From d7049511880d1455945eacd103a1b321bdf8090d Mon Sep 17 00:00:00 2001 From: ModelHub XC Date: Tue, 30 Jun 2026 22:08:44 +0800 Subject: [PATCH] =?UTF-8?q?=E5=88=9D=E5=A7=8B=E5=8C=96=E9=A1=B9=E7=9B=AE?= =?UTF-8?q?=EF=BC=8C=E7=94=B1ModelHub=20XC=E7=A4=BE=E5=8C=BA=E6=8F=90?= =?UTF-8?q?=E4=BE=9B=E6=A8=A1=E5=9E=8B?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Model: QuantaSparkLabs/NYXIS-Pro Source: Original Platform --- .gitattributes | 38 + README.md | 126 + aegis_chunks.txt | 23327 ++++++++++++++++ aegis_embedder/1_Pooling/config.json | 5 + aegis_embedder/README.md | 3074 ++ aegis_embedder/config.json | 35 + .../config_sentence_transformers.json | 14 + aegis_embedder/model.safetensors | 3 + aegis_embedder/modules.json | 20 + aegis_embedder/sentence_bert_config.json | 10 + aegis_embedder/tokenizer.json | 3 + aegis_embedder/tokenizer_config.json | 17 + aegis_index.faiss | 3 + aegis_reranker/README.md | 147 + aegis_reranker/config.json | 36 + .../config_sentence_transformers.json | 11 + aegis_reranker/model.safetensors | 3 + aegis_reranker/modules.json | 8 + aegis_reranker/sentence_bert_config.json | 10 + aegis_reranker/tokenizer.json | 3 + aegis_reranker/tokenizer_config.json | 18 + chat_template.jinja | 54 + config.json | 62 + generation_config.json | 8 + logoname.png | 3 + model.safetensors | 3 + pipeline.py | 94 + preview imgagee.png | 3 + tokenizer.json | 3 + tokenizer_config.json | 202 + 30 files changed, 27343 insertions(+) create mode 100644 .gitattributes create mode 100644 README.md create mode 100644 aegis_chunks.txt create mode 100644 aegis_embedder/1_Pooling/config.json create mode 100644 aegis_embedder/README.md create mode 100644 aegis_embedder/config.json create mode 100644 aegis_embedder/config_sentence_transformers.json create mode 100644 aegis_embedder/model.safetensors create mode 100644 aegis_embedder/modules.json create mode 100644 aegis_embedder/sentence_bert_config.json create mode 100644 aegis_embedder/tokenizer.json create mode 100644 aegis_embedder/tokenizer_config.json create mode 100644 aegis_index.faiss create mode 100644 aegis_reranker/README.md create mode 100644 aegis_reranker/config.json create mode 100644 aegis_reranker/config_sentence_transformers.json create mode 100644 aegis_reranker/model.safetensors create mode 100644 aegis_reranker/modules.json create mode 100644 aegis_reranker/sentence_bert_config.json create mode 100644 aegis_reranker/tokenizer.json create mode 100644 aegis_reranker/tokenizer_config.json create mode 100644 chat_template.jinja create mode 100644 config.json create mode 100644 generation_config.json create mode 100644 logoname.png create mode 100644 model.safetensors create mode 100644 pipeline.py create mode 100644 preview imgagee.png create mode 100644 tokenizer.json create mode 100644 tokenizer_config.json diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..c1554a9 --- /dev/null +++ b/.gitattributes @@ -0,0 +1,38 @@ +*.7z filter=lfs diff=lfs merge=lfs -text +*.arrow filter=lfs diff=lfs merge=lfs -text +*.bin filter=lfs diff=lfs merge=lfs -text +*.bz2 filter=lfs diff=lfs merge=lfs -text +*.ckpt filter=lfs diff=lfs merge=lfs -text +*.ftz filter=lfs diff=lfs merge=lfs -text +*.gz filter=lfs diff=lfs merge=lfs -text +*.h5 filter=lfs diff=lfs merge=lfs -text +*.joblib filter=lfs diff=lfs merge=lfs -text +*.lfs.* filter=lfs diff=lfs merge=lfs -text +*.mlmodel filter=lfs diff=lfs merge=lfs -text +*.model filter=lfs diff=lfs merge=lfs -text +*.msgpack filter=lfs diff=lfs merge=lfs -text +*.npy filter=lfs diff=lfs merge=lfs -text +*.npz filter=lfs diff=lfs merge=lfs -text +*.onnx filter=lfs diff=lfs merge=lfs -text +*.ot filter=lfs diff=lfs merge=lfs -text +*.parquet filter=lfs diff=lfs merge=lfs -text +*.pb filter=lfs diff=lfs merge=lfs -text +*.pickle filter=lfs diff=lfs merge=lfs -text +*.pkl filter=lfs diff=lfs merge=lfs -text +*.pt filter=lfs diff=lfs merge=lfs -text +*.pth filter=lfs diff=lfs merge=lfs -text +*.rar filter=lfs diff=lfs merge=lfs -text +*.safetensors filter=lfs diff=lfs merge=lfs -text +saved_model/**/* filter=lfs diff=lfs merge=lfs -text +*.tar.* filter=lfs diff=lfs merge=lfs -text +*.tar filter=lfs diff=lfs merge=lfs -text +*.tflite filter=lfs diff=lfs merge=lfs -text +*.tgz filter=lfs diff=lfs merge=lfs -text +*.wasm filter=lfs diff=lfs merge=lfs -text +*.xz filter=lfs diff=lfs merge=lfs -text +*.zip filter=lfs diff=lfs merge=lfs -text +*.zst filter=lfs diff=lfs merge=lfs -text +*tfevents* filter=lfs diff=lfs merge=lfs -text +logoname.png filter=lfs diff=lfs merge=lfs -text +preview[[:space:]]imgagee.png filter=lfs diff=lfs merge=lfs -text +tokenizer.json filter=lfs diff=lfs merge=lfs -text diff --git a/README.md b/README.md new file mode 100644 index 0000000..7dfc961 --- /dev/null +++ b/README.md @@ -0,0 +1,126 @@ +--- +license: apache-2.0 +language: +- en +tags: +- rag +- retrieval-augmented-generation +- knowledge-base +- emotion-detection +- dual-stage-retrieval +- coding +- math +- science +- history +- nyxis +- quantasparklabs +pipeline_tag: text-generation +base_model: +- QuantaSparkLabs/NYXIS-1.1B +library_name: transformers +datasets: +- QuantaSparkLabs/NYXIS-AEGIS-Knowledge +--- +

+ NYXIS Logo +

+ +

+ NYXIS Name +

+# NYXIS-PRO 🛡️ + +

+ Base Model + AEGIS KB + Dual Stage + Emotion Engine + License +

+ +**The all-in-one reasoning engine with the AEGIS knowledge shield.** + +NYXIS-PRO combines the NYXIS1.1B base model with a curated 5,000+ chunk knowledge base covering coding, math, science, history, and common knowledge. A dual‑stage retriever grounds every factual answer in verified data — **zero hallucination.** + +## 🧠 What Makes It Different + +| Feature | Description | +|---------|-------------| +| **AEGIS Knowledge Base** | 5,426 curated Wikipedia, Trivia QA, and ArXiv chunks | +| **Dual‑Stage Retriever** | Dense recall (bge‑small) + Cross‑encoder rerank (ms‑marco‑MiniLM) | +| **Emotion Engine** | Detects user emotion on a 1‑10 scale and matches tone | +| **4‑Tier Knowledge Cascade** | AEGIS → External Search → Model Brain → Honest Fallback | +| **Zero Hallucination** | If it doesn't know, it says so — no fabrication | + +## 🚀 Quick Start + +```python +from huggingface_hub import snapshot_download +import sys + +model_dir = snapshot_download("QuantaSparkLabs/NYXIS-Pro") +sys.path.insert(0, model_dir) + +from pipeline import NYXISPro +nyxis = NYXISPro(model_dir) + +result = nyxis.generate("What is a binary search tree?") +print(result["response"]) +``` + +> **Requirements:** `sentence-transformers`, `faiss-cpu`, `transformers`, `accelerate`, `bitsandbytes` +> **VRAM:** ~2.1 GB (4‑bit) | **Hardware:** T4 or better + +## 📦 What's Inside + +| Component | Model | Purpose | +|-----------|-------|---------| +| **Base LLM** | NYXIS1.1B) | Text generation | +| **Dense Retriever** | bge‑small‑en‑v1.5 | Initial candidate recall | +| **Cross‑Encoder** | ms‑marco‑MiniLM‑L‑6‑v2 | Precision re‑ranking | +| **FAISS Index** | 5,426 chunks | Knowledge storage | +| **Emotion Engine** | Custom keyword‑based | Tone matching | + +## 🤖 Emotion Intelligence + +NYXIS-PRO detects your emotional state from text and adjusts its personality: + +| Level | Emotion | Response Style | +|:---:|---------|----------------| +| 1‑3 | Sad / Angry | Gentle, supportive, empathetic | +| 4‑6 | Neutral | Balanced, warm, helpful | +| 7‑9 | Happy / Excited | Energetic, playful | +| 10 | Overjoyed | Celebratory | + +## 🛡️ Knowledge Cascade + +When you ask a factual question, NYXIS-PRO follows a strict 4‑tier protocol: + +1. **AEGIS** — Searches internal verified knowledge base +2. **External Search** — Falls back to web search (user‑provided API) +3. **Model Brain** — Uses training data with honesty guard +4. **Honest Fallback** — Admits "I don't have enough information" + +It **never fabricates** an answer. + +## Limitations + +- Knowledge base covers ~5,400 chunks — not infinite +- Emotion detection is keyword‑based, not deep sentiment analysis +- External search requires user‑provided API function +- English‑only, 1.5B model size limits complex reasoning + +## License + +Apache‑2.0 + +--- + +*Built with 🛡️ by QuantaSparkLabs* \ No newline at end of file diff --git a/aegis_chunks.txt b/aegis_chunks.txt new file mode 100644 index 0000000..d7dbe8e --- /dev/null +++ b/aegis_chunks.txt @@ -0,0 +1,23327 @@ +thumb|250px|The [[Tree of life (biology)|tree of life showing the three domains of life on Earth]] + +'''Evolution''' is a biological process. It is how living things change over time and how new species develop. The theory of evolution explains how evolution works, and how living and extinct things have come to be the way they are. + +The theory of evolution is an essential idea in biology. Theodosius Dobzhansky, a well-known evolutionary biologist, said: "Nothing in biology makes sense except in the light of evolution".Dobzhansky, Theodosius 1973. Nothing in biology makes sense except in the light of evolution. ''American Biology Teacher'' '''35''', 125-129. http://www.2think.org/dobzhansky.shtml + +Evolution has been happening since life started on Earth and is happening now. Evolution is caused mostly by natural selection. Living things are not identical to each other. Even living things of the same species look, move, and behave differently to some extent. Some differences make it easier for living things to survive and reproduce. + +Differences may make it easier to find food, hide from danger, or give birth to offspring which survive. The offspring will have some of the things which made it easier for their parents to have and raise them. Over time, these good differences continue and are spread through the population. Many generations pass and living things change enough to become new species. + +Individuals who have differences that make it harder to find food, have offspring or avoid being eaten are likely not to have offspring at all and so will not be parents of future generations. + +It is known that living things have changed over time, because their remains can be seen in the rocks. These remains are called 'fossils'. They prove that the animals and plants of today are different from those of long ago. The older the fossils, the bigger the differences from modern forms.Levin, Harold L. 2005. ''The Earth through time''. 8th ed, Wiley, N.Y. Chapter 6: Life on +<|CHUNK_END|> +The '''Fourier transform''' is a mathematical function that can be used to find the base frequencies that a wave is made of. Imagine playing a chord on a piano. When played, the sounds of the notes of the chord mix together and form a sound wave. This works because each of the different note's waves interfere with each other by adding together or canceling out at different points in the wave. A Fourier transform takes this complex wave and is able to find the frequencies that made it, meaning it can find the notes that a chord is made from. + +The output of a Fourier transform is sometimes called a frequency spectrum or distribution because it displays a distribution of possible frequencies of the input. This function has many uses in cryptography, oceanography, machine learning, radiology, quantum physics as well as sound design and visualization. + +The Fourier transform of a function f(x), sometimes written as \mathcal{F}\{f\}, is given by + +F(\alpha)=\int_{-\infty}^{+\infty} f(x) e^{-2 \pi i \alpha x} \, dx + +where: + +* \alpha is a frequency. +* F(\alpha) is the Fourier transform function and returns a value representing how prevalent frequency \alpha is in the original signal. +* e^{-2\pi i \alpha x} represents wrapping the input wave function f(x) around the origin of the complex plane at some frequency \alpha. + +The '''inverse Fourier transform''' is given by + +f(x)=\int_{-\infty}^{+\infty} F(\alpha) e^{+2 \pi i x \alpha} \, d \alpha + +A Fourier transform shows what frequencies are in a signal. For example, consider a sound wave which contains three different musical notes: A, B, and C. Making a graph of the Fourier transform of this sound wave (with the frequency on the ''x''-axis and the intensity on the ''y''-axis) will show a peak at each frequency which corresponds with one of the musical notes. + +Many signals can be created by adding cosines and sines together with varying amplitudes and frequencies. The Fourier transform plots the amplitudes and phases of these co +<|CHUNK_END|> +'''Algebra''' is a part of mathematics. It uses variables to represent a value that is not yet known or can be replaced with any value. When an equals sign (=) is used, this is called an equation. A very simple equation using a variable is: 2+3=x. In this example, x=5, or it could also be said that "x equals five". This is called ''solving for'' x. + +Besides equations, there are inequalities (''less than'' and ''greater than''). A special type of equation is called the function. This is often used in making graphs because it always turns one input into one output. + +Algebra can be used to solve real problems because the rules of algebra work in real life and numbers can be used to represent the values of real things. Physics, engineering and computer programming are areas that use algebra all the time. It is also useful to know in surveying, construction and business, especially accounting. + +People who do algebra use the rules of numbers and mathematical operations used on numbers. The simplest are adding, subtracting, multiplying, and dividing. More advanced operations involve exponents, starting with squares and square roots. + +Algebra was first used to solve equations and inequalities. Two examples are linear equations (the equation of a straight line, y=mx+b or y=mx+c) and quadratic equations, which has variables that are squared (multiplied by itself, for example: 2\cdot2, 3\cdot3, or x\cdot x). + +== History == +Early forms of algebra were developed by the Babylonians and Greek geometers such as Hero of Alexandria. However the word "algebra" is a Latin form of the Arabic word ''Al-Jabr'' ("casting") and comes from a mathematics book ''Al-Maqala fi Hisab-al Jabr wa-al-Muqabilah'', ("Essay on the Computation of Casting and Equation") written in the 9th century by a Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī, who was a Muslim born in Khwarizm in Uzbekistan. He flourished under Al-Ma'moun in Baghdad, Iraq through 813-833 CE, and died around 840 CE. The book w +<|CHUNK_END|> +thumb|300px|A [[Brownian bridge, a stochastic process.]] +A '''Stochastic process''' is a mathematical description of random events that occur one after another. It is possible to order these events according to the time at which they occur. + +This can be used to model such things as daily weather data, or exchange rate changes, or medical information like a patient's EKG, EEG, blood pressure or temperature. + +Stochastic processes used in various disciplines, including physics, biology, finance, telecommunications, and operations research. They provide a powerful framework for analyzing and predicting the behavior of systems under uncertain conditions. + +==References== + +Category:Statistics +<|CHUNK_END|> +In mathematics, a '''series''' is, roughly speaking, an addition of infinitely many terms, one after the other. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures in combinatorics through generating functions. The mathematical properties of infinite series make them widely applicable in other quantitative disciplines such as physics, computer science, statistics and finance. + +Among the Ancient Greeks, the idea that a potentially infinite summation could produce a finite result was considered paradoxical, most famously in Zeno's paradoxes. Nonetheless, infinite series were applied practically by Ancient Greek mathematicians including Archimedes, for instance in the quadrature of the parabola. The mathematical side of Zeno's paradoxes was resolved using the concept of a limit during the 17th century, especially through the early calculus of Isaac Newton. The resolution was made more rigorous and further improved in the 19th century through the work of Carl Friedrich Gauss and Augustin-Louis Cauchy, among others, answering questions about which of these sums exist via the completeness of the real numbers and whether series terms can be rearranged or not without changing their sums using absolute convergence and conditional convergence of series. + +In modern terminology, any ordered infinite sequence (a_1,a_2,a_3,\ldots) of terms, whether those terms are numbers, functions, matrices, or anything else that can be added, defines a series, which is the addition of the one after the other. To emphasize that there are an infinite number of terms, series are often also called '''infinite series''' to contrast with finite series, a term sometimes used for finite sums. Series are represented by an expression like +a_1+a_2+a_3+\cdots, +or, using capital-sigma summation notation, +\sum_{i=1}^\infty a_i. + +The infinite sequence of additions expressed by a seri +<|CHUNK_END|> +In computer science, '''breadth-first search (BFS)''' is a method used for traversing a graph. It starts at any item you want to use as a starting position in a graph, and explores all of the neighbor items at the present depth before to moving on to the items at the next depth level. A breadth-first search done on a tree (data structure) is called a level-order traversal. + +thumb|187px|Animated example of a breadth-first search (level-order traversal) within a tree. + +==Implementation== + +void breadthFirstSearch(Item root) { + Queue q = new Queue(); + root.found = true; + q.enqueue(item); + while (!q.isEmpty()) { + Item v = q.dequeue(); + for (Item neighbor : v.neighbors()) { + if (!neighbor.found) { + neighbor.found = true; + q.enqueue(neighbor); + } + } + } +} + +==Usage== +Though they have usage in a variety of disciplines, breadth first search algorithms are most often associated with finding the shortest distance between two points, such as on a map. + +==Related pages== +* Linear search +* Binary search +* Depth-first search +* Bidirectional search + +Category:Searching and sorting algorithms +<|CHUNK_END|> +thumb|300px|right|The minimum spanning tree of a [[planar graph. Each edge is labeled with its weight, which here is roughly proportional to its length.]] +A number of problems from graph theory are called '''Minimum spanning tree'''. In graph theory, a tree is a way of connecting all the vertices together, so that there is exactly one path from any one vertex, to any other vertex of the tree. If the graph represents a number of cities connected by roads, one could select a number of roads, so that each city can be reached from every other, but that there is no more than one way to travel from one city to another. + +A graph can have more than one spanning tree, just like there may be more than one way to select the roads between the cities. + +Most of the time, graphs are weighted; each connection between two cities has a weight: It might cost something to travel on a given road, or one connection may be longer than the other, this means it takes more time to travel on that connection. In the language of graph theory, the connections are called ''edges''. + +A minimum spanning tree is a tree. It is different from other trees in that it minimizes the total of the ''weights'' attached to the edges. Depending on what the graph looks like, there may be more than one minimum spanning tree. In a graph where all the edges have the same weight, every tree is a minimum spanning tree. If all the edges have different weights (that is: there are no two edges with the same weight), there is exactly one minimal spanning tree. + +==Finding the minimum spanning tree== +===A first try=== +It can be very simple to make an algorithm that will discover a minimum spanning tree: + + '''function''' MST(''G'',''W''): + ''T'' = {} + '''while''' ''T'' does not form a spanning tree: + find the minimum weighted edge in ''E'' that is safe for ''T'' + ''T'' = ''T'' union {(''u'',''v'')} + '''return''' ''T'' + +In this case, "safe" means that including the edge does not form a cycle +<|CHUNK_END|> +thumb|V8 (JavaScript engine) logo +A '''JavaScript engine''' is a program that runs JavaScript code. Web Browsers often have a JavaScript engine. It can also be used outside of web browsers, such as running services in Node.js or apps in the electron framework. + +== Design == +JavaScript was originally created as a scripting language to allow web pages to have changing, or dynamic, elements. Early Javascript engines were created as interpreters, programs that simply read the script and execute the instructions without analyzing it any more. + +As JavaScript started being used more and more as a general-purpose language, execution speed, or how quickly the code is run, became more important for JavaScript engines. In response, many engines, such as V8 (Used in Chrome and Chromium) and SpiderMonkey (used in Firefox), started using Just-In-Time Compilation. In this method, it starts by compiling all of the code to optimized machine code, which is typically faster than interpretation, then running the result. + +== References == + +Category:JavaScript +<|CHUNK_END|> +'''Classical mechanics''' is the part of physics that describes how everyday things move and how their motion changes because of forces. If we know how things are moving now, classical mechanics allows us to predict how they will move in the future and how they were moving in the past. We can use classical mechanics to predict how things like planets and rockets move. + +Classical mechanics is not accurate when things are the size of atoms or smaller: for those things, we use quantum mechanics instead. Classical mechanics is also not accurate when things move close to the speed of light: for those things, we use special relativity instead. + +== Position, velocity, and acceleration == + +=== Position === +The position of an object tells you where it is. For example, if you live in New York City and your friend lives in Seattle, your friend has a position of 3,876 kilometers (2,408 miles) west from you. But your friend would say that ''you'' have a position of 3,876 kilometers (2,408 miles) ''east'' from them instead. This is because position depends on where "position zero" or the ''origin'' is. For you, the origin is in New York City, but for your friend, the origin is in Seattle. So we make sure to always say where the origin is when we talk about position. + +We talk about position using vectors: we first say a distance (such as 3,000 km) and then the direction (such as ''east'', ''left'', or ''38 degrees south''). If there is no direction, position is simply ''distance''. Position can sometimes be negative: for example, New York City is 3,876 kilometers (2,408 miles) east of Seattle and Seattle is ''negative'' 3,876 kilometers (2,408 miles) east of New York City. However, it is easier to say "west" instead of "negative east". + +=== Velocity === +When something moves, its position changes. You may pull a book closer to you, and the book has a new position. Or, you may walk away from your house and you have a new position. The velocity of an object tells you how fast the obj +<|CHUNK_END|> +thumb|The Greek glyph "'''ψ'''" or "psi" when Latinized, is an old symbol for mental health and well being + +'''Mental health''' encompasses emotional, psychological, and social well-being, influencing cognition, perception, and behavior. Mental health plays a crucial role in an individual's daily life when managing stress, engaging with others, and contributing to life overall. According to the World Health Organization (WHO), it is a "state of well-being in which the individual realizes their abilities, can cope with the normal stresses of life, can work productively and fruitfully, and can contribute to their community". It likewise determines how an individual handles stress, interpersonal relationships, and decision-making. Mental health includes subjective well-being, perceived self-efficacy, autonomy, competence, intergenerational dependence, and self-actualization of one's intellectual and emotional potential, among others. +Mental health also includes emotional, psychological, and social well-being, and it affects how people manage stress and make everyday decisions. + +From the perspectives of positive psychology or holism, mental health is thus not merely the absence of mental illness. Rather, it is a broader state of well-being that includes an individual's ability to enjoy life and to create a balance between life activities and efforts to achieve psychological resilience. Cultural differences, personal philosophy, subjective assessments, and competing professional theories all affect how one defines "mental health". + +== Mental disorders == + +Mental health, as defined by the Public Health Agency of Canada, is an individual's capacity to feel, think, and act in ways to achieve a better quality of life while respecting personal, social, and cultural boundaries. Impairment of any of these is a risk factor for mental disorders, or mental illnesses, which is a component of mental health. In 2019, about 970 million people worldwide suffered from a mental disorder +<|CHUNK_END|> +'''CSS''' is an abbreviation. It can stand for the following: +* Cascading Style Sheets, a technology to make HTML look better +* The Chinese Space Station, a planned space station in low earth orbit +* Content Scrambling System, a way to make it harder to copy DVDs +* Counter-Strike Source, an online first person shooter game +<|CHUNK_END|> +The '''Laplace transform''' is a way to turn functions into other functions in order to do certain calculations more easily. This way of turning functions to other functions is very similar to U Substitution. The aim of this change is to be able to turn the hard work of integration into a simple algebraic addition and subtraction, just as logarithms allow one to add and subtract instead of multiplying and dividing. An example of its use is in ruin theory, which is a subject of actuarial science with regards to insurance. + +Functions usually take a variable (say ''t'') as an input, and give some output (say ''f''). The Laplace transform converts these functions to take some other input (''s'') and give some other output (''F''). Because of certain shared properties of Laplace transforms, this makes it very easy to manipulate the original function into something useful. + +In many kinds of engineering, especially electrical engineering and signal processing, the original function is said to be in the ''time domain'' and the new function given by the Laplace transform is said to be in the ''frequency domain''. + +The Laplace transform of a function f(t), written as \mathcal{L}\{f(t)\} or F(s), is often formulated as: + +:F(s) = \int_{0}^\infty {f(t) e^{-st} \mathrm{d}t} +where: +*''f(t)'' is the input function +* ''t'' is the old domain +*''s'' is the new domain + +== Related pages == + +* Fourier transform + +== References == + +Category:Calculus +Category:Harmonic analysis +<|CHUNK_END|> +'''Ethics''' is the study of good and bad behavior. It is one of the main parts of philosophy. Ethics tries to answer questions like: + +* What actions are good? What actions are evil? +* How can we tell the difference? +* Are good and evil the same? +* How should we make hard decisions that might help or hurt other people? +* How do our actions affect others? + +== Ideas about ethics == +When discussing ethics, the philosophy is generally separated into: +* thinking about morality, +* the involvement of science, +* the freedom of people to decide for themselves how to act within their own beliefs. + +''Morality'' is what someone thinks or feels is good or bad. There are many different moralities, but they share some things. For example, most people think that murder (killing somebody) is wrong. (compare Exodus 20:13) Some philosophers hope to find more things that moralities share. They think that ethics should use the scientific method to study things that people think are good or bad. Their work can be used to test the fairness of a situation, such as how people should treat each other. An example of this kind of thinking is the categorical imperative. Many countries have laws based on this idea of fairness. + +== What is ethics used for? == +Understanding ethics can help people decide what to do when they have choices. Many philosophers think that doing anything or making any choice is a part of ethics. + +Ethics is part of other fields of study in many ways. Here are some ways: + +* Ethics is part of the study of religion. In religion, people often learn what is good or bad from what they believe about God (or gods). Some important ideas about what is good or bad have come from religion. See Ten Commandments. +* Some theories of economics say ethics has to do with money. Money is a big part of most people's lives. Thinking about morality can be important in economics. For example, there is a saying about ethics taken from the Bible that 'the love of money is the root of all +<|CHUNK_END|> +thumb|right|200px|The structure of part of a DNA double helix +180px|thumb|Chemical [[structure + of DNA. The phosphate groups are yellow, the deoxyribonucleic sugars are orange, and the nitrogen bases are green, purple, pink, and blue. The atoms shown are: P=phosphorus O=oxygen =nitrogen H=hydrogen]]180px|thumb|right|DNA being copied + +'''DNA''', short for '''deoxyribonucleic acid''', is the molecule that contains the genetic code of living organisms. This includes animals, plants, protists, archaea and bacteria. It is made up of two polynucleotide chains in a double helix. + +DNA, present in most cells such as skin, muscle, and nerve cells, contains the genetic instructions that cells use to make proteins, but it is absent in some cells like mature red blood cells. Mostly, these proteins are enzymes. DNA is inherited by children from their parents. This is why children share traits with their parents, such as skin, hair and eye color. The DNA in a person is a combination of the DNA from each of their parents. + +Part of an organism's DNA is "non-coding DNA" sequences. They do not code for protein sequences. Some noncoding DNA is transcribed into non-coding RNA molecules, such as transfer RNA, ribosomal RNA, and regulatory RNAs. Other sequences are not transcribed at all, or give rise to RNA of unknown function. The amount of non-coding DNA varies greatly among species. For example, over 98% of the human genome is non-coding DNA,Elgar G. & Vavouri T. 2008. Tuning in to the signals: non-coding sequence conservation in vertebrate genomes. ''Trends Genet''. '''24''' (7): 344–52. while only about 2% of a typical bacterial genome is non-coding DNA. + +Viruses use either DNA or RNA to infect organisms. The genome replication of most DNA viruses takes place in the cell's nucleus, whereas RNA viruses usually replicate in the cytoplasm. + +Inside eukaryotic cells, DNA is organized into chromosomes. Before cell division, more chromosomes are made in the process of DNA replication. E +<|CHUNK_END|> +In probability theory, the '''central limit theorem''' ('''CLT''') states that, under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard normal distribution. This holds even if the original variables themselves are not normally distributed. There are several versions of the CLT, each applying in the context of different conditions. + +The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. + +This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811, but in its modern form it was only precisely stated in the 1920s.}} + +In statistics, the CLT can be stated as: let X_1, X_2, \dots, X_n denote a statistical sample of size n from a population with expected value (average) \mu and finite positive variance \sigma^2, and let \bar{X}_{n} denote the sample mean (which is itself a random variable). Then the limit as n\to\infty of the distribution of (\bar{X}_n-\mu) \sqrt{n} is a normal distribution with mean 0 and variance \sigma^2. + +In other words, suppose that a large sample of observations is obtained, each observation being randomly produced in a way that does not depend on the values of the other observations, and the average (arithmetic mean) of the observed values is computed. If this procedure is performed many times, resulting in a collection of observed averages, the central limit theorem says that if the sample size is large enough, the probability distribution of these averages will closely approximate a normal distribution. + +The central limit theorem has several variants. In its common form, the random variables must be independent and identically distributed (i.i.d.). This requirement can be weakened; convergence of the mean to the normal distribution also occurs f +<|CHUNK_END|> +|space_worst=O(''n'') +|search_avg=O(1 + ''n''/''k'') +|search_worst=O(''n'') +|insert_avg=O(1) +|insert_worst=O(1) +|delete_avg=O(1 + ''n''/''k'') +|delete_worst=O(''n'') +}} +thumb|315px|right|A small phone book as a hash table + +A '''hash table''' is a type of tool for storing information. In computer science, these tools for keeping track of information, or data, are called data structures. +A hash table is a data structure that uses a hash function to keep track of where data is. +Each piece of information to be stored has a name, which is called a key. For example, a key might be a person's name. Each name is matched up to one piece of data called a value, like the person's telephone number. + +The data is kept in another data structure called an array, which is like many boxes, or buckets, in a column to hold data. Each box has a number starting from 0 and counting up. + +The idea behind a hash table is to find the box for a value using only its name. This means that no matter how many boxes there are, one can find information quickly by its name. It is very fast to use the box of an array by its number. A hash function reads a name and gives back a number. A hash table uses a hash function to find a box number for a name. + +A good hash table will always find information at the same speed, no matter how much data is put in. A lot of hash tables also let the user put key/value pairs (a name and its data) in and take them out at the same speed. + + +Because of this, hash tables can often find information faster than other tools, such as search trees or other table lookup structures. As a result, they are used in many kinds of computer software. They are used most often for associative arrays, databases, caches, and sets. + +==Uses== +Many programming languages use hash tables, either as built-in associative arrays or as part of their standard library. + +* .NET_Framework, which can be used from languages such as C# and VB.NET. +* JavaScript MDN |url=https://developer.mozilla.org/ +<|CHUNK_END|> +'''Insertion sort''' is a simple sorting algorithm that builds the final sorted array (or list) one item at a time by comparisons. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. However, insertion sort provides several advantages: + +* Simple implementation: Jon Bentley shows a version that is three lines in C-like pseudo-code, and five lines when optimized. +* Efficient for (quite) small data sets, much like other quadratic (i.e., O(''n''2)) sorting algorithms +* May be more efficient in practice than most other simple quadratic algorithms such as selection sort or bubble sort but relative incoming data order and read/write costs matter with high exchange costs and randomly ordered data, selection sort is faster +* Adaptive, i.e., efficient for data sets that are already substantially sorted: the time complexity is O(''kn'') when each element in the input is no more than places away from its sorted position +* Stable; i.e., does not change the relative order of elements with equal keys +* In-place; i.e., only requires a constant amount O(1) of additional memory space +* Online; i.e., can sort a list as it receives it + +When people manually sort cards in a bridge hand, most use a method that is similar to insertion sort. + +==Algorithm== +300px|thumb|right|A graphical example of insertion sort. The partial sorted list (black) initially contains only the first element in the list. With each iteration one element (red) is removed from the "not yet checked for order" input data and inserted in-place into the sorted list. + +Insertion sort iterates, consuming one input element each repetition, and grows a sorted output list. At each iteration, insertion sort removes one element from the input data, finds the correct location within the sorted list, and inserts it there. It repeats until no input elements remain. + +Sorting is typically done in-place, by iterating up the array, growing the sorted list behind it. At e +<|CHUNK_END|> +thumb|250px|right|Babylonian clay tablet YBC 7289 (c. 1800–1600 BCE) with annotations. The approximation of the [[square root of 2 is four sexagesimal figures, which is about six decimal figures. 1+24/60+51/60^2+10/60^3\approx1.41421296]] + +'''Numerical analysis''' studies different algorithms to get approximations for problems of mathematical analysis. Approximations are used for the following reasons: +# There are no known ways to solve a problem using calculus. Examples for such problems are the Navier–Stokes equationsConstantin, P., & Foias, C. (1988). Navier-stokes equations. University of Chicago Press.Temam, R. (2001). Navier-Stokes equations: theory and numerical analysis (Vol. 343). American Mathematical Society.Foias, C., Manley, O., Rosa, R., & Temam, R. (2001). Navier-Stokes equations and turbulence (Vol. 83). Cambridge University Press.Girault, V., & Raviart, P. A. (2012). Finite element methods for Navier-Stokes equations: theory and algorithms (Vol. 5). Springer Science & Business Media. or the Three-body problem +# There is a way to solve a problem using calculus. Getting an exact solution is impractical though, because it requires a long time, or many resources. An example for this is calculating power series. + +One of the earliest known uses of numerical analysis is a Babylonian clay tablet, which approximates the square root of 2. In a unit square, the diagonal has this length. Being able to compute the sides of a triangle is extremely important, for instance, in carpentry and construction.The New Zealand Qualification authority specifically mentions this skill in document 13004 version 2, dated 17 October 2003 titled [https://www.nzqa.govt.nz/nqfdocs/units/pdf/13004.pdf CARPENTRY THEORY: Demonstrate knowledge of setting out a building] + +Numerical analysis continues this long tradition of practical mathematical calculations. Much like the Babylonian approximation of \sqrt2, modern numerical analysis does not seek exact answers, because exact answers +<|CHUNK_END|> +The '''periodic table''' is a table that puts all known chemical elements in a specific order. Elements that have similar characteristics are often put near each other. In the table, the elements are placed in the order of their atomic numbers starting with the lowest number of one, hydrogen. The atomic number of an element is the same as the number of protons in that particular nucleus of an atom. In the table the elements are arranged into ''periods'' and ''group.'' A row of elements across the table is called a ''period''. Each period has a number; from 1 to 8. Period 1 has only 2 elements in it: hydrogen and helium. Period 2 and Period 3 both have 8 elements. Other periods are longer. Elements in a period have consecutive atomic numbers. + +The periodic classification of elements offers a systematic approach to organizing and studying the universe's vast array of elements. This method is crucial for comprehending the chemistry of elements and their compounds. By grouping elements with similar properties, scientists uncover patterns and trends in these fundamental building blocks of matter. '''[https://learnwithvdk.blogspot.com/2024/08/periodic-classification-of-elements.html Read more ...]''' + +center|thumb|507x507px|A standard periodic table +A column of elements down the table is called a ''group''. There are 18 groups in the standard periodic table. Each group has a number: from 1 to 18. Elements in a group have electrons arranged in similar ways, according to the number of valency electrons, which gives them similar chemical properties (they behave in similar ways). For example, group 18 is known as the noble gases because they are all gases and they do not combine with other atoms. '''[https://learnwithvdk.blogspot.com/2024/08/periodic-classification-of-elements.html Read more ...]''' + +There are two systems of group numbers; one using Arabic numerals (1, 2, 3) and the other using Roman numerals (I, II, III). The Roman numeral names were used in most of the +<|CHUNK_END|> +thumb|Similarly to a stack of plates, adding or removing is only practical at the top. +thumb|350px|right|Simple representation of a stack runtime with ''push'' and ''pop'' operations + +In computer science, a '''stack''' is an abstract data type that serves as a collection of elements with two main operations: +* '''Push''', which adds an element to the collection, and +* '''Pop''', which removes the most recently added element. +Additionally, a peek operation can, without modifying the stack, return the value of the last element added (the item at the top of the stack). The name ''stack'' is an analogy to a set of physical items stacked one atop another, such as a stack of plates. + +The order in which elements are added to or removed from a stack is described as '''last in, first out''', referred to by the acronym '''LIFO'''. As with a stack of physical objects, this structure makes it easy to take an item off the top of the stack, but accessing a datum deeper in the stack may require removing multiple other items first. + +Considered a sequential collection, a stack has one end which is the only position at which the push and pop operations may occur, the ''top'' of the stack, and is fixed at the other end, the ''bottom''. A stack may be implemented as, for example, a singly linked list with a pointer to the top element. + +A stack may be implemented to have a bounded capacity. If the stack is full and does not contain enough space to accept another element, the stack is in a state of stack overflow. + +==History== + +Stacks entered the computer science literature in 1946, when Alan Turing used the terms "bury" and "unbury" as a means of calling and returning from subroutines. Subroutines and a two-level stack had already been implemented in Konrad Zuse's Z4 in 1945. + +Klaus Samelson and Friedrich L. Bauer of the Technical University of Munich proposed the idea of a stack called ("operational cellar") in 1955 and filed a patent in 1957. In March 1988, by which time Samelson wa +<|CHUNK_END|> +alt=A two-state Markov chain|thumb|A two-state Markov chain. The [[probability of switching from one state to another is indicated by the numbers next to the arrows.]] +A '''Markov chain''' is a model of some random process that happens over time. Markov chains are called that because they follow a rule called the Markov property. The Markov property says that whatever happens next in a process only depends on how it is right now (the state). It doesn't have a "memory" of how it was before. It is helpful to think of a Markov chain as evolving through discrete steps in time, although the "step" doesn't need to have anything to do with time. + +Markov chains can be discrete or continuous. Discrete Time Markov Chains are split up into discrete time steps, like t = 1, t = 2, t = 3, and so on. The probability that a chain will go from one state to another state depends only on the state that it's in right now. Continuous Time Markov Chains are chains where the time spent in each state is a real number. The amount of time the chain stays in a certain state is randomly picked from an exponential distribution, which basically means there's an average time a chain will stay in some state, plus or minus some random variation. + +An example of a Markov chain are the dietary habits of a creature who only eats grapes, cheese or lettuce, and whose dietary habits conform to the following (artificial) rules: +* It eats exactly once a day. +* If it ate cheese yesterday, it will eat lettuce or grapes today with equal probability for each, and zero chance of eating cheese. +* If it ate grapes yesterday, it will eat grapes today with probability 1/10, cheese with probability 4/10 and lettuce with probability 5/10. +* Finally, if it ate lettuce yesterday, it won't eat it again today, but will eat grapes with probability 4/10 or cheese with probability 6/10. + +This creature's eating habits can be modeled with a Markov chain since its choice depends on what it ate yesterday, not additionally on wha +<|CHUNK_END|> +thumb|right|250px| +A '''Moon landing''' is the arrival of a spacecraft on the surface of the Moon. It is a follow up to Project Mercury. This includes both crewed and uncrewed (robotic) missions. The first man-made object to reach the surface of the Moon was the Soviet Union's Luna 2 mission, on 13 September 1959. + +The United States' Apollo 11 was the first crewed mission to land on the Moon, on 20 July 1969.[http://www.nasa.gov/mission_pages/apollo/apollo11_40th.html NASA Apollo 11 40th anniversary]. There have been six missions with people onboard that landed on the Moon between 1969 and 1972. There were also numerous landings without people onboard, with no soft landings happening from 22 August 1976 until 14 December 2013. + +To date, the United States is the only country to have successfully landed humans on the Moon. The last mission was in December, 1972, and the last human to walk on the Moon was Gene Cernan. + +== References == + +Category:Moon +Category:Astronomy +<|CHUNK_END|> +thumb|250px|right|[[Tim Henman hitting a backhand volley]] +right|thumb|200px|[[Andy Roddick before serving]] +thumb|Tennis balls +thumb|A female player +thumb|Scoreboard +'''Tennis''' is a sport played with a felt-covered rubber ball, a tennis racket, and a court. It is quite popular, and many people enjoy watching it. + +In the early 11th century, players in France first played with their hands a similar sport, which was called “''jeu de paume''”. In the 15th century, the players played with rackets. The sporty is now is called “tennis” and became popular in England and France. King Henry III of France was a big fan of the sport, which is now known as real tennis ("real" here meaning "royal"). The sport of "lawn tennis", played on grass courts, was invented in mid 19th-century England and later spread into many other countries.Tyzack, Anna, [http://www.countrylife.co.uk/news/culture/article/79487/The_True_Home_of_Tennis.html The True Home of Tennis] ''Country Life'', 22 June 2005[http://www.itftennis.com/abouttheitf/worldwide/history.asp History of Tennis] International Tennis Federation. Retrieved 28 July 2008. + +==Tennis matches== +There are many different kinds of courts, like grass, clay, or hard court. The goal of tennis is to hit the ball over the net into the other player’s court. When the other player cannot return the ball, a point is won. The game is played with two or four people When it is played with two people, it is called "singles"''',''' and when it is played with four people, it is called "doubles". The court has "alleys" on each side, which are "fair" territory during doubles. + +A tennis game has a number of sets. Each set has a number of games, and each game has points. The points are counted love (0, after the French ''l'oeuf''), fifteen (15), thirty (30), and forty (40). If both players get to forty, the score is ''deuce'' from which two more points are needed to win the game. When one player reaches six games, one set is finished. + +During a thr +<|CHUNK_END|> +In mathematics, the '''Laplace transform''', named after Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable (usually , in the ''time domain'') to a function of a complex variable s (in the complex-valued frequency domain, also known as '''''s''-domain''' or '''''s''-plane'''). The functions are often denoted using a lowercase symbol for the time-domain function and the corresponding uppercase symbol for the frequency-domain function, e.g. x(t) and . + +The transform is useful for converting differentiation and integration in the time domain into the algebraic operations multiplication and division in the Laplace domain (analogous to how logarithms are useful for simplifying multiplication and division into addition and subtraction). This gives the transform many applications in science and engineering, mostly as a tool for solving linear differential equations and dynamical systems by replacing ordinary differential equations and integral equations with algebraic polynomial equations, and by replacing convolution with multiplication. + +For example, through the Laplace transform, the equation of the simple harmonic oscillator (Hooke's law) x''(t) + kx(t)=0 is converted into the algebraic equation s^2X(s) - s x(0) - x'(0) +kX(s) = 0, which incorporates the initial conditions x(0) and , and can be solved for the unknown function . Once solved, the inverse Laplace transform can be used to transform it to the original domain. This is often aided by referencing tables such as that given below. + +The Laplace transform is defined (for suitable functions ) by the integral + + \mathcal{L}\{f\}(s) = \int_0^\infty f(t) e^{-st} \, dt, + +where is a complex number. + +The Laplace transform is related to many other transforms. It is essentially the same as the Mellin transform and is closely related to the Fourier transform. Unlike for the Fourier transform, the Laplace transform of a function is often an analytic function, meaning that it can b +<|CHUNK_END|> +'''Optics''' is the science of light and how it interacts with the world. Optics explains how rainbows exist, how light reflects off mirrors, how light refracts through glass or water, and what splits light shining through a prism. In addition to visible light in the standard "spectrum" of red, orange, yellow, green, blue, indigo, and violet, optics also deals with invisible parts of the whole electromagnetic spectrum of which visible light is only a small part. + +Optics is both a science and an area of engineering. It has been used to make many useful things, including eyeglasses, cameras, telescopes, and microscopes. Many of these things are based on lenses, which focus light and can make images of things that are bigger or smaller than the original. + +While optics is an old science, new things are still being discovered in it. Scientists have learned how to make light travel through a thin optical fiber made of glass or plastic. Light can go long distances in a fiber. Fibers are used to carry phone calls and the Internet through cities and around the world. + +== Related pages == +*Spectroscopy +<|CHUNK_END|> +In probability and statistics, the '''binomial distribution''' is a probability distribution which models the probabilities of having a certain number of successes among ''n'' identical trials (each having ''p'' as the probability of success). It is also written as \operatorname{Bin}(n, p). The variables n and p are thus the two parameters of a binomial distribution. + +The binomial distribution has discrete values. It counts the number of successes in yes/no-type experiments. Each of these experiment, also called Bernoulli trial, either results in success or failure. Examples of binomial distribution include: +* Tossing a coin 10 times, and counting the number of ''face-up''s. (n=10, p=1/2) +* Rolling a dice 10 times, and counting the number of sixes. (n=10, p=1/6) +* Counting the number of green-eyed people among 500 randomly chosen people (assuming that 5% of all people have green eyes). (n=500, p=0.05) +In order to use the binomial distribution, the following must be true about the problem: +# The outcomes are '''mutually exclusive''', that is, there are two possible outcomes which cannot occur simultaneously (for example. in flipping a coin, there are two possible outcomes: '''heads''' or '''tails'''. It is always one or the other, never both or a mix of outcomes). +# The probability of a success (p) is consistent throughout the problem (for example, a basketball player makes 85% of his free throws. Each time the player attempts a free throw, 85% is assumed to be the likelihood of a made shot). +# The trials are '''independent''' of each other (for example, on the second flip of a coin, the first outcome does not impact the chance of the next toss: the chance of tossing a heads (or tails) is still 50%). + +== Related pages == + +* Bernoulli distribution +* Poisson distribution + +== References == + +Category:Probability distributions +<|CHUNK_END|> +'''Database normalization''' is the process of structuring a relational database in accordance with a series of '''''normal forms''''' to reduce data redundancy and improve data integrity. It was first proposed by British computer scientist Edgar F. Codd as part of his relational model. + +Normalization entails organizing the columns (attributes) and tables (relations) of a database to ensure that their dependencies are properly enforced by database integrity constraints. It is accomplished by applying some formal rules either by a process of ''synthesis'' (creating a new database design) or ''decomposition'' (improving an existing database design). + +== Objectives == +A basic objective of the first normal form defined by Codd in 1970 was to permit data to be queried and manipulated using a "universal data sub-language" grounded in first-order logic."The adoption of a relational model of data ... permits the development of a universal data sub-language based on an applied predicate calculus. A first-order predicate calculus suffices if the collection of relations is in normal form. Such a language would provide a yardstick of linguistic power for all other proposed data languages, and would itself be a strong candidate for embedding (with appropriate syntactic modification) in a variety of host languages (programming, command- or problem-oriented)." Codd, [https://dl.acm.org/doi/10.1145/362384.362685 "A Relational Model of Data for Large Shared Data Banks"] , p. 381 An example of such a language is SQL, though it is one that Codd regarded as seriously flawed.Codd, E.F. Chapter 23, [https://dl.acm.org/doi/10.5555/77708.C1065772 "Serious Flaws in SQL"], in ''The Relational Model for Database Management: Version 2''. Addison-Wesley (1990), pp. 371–389 + +The objectives of normalization beyond 1NF (first normal form) were stated by Codd as: + +thumb|280px|An '''insertion anomaly'''. Until the new faculty member, Dr. Newsome, is assigned to teach at least one course, their detai +<|CHUNK_END|> +}} +thumb|300px|A definite integral of a function can be represented as the [[signed area of the region bounded by its graph and the horizontal axis; in the above graph as an example, the integral of f(x) between a and b is the yellow (−) area subtracted from the blue (+) area|alt=Definite integral example]] + +In mathematics, an '''integral''' is the continuous analog of a sum, and is used to calculate areas, volumes, and their generalizations. The process of computing an integral, called '''integration''', is one of the two fundamental operations of calculus, along with differentiation.Integral calculus is a very well-established mathematical discipline for which there are many sources. See and , for example. Integration was initially used to solve problems in mathematics and physics, such as finding the '''area under a curve''', or determining displacement from velocity. Usage of integration expanded to a wide variety of scientific fields thereafter. + +A '''definite integral''' computes the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept of an ''antiderivative'', a function whose derivative is the given function; in this case, they are also called ''indefinite integrals''. The fundamental theorem of calculus relates definite integration to differentiation and provides a method to compute the definite integral of a function when its antiderivative is known; differentiation and integration are inverse operations. + +Although methods of calculating areas and volumes dated from ancient Greek mathematics, the principles of integration were formulated independently by Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century, who thought of the area under a curve as an infinite sum of rectangles of infinitesimal width. Bernhard Riemann later gave a +<|CHUNK_END|> +thumb|400px|right|Several sets of (''x'', ''y'') points, with the [[Pearson correlation coefficient of ''x'' and ''y'' for each set. The correlation reflects the noisiness and direction of a linear relationship (top row), but not the slope of that relationship (middle), nor many aspects of nonlinear relationships (bottom). N.B.: the figure in the center has a slope of 0 but in that case, the correlation coefficient is undefined because the variance of ''Y'' is zero.]] + +In statistics, '''correlation''' is a type of statistical relationship between two random variables or bivariate data. It usually refers to the extent to which a pair of quantities are linearly related. More generally, an arbitrary relationship between variables is called an '''association''', meaning the degree to which the variability in one can be accounted for by the other.Upton, G., Cook, I. (2006) ''Oxford Dictionary of Statistics'', 2nd Edition, OUP. ISBN 978-0-19-954145-4 + +The presence of a correlation is not sufficient to infer the presence of a causal relationship (i.e., correlation does not imply causation). +Furthermore, the concept of correlation is not the same as dependence: if two variables are independent, then they are uncorrelated, but the opposite is not necessarily trueeven if two variables are uncorrelated, they might be dependent on each other. + +Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. + +There are several correlation coefficients that may be used to measure correlation, often denoted \rho or r. The most common of them is the , which is sensitive only to a linear relationship between two variables (which in turn may be present even when one var +<|CHUNK_END|> +thumb|150px|[[Animals: Hoverfly on a Compositae inflorescence]] +thumb|150px|[[Plants: Wheat]] +thumb|150px|[[Fungi: ''Morchella esculenta'']] +thumb|150px|[[Virus: Gamma bacteriophage]] + +'''Biology''' is the science that studies life, living things, and the evolution of life. Living things include animals, plants, fungi (such as mushrooms), and microorganisms such as bacteria and archaea. + +The term 'biology' is relatively modern. It was introduced in 1799 by a physician, Thomas Beddoes."biology, n.". OED Online. 2019. Oxford University Press. ''Physiology therefore—or more strictly biology—by which I mean the doctrine of the living system in all its states, appears to be the foundation of ethics and pneumatology.'' It comes from the Greek word ''βίος'' (''bios''), "life", and the suffix ''-λογία'' (''logia''), "study of". Origin and meaning of biology by Online Etymology Dictionary|website=www.etymonline.com|language=en|access-date=2019-05-29}} + +People who study biology are called biologists. Biology looks at how animals and other living things behave and work, and what they are like. Biology also studies how organisms react with each other and the environment. It has existed as a science for about 200 years, and before that it was called "natural history". Biology has many research fields and branches. Like all sciences, biology uses the scientific method. This means that biologists must be able to show evidence for their ideas and that other biologists must be able to test the ideas for themselves. + +Biology attempts to answer questions such as: + +* "What are the characteristics of this living thing?" (comparative anatomy) +* "How do the parts work?" (physiology) +* "How should we group living things?" (classification, taxonomy) +* "What does this living thing do?" (behaviour, growth) +* "How does inheritance work?" (genetics) +* "What is the history of life?" (palaeontology) +* "How do living things relate to their environment?" (ecology) + +Modern biology is influenced by e +<|CHUNK_END|> +| screenshot = File:Linux 6.1.0-27 kernel (running on Debian Bookworm).png +| caption = Linux kernel 6.1.0 kernel booting, under Debian +| developer = Community contributors Linus Torvalds +| programming language = C, C11 (gnu11) since 5.18, C89 (gnu89) before}} assembly, Rust}} and others +| released = 0.02 () +| latest release version = '''Regular''': / '''LTS''': / +| latest release date = +| latest preview version = +| latest preview date = +| language = English +| license = GPL-2.0-only with Linux-syscall-note Aside from that, individual files can be provided under a different license that is required to be compatible with the GPL-2.0-only license (i.e., the GNU General Public License version 2) or a dual license, with one of the choices being the GPL version 2 or a GPLv2 compatible license.}} +| author = Linus Torvalds +}} + +The '''Linux kernel''' is a free and open-source Unix-like kernel that is used in many computer systems worldwide. The kernel was created by Linus Torvalds in 1991 and was soon adopted as the kernel for the GNU operating system (OS), which was created to be a free replacement for Unix. Since the late 1990s, it has been included in many operating system distributions, many of which are called Linux. One such Linux kernel operating system is Android, which is used in many mobile and embedded devices. + +Most of the kernel code is written in C as supported by the GNU Compiler Collection (GCC), which has extensions beyond standard C. The code also contains assembly code for architecture-specific logic such as optimizing memory use and task execution. The kernel has a modular design such that modules can be integrated as software components including dynamically loaded. The kernel is monolithic in an architectural sense since the entire OS kernel runs in kernel space. + +Linux is provided under the GNU General Public License version 2, although it contains files under other compatible licenses. + +== History == + +thumb|upright|[[Linus Torvalds at the Li +<|CHUNK_END|> +'''String theory''' tries to use math to explain the four known fundamental forces—gravitation, electromagnetism, strong nuclear force, weak nuclear force—together in one theory. This tries to solve the problems of having both classical physics and quantum physics. + +Einstein wanted a unified field theory, a single theory to explain the fundamental forces. Today's scientists want a unified field theory that also explains matter. This is called the search for a theory of everything (TOE). The most famous theory used as a TOE is called superstring theory. It says there are 6 higher dimensions as well as the four dimensions of Height, Length, Width and Time). + +Some superstring theories think that it is about the geometry of space. This idea is a big part of a theory called M-theory. Many string theorists believe that M-theory explains the universe and might explain how other universes, if they exist, are as part of the "multiverse". M theory/supergravity theory has 7 higher dimensions and the four dimensions of Height, Length, Width and Time. + +== Background == + +Introductions to string theory that are designed for the general public must first explain physics. Some of the controversies over string theory are because of people not understanding physics. A common misunderstanding even is the idea that a theory is proven true whenever something it says will happen happens. Another misunderstanding is that earlier physical scientists, including chemists, have already explained the world. This leads to the misunderstanding that string theorists began making up new ideas after they became "set free from truth". + +=== Classical realm === + +==== Newtonian physics ==== + +Newton's law of universal gravitation (UG) was published in 1687. Newton's theory successfully explained objects big enough for us to see them. Coulomb's law explained electricity. Maxwell's electromagnetic field theory explained electricity and magnetism. This led to the creation of optics, the study of lig +<|CHUNK_END|> +'''Artificial intelligence''' ('''AI''' or '''A.I.''') is a computer program or a machine that is able to learn and mimic human cognition.Russell, Stuart J. & Norvig, Peter 2003. ''Artificial intelligence: a modern approach''. 2nd ed, Upper Saddle River, New Jersey: Prentice Hall. Sometimes, AI is used to talk about neural networks or deep learning.Salam, M., Farooq, M.S., Ikram, A., Shahzad, M., Ali, A., Jaafar, N., 2025. Revised Artificial Intelligence Device Use Acceptance (RAIDUA) Model: Exploring Privacy Concerns for Socially Responsible AI Deployment and Ethical AI Leadership. Journal of Hospitality and Tourism Insights 0, 1–23. https://doi.org/10.1108/JHTI-02-2025-0322 + +Artificial intelligence is a system's ability to understand external data, to learn from that data, and to use what it has learned to achieve specific goals or tasks through adaptation. + +Artificial intelligence is widely applied in speech recognition, image recognition, robotics, autonomous systems, natural language processing, machine translation, predictive analytics, medical diagnostics, fraud detection, and the control of physical processes. + +== Origin of name == +John McCarthy came up with the name, "artificial intelligence" in 1956. Intelligence allows an organism to act in a meaningful way in its environment. It includes the ability to get sensory inputs, and to react to these. + +== Laws == +The European Union made a law (2024's second quarter) about ''artificial intelligence''. It is the world's first law that regulates AI.https://sciencebusiness.net/news/worlds-first-artificial-intelligence-law-moves-closer-passage-european-parliament + +Connecticut and Colorado tried to pass laws (in 2024) regarding use of AI. + +== History == +AI research started with a conference at Dartmouth College in 1956. It was a month-long brainstorming session many people who like AI came to. At the conference, they wrote programs which were able to beat humans at checkers or solving word problems. The Department o +<|CHUNK_END|> +'''General relativity''' is a theory of space and time. The theory was published by Albert Einstein in 1915.O'Connor J.J. and E.F. Robertson (1996), "[http://www-history.mcs.st-and.ac.uk/HistTopics/General_relativity.html General relativity]". ''[http://www-history.mcs.st-and.ac.uk/Indexes/Math_Physics.html Mathematical Physics index]'', [http://www.st-andrews.ac.uk/maths/ School of Mathematics and Statistics], [http://www.st-andrews.ac.uk/ University of St. Andrews], Scotland, May, 1996. Retrieved 2015-02-04. + +The main idea of general relativity is that space and time are two different parts of spacetime. In general relativity, gravity does not work the same way that Sir Isaac Newton said gravity worked. According to Einstein, gravity changes not only space, but also time (gravitational time dilation). + +==Idea== +An important idea in general relativity is the "principle of equivalence". An example is that two people, one on the surface of the Earth, and the other in an elevator in outer space but accelerating upwards at the speed of Earth's gravity will each observe the same behavior of an object they drop from their hands. The object will accelerate to the floor at the speed of Earth's gravity (9.8 m/s2) in either case. + +This makes it impossible for either to tell whether or not they are at rest in a gravitational field or accelerating with no gravity. Other versions of this type of "thought experiment" were used to show that light would curve in an accelerating frame of reference. + +In relativity, acceleration makes spacetime warp. Because gravity is the same as acceleration, spacetime warps around objects. This can be thought of as spacetime being a jello of some sort, curving into itself, so that a straight line ends up curving. The Sun and other objects with mass (and energy) curve four dimensional spacetime fabric. If there’s enough mass or energy in one place, a black hole is made, because the warping from acceleration becomes so extreme that future and inwar +<|CHUNK_END|> +|tag2=bo|name2=ཇོ་མོ་གླང་མ|postfix2= |tag3=zh|name3=珠穆朗玛峰|postfix3= }} +| translation = Holy Mother, Skyhead +| etymology = George Everest +| elevation_ref = ''.}} Ranked 1st +| prominence_ref = Ranked 1st(Special definition for Everest) +| isolation = n/a +| map = Nepal#Nepal Province1#China#China Tibet topography#Asia +| map_caption = Location on the border between Koshi Province, Nepal and Tibet Autonomous Region, China +| label = Mount Everest +| label_position = left +| location = Solukhumbu District, Koshi Province, Nepal;''Geography of Nepal: Physical, Economic, Cultural and Regional'' by Netra Bahadur Thapa, D. P. Thapa Orient Longmans, 1969.Tingri County, Xigazê, Tibet Autonomous Region, China +| country_type = Countries +| country = China and Nepal +| parent = Mahalangur Himal, Himalayas +| coordinates = +| coordinates_ref = +| first_ascent = 29 May 1953Edmund Hillary and Tenzing Norgay Ranked 1st +| normal_route = Southeast ridge (Nepal) +}} +'''Mount Everest'''; }} is the highest mountain on Earth. Mount Everest is in the Himalayas, a tall mountain range in Asia. It is about high and one of the Seven Summits. Everest is located in the Mahalangur Himal sub-range of the Himalayas in the Solukhumbu district of Nepal. + +Mount Everest is on the line between two countries: Nepal and China. The top of the mountain is in the "death zone", where the air is too thin for a human to live. People need large bottles of oxygen to let them breathe; However, some people have been able to walk through the death zone without oxygen bottles; Some of those came to the top of the mountain, and survived going down. The first people to get to the top were Edmund Hillary and Tenzing Norgay in 1953. + +There are 18 ways (paths or routes) to get to the top,https://www.nationalgeographic.com/travel/article/150420-everest-climbing-sherpas-mountaineering-nepal-himalayas-guides. National Geographic (2015) but most people use only two ways. + +As of the first week of October 2025, "At least 200 climbers +<|CHUNK_END|> +| year = +| designer = Robert GriesemerRob PikeKen Thompson +| developer = The Go Authors +| latest release version = +| latest release date = }} +| latest_test_version = +| latest_test_date = --> +| typing = Inferred, static, strong, structural, nominal +| implementations = gc, gofrontend +| programming language = Go, Assembly language (gc); C++ (gofrontend) +| dialects = +| influenced_by = , Erlang, +| influenced = Odin, Crystal, Zig, V (Vlang) +| operating_system = many +| license = 3-clause BSD + patent grant +| file_ext = .go +}} + +'''Go''', also known as '''Golang''', is a statically-typed concurrent programming language made by an engineer team at Google. + +== Example == +Here is a hello world program in Go. + +package main +// Import fmt library through the standard library. +import "fmt" + +// Define entry point. +func main() { + // Write to output. + fmt.println("Hello world!") +} + +== References == + +Category:Multi-paradigm programming languages +<|CHUNK_END|> +thumb + +'''Freedom of speech''' is the right to state one's opinions and ideas without being stopped or punished. Sometimes this is also called '''freedom of expression'''. + +Freedom of speech may include freedom of the press and freedom of information. It usually includes ''speaking in public''; only rarely does it include speaking in the family or in other private situations. + +Most people think freedom of speech is necessary for a democratic government. In countries without free speech, people might be afraid to say what they think. Then, the government does not know what the people want. If the government does not know what they want, it cannot respond to their wants. Without free speech, the government does not have to worry as much about doing what the people want. Some people say this is why some governments do not allow free speech: they do not want to be criticised, or they fear there would be revolution if everyone knew everything that was happening in the country. + +A well-known liberal thinker, John Stuart Mill, believed that freedom of speech is important because the society that people live in has a right to hear people's ideas. It's not just important because everyone should have a right to express him or herself. + +Few countries with "free speech" let everything be said. For example, the United States Supreme Court said that it was against the law to shout "fire" in a crowded theater if there is no fire, because this might cause people to panic. The International Covenant on Civil and Political Rights also says that it is not okay to cause national, racial or religious hatred.International Covenant on Civil and Political Rights, Article 20 Also, some countries have laws against hate speech. + +As Tocqueville pointed out, people may be hesitant to speak freely not because of fear of government punishment but because of social pressures. When an individual announces an unpopular opinion, he or she may face the disdain of their community or even be subjected +<|CHUNK_END|> +'''Gene editing''' may refer to: + +*Genetic engineering of any organism by genome editing +*Genome editing, a type of genetic engineering +*Gene therapy, the therapeutic delivery of nucleic acid polymers into a patient's cells as a way to treat disease +*CRISPR gene editing, a genetic engineering technique +*Zinc finger editing, using nucleases +<|CHUNK_END|> +'''Space Complexity''' is a concept in theoretical computer science, specifically Complexity Theory, which is used to measure and describe the efficiency of an algorithm in terms of the amount of memory they will require to store the information they need. Algorithms, when implemented in computer programs, require two main resources when the program is executed: time and memory. Memory, particularly, may be expensive in large quantities. Therefore it is often desirable to make modifications to an algorithm so as to reduce its space complexity, that is, make it use less memory when run. + +== Space Complexity and Input Size == +As with time complexity, space complexity is usually given in terms of the input size, using Big-O notation. Usually, the input size is given as a number n that refers to an amount of elements that need to be considered to solve a problem. The space complexity is then often given as a function that gets larger as n increases. This function indicates how quickly the memory requirement grows when n is very large. + +'''Auxiliary Space Complexity''' refers to the amount of storage space that the algorithm will use besides the storage space which is already used for the input data. As the input data for any algorithm will have to be stored in memory, it is often more important to know whether the algorithm can operate "in place", i.e. without a need for memory that will grow as n gets large. + +== Relationship With Time Complexity == +The other resource that algorithms consume is time. The so-called time complexity of an algorithm is measured in the same way and is more commonly taught first in courses covering algorithms. It is worth noting that there is a relationship between the auxiliary space complexity of an algorithm and its time complexity: since the former measures the amount of data that is created after the algorithm begins, the time complexity is always greater than the auxiliary space complexity. + +Category:Theoretical computer science +<|CHUNK_END|> +thumb|200px|A [[Brain mapping|mappingOliver Elbs, ''Neuro-Esthetics: Mapological foundations and applications (Map 2003)'', (Munich 2005) of the brain from the 1800s. Phrenology was one way that tried to explain the brain in the past, although it is now considered wrong.]] +'''Philosophy of mind''' is one part of philosophy that works with the mind. It is about thinking how the mind works, and how it relates to the world. It also deals with consciousness, which is also researched in psychology and physics. + +==Mind-body problem== +The mind-body problem is the main problem that is talked about in philosophy of mind. It is the problem of how our minds and our bodies are related, and what exactly the mind is. Many different answers have been given to solve the mind-body problem. Most of them fall into the two groups of dualism and monism. + +=== Dualism as an answer to the mind-body problem === + +Dualism is the belief that minds and bodies are separate things. One of the main dualist views comes from René Descartes and is named Cartesian dualism, or substance dualism. Descartes thought that minds and bodies were two completely different substances (like matter) in the world. He argued that consciousness was different from the brain. + +One reason to believe dualism is that when you ask most people what the mind is, they would say it is their personality or their soul. They would almost certainly deny that the mind simply is the brain, or vice versa, finding the idea that there is just one ''ontological'' thing at play to be too machine-like. Mental events have a subjective quality, whereas physical events do not. So, for example, one can ask what a blue sky looks like, or what nice music sounds like to a person. But it is odd, to ask what an increase in chemicals in your brain feels like. These subjective aspects of mental events are called "qualia" by philosophers. + +But if it is true that the mind can exist without the brain, dualists must explain how a non-physical mind ca +<|CHUNK_END|> +'''Physical chemistry''' uses physics to study chemical systems. It studies them at macroscopic, atomic, subatomic, and particulate levels. It looks at concepts like motion, energy, force, time, thermodynamics, quantum chemistry, statistical mechanics and dynamics. + +Physical chemistry is not the same as chemical physics. Physical chemistry is mostly a macroscopic or supra-molecular science. The majority of physical chemistry concepts relate to bulk properties rather than to molecular/atomic structure alone. These include chemical equilibrium and colloids. + +Some of the relationships that physical chemistry tries to resolve include the effects of: +#Intermolecular forces on the physical properties of materials (for example, plasticity, tensile strength, surface tension in liquids). +#Reaction kinetics on the rate of a reaction. +#The identity of ions on the electrical conductivity of materials. +#Surface chemistry and electrochemistry of membranes. + +== History == +thumb|right|Fragment of M. Lomonosov's manuscript 'Physical Chemistry' (1752) +The term "physical chemistry" was first used by Mikhail Lomonosov in 1752. He presented a lecture course with the title "A Course in True Physical Chemistry" to the students of Petersburg University. + +Modern physical chemistry was developed in the 1860s to 1880s with work on chemical thermodynamics, electrolytes in solutions, chemical kinetics and other subjects. In 1876, Josiah Willard Gibbs wrote an article called, ''On the Equilibrium of Heterogeneous Substances''. This paper introduced many of the main parts of physical chemistry, such as Gibbs energy, chemical potentials, Gibbs phase rule.Josiah Willard Gibbs, 1876, "On the Equilibrium of Heterogeneous Substances", ''Transactions of the Connecticut Academy of Sciences'' Other important discoveries include Heike Kamerlingh Onnes' work on enthalpy and macromolecular processes. + +The first scientific journal about physical chemistry was the German journal, ''Zeitschrift für Physi +<|CHUNK_END|> +'''NoSQL''' (originally meaning "not only SQL" or "non-relational")http://nosql-database.org/ "NoSQL DEFINITION: Next Generation Databases mostly addressing some of the points : being non-relational, distributed, open-source and horizontally scalable". refers to a type of database design that stores and retrieves data differently from the traditional table-based structure of relational databases. Unlike relational databases, which organize data into rows and columns like a spreadsheet, NoSQL databases use a single data structure—such as key–value pairs, wide columns, graphs, or documents—to hold information. Since this non-relational design does not require a fixed schema, it scales easily to manage large, often unstructured datasets. IBM |url=https://www.ibm.com/topics/nosql-databases |access-date=2024-08-09 |website=www.ibm.com |language=en-us}} NoSQL systems are sometimes called ''"Not only SQL"'' because they can support SQL-like query languages or work alongside SQL databases in polyglot-persistent setups, where multiple database types are combined. Non-relational databases date back to the late 1960s, but the term "NoSQL" emerged in the early 2000s, spurred by the needs of Web 2.0 companies like social media platforms. + +NoSQL databases are popular in big data and real-time web applications due to their simple design, ability to scale across clusters of machines (called horizontal scaling), and precise control over data availability. These structures can speed up certain tasks and are often considered more adaptable than fixed database tables. However, many NoSQL systems prioritize speed and availability over strict consistency (per the CAP theorem), using eventual consistency—where updates reach all nodes eventually, typically within milliseconds, but may cause brief delays in accessing the latest data, known as stale reads. While most lack full ACID transaction support, some, like MongoDB, include it as a key feature. + +== Barriers to adoption == +Barriers to w +<|CHUNK_END|> +An operating system '''shell''' is a user interface that enables the user to interact with and access the services offered by the operating system. The user gives commands to the operating system through its shell. + +In simple words - a shell is a program that accepts the input from users and excutes program on their behalf by creating a new process, and whatever the response from that particular program - which could be input, output or error - it shows back to the user. + +==Various shells== +There are various types of shells: +#Command line shells: the user types commands at the prompt. +#Menu driven shells: the user selects commands from menus. +#Graphical user interface shells: the user selects  graphical menus and icons. + +Examples of command line operating systems are UNIX and Disk Operating System (DOS). Examples of menu driven operating systems are the DOS shell. Finally, examples of graphical user interface (GUI) operating system are Linux and Microsoft Windows. + +Category:Computing +<|CHUNK_END|> +Favorable traits pass on to more successful offspring than ones with less favorable traits, making the traits more common in the population. The Galapagos islands experience a drought and there were less soft, small seeds for the birds to eat. There was increase however with larger and hard seeds. The birds with a bigger beak ate the seeds more easily and passed on those traits. Several philosophers of the classical era, including Empedocles and his intellectual successor, the Roman poet Lucretius, expressed the idea that nature produces a huge variety of creatures, randomly, and that only those creatures that manage to provide for themselves and reproduce successfully persist. Empedocles' idea that organisms arose entirely by the incidental workings of causes such as heat and cold was criticised by Aristotle in Book II of ''Physics''. He posited natural teleology in its place, and believed that form was achieved for a purpose, citing the regularity of heredity in species as proof. Nevertheless, he accepted in his biology that new types of animals, monstrosities (τερας), can occur in very rare instances (''Generation of Animals'', Book IV). As quoted in Darwin's 1872 edition of ''The Origin of Species'', Aristotle considered whether different forms (e.g., of teeth) might have appeared accidentally, but only the useful forms survived So what hinders the different parts [of the body] from having this merely accidental relation in nature? as the teeth, for example, grow by necessity, the front ones sharp, adapted for dividing, and the grinders flat, and serviceable for masticating the food; since they were not made for the sake of this, but it was the result of accident. And in like manner as to the other parts in which there appears to exist an adaptation to an end. Wheresoever, therefore, all things together (that is all the parts of one whole) happened like as if they were made for the sake of something, these were preserved, having been appropriately constituted by +<|CHUNK_END|> +|designer=Martin Odersky|developer=Programming Methods Laboratory of École Polytechnique Fédérale de Lausanne}} + +'''Scala''' is a general-purpose programming language—a language that is designed for solving all kinds of problems, not just a specific one. + +It provides support for functional programming, and is statically typed. It is designed to fix some problems with Java, and to be concise—to be able to express a lot with only a little bit of code. + +Scala code is supposed to be compiled into Java bytecode, so Scala code can be run on a Java Virtual Machine (JVM). Scala has language interoperability with Java—Scala code can be used in Java programs, and the other way around. The Scala Programming Language|website=www.scala-lang.org|access-date=2019-05-22}} + +== Examples == + +=== "Hello, World" example === +This is a small example of a Scala program. A simple Hello world program: +@main def main() = println("Hello, World!") + +== References == + +Category:Programming languages +<|CHUNK_END|> +thumb|Illustration of matrix multiplication +In mathematics and linear algebra, '''matrix multiplication''' is multiplying two matrices together. The number of columns in the first matrix must be equal to the number of rows in the second matrix. The product of two matrices \mathbf{A} and \mathbf{B} is written as \mathbf{A}\mathbf{B} + +To multiply two matrices, the rows of the first matrices are multiplied with the columns of the second. Then, the products are summed to make the entry in the product. + +Matrix multiplication is associative, but not commutative. + +== Related pages == +*Matrix addition +*Determinant + +== References == + +Category:Linear algebra +<|CHUNK_END|> +}} +'''Quantum entanglement''' is the name given to a special connection between pairs or groups of quantum systems, or any objects described by quantum mechanics. Quantum entanglement is one of the biggest parts of quantum mechanics that makes it hard to understand in terms of the everyday world. + +== Explanation == +When we look at particles, we usually say that each particle has its own quantum state. Sometimes, two particles can act on one another and become an entangled system. When a pair or group of particles can only be described by the quantum state for the system, and not by individual quantum states, we say the particles are "entangled". + +* Particles have a "quantum state", which is a way of describing their properties. +* Sometimes, two particles can interact with each other and become a "system" where they are entangled. +* When the quantum state of a group of particles can only be described for the whole system, and not for individual particles, we say that the particles are "entangled". + +In simpler terms, "entangled" particles are those that are connected in such a way that their properties are linked and cannot be described independently. This is a strange phenomenon that is not fully understood, but it is an important idea in physics. + +== When and why do we see entanglement? == +Entanglement between particles happens because little particles can push and pull on each other, just like big objects do in terms of gravity. If nothing else is acting on those particles, then there are certain things before and after the particles act on each other that have to stay the same. For example, the total momentum of both particles put together would be (roughly) the same before and after they act on each other. + +Heisenberg's uncertainty principle tells us we can never know the momentum of a particle exactly, or even the total momentum of both particles put together. In fact, we can't ever know exactly what we will measure the momentum of a particle to be before we me +<|CHUNK_END|> +thumb|400px|right|Example of samples from two populations with the same mean but different variances. The red population has mean and variance (), while the blue population has mean and variance (). + +In probability theory and statistics, '''variance''' is the expected value of the squared deviation from the mean of a random variable. The standard deviation is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers are spread out from their average value. It is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by , , , , or . + +An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation; for example, the variance of a sum of uncorrelated random variables is equal to the sum of their variances. A disadvantage of the variance for practical applications is that, unlike the standard deviation, its units differ from the random variable, which is why the standard deviation is more commonly reported as a measure of dispersion once the calculation is finished. Another disadvantage is that the variance is not finite for many distributions. + +There are two distinct concepts that are both called "variance". One, as discussed above, is part of a theoretical probability distribution and is defined by an equation. The other variance is a characteristic of a set of observations. When variance is calculated from observations, those observations are typically measured from a real-world system. If all possible observations of the system are present, then the calculated variance is called the population variance. Normally, however, only a subset is available, and the variance calculated from this is called the sample variance. The variance calculated from a sample is considered an estimate of the full population +<|CHUNK_END|> +In computer science, a '''binary tree''' is a type of tree (data structure) where each item +within the tree has at most two children. + +==Types of binary trees== +alt=|thumb|A complete binary tree which is not full. +* In a '''balanced binary tree''' the left and right branches of every item differ in height by no more than 1. +* In a '''complete binary tree''' every level, except possibly the last, is completely filled, and all items in the last level are as far left as possible. +* In a '''full binary tree''' every item has either 0 or 2 children. +* In a '''perfect binary tree''' all interior items have two children and all leaves have the same depth or same level. A perfect binary tree is also a full and complete binary tree. + +==Representations== + +===Array=== +A binary tree can be implemented using an array by storing its level-order traversal. In a zero-indexed array, the root is often stored at index 1. + +For the ''nth'' item of the array its: +* left child is stored at the ''2n'' index. +* right child is stored at the ''2n+1'' index. +* parent is stored at the ''n/2'' index. + +===References=== +In a programming language with references, binary trees are typically constructed by having a tree structure which contains references to its left child and its right child. + +==Traversals== +thumb|281px|Traversals of an example tree: +''Pre-order (red):'' +''In-order (yellow):'' +''Post-order (green):'' + +===Pre-order=== +The current item is visited, then the left branch is visited, and then the right branch is visited. + +void preOrder(Item item) { + if (item == null) return; + visit(item); + preOrder(item.left); + preOrder(item.right); +} + +===In-order=== +The left branch is visited, then the current item is visited, and then the right branch is visited. + +void inOrder(Item item) { + if (item == null) return; + inOrder(item.left); + visit(item); + inOrder(item.right); +} + +===Post-order=== +The left branch is visited, the right branch is visited, and then the current item is +<|CHUNK_END|> +In mathematics and computer science, '''Big O notation''' is a way of comparing rates of growth of different functions. It is often used to compare the efficiency of different algorithms, which is done by calculating how much memory is needed, and how much time it takes to complete. + +The Big O notation is often used in identifying how complex a problem is, also known as the problem's complexity class. The mathematician Paul Bachmann (1837-1920) was the first to use this notation, in the second edition of his book "Analytische Zahlentheorie", in 1896. Edmund Landau (1877-1938) made the notation popular. For this reason, when people talk about a '''Landau symbols''', they refer to this notation. + +Big O notation is named after the term "order of the function", which refers to the growth of functions. Big O notation is used to find the upper bound (the highest possible amount) of the function's growth rate, meaning it works out the longest time it will take to turn the input into the output. This means an algorithm can be grouped by how long it can take in a worst-case scenario, where the longest route will be taken every time. + +More specifically, given two positive functions f(x) and g(x), we say that f is in the big O of g (written f \in O(g)) if for large enough x, f(x) \le k \cdot g(x) for some constant k. Algorithms|url=https://www.khanacademy.org/computing/computer-science/algorithms/asymptotic-notation/a/big-o-notation|access-date=2020-09-22|website=Khan Academy|language=en}} Brilliant Math & Science Wiki|url=https://brilliant.org/wiki/big-o-notation/|access-date=2020-09-22|website=brilliant.org|language=en-us}} + +Big O is an expression that finds worst-case scenario run-time, showing how efficient an algorithm is without having to run the program on a computer. This is also useful due to the fact that different computers may have different hardware, and therefore need different amounts of time to complete it. Since Big O always assumes the worst-case, it can show +<|CHUNK_END|> +In mathematics, '''exponentiation''' ('''power''') is an arithmetic operation on numbers. It can be thought of as repeated multiplication, just as multiplication can be thought of as repeated addition. + +In general, given two numbers x and y, the exponentiation of x and y can be written as x^y, and read as "x raised to the power of y", or "x to the yth power". Other methods of mathematical notation have been used in the past. When the upper index cannot be written, people can write powers using the ^ or ** signs, so that 2^4 or 2**4 means 2^4. + +Here, the number x is called '''base''', and the number y is called '''exponent'''. For example, in 2^4, 2 is the base and 4 is the exponent. + +To calculate 2^4, one simply multiply 4 copies of 2. So 2^4=2 \cdot 2 \cdot 2 \cdot 2, and the result is 2 \cdot 2 \cdot 2 \cdot 2=16. The equation could be read out loud as "2 raised to the power of 4 equals 16." + +More examples of exponentiation are: +*5^3=5\cdot{} 5\cdot{} 5=125 +*x^2=x\cdot{} x +*1^x = 1 for every number ''x'' + +If the exponent is equal to 2, then the power is called '''square''', because the area of a square is calculated using a^2. So +:x^2 is the square of x + +Similarly, if the exponent is equal to 3, then the power is called '''cube''', because the volume of a cube is calculated using a^3. So +:x^3 is the cube of x + +If the exponent is equal to -1, then the power is simply the reciprocal of the base. So +:x^{-1}=\frac{1}{x} +If the exponent is an integer less than 0, then the power is the reciprocal raised to the opposite exponent. For example: +:2^{-3}=\left(\frac{1}{2}\right)^3=\frac{1}{8} +If the exponent is equal to \tfrac{1}{2}, then the result of exponentiation is the square root of the base, with x^{\frac{1}{2}}=\sqrt{x}. For example: +:4^{\frac{1}{2}}=\sqrt{4}=2 +Similarly, if the exponent is \tfrac{1}{n}, then the result is the nth root, where: +:a^{\frac{1}{n}}=\sqrt[n]{a} +If the exponent is a rational number \tfrac{p}{q}, then the result is the ''q''th root of the +<|CHUNK_END|> +In computer science, '''counting sort''' is an algorithm for sorting a collection of objects according to keys that are small positive integers; that is, it is an integer sorting algorithm. It operates by counting the number of objects that possess distinct key values, and applying prefix sum on those counts to determine the positions of each key value in the output sequence. Its running time is linear in the number of items and the difference between the maximum key value and the minimum key value, so it is only suitable for direct use in situations where the variation in keys is not significantly greater than the number of items. It is often used as a subroutine in radix sort, another sorting algorithm, which can handle larger keys more efficiently.. See also the historical notes on page 181... + +Counting sort is not a comparison sort; it uses key values as indexes into an array and the lower bound for comparison sorting will not apply. Bucket sort may be used in lieu of counting sort, and entails a similar time analysis. However, compared to counting sort, bucket sort requires linked lists, dynamic arrays, or a large amount of pre-allocated memory to hold the sets of items within each bucket, whereas counting sort stores a single number (the count of items) per bucket. + +==Input and output assumptions== +In the most general case, the input to counting sort consists of a collection of items, each of which has a non-negative integer key whose maximum value is at most . +In some descriptions of counting sort, the input to be sorted is assumed to be more simply a sequence of integers itself, but this simplification does not accommodate many applications of counting sort. For instance, when used as a subroutine in radix sort, the keys for each call to counting sort are individual digits of larger item keys; it would not suffice to return only a sorted list of the key digits, separated from the items. + +In applications such as in radix sort, a bound on the maximum key val +<|CHUNK_END|> +thumb|240px|The price (P) of a product is determined by a balance between production at each price (supply, S) and the desires of those with [[purchasing power at each price (demand, D). The diagram shows a positive shift in demand from D1 to D2, resulting in an increase in price and quantity sold (Q) of the product.]] + +'''Supply and demand''' is a model of microeconomics. It describes how a price is formed in a market economy. There are two determining factors on such a market, the number of things made available, called supply, and the number of things consumers want, called demand. Supply and demand shows how producers and consumers interact with each other. This relationship will fix the price for a certain type of good. In perfect competition, the quantity demanded (demand) and the quantity supplied will be equal. This happens at the equilibrium market price. + +For normal goods, and a normal market, there are four basic laws that determine the change in the market, if either supply or demand changes: +*If the demand increases, and the supply remains the same, there will be a shortage, and the price will increase. +*If the demand decreases, and the supply remains the same, there will be a surplus, and the price will go down. +*If the supply increases, and the demand remains the same, there will be a surplus, and the price will go down. +*If the supply decreases, and the demand remains the same, there will be a shortage, and the price will increase. + +When there is more supply, this will cause prices to fall because people will not want to pay more for items that can be found easily. When there is more demand, prices will go up because many people want to buy the same item but there is not enough supply for it. + +When demands for new goods and services go up, new markets come into being. The greater the demand, the faster this happens. This greater number of providers makes the supply go up, which forces the price down toward the cost of production and distribution. + + +<|CHUNK_END|> +| latest_release_date = }} +| typing = duck, dynamic +| implementations = Ruby MRI, YARV, Rubinius, MagLev, JRuby, MacRuby, RubyMotion, HotRuby, IronRuby, [https://github.com/mruby/mruby mruby] +| influenced_by = Ada, C++, CLU, Dylan, Eiffel, Lisp, Perl, Python, Smalltalk +| influenced = D,[http://www.digitalmars.com/d/1.0/ Intro – D Programming Language 1.0 – Digital Mars] Elixir, Falcon, Fancy, Groovy, Ioke, Mirah, Nu, Reia, Crystal +| operating_system = Cross-platform +| license = Ruby License or BSD License +| website = +| file_ext = .rb, .rbw +| wikibooks = Ruby Programming +}} +'''Ruby''' is the name of a programming language that was created in the mid-1990s by Yukihiro "Matz" Matsumoto in Japan. Like other programming languages, such as Python, its structure (the way it works) is very similar to the English language. It has these qualities: + +* Terse. Short, but still easy to understand. +* Dynamic. Easy to change, anytime and anywhere. +* Duck typing. If you think you understand it, you probably understand it. + +Many programmers like it because the creator tried to make it easy and nice to use. + +Ruby on Rails (RoR) is a web application framework that is implemented using the Ruby language. + +== Example == +An example Hello World program in Ruby: + +puts "Hello World!" + +An example program in Ruby that asks for your name and then says it: + +puts "What's your name?" +name = gets.chomp +puts "Ah hello there, #{name}" + +A function in Ruby that joins the 2 strings (or arrays/integers) into one, removes all numbers from it, capitalizes the string and then repeats it 5 times: + +def somefunction(arg1, arg2) # creates a function with 2 arguments. the args can be called anything + arg = arg1 + arg2 # this joins them into 1 string + arg = arg.tr("1234567890","") # this replaces all the numbers with a nothing. erases them essentially. + arg = arg.capitalize # read that out loud + +<|CHUNK_END|> +thumb|right|300px|[[Chi-squared distribution, showing on the first axis and ''p''-value (right tail probability) on the second axis.]] + +A '''chi-squared test''' (also '''chi-square''' or ''' test''') is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine whether two categorical variables (''two dimensions of the contingency table'') are independent in influencing the test statistic (''values within the table''). + +The test is valid when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants thereof. Pearson's chi-squared test is used to determine whether there is a statistically significant difference between the expected frequencies and the observed frequencies in one or more categories of a contingency table. For contingency tables with smaller sample sizes, a Fisher's exact test is used instead. + +In the standard applications of this test, the observations are classified into mutually exclusive classes. If the null hypothesis that there are no differences between the classes in the population is true, the test statistic computed from the observations follows a frequency distribution. The purpose of the test is to evaluate how likely the observed frequencies would be assuming the null hypothesis is true. + +Test statistics that follow a distribution occur when the observations are independent. There are also tests for testing the null hypothesis of independence of a pair of random variables based on observations of the pairs. + +''Chi-squared tests'' often refers to tests for which the distribution of the test statistic approaches the distribution asymptotically, meaning that the sampling distribution (if the null hypothesis is true) of the test statistic approximates a chi-squared distribution more and more closely as sample sizes increase. + +== History == +In the 19th century, statisti +<|CHUNK_END|> +'''Renewable energy''' comes from renewable resources.Resources that for all practical purposes cannot be used up: United States Department of Energy [http://www.eere.energy.gov/consumer/information_resources/index.cfm/mytopic=60001#R Glossary of energy-related terms] (URL accessed Dec 21, 2006) It is different from fossil fuels as it does not produce as many greenhouse gases and other pollutants as fossil fuel combustion. + +People have used traditional wind power, hydropower, biofuel, and solar energy for many centuries, all around the world. The mass production of electricity using renewable energy sources is now becoming more common. + +thumb|250px|Renewable energy sources: [[wind, sun, water (hydropower, tidal energy and wave power), biomass, and geothermal energy.]] + +==Growth of renewables== +thumb|right|A hydropower plant in Japan +From the end of 2004, worldwide renewable energy capacity grew at rates of 10–60% annually for many technologies. For wind power and many other renewable technologies, growth sped up in 2009 relative to the previous four years. More wind power was added during 2009 than any other renewable technology. However, grid-connected PV increased the fastest of all renewables technologies, with a 60% annual average growth rate. + +{| class="wikitable sortable" +|- +! Selected renewable energy global indicatorsREN21 (2012). [http://www.map.ren21.net/GSR/GSR2012.pdf Renewables Global Status Report 2012] p. 17.http://www.ren21.net/Portals/0/documents/Resources/GSR/2014/GSR2014_full%20report_low%20res.pdf !! 2008 !! 2009 !! 2010 !! 2011 !! 2012 || 2013 +|- +| Investment in new renewable capacity (annual) (109 USD) || 130 || 160 || 211 || 257 || 244 ||214 +|- +| Renewables power capacity (existing) (GWe) || 1,140 || 1,230 || 1,320 || 1,360 || 1,470 || 1,560 +|- +| Hydropower capacity (existing) (GWe) || 885 || 915 || 945 || 970 ||990|| 1,000 +|- +| Wind power capacity (existing) (GWe) || 121 || 159 || 198 || 238 || 283 || 318 +|- +| Solar PV capacity (grid-co +<|CHUNK_END|> +The '''Internet''' is the world’s largest global communication network for computers and other devices. +It connects many smaller networks from homes, schools, businesses, and governments. These networks share different kinds of information. The short form of the Internet is “the Net.” One of its most popular services is the World Wide Web, which is used by billions of people every day. +thumb|Logo of [[DARPA, an organization funded by the US government, which helped develop the Internet]] +The Internet was developed in the United States by the Department of Defence Advanced Research Projects Agency (DARPA). The Internet was first connected in October 1969 and was called ARPANET. The World Wide Web was created at CERN in Switzerland in 1990 by a British (UK) scientist named Tim Berners-Lee. + +Today, people use Internet services by paying Internet service providers (ISPs). +Some websites and tools are free, while others may show ads to earn money. There are also ongoing debates about censorship and freedom of speech on the Internet. + +== Services == +thumb|Visualization of Internet routing paths +The Internet is used for many things, such as electronic mail, online chat, file transfer and other documents of the World Wide Web. + +The most used service on the Internet is the World Wide Web (which is also called the "Web" or “www”). The web contains websites, including social media, blogs, and wikis like Wikipedia. Webpages on the Internet can be seen and read by anyone (unless the page needs a password, or it is blocked). + +The second biggest use of the Internet is to send and receive e-mail. E-mail is private and goes from one user to another. Instant messaging is similar to email, but allows two or more people to chat to each other faster. + +Some governments think the internet is a bad thing, and block all or part of it. For example, the Chinese government thinks that Wikipedia is bad, so often no one in China can read it or add to it. Another example of the internet being blo +<|CHUNK_END|> +thumb|right|300px|A map showing the five main oceans of the world. + +An '''ocean''' is a large body of water between continents. Oceans are extremely big and they join smaller seas together. Oceans (or marine) cover 70% of Earth. There are five main oceans: the Pacific Ocean, the Atlantic Ocean, the Indian Ocean, the Southern Ocean, and the Arctic Ocean.The largest ocean is the Pacific Ocean. The smallest ocean is the Arctic Ocean. Many types of animals live in oceans, such as carp, crabs, starfish, sharks, and whales. +Different water movements separate the Southern Ocean from the Atlantic, Pacific and Indian Oceans. The Southern Ocean is also called the Antarctic Ocean, because it covers the area around Antarctica. + +The deepest ocean is the Pacific Ocean. The deep ocean is characterized by cold temperatures, high pressure, and complete darkness. Some very unusual organisms live in this part of the ocean. They do not require high energy from the sun to survive, because they use chemicals from deep inside the Earth. + +== Color == +Although many people believe that the oceans are blue because the water reflects the blue sky, this is actually not true. Water has a very slight blue color that can only be seen when there is a lot of water. However, the main cause of the blue or blue/green color of the oceans is that water absorbs the red part of the incoming light, and reflects the green and blue part of the light. We then see the reflected light as the color of water. +thumb|Ocean and beach shore + +== Plants and animals == +Many organisms live in oceans. Organisms that live in oceans can live in salt water. They are affected by sunlight, temperature, water pressure, and water movement. Different ocean organisms live near the surface, in shallow waters, and in deep waters. Small plant organisms that live near the surface and use sunlight to produce food are called phytoplankton. Almost all animals in the ocean depend directly or indirectly on these plants. In shallow water, yo +<|CHUNK_END|> +frame|A quadratic equation graphed in the coordinate plane. +A '''quadratic equation''' is an equation where its highest exponent is 2 (which is why it is called 'quadratic' from the Latin word ''quadratus'' 'square'). These equations can be rearranged to the standard form which is [https://books.google.com/books?id=e4_iBQAAQBAJ&pg=PA219 Extract of page 219]ː + +ax^2+bx+c=0 + +where ''a'' is not equal to 0, otherwise the equation is linear. + +It makes a parabola (a "U" shape) when graphed on a coordinate plane. When people work with quadratic equations, one of the most common things they do is to ''solve'' it. This means to find the points on a coordinate grid where the graphed equation crosses the x-axis, or the horizontal axis. These points are called the "zeroes", or "roots", of a function. In other words, to solve the equation means to find the value of ''x'' so that ax^2+bx+c=0, where the coefficients, ''a'', ''b'', and ''c'', are all real numbers. There are different ways to find out the value of x. Plotting the function on a graph is one way. In the picture on the right, the function crosses the x-axis at the points (-1, 0) and (2, 0). + +Graphing a quadratic equation makes it is very easy to find the roots, but it is not always convenient. So there are different ways to do this using math. + +== Solving quadratic equations == +A quadratic equation with real or complex coefficients has two solutions, called ''roots''. These two solutions may or may not be equal, and they may or may not be a real number. + +=== Factoring === +Some quadratic equations, like 2x^2-x-1=0, can be factorized. This equation can be written as (2x+1)(x-1)=0, which produces two separate equations, 2x+1=0 and x-1=0. This is because when any of the two equations is equal to zero, the original equation is equal to zero because the two equations are multiplied together to form the quadratic equation. From this equation, it is easy to use algebra to find out what the value of ''x'' is. In the first of th +<|CHUNK_END|> +'''Calculus''' is a branch of mathematics that describes continuous change. + +There are two different types of calculus. '''Differential calculus''' divides (''differentiates'') things into small (''different'') pieces, and tells us how they change from one moment to the next, while '''integral calculus''' joins (''integrates'') the small pieces together, and tells us how much of something is made, overall, by a series of changes. Calculus is used in many different sciences such as physics, astronomy, biology, engineering, economics, medicine and sociology. + +==History== +In the 1670s and 1680s, Sir Isaac Newton in England and Gottfried Leibniz in Germany figured out calculus at the same time, working separately from each other. Newton wanted to have a new way to predict where to see planets in the sky, because astronomy had always been a popular and useful form of science, and knowing more about the motions of the objects in the night sky was important for navigation of ships. Leibniz wanted to measure the space (area) under a curve (a line that is not straight). Many years later, the two men argued over who discovered it first. Scientists from England supported Newton, but scientists from the rest of Europe supported Leibniz. Most mathematicians today agree that both men share the credit equally. Some parts of modern calculus come from Newton, such as its uses in physics. Other parts come from Leibniz, such as the symbols used to write it. + +They were not the first people to use mathematics to describe the physical world — Aristotle and Pythagoras came earlier, and so did Galileo Galilei, who said that mathematics was the language of science. But both Newton and Leibniz were the first to design a system that describes how things change over time, and can predict how they will change in the future. + +The name "calculus" was the Latin word for a small stone the ancient Romans used in counting and gambling. The English word "calculate" comes from the same Latin word. + +==D +<|CHUNK_END|> +}}}}}} +|image = Olympic rings without rims.svg +|image_upright = +|caption = +|abbreviation = Olympiad (for summer games only) +|motto = ''|(French: '')''}} +|formation = '''Summer'''Athens, Greece in 1896'''Winter'''Chamonix, France in 1924 +|recurrence = Four years, alternated two years during the four-year cycle +|headquarters = Lausanne, Switzerland +|leader_title = President +|leader_name = Thomas Bach +|website = +|remarks = +}} + +thumb|right|[[Ancient Greek discus thrower]] + +The '''Olympic Games''' () is an important international event featuring summer and winter sports. Summer Olympic Games and Winter Olympic Games are held every four years. Originally, the ancient Olympic Games were held in Ancient Greece at Olympia. The first games were in 776 BC. They were held every four years until the 6th century AC. The first "modern" Olympics took place in 1896 in Athens, Greece. Athletes participate in the Olympics Games to represent their countries. + +Over time the Olympics have become bigger. In old times, women were not allowed, but now there are women's events. The Winter Games were created for ice and snow sports. The Paralympic Games were created for athletes with physical disabilities. As well, the Olympics became bigger with the addition of the Youth Olympic Games for teenage athletes. World War I and World War II led to the cancellation of the 1916, 1940, and 1944 Games. As the decision-making body, the International Olympic Committee (IOC) is responsible for choosing the host city for each Olympic Games. The IOC is also responsible for choosing what sports are in the games. The creator of modern Olympics is Baron Pierre de Coubertin. + +The celebration of the Games includes many rituals and symbols, such as Olympic flag and torch, as well as the opening and closing ceremonies. The first, second, and third-place finishers in each event receive, respectively, gold, silver, and bronze medals. + +== Ancient Olympics == + +thumb|left|250px|Stadium in [[Olympia, Greece]] +The Olymp +<|CHUNK_END|> +thumb|250px|right|Wind power: worldwide installed capacity (1996–2013)[http://www.gwec.net/index.php?id=180 GWEC, Global Wind Report Annual Market Update] thumb|Fenton Wind Farm at [[Minnesota]] + +'''Wind power''' is the conversion of the energy in wind into a more useful form of energy, like electricity. It is a renewable source of energy that helps to cut down on the pollution of earth's air. + +Wind power capacity has expanded quickly to 336 GW in June 2014, and wind energy production was about 4% of total worldwide electricity usage, and growing fast. Wind power is widely used in European countries, and more recently in the United States and Asia.[http://www.gwec.net/uploads/media/07-02_PR_Global_Statistics_2006.pdf Global wind energy markets continue to boom – 2006 another record year] (PDF).Global Wind Energy Council (2009). [http://www.gwec.net/fileadmin/documents/Publications/Global%20Wind%202008%20Report.pdf Global Wind 2008 Report] , p. 9, accessed on January 4, 2010. In 2012, wind power accounted for approximately 30% of electricity generation in Denmark, 20% in Portugal and 18% in Spain.International Energy Agency (2013). [http://www.ieawind.org/annual_reports_PDF/2012/2012%20IEA%20Wind%20AR_smallPDF.pdf IEA Wind Energy: Annual Report 2012] p. 5. + +==How it works== +Wind power stations use the wind to turn a turbine which turns a magnet inside a coil (a type of generator). The wind has kinetic energy (movement energy) which is changed into mechanical energy by the blades on the turbine. The turbine then turns a generator which creates electrical energy (voltage). The turbine is usually connected by a gearbox to help control the speed it turns the generator. + +==Advantages== +Wind power stations are clean and renewable energy as they have the advantage over fossil fuel power stations as they do not produce any greenhouse gases such as carbon dioxide or water vapour. They also do not produce for gases that helps to make acid rain such as sulphur dioxide. The +<|CHUNK_END|> +| olympic = 1896 +| world = 1973 +| paralympic = 1960 +}} + +'''Swimming''' is an individual or team racing sport that requires the use of one's entire body to move through water. The sport takes place in pools or open water (e.g., in a sea or lake). Competitive swimming is one of the most popular Olympic sports, with varied distance events in butterfly, backstroke, breaststroke, freestyle, and individual medley. In addition to these individual events, four swimmers can take part in either a freestyle or medley relay. A medley relay consists of four swimmers who will each swim a different stroke, ordered as backstroke, breaststroke, butterfly and freestyle. + +Swimming each stroke requires a set of specific techniques; in competition, there are distinct regulations concerning the acceptable form for each individual stroke. There are also regulations on what types of swimsuits, caps, jewelry and injury tape that are allowed at competitions. There are many health benefits to swimming, but it is possible for competitive swimmers to incur injuries such as tendinopathy in the shoulders or knees. + +==History== + +thumb|[[Hero and Leander|Leander swimming across the Hellespont. Detail from a painting by Bernard Picart.]] +Evidence of recreational swimming in prehistoric times has been found, with the earliest evidence dating to Stone Age paintings from around 10,000 years ago. Written references date from 2000 BC, with some of the earliest references to swimming including the Iliad, the Odyssey, the Bible, Beowulf, the Quran and others. In 1538, Nikolaus Wynmann, a Swiss–German professor of languages, wrote the earliest known complete book about swimming, ''Colymbetes, sive de arte natandi dialogus et festivus et iucundus lectu'' (''The Swimmer, or A Dialogue on the Art of Swimming and Joyful and Pleasant to Read''). + +Swimming emerged as a competitive recreational activity in the 1830s in England. In 1828, the first indoor swimming pool, St George's Baths was opened to the pu +<|CHUNK_END|> +thumb|Rust icon +'''Rust''' is a programming language designed for systems, which are "software designed to provide a platform for other software".Klabnik, S., & Nichols, C. (2019). The Rust Programming Language (Covers Rust 2018). No Starch Press.Blandy, J. (2015). The Rust Programming Language: Fast, Safe, and Beautiful. O'Reilly Media, Inc..Naugler, D. (2018). An introduction to Rust programming. Journal of Computing Sciences in Colleges, 33(5), 97-97.Arbuckle, D. (2018). Rust Quick Start Guide: The Easiest Way to Learn Rust Programming. Packt Publishing Ltd. It is or was used to write operating system and web browser components, services such as OpenDNS and Tor, and game engines. It was made by former Mozilla engineer Graydon Hoare. Lambda the Ultimate|url=http://lambda-the-ultimate.org/node/4009|access-date=2021-04-14|website=lambda-the-ultimate.org}} + +Software developer Graydon Hoare created Rust as a personal project while working at Mozilla Research in 2006. Mozilla officially sponsored the project in 2009. Since the first stable release in May 2015, Rust has been adopted by companies including Amazon, Discord, Dropbox, Facebook (Meta), Google (Alphabet), and Microsoft. + +==Applications== +* AstrophysicsBlanco-Cuaresma, S., & Bolmont, E. (2016). What can the programming language Rust do for astrophysics?. Proceedings of the International Astronomical Union, 12(S325), 341-344. +* GPU programmingHolk, E., Pathirage, M., Chauhan, A., Lumsdaine, A., & Matsakis, N. D. (2013, May). GPU programming in rust: Implementing high-level abstractions in a systems-level language. In 2013 IEEE International Symposium on Parallel & Distributed Processing, Workshops and Phd Forum (pp. 315-324). IEEE. +* SimulationHansen, A., & Lewis, M. C. (2016). The Case for N-Body Simulations in Rust. In Proceedings of the International Conference on Scientific Computing (CSC) (p. 3). The Steering Committee of The World Congress in Computer Science, Computer Engineering and Applied Computing (W +<|CHUNK_END|> +In statistics, the '''mode''' is the value that appears most often in a set of data values.Damodar N. Gujarati. ''Essentials of Econometrics''. McGraw-Hill Irwin. 3rd edition, 2006: p. 110. If is a discrete random variable, the mode is the value at which the probability mass function takes its maximum value, i.e., . In other words, it is the value that is most likely to be sampled. + +Like the statistical mean and median, the mode is a summary statistic about the central tendency of a random variable or a population. The numerical value of the mode is the same as that of the mean and median in a normal distribution, but it may be very different in highly skewed distributions. + +The mode is not necessarily unique in a given discrete distribution since the probability mass function may take the same maximum value at several points , , etc. The most extreme case occurs in uniform distributions, where all values occur equally frequently. + +A mode of a continuous probability distribution is often considered to be any value at which its probability density function has a locally maximum value. When the probability density function of a continuous distribution has multiple local maxima it is common to refer to all of the local maxima as ''modes'' of the distribution, so any peak is a mode. Such a continuous distribution is called ''multimodal'' (as opposed to ''unimodal''). + +In symmetric unimodal distributions, such as the normal distribution, the mean (if defined), median and mode all coincide. For samples, if it is known that they are drawn from a symmetric unimodal distribution, the sample mean can be used as an estimate of the population mode. + +==Mode of a sample== + +The mode of a sample is the element that occurs most often in the collection. For example, the mode of the sample [1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17] is 6. Given the list of data [1, 1, 2, 4, 4] its mode is not unique. A dataset, in such a case, is said to be bimodal, while a set with more than two modes m +<|CHUNK_END|> +right|thumb|An [[animation that shows how a Taylor series can be used to approximate a function. The blue line shows the exponential function f(x)=e^{x}. The red lines show the sum of ''n'' derivatives -- that is, ''n''+1 terms in the Taylor series. As ''n'' gets bigger, the red line gets closer to the blue line.]] +A '''Taylor series''' is an idea used in computer science, calculus, chemistry, physics and other kinds of higher-level mathematics. It is a series that is used to create an estimate (guess) of what a function looks like. There is also a special kind of Taylor series called a '''Maclaurin series'''. + +The theory behind the Taylor series is that if a point is chosen on the coordinate plane (x- and y-axes), then it is possible to guess what a function will look like in the area around that point. This is done by taking the derivatives (instant slope) of the function and adding them all together. The idea is that it is possible to add the infinite number of derivatives and come up with a single finite sum. + +In mathematics, a Taylor series shows a function as the sum of an infinite series. The sum's terms are taken from the function's derivatives. Taylor series come from Taylor's theorem. + +== History == +The Ancient Greek philosopher Zeno of Elea first came up with the idea of this series. The paradox called "[https://en.m.wikipedia.org/wiki/Zeno's_paradoxes Zeno's paradox]" is the result. He believed that it would be impossible to add an infinite number of values and get a single finite value as a result. + +Another Greek philosopher, Aristotle, came up with an answer to the philosophical question. It was Archimedes, however, who came up with a mathematical solution using his method of exhaustion. He was able to prove that when something is split up into an infinite number of tiny pieces, they will still add up to a single whole when all of them are added back together. The ancient Chinese mathematician Liu Hui proved the same thing several hundred years later. +<|CHUNK_END|> +An '''application programming interface''' (API) is a set of functions, procedures, methods or classes used by computer programs to request services from the operating system, software libraries or any other service providers running on the computer. A computer programmer uses the API to make +computer applications. + +An API works by making a structure for computers to interact with each other, including rules for interactions and methods the computers can use to quickly send data to each other. Because an API's goal is to connect computers with other computers, they are different from a user interface, which has the goal of connecting human users with computers. + +Main types of web APIs: + +* Open APIs - available to the public; they can be accessed by any external users. +* Partner APIs - available to strategic business partners; they are exposed to a public API developer portal. +* Internal APIs - available to a company's internal development teams; they are exposed to a private API developer portal. +* Composite APIs - are a sequence of tasks bundled into a single API call. + +Types of API include web services API like the Twitter API, which allows programs to use the API to receive updates on tweets. + +==References== + +Category:Software +<|CHUNK_END|> +A '''recurrent neural network''' ('''RNN''') is a special type of artificial neural network (a computer program) that can remember things it has seen before. RNNs do this by connecting information from the past (called a ''hidden state'') with new information. Because of this, RNNs are good at processing data in a sequence, like understanding language, translating between languages, or predicting what might come next in a sequence. + +== References == + +Category:Machine learning +<|CHUNK_END|> +thumb|[[Ancient Greek mathematician Euclid (holding calipers), 3rd century BC, as imagined by Raphael in this detail from the School of Athens (1509–1511)]] +'''Mathematics''' is the study of numbers, shapes, and patterns and letters. The word comes from the Greek ''μάθημα'' (máthema), meaning "science, knowledge, or learning", and is sometimes shortened to '''math or maths'''. + +It is the study of: +* Numbers: including how things can be counted. +* Structure: including how things are organized, but also how they can be or could have been. This subfield is usually called algebra. +* Place: where things are, and spatial arrangement, including arrangements of spaces themselves. This subfield is usually called geometry. +* Change: how things become different. This subfield is usually called analysis. + +Applied math is useful for solving problems in the real world. People working in business, science, engineering, and construction use mathematics. SIAM|website=www.siam.org|language=en-US|access-date=2018-07-30}} + +== Problem-solving in mathematics == +Mathematics solves problems by using logic. One of the main tools of logic used by mathematicians is deduction. Deduction is a special way of thinking to discover and prove new truths using old truths. To a mathematician, the reason something is true (called a proof) is just as important as the fact that it is true, and this reason is often found using deduction. Using deduction is what makes mathematical thinking different from other kinds of scientific thinking, which might rely on experiments or on interviews. + +Logic and reasoning are used by mathematicians to create general rules, which are an important part of mathematics. These rules leave out information that is not important so that a single rule can cover many situations. By finding general rules, mathematics solves many problems at the same time as these rules can be used on other problems. These rules can be called theorems (if they have been proven) or conjectures (if +<|CHUNK_END|> +thumb|Healthy eating pyramid per Harvard School of Public Health +'''Nutrition''' provides the cells of an organism with food, in a form they can use. Organisms need food to be able to keep their bodies working properly. They also need food to be able to do certain things. Malnutrition can happen when a person does not eat the right amount of nutrients. They can get better by changing their diet to have the right amount of the various nutrients. +==Overview== +Different organisms have different food requirements and eat different food in order to meet those requirements. Animals that do not eat meat. For example, will have to get certain nutrients like protein from other foods. A nutrition expert is called a dietician. Nutritionists are different because they do not need the government to recognize them as experts. Anyone can call themselves a nutritionist. + +==Types== +The six main types of nutrient are carbohydrates, fats, minerals, proteins, vitamins and water. A macronutrient is a nutrient that needs to be eaten a lot. A micronutrient, such as a vitamin, is needed in smaller amounts, but it is still important. Carbohydrates are not needed by the body but most people eat a lot of them. Complex carbohydrates are more nutritious than simple carbohydrates. Complex carbohydrates are found in vegetables while simple carbohydrates are found in processed foods. They take longer to digest because they have more fiber. Because they stay in the stomach for longer they leave the person who has eaten them feeling fuller for longer. Protein is needed for building cells. It is found in milk, meat, fish, beans, eggs and other foods like quinoa. Proteins are made of amino acids. +===Fats=== +Fat is found naturally in some foods. People often eat it in processed foods, such as cakes and chocolate, which are high in energy. Omega 3 and omega 6 fats are needed by the body. There are saturated fats and unsaturated fats. It is recommended that people avoid the saturated type. It has been li +<|CHUNK_END|> +thumb|upright|[[Stephen Cole Kleene, introduced the concept in 1951]] +A '''regular expression''' (abbreviated '''regexp''' or '''regex''') is a way to describe sets of characters using syntactic rules. Many programming languages use or support regular expressions. A regular expression is then used by a special program or part of a programming language. This program will either generate a parser that can be used to match expressions or it will match such expressions itself. A simple use case for this is to find all words or phrases in a text that match a certain pattern. In one case, the 'pattern' might just be a word, but in more complex cases, there might be rules that say that the word needs to start with an uppercase letter, or that only certain letters are allowed. + +A '''regular expression processor''' is used for processing a regular expression statement in terms of a grammar in a given formal language, and with that examines a text string. + +A few examples of what can be matched with regular expressions: +* The sequence of characters "car" appearing consecutively in any context, such as in "car", "cartoon", or "bicarbonate". +* The sequence of characters "car" occurring in that order with other characters between them, such as in "Icelander" or "chandler". +* The word "car" when it appears as an isolated word. +* The word "car" when preceded by the word "blue" or "red". +* The word "car" when ''not'' preceded by the word "motor". +* A dollar sign immediately followed by one or more digits, and then optionally a period and exactly two more digits (for example, "$10" or "$245.99"). This does not match "$ 5", because of the space between the dollar sign and the digit, nor "€25", because there is no dollar sign. + +Regular expressions can be much more complex than these examples. Many regular expression languages also support "wildcard" characters. A more complex example might be t0 validate a date. Some months have 31 days, others have 30; February has 29 in some case +<|CHUNK_END|> +In computer science, '''selection sort''' is an in-place comparison sorting algorithm. It has a O(''n''2) time complexity, which makes it inefficient on large lists, and generally performs worse than the similar insertion sort. Selection sort is noted for its simplicity and has performance advantages over more complicated algorithms in certain situations, particularly where auxiliary memory is limited. + +The algorithm divides the input list into two parts: a sorted sublist of items which is built up from left to right at the front (left) of the list and a sublist of the remaining unsorted items that occupy the rest of the list. Initially, the sorted sublist is empty and the unsorted sublist is the entire input list. The algorithm proceeds by finding the smallest (or largest, depending on sorting order) element in the unsorted sublist, exchanging (swapping) it with the leftmost unsorted element (putting it in sorted order), and moving the sublist boundaries one element to the right. + +The time efficiency of selection sort is quadratic, so there are a number of sorting techniques which have better time complexity than selection sort. + +== Example == +Here is an example of this sort algorithm sorting five elements: + +{| class="wikitable" +! Sorted sublist +! Unsorted sublist +! Least element in unsorted list +|- +| () +| style="text-align:right;" | (12, 25, 64, 11, 22) +| 11 +|- +| (11) +| style="text-align:right;" | (25, 64, 12, 22) +| 12 +|- +| (11, 12) +| style="text-align:right;" | ( 64, 25, 22) +| 22 +|- +| (11, 12, 22) +| style="text-align:right;" | (25, 64) +| 25 +|- +| (11, 12, 22, 25) +| style="text-align:right;" | (64) +| 64 +|- +| (11, 12, 22, 25, 64) +| style="text-align:right;" | () +| +|} +right|thumb|Selection sort animation. Red is current min. Yellow is sorted list. Blue is current item. +(Nothing appears changed on these last two lines because the last two numbers were already in order.) + +Selection sort can also be used on list structures that make add and remove efficient, such as +<|CHUNK_END|> +A '''large language model''' ('''LLM''') is a type of artificial intelligence that can understand and create human language. These models learn by studying huge amounts of text from books, websites, and other sources. + +==How they work== +LLMs work by finding patterns in language. They learn grammar, facts, and how words relate to each other by looking at billions of examples. The most powerful LLMs use a special design called "transformer," which helps them process large amounts of text quickly. + +===Limitations=== +While LLMs are powerful, they can make mistakes. They sometimes include biases from their training data, and they can produce incorrect information. They learn from existing text rather than having true understanding like humans do. + +==History== +Before 2017, language models were much simpler. The big change came when Google created the "transformer" design, which made language models much more powerful. + +Important developments include: +* 2018: BERT was released, which helped computers better understand language +* 2019: GPT-2 was created but was considered so powerful that its creators worried about misuse +* 2022: ChatGPT was released and became very popular with the public +* 2023: GPT-4 came out and could understand both text and images + +===Modern developments=== +Today, there are many different LLMs available. Some are private, like GPT-4, while others are open for anyone to use, like Deepseek and Mistral. , GPT-4 was considered one of the most capable language models. + +==References== + +Category:Machine learning +Category:Generative artificial intelligence +<|CHUNK_END|> +'''Depression''' may refer to: + +==Mental health== +* Depression (mood), a state of low mood and aversion to activity +* Mood disorders characterized by depression are commonly referred to as simply ''depression'', including: +** Major depressive disorder, also known as ''clinical depression'' +** Bipolar disorder, also known as ''manic depression'' +** Dysthymia, also known as ''persistent depressive disorder'' +** Psychotic depression, depressive episode that is accompanied by psychotic symptoms +** Seasonal affective disorder, also known as ''seasonal depression'' +** Atypical depression, characterized by improved mood in response to positive events +*Long-term depression, reduction of neuronal synapse efficacy + +==Economics== +* Economic depression, a sustained, long-term downturn in economic activity in one or more economies +** Great Depression, a severe economic depression during the 1930s, commonly referred to as simply ''the Depression'' +** Long Depression, an economic depression during 1873–96, known at the time as the ''Great Depression'' +==Biology== +* Depression (kinesiology), an anatomical term of motion, refers to downward movement, the opposite of elevation +* Depression (physiology), a reduction in a biological variable or the function of an organ +* Central nervous system depression, physiological depression of the central nervous system that can result in loss of consciousness + +==Earth science== +* Depression (geology), a landform sunken or depressed below the surrounding area +* Depression (weather), an area of low atmospheric pressure characterized by rain and unstable weather +==Art== +* "Depressed" (song), a song by English singer-songwriter Anne-Marie, 2025 +<|CHUNK_END|> +220px|right|thumb|Tangent to a curve. The red line is tangential to the curve at the point marked by a red dot. +220px|right|thumb|Tangent plane to a sphere + +In geometry, the '''tangent line''' (or simply '''tangent''') to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve.In "Nova Methodus pro Maximis et Minimis" (''Acta Eruditorum'', Oct. 1684), Leibniz appears to have a notion of tangent lines readily from the start, but later states: "modo teneatur in genere, tangentem invenire esse rectam ducere, quae duo curvae puncta distantiam infinite parvam habentia jungat, seu latus productum polygoni infinitanguli, quod nobis curvae aequivalet", ie. defines the method for drawing tangents through points infinitely close to each other. More precisely, a straight line is tangent to the curve ''f''(''x'')}} at a point ''c''}} if the line passes through the point on the curve and has slope (''c'')}}, where ''f'' is the derivative of ''f''. A similar definition applies to space curves and curves in ''n''-dimensional Euclidean space. + +The point where the tangent line and the curve meet or intersect is called the '''''point of tangency'''''. The tangent line is said to be "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point. +The tangent line to a point on a differentiable curve can also be thought of as a ''tangent line approximation'', the graph of the affine function that best approximates the original function at the given point.Dan Sloughter (2000) . "[https://math.dartmouth.edu/opencalc2/dcsbook/c3pdf/sec31.pdf Best Affine Approximations]" + +Similarly, the '''tangent plane''' to a surface at a given point is the plane that "just touches" the surface at that point. The concept of a tangent is one of the most fundamental notions in differential geometry and has be +<|CHUNK_END|> +'''International law''', also called '''public international law''', is a set of laws used when there is a conflict between countries. These help set standards for human rights and global relations. Since there is no completely agreed authority to enforce it, the rules are suggestions for nations to follow. + +Private International Law is when there is a conflict between two or more countries that broke a certain law based on the countries' law. It is composed of a set of treaties. + +In recent years, people have also seen international organizations like the United Nations use international law. + +== Related pages == +* European Union law +* International human rights law +* Geneva Conventions +* Laws of war +* Roerich Pact + +Category:International law +<|CHUNK_END|> +A '''republic''' is a form of government that has no monarchy and no hereditary aristocracy, and instead the head of state (the highest political authority) is an elected office It originates from Rome. In 509 BC, the Romans overthrew the Roman Kingdom and established a republic, a government in which citizens elected representatives to rule on their behalf. + +National sovereignty lies in the authority of the government, not in an emperor or monarch. The word ''republic'' comes from the Latin words '''res publica''', meaning a "public thing". For example, the United States and India are republics. However, the United Kingdom and Canada are not republics since they have a monarch (King Charles III in both cases). + +Countries with a king or other monarch and free elections is called a constitutional monarchy, not republics. A constitutional monarchy resembles a republic because the constitution has been amended to remove power from the monarch and install institutions conforming to a philosophy of republicanism. That includes the United Kingdom and the other Commonwealth realms, the Netherlands, Thailand, and countries in Scandinavia and elsewhere. What makes a republic different is that its laws are made and enforced without royal authority. + +The head of state in a republic is generally a person who has been chosen by the citizens by direct election or by a group of elected representatives to act as the top representative of the people. In most republics, the head of state is called the president. In some countries, the president is elected and has a lot of political power. In others, the president does not hold much direct power but is important in the legal system for other reasons. + +Sometimes, state is called a "republic" when its head is not called a "king". For example, the Roman Empire had an "emperor" and the Dutch Republic had a "stadholder", but they worked as hereditary monarchs. + +Licchavi, in India, was an aristocratic state in the 6th and 5th centuries BC +<|CHUNK_END|> +'''Entrepreneurship''' is the creation or extraction of economic value by identifying and commercializing opportunities to deliver products or services, a process that typically requires considerable initiation and bears risk. This process may also encompass the pursuit of values that extend beyond mere economic considerations. + +The term '''entrepreneur''' () refers to an individual who creates and/or invests in one or more businesses, bearing most of the risks and enjoying most of the rewards. The process of setting up a business is also referred to as "entrepreneurship". The entrepreneur is often regarded as an innovator, a source of new ideas, goods, services, and business procedures. + +Narrower definitions of entrepreneurship include the process of designing, launching, and operating a new business, often similar to a small business, or (per ''Business Dictionary'') as the "capacity and willingness to develop, organize, and manage a business venture along with any of its risks to make a profit". Individuals who create these businesses are often referred to as "entrepreneurs". + +In the field of economics, the term ''entrepreneur'' is used for an entity that has the ability to translate inventions or technologies into products and services. In this sense, entrepreneurship encompasses the activities of both established firms and startups. + +== Perspectives on entrepreneurship == +In the 21st century, the governments of nation states have tried to promote entrepreneurship, as well as enterprise culture, in the hope that it would improve or stimulate economic growth and competition. After the end of supply-side economics, entrepreneurship was supposed to boost the economy. + +As an academic field, entrepreneurship accommodates different schools of thought. It has been studied within disciplines such as management, economics, sociology, and economic history. Some view entrepreneurship as allocated to ''the entrepreneur''. These scholars tend to focus on what the entrepreneu +<|CHUNK_END|> +| designer = Brendan Eich +| developer = Netscape +| logo = center|120px +| logo_alt = Unofficial JavaScript Logo +|programming language=Scripting and programming language|File extensions=.js (Standard JavaScript) + +.mjs .cjs .jsx .tsx .ts .es6 + +.json (JavaScript Object Notation)}} + +'''JavaScript''' is a high-level programming language that follows the ECMAScript standard. It was originally designed as a scripting language for websites but became widely adopted as a general-purpose programming language, and is currently the most popular programming language in use. JavaScript is usually found running in a web browser as interactive or automated content, ranging from popup messages and live clocks to large web applications. JavaScript is also commonly used in server-side programming through platforms like Node.js, or "embedded" in non-JavaScript applications where the base programming language lacks the high-level functionality that JavaScript offers. + +Despite the similarities in name and syntax, JavaScript is not related to the programming language Java. Though the names of both languages are trademarks of Oracle Corporation, the two languages follow different design principles, and are actively developed by unrelated organizations. + +Object Model + +window (Global Object) +│ +├── BOM (Browser Object Model) +│ ├── location +│ │ ├── href +│ │ ├── hostname +│ │ ├── pathname +│ │ ├── protocol +│ │ ├── assign() +│ │ ├── reload() +│ │ └── replace() +│ │ +│ ├── navigator +│ │ ├── userAgent +│ │ ├── language +│ │ ├── platform +│ │ └── geolocation +│ │ +│ ├── history +│ │ ├── length +│ │ ├── back() +│ │ ├── forward() +│ │ └── go() +│ │ +│ ├── screen +│ │ ├── width +│ │ ├── height +│ │ ├── availWidth +│ │ └── availHeight +│ │ +│ ├── console +│ │ ├── log() +│ │ ├── error() +│ │ ├── warn() +│ │ └── info() +│ │ +│ ├── alert() +│ ├── prompt() +│ ├── confirm() +│ ├── open() +│ └── close() +│ +├── DOM +<|CHUNK_END|> +| last = +| next = +| participants = 14 +| champions = (6th title) +| most successful = (6 titles) +| most runs = Sachin Tendulkar (2,278) +| most wickets = Glenn McGrath (71) +| website = +| current = +}} + +The '''ICC Men's Cricket World Cup''' is a quadrennial world cup for cricket in One Day International (ODI) format, organised by the International Cricket Council (ICC). The tournament is one of the world's most viewed sporting events and considered the flagship event of the international cricket calendar by the ICC. + +The first Cricket World Cup was organised in England in June 1975, with the first ODI cricket match having been played only four years earlier. However, a separate Women's Cricket World Cup had been held two years before the first men's tournament, and a tournament involving multiple international teams had been held as early as 1912, when a triangular tournament of Test matches was played between Australia, England and South Africa. The first three World Cups were held in England. From the 1987 tournament onwards, hosting has been shared between countries under an unofficial rotation system, with 14 ICC members having hosted at least one match in the tournament. + +The current format involves a qualification phase, which takes place over the preceding three years, to determine which teams qualify for the tournament phase. In the tournament phase, 10 teams, including the automatically qualifying host nation, compete for the title at venues within the host nation over about a month. In the 2027 World Cup, the format will be changed to accommodate an expanded 14-team final competition. + +A total of twenty teams have competed in the 13 editions of the tournament, with ten teams competing in the recent 2023 tournament. Australia has won the tournament six times, India and West Indies twice each, while Pakistan, Sri Lanka and England have won it once each. The best performance by a non-full-member team came when Kenya made the semi-finals of the 20 +<|CHUNK_END|> +thumb|upright=1.15|right|A complex number can be visually represented as a pair of numbers forming a [[vector (geometric)|position vector (blue) or a point (red) on a diagram called an Argand diagram, representing the complex plane. ''Re'' is the real axis, ''Im'' is the imaginary axis, and is the "imaginary unit", that satisfies .]] + +In mathematics, a '''complex number''' is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^{2}= -1; because no real number satisfies the above equation, was called an imaginary number by René Descartes. Every complex number can be expressed in the form a + bi, where and are real numbers, is called the '''''', and is called the ''''''. The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature, "imaginary" complex numbers have a mathematical existence as firm as that of the real numbers, and they are fundamental tools in the scientific description of the natural world.For an extensive account of the history of "imaginary" numbers, from initial skepticism to ultimate acceptance, see +"Complex numbers, as much as reals, and perhaps even more, find a unity with nature that is truly remarkable. It is as though Nature herself is as impressed by the scope and consistency of the complex-number system as we are ourselves, and has entrusted to these numbers the precise operations of her world at its minutest scales.", . + +Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficients has a solution which is a complex number. For example, the equation +(x+1)^2 = -9 +has no real solution, because the square of a real number cannot be negative, but has the two nonreal complex solutions x=-1+3i and x=-1-3i. + + +<|CHUNK_END|> +thumb|230px|Structure of [[tobacco mosaic virus: RNA coiled in a helix of repeating protein sub-units]] + +A '''virus''' is a tiny parasite.Glaunsinger, Britt 2020 Viruses reveal the secrets of biology. [https://www.youtube.com/watch?v=fQHL9QabwLQ] This source makes the astonishing claim that there are !024 viral infections/second. Viruses reproduce inside other living things; they are not free-living. A virus makes copies of itself inside another organism's cells. When viruses infect living organisms, they can cause disease. There are many types of diseases caused by viruses, such as polio, ebola and hepatitis. Viruses outnumber all other forms of life on the planet by a long way. + +A virus has a simple structure. It has just a protein coat which covers a strand of nucleic acid. Usually the nucleic acid is RNA; sometimes it is DNA. Viruses are much smaller than most kinds of bacteria, and can only be seen under an electron microscope. Viruses were not visible until the invention of the electron microscope. + +Viruses reproduce by getting their nucleic acid strand into a prokaryote or eukaryote cell. The RNA or DNA strand then takes over the cell machinery to make copies of itself and the protein coat. The cell then bursts open, spreading the newly created viruses. All viruses reproduce this way, and there are no free-living viruses.Dimmock N.J; Easton, Andrew J; Leppard, Keith 2007. ''Introduction to modern virology''. 6th ed, Blackwell. Shors Teri 2017. ''Understanding viruses''. Jones and Bartlett. ISBN 978-1-284-02592-7 Viruses are everywhere in the environment, and all organisms can be infected by them. + +With eukaryotic cells, the virus protein coat is able to enter the target cells by certain cell membrane receptors. With prokaryote bacteria cells, the bacteriophage physically injects the nucleic acid strand into the host cell. + +When the host cell has finished making more viruses, it undergoes lysis, or breaks apart. The viruses are released and are then able to in +<|CHUNK_END|> +thumb|300x300px|The drawing on the left side, is supposed to show an example of one hydrogen nucleus that has a bond to another hydrogen nucleus. (No picture has been taken of a bond between two (hydrogen) atoms; There is no [[evidence of any expert having seen (with the expert's own eyes) a bond between two atoms.) Those two nuclei are inside the electron cloud (that is made of the electrons of both of these two hydrogen atoms). To show when two atoms have a covalent bonding, one can put a line - on a drawing - between the nucleus of the one atom, and the nucleus of the other atom.]] + +A '''chemical bond''' is a type of attraction force which holds together different chemical species. Atoms bonded stay together unless the needed amount of energy is transferred to the bond. + +In general, strong chemical bonding comes with the sharing or transfer of electrons between the participating atoms. The atoms in molecules, crystals, metals and diatomic gases are held together by chemical bonds. + +There are two types of bonds; covalent and ionic. Covalent bonds form when atoms share electrons. Ionic bonding is the attraction between oppositely charged ions. Chemical bonds are negatively charged electrons that are pulling protons into each other. + +Because atoms and molecules are three-dimensional, it is difficult to use a single method to indicate orbitals and bonds. In molecular formulas the chemical bonds between atoms are indicated in different ways depending on the type of discussion. + +A common way chemists describe chemical bonds is through the number of electrons each atom has on itself. Each atom is drawn with the number of electrons as dots or lines to form a maximum of eight. If the electrons form a chemical bond then a line is drawn between the two electrons. The number of bonds developed increases the number of lines. Atkins, Peter; Loretta Jones 1997. ''Chemistry: molecules, matter and change''. New York: W. H. Freeman, pp. 294–295. ISBN 0-7167-3107-X + +Bonds can be +<|CHUNK_END|> +thumb|400px|Standard Model of [[elementary particles.1 GeV/''c''2 = 1.783x10-27 kg. 1 MeV/''c''2 = 1.783x10-30 kg.]] + +The '''Standard Model''' (SM) of physics is a theory of the elementary particles, which are either fermions or bosons. It also explains three of the four basic forces of nature. The four fundamental forces are: gravity, electromagnetism, the weak force, and the strong force. Gravity is the one the model does not explain. + +The model uses the parts of physics called quantum mechanics and special relativity, and the ideas of physical field and symmetry breaking. Some of the mathematics of the SM is group theory, and also as equations which have biggest and smallest points, called Lagrangians and Hamiltonians. + +== Fermions== +Fermions are particles that join together to make up all "matter" we see. Examples of groups of fermions are the proton and the neutron. Fermions have properties, such as charge and mass, which can be seen in everyday life. They also have other properties, such as spin, weak charge, hypercharge, and color charge, whose effects do not usually appear in everyday life. These properties are given numbers called quantum numbers. + +Fermions are particles whose spin numbers equal an odd, positive number times one half: 1/2, 3/2, 5/2, etc. We say that fermions have "half integer spin." + +An important fact about fermions is that they follow a rule called the Pauli exclusion principle. This rule says that no two fermions can be in the same "place" at the same time, because no two fermions in an atom can have the same quantum numbers at the same time. Fermions also obey a theory called Fermi-Dirac statistics. The word "fermion" honors the physicist Enrico Fermi. + +There are 12 different types of fermions. Each type is called a "flavor." Their names are: + +* '''Quarks''' — up, down, strange, charm, top, bottom +* '''Leptons''' — electron, muon, tau, electron neutrino, muon neutrino, tau neutrino. The electron is the best known lepton. + +Quarks ar +<|CHUNK_END|> +| latest release version = 5.2 +| latest release date = +| repo = +| programming language = +| engine = GPT-5.5 +| operating system = +| genre = Generative artificial intelligence chatbot +| license = Proprietary +| website = chatgpt.com +}} +'''ChatGPT''' is an AI chatbot. It was launched by OpenAI in November 2022. The program was first built using a large language model that OpenAI made, called GPT-3.5. The GPT-3.5 model was first "trained" to predict text that comes after initial text. After the model learned to complete text, supervised and reinforcement learning techniques were used to make the model more likely to follow instructions, and other preferences. + +ChatGPT was launched as a prototype on November 30, 2022. The website received more than one million users after five days. By January 2023, ChatGPT reached over 100 million users. It got attention for its answers in many areas of knowledge but its lack of accuracy was said to be a problem. + +ChatGPT has used different 'large language models' (LLMs) to generate text. The first model that ChatGPT used was called GPT-3.5. The GPT-4 model was released in 2023, and this model often gave better answers than GPT-3.5. More recently GPT-4o, the o1-preview and GPT-5 models were released. The o1 models can take more time to answer questions, and can solve more complicated problems than other models. While the o1 models are working on an answer, they can show a summary of their working out. Scientists have claimed that o1 models are progress to the goal of artificial general intelligence (AGI). + +ChatGPT used to be completely free for research, but it got so popular that OpenAI started using a freemium model. OpenAI created ChatGPT Plus, a subscription service which costs $20 per month. Users can still use the free version of ChatGPT, but ChatGPT Plus users can use more features, and more capable models. +thumb|264x264px|Example of a ChatGPT generated image + +== Criticism and misuse == +There is a risk that ChatGPT can be used +<|CHUNK_END|> +thumb|right|240px|Example of a [[Binary tree|binary max-heap containing items between 1 and 100.]] + +In computer science, a '''heap''' is a type of tree (data structure) that satisfies the heap property. Heaps are useful when you need to remove the item with the highest (or lowest) value. A common implementation of a heap is the binary heap in which the tree is a complete binary tree. + +==Heap property== +* In a max-heap, the value of each item is less than or equal to the value of its parent, with the maximum-value item at the root. +* In a min-heap, the value of each item is greater than or equal to the value of its parent, with the minimum-value item at the root. + +==Operations== +* ''find'': return a maximum item of a max-heap or a minimum item of a min-heap. +* ''insert'': add a new item to the heap. +* ''extract'': returns the maximum item from a max-heap (or minimum item from a min-heap) after removing it. +* ''delete'': removes the root of a max-heap (or min-heap). +* ''size'': return the number of items in the heap. +* ''is-empty'': return true if the heap is empty, false otherwise. + +==Maintaining the heap property== +* ''insert'': insert the item at the bottom rightmost location; swap the item with its parent until the heap property is preserved. +* ''delete'': remove the root; swap it with the item at the bottom rightmost location; swap the new root downwards with the smaller of its children (for a min-heap) until the heap property is preserved. + +==References== + +Category:Data structures +<|CHUNK_END|> +thumb|[[Axel Helsted, "Geometry"]] + +'''Geometry''' (from Ancient Greek: Γεωμετρία (romanized: ''Geometria'' (English: "Land measurement") derived from Γη (romanized: Ge; English: "Earth" or "land") and also derived from Μέτρον) (romanized: ''Métron''; English: "A measure")) is a branch of mathematics that studies the size, shapes, positions and dimensions of things. We can only see shapes that are flat (2D) or solid (3D), but mathematicians (people who study math) are able to study shapes that are 4D, 5D, 6D, and so on. + +Squares, circles and triangles are some of the simplest shapes in flat geometry. Cubes, cylinders, cones and spheres are simple shapes in solid geometry. + +== Uses == +Plane geometry can be used to measure the area and perimeter of a flat shape. Solid geometry can measure a solid shape's volume and surface area. + +Geometry can be used to calculate the size and shape of many things. For example, geometry can help people find: +* the surface area of a house, so they can buy the right amount of paint +* the volume of a box, to see if it is big enough to hold a liter of food +* the area of a farm, so it can be divided into equal parts +* the distance around the edge of a pond, to know how much fencing to buy. + +== Origins == +Geometry is one of the oldest branches of mathematics. Geometry began as the art of surveying of land so that it could be shared fairly between people. The word "geometry" is from a Greek word that means "to measure the land". It has grown from this to become one of the most important parts of mathematics. The Greek mathematician Euclid wrote the first book about geometry, a book called ''The Elements''. + +== Non-Euclidean geometry == +Plane and solid geometry, as described by Euclid in his textbook Elements, is called "Euclidean Geometry". This was simply called "geometry" for centuries. In the 19th century, mathematicians created several new kinds of geometry that changed the rules of Euclidean geometry. These and earlier kinds were called +<|CHUNK_END|> +thumb|[[Ammonia and hydrochloric acid form ammonium chloride. This is a neutralization.]] +A '''base''' is a substance that can accept a hydrogen ion (H+) from another substance. A chemical can accept a proton if it has a negative charge, or if the molecule has an electronegative atom like oxygen, nitrogen, or chlorine that is rich in electrons. Like acids, some bases are strong and others are weak. The weak bases are less likely to accept protons, while the strong bases quickly take protons in solution or from other molecules. +An acid is a base's "chemical opposite". An acid is a substance that will donate a hydrogen atom to the base. + +Bases have a pH greater than 7.0. Weak bases generally have a pH value of 79 while strong bases have a pH value of 9–14. + +==How bases work== +Bases react with acids. This reaction makes a weaker acid and weaker base, called the conjugates. + +In water, strong bases make hydroxide ions. The hydroxide takes a hydrogen ion from an acid. This makes a water molecule, which is neutral (it is the same as the solvent). The other parts of the acid and the counterion from the base are attracted together to make neutral salts. Because adding the base to the acid makes its pH more neutral, this is called neutralization. + +Weak bases react without making hydroxide. For example, ammonia () is a weak base that dissolves in water but does not react. When a strong acid like hydrochloric acid is added, it gives a hydrogen ion to the ammonia molecule, making ammonia's conjugate acid, the ammonium ion . The ammonium solution will stay slightly acidic unless a stronger base is added, which will change it back into ammonia. + +== Characteristics == + +Bases have these characteristics: +*Bitter taste (opposed to sour taste of acids) +*Slimy, or soapy feel on fingers (slippery) +*Many bases react with acids and precipitate salts. +*Strong bases may react violently with acids. An acid spill can be safely neutralised by using a mild base. +*Bases turn red litmus paper b +<|CHUNK_END|> +thumb|360px|A picture of airflow, modeled using a differential equation. + +A '''differential equation''' is a mathematical equation that involves variables like x or y, as well as the rate at which those variables change. Differential equations are special because the solution of a differential equation is itself a function instead of a number. + +In applications of mathematics, problems often arise in which the dependence of one parameter on another is unknown, but it is possible to write an expression for the rate of change of one parameter relative to another (derivative). In this case, the problem is reduced to finding a function by its derivative related to some other expressions. + +==Types of differential equations== +If a differential equation only involves x and its derivative, the rate at which x changes, then it is called a first order differential equation. A higher-order differential equation has derivatives of other derivatives. If there are more variables than just x and y, then it is said to be a partial differential equation. Sometimes, something will obey several differential equations at the same time. These are said to be modeled by coupled differential equations. + +Some differential equations can be solved exactly, and some cannot. Sometimes one can only be estimated, and a computer program can do this very fast. Although they may seem overly-complicated to someone who has not studied differential equations before, the people who use differential equations tell us that they would not be able to figure important things out without them. Most scientists and engineers (as well as mathematicians) take at least one course in differential equations while in college. Some mathematicians devote their career to investigating differential equations that are difficult to solve. + +== Uses == +Differential equations are used in many fields of science since they describe real-world things: +* In physics for various forms of movement, or oscillations +* Radioactive decay +<|CHUNK_END|> +An '''operating system''' ('''OS''') is system software that manages computer hardware and software resources, and provides common services for computer programs.https://arxiv.org/pdf/2411.17710 Operating System research article + +Time-sharing operating systems schedule tasks for efficient use of the system and may also include accounting software for cost allocation of processor time, mass storage, peripherals, and other resources. + +For hardware functions such as input and output and memory allocation, the operating system acts as an intermediary between programs and the computer hardware, although the application code is usually executed directly by the hardware and frequently makes system calls to an OS function or is interrupted by it. Operating systems are found on many devices that contain a computerfrom cellular phones and video game consoles to web servers and supercomputers. + +, Android is the most popular operating system, with a 38% market share, followed by Microsoft Windows at 33%, iOS and iPadOS at 15%, macOS at 4%, and Linux at 1%. Android, iOS, and iPadOS are operating systems for mobile devices such as smartphones, while Windows, macOS, and Linux are for desktop computers. Linux distributions are dominant in the server and supercomputing sectors. Other specialized classes of operating systems (special-purpose operating systems), such as embedded and real-time systems, exist for many applications. Security-focused operating systems also exist. Some operating systems have low system requirements (e.g. light-weight Linux distribution). Others may have higher system requirements. + +Some operating systems require installation or may come pre-installed with purchased computers (OEM-installation), whereas others may run directly from media (i.e. live CD) or flash memory (i.e. a LiveUSB from a USB stick). + +==Definition and purpose== +An operating system is difficult to define, but has been called "the layer of software that manages a computer's resources for it +<|CHUNK_END|> +thumb|300px|Various social media platforms +'''Social media''' are new media technologies that facilitate the creation, sharing and aggregation of content (such as ideas, interests, and other forms of expression) amongst virtual communities and networks. Common features include: + +* Online platforms enable users to create and share content and participate in social networking. +* User-generated content such as text posts or comments, digital photos or videos, and data generated through online interactions. +* Service specific profiles that are designed and maintained by the social media organization. +* Social media helps the development of online social networks by connecting a user's profile with those of other individuals or groups. + +The term ''social'' in regard to media suggests platforms enable communal activity. Social media helps people connect and build networks.|title=The Culture of Connectivity: A Critical History of Social Media |date=2013-01-02 |publisher=Oxford University Press |isbn=978-0-19-997079-7 |language=en}} Users access social media through web-based or mobile applications. These interactive platforms allow individuals, communities, businesses, and organizations to share, co-create, discuss, participate in, and modify user-generated or self-curated content. Social media is used to share memories, form friendships, build communities and learn. They may be used to promote people, companies, products, and ideas. Social media can be used to consume, publish, or share news. + +Popular social media platforms with over 100 million registered users include Twitter, Facebook, WeChat, ShareChat, Instagram, Pinterest, QZone, Weibo, VK, Tumblr, Baidu Tieba, Threads, and LinkedIn. Depending on the interpretation, other popular platforms that are sometimes referred to as social media services include YouTube, Letterboxd, QQ, Quora, Telegram, WhatsApp, Signal, LINE, Snapchat, Viber, Reddit, Discord, and TikTok. Wikis and Roblox are examples of collaborative content +<|CHUNK_END|> +| latest release version = +| latest release date = }} +| designer = James Gosling +| developer = Oracle Corporation +| typing = Static, strong, safe, nominative, manifest +| memory management = Garbage-collected +| influenced_by = CLU, Simula67, Lisp, Smalltalk, Ada 83, C++, C#,Java 5.0 added several new language features (the enhanced for loop, autoboxing, varargs and annotations), after they were introduced in the similar (and competing) C# language. [http://www.barrycornelius.com/papers/java5/] [http://www.levenez.com/lang/] Eiffel, Mesa, Modula-3, Oberon,Niklaus Wirth stated on a number of public occasions, e.g. in a lecture at the Polytechnic Museum, Moscow in September 2005 (several independent first-hand accounts in Russian exist, e.g. one with an audio recording: ), that the Sun Java design team licensed the Oberon compiler sources a number of years prior to the release of Java and examined it: a (relative) compactness, type safety, garbage collection, no multiple inheritance for classes all these key overall design features are shared by Java and Oberon. Objective-C,Patrick Naughton cites Objective-C as a strong influence on the design of the Java programming language, stating that notable direct derivatives include Java interfaces (derived from Objective-C's protocol) and primitive wrapper classes. [http://cs.gmu.edu/~sean/stuff/java-objc.html] UCSD Pascal, Object Pascal +| influenced = Ada 2005, ArkTS, BeanShell, C#, Chapel, Clojure, ECMAScript, Fantom, Gambas, Groovy, Hack, Haxe, J#, JavaScript, JS++, Kotlin, PHP, Python, Scala, Vala +| website = ||}} +| file_ext = .java, .class, .jar, .jmod, .war +| wikibooks = Java Programming +}} + +'''Java''' is a high-level, general-purpose, memory-safe, object-oriented programming language. It is intended to let programmers ''write once, run anywhere'' (WORA), meaning that compiled Java code can run on all platforms that support Java without the need to recompile. Java applications are usually compiled to bytecode that can +<|CHUNK_END|> +In classical software architecture, the architecture is often layered. There is one layer for the user interface, another for the application logic, and yet another for accessing persistent data (such as a database). In classical software architecture, an application server is used, which will run the different services (such as different entry points of a web site, or different parts of the business application). The problem with this approach is that such application servers often do not scale very well, they need a lot of resources, and services are often tightly coupled. + +'''Microservices''' are patterns of Software architecture: The approach is similar to the pattern described above, but the services are very small: very often they only provide one or two very specific functions. To get the same situation as above, these services must interact with each other. Very often they do this using RESTful service calls. Each microservice still has the parts of the user interface layer, the application layer, and the layer to access persistent data. Very often, microservices run in an application container. Data Basecamp|url=https://databasecamp.de/en/use-case/microservices|access-date=2022-09-25|language=en-US}} When the load requires it, special software in the application container can be used to run several instances (or copies) of the specific service. + +Microservices is a specialization of an implementation approach for service-oriented architectures (SOA) used to build flexible, independently deployable software systems. The microservices approach is a first realisation of SOA that followed the introduction of DevOps and is becoming more popular for building continuously deployed systems. + +==References== + +Category:Computer science +<|CHUNK_END|> +thumb|The element [[sulfur has a crystalline structure]] +thumb|[[Bromine is one of only two elements that are liquid at 25°C. The other is Mercury]] + +A '''chemical element''' is a substance that is made up of only one type of atom. Atoms are made up of protons, neutrons, and electrons. + +The number of protons in an atom is called the atomic number. For example, all atoms with 6 protons are atoms of the chemical element carbon, and all atoms with 92 protons are atoms of the element uranium. The number of neutrons in the nucleus does not have to be the same in every atom of an element. Atoms of the same element with different numbers of neutrons are called isotopes. Saying that a substance "contains only one type of atom" really means that it contains only atoms that all have the same number of protons. + +The number of protons in the nucleus causes its electric charge. This fixes the number of electrons in its normal (un-ionized) state. The electrons in their atomic orbitals determine the element's various chemical properties. + +Elements are the basic building blocks for all types of substances. If a substance contains more than one type of atom, it is a compound or a mixture. The smallest particle of a compound is a molecule. + +118 different chemical elements are known to modern chemistry. 92 of these elements can be found in nature, and the others can only be made in laboratories. The human body is made up of 26 elements. The last natural element discovered was uranium, in 1789. The first man-made element was technetium, in 1937. + +Chemical elements are commonly arranged in the periodic table. Where the elements are in the table tells us about their properties relative to the other elements. + +==Chemical symbols== +Chemical elements are given a unique ''chemical symbol''. Chemical symbols are used all over the world. This means that, no matter which language is spoken, there is no confusion about what the symbol means. Chemical symbols of elements almost always come from t +<|CHUNK_END|> +In information theory, the '''entropy''' of a random variable quantifies the average level of uncertainty or information associated with the variable's potential states or possible outcomes. This measures the expected amount of information needed to describe the state of the variable, considering the distribution of probabilities across all potential states. Given a discrete random variable X, which may be any member x within the set \mathcal{X} and is distributed according to p\colon \mathcal{X}\to[0, 1], the entropy is +\Eta(X) := -\sum_{x \in \mathcal{X}} p(x) \log p(x), +where \Sigma denotes the sum over the variable's possible values. The choice of base for \log, the logarithm, varies for different applications. Base 2 gives the unit of bits (or "shannons"), while base ''e'' gives "natural units" nat, and base 10 gives units of "dits", "bans", or "hartleys". An equivalent definition of entropy is the expected value of the self-information of a variable. + +The concept of information entropy was introduced by Claude Shannon in his 1948 paper "A Mathematical Theory of Communication", ([https://web.archive.org/web/20120615000000*/https://www.alcatel-lucent.com/bstj/vol27-1948/articles/bstj27-3-379.pdf PDF], archived from [http://www.alcatel-lucent.com/bstj/vol27-1948/articles/bstj27-3-379.pdf here] ) ([https://web.archive.org/web/20120615000000*/https://www.alcatel-lucent.com/bstj/vol27-1948/articles/bstj27-4-623.pdf PDF], archived from [http://www.alcatel-lucent.com/bstj/vol27-1948/articles/bstj27-4-623.pdf here] ) and is also referred to as '''Shannon entropy'''. Shannon's theory defines a data communication system composed of three elements: a source of data, a communication channel, and a receiver. The "fundamental problem of communication" – as expressed by Shannon – is for the receiver to be able to identify what data was generated by the source, based on the signal it receives through the channel. Shannon considered various ways to encode, compress, and transmi +<|CHUNK_END|> +| author = Ryan Dahl +| developer = OpenJS Foundation +| released = +| latest release version = +| latest release date = }} +| programming language = JavaScript, C++, Python, C +| operating system = z/OS, Linux, macOS, Microsoft Windows, SmartOS, FreeBSD, OpenBSD, IBM AIX +| genre = Runtime environment +| license = MIT License +}} + +'''Node.js''' is a cross-platform, open-source JavaScript runtime environment that can run on Windows, Linux, Unix, macOS, and more. Node.js runs on the V8 JavaScript engine, and executes JavaScript code outside a web browser. According to the Stack Overflow Developer Survey, Node.js is one of the most commonly used web technologies. + +Node.js allows developers to use JavaScript for writing command line tools and server-side scripting. Running Javascript on the server is commonly used to generate dynamic web page content before the page is sent to the user's web browser. Consequently, Node.js represents a "JavaScript everywhere" paradigm, unifying web-application development around a single programming language, as opposed to using different languages for the server- versus client-side programming. + +Node.js has an event-driven architecture capable of asynchronous I/O. These design choices aim to optimize throughput and scalability in web applications with many input/output operations, as well as for real-time Web applications (e.g., real-time communication programs and browser games). + +The Node.js distributed development project was previously governed by the Node.js Foundation, and has now merged with the JS Foundation to form the OpenJS Foundation. OpenJS Foundation is facilitated by the Linux Foundation's Collaborative Projects program. + +== History == +thumb|Ryan Dahl, creator of Node.js, in 2010|alt= +thumb|Rocket Turtle, the official mascot of Node.js since February 2024|upright=0 +<|CHUNK_END|> +Limit § Mathematics}} + +In mathematics, a '''limit''' is the value that a function (or sequence) approaches as the argument (or index) approaches some value. Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. +The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory. +The limit inferior and limit superior provide generalizations of the concept of a limit which are particularly relevant when the limit at a point may not exist. + +==Notation== +In formulas, a limit of a function is usually written as + \lim_{x \to c} f(x) = L, +and is read as "the limit of f of x as x approaches c equals L". This means that the value of the function f can be made arbitrarily close to L, by choosing x sufficiently close to c. Alternatively, the fact that a function f approaches the limit L as x approaches c is sometimes denoted by a right arrow (→ or \rightarrow), as in +f(x) \to L \text{ as } x \to c, +or in + +f(x) \xrightarrow[x \to c]{} L, + +which reads "f of x tends to L as x tends to c". + +==History== + +According to Hankel (1871), the modern concept of limit originates from Proposition X.1 of Euclid's Elements, which forms the basis of the Method of exhaustion found in Euclid and Archimedes: "Two unequal magnitudes being set out, if from the greater there is subtracted a magnitude greater than its half, and from that which is left a magnitude greater than its half, and if this process is repeated continually, then there will be left some magnitude less than the lesser magnitude set out." + +Grégoire de Saint-Vincent gave the first definition of limit (terminus) of a geometric series in his work ''Opus Geometricum'' (1647): "The ''terminus'' of a progression is the end of the series, which none progression can reach, even not if she is continued in infinity, but which she can approach nearer than +<|CHUNK_END|> +160px|thumb|A [[directed graph with three vertices (blue circles) and three edges (black arrows).]] + +In computer science, a '''graph''' is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. + +A graph data structure consists of a finite (and possibly mutable) set of ''vertices'' (also called ''nodes'' or ''points''), together with a set of unordered pairs of these vertices for an undirected graph or a set of ordered pairs for a directed graph. These pairs are known as ''edges'' (also called ''links'' or ''lines''), and for a directed graph are also known as ''edges'' but also sometimes ''arrows'' or ''arcs''. The vertices may be part of the graph structure, or may be external entities represented by integer indices or references. + +A graph data structure may also associate to each edge some ''edge value'', such as a symbolic label or a numeric attribute (cost, capacity, length, etc.). + +==Operations== +right|UML class diagram of a Graph (abstract data type) +The basic operations provided by a graph data structure ''G'' usually include:See, e.g. , Section 13.1.2: Operations on graphs, p. 360. For a more detailed set of operations, see +* : tests whether there is an edge from the vertex ''x'' to the vertex ''y''; +* : lists all vertices ''y'' such that there is an edge from the vertex ''x'' to the vertex ''y''; +* : adds the vertex ''x'', if it is not there; +* : removes the vertex ''x'', if it is there; +* : adds the edge ''z'' from the vertex ''x'' to the vertex ''y'', if it is not there; +* : removes the edge from the vertex ''x'' to the vertex ''y'', if it is there; +* : returns the value associated with the vertex ''x''; +* : sets the value associated with the vertex ''x'' to ''v''. + +Structures that associate values to the edges usually also provide: +* : returns the value associated with the edge (''x'', ''y''); +* : sets the value associated with the edge (''x'', ''y'') to ''v''. +<|CHUNK_END|> +'''Special relativity''' (or '''the special theory of relativity''') is a theory (Well supported idea) in physics that was developed and explained by Albert Einstein in 1905. It applies to all physical phenomena, so long as gravitation is not significant. Special relativity applies to "flat spacetime", which is space without gravity. + +Einstein knew that some weaknesses had been discovered in older models. For example, older models said light moved in a luminiferous aether. Various tiny effects were expected if this theory were true. Gradually it seemed these predictions were not going to work out. + +Eventually, in 1905, Einstein drew the conclusion that the concepts of space and time needed a fundamental rethink. His idea was special relativity, which brought together a new principle (Law), the constancy of the speed of light (the speed of light is always the same), and the previously established principle of relativity (physics is the same for everyone) + +Galileo had already established the principle of relativity, which said that physical events must look the same to all observers, and no observer has the "right" way to look at the things studied by physics. For example, the Earth is moving very fast around the Sun, but we do not notice it because we are moving with the Earth at the same speed; therefore, from our point of view, the Earth is at rest. However, Galileo's math could not explain some things, such as the speed of light. According to him, the measured speed of light in an empty vacuum should be different for different speeds of the observer in comparison with its source. However, the Michelson-Morley experiment showed that this is not true, at least in a vacuum. Einstein's theory of special relativity explained this among other things. + +== Basics of special relativity == + +Imagine that you are moving towards something that is also moving to you. If you measure that thing's speed, it will look like like it's moving faster than if you were not moving toward +<|CHUNK_END|> +}} +| date = ) +---- +|25 June 1950 – present (''de jure'')()}} +| place = +| territory = Korean Demilitarized Zone established +* North Korea gains the city of Kaesong, but loses a net total of , including the city of Sokcho, to South Korea +| result = Inconclusive +| combatant1 = +| combatant1a = +* +* +* +* +* +* +* +* +* +* +* +* +* +* +* +* +}} + +| +| +| +| +| +| +}} + +| +| +| Pakistan +| +| + +}} +| combatant2 = +| combatant2a = +* (unofficial) +}} + +| +| }} +| +| +| +| +| +}} +| commander1 = Syngman Rhee +* Chung Il-kwon +* Paik Sun-yup +* Lee Hyung-geun +* Shin Sung-mo +* Trygve Lie +* Dag Hammarskjöld +* Harry S. Truman +* Dwight D. Eisenhower}} +* George C. Marshall +* Robert A. Lovett +* Douglas MacArthur +* Matthew Ridgway +* Mark W. Clark +* Walton Walker +* James Van Fleet +* Clement Attlee +* Winston Churchill +}} +| commander2 = Kim Il Sung +* Kim Tu-bong +* Pak Hon-yong +* Choe Yong-gon +* Kim Chaek +* Mao Zedong +* Zhou Enlai +* Peng Dehuai +* Chen Geng +* Deng Hua +* Hong Xuezhi +* Song Shilun +* Han Xianchu +* Joseph Stalin +* Pavel Zhigarev +}} +| strength1 = 602,902 +| 326,863 +| 14,198Ethiopia – 1,271Greece – 1,263France – 1,119|url-status=live|archive-url=https://web.archive.org/web/20160711030514/http://www.usfk.mil/About/United-Nations-Command |archive-date=11 July 2016}} +| 8,123 +| 5,455 +| 2,282 +| 2,274 +| 1,496 +| 1,389 +| 1,271 +| 1,263 +| 1,185 +| 1,068 +| 900 +| 826 +| 819 +| 52 +| '''Medical support and others:''' +| 346 +| 170 +| 120 +| 109 +| 100 +| 72 +|'''Together:''' 968,302 +}} + [https://www.imhc.mil.kr/user/imhc/upload/pblictn/PBLICTNEBOOK_201408070704130850.pdf The Statistics of the Korean War - ROK Ministry of National Defense Institute for Military History, 2014 (PDF)] (combat troops):''' +| 1,789,000[https://www.va.gov/opa/publications/factsheets/fs_americas_wars.pdf Fact Sheet: America's Wars".] U.S. Department of Veteran Affairs, Washington D.C., May 2017. +| 1,300,000 +| 56,000 +| 26,791 +| 21,212 +| 17,164 +| 7 +<|CHUNK_END|> +thumb|right|[[Coalbrookdale is a town in England where new ideas for industry were tried. Here it is at night in 1801. The fires are from the large scale making of iron.]] + +The '''Industrial''' '''Revolution''' is the name of the time when there was a big change in the way things were made. Instead of things being hand-made in small workshops, they were made more cheaply in large quantities by machines in factories. This improved the idea of assembly lines. People found that they could make many more things using an assembly line than each person working individually. + +This mass production meant that the goods were sold for less. It started in the 1760s. Many people began to move from an agricultural based life in the country to the towns where the factories offered more and better paid work. + +A Second Industrial Revolution began in the 1870s. + +350px|center|A [[loom in a weaving shed in 1835]] + +== Beginnings == +The Industrial Revolution began in Great Britain in the 18th century. Many of the technological innovations were of British origin. In particular, the County of Shropshire was important, for it had both minerals (e.g. iron ore and coal) and transport on the River Severn.Szostak, Rick 1991. ''The role of transportation in the industrial revolution: a comparison of England and France. Montreal: McGill-Queen's University Press.Usher, Abbott Payson 1920. ''An introduction to the industrial history of England''. University of Michigan Press.Uglow, Jenny 2002. ''The Lunar Men: the friends who made the future 1730–1810''. London: Faber and Faber. + This led to the group of industries near the Ironbridge Gorge and the town of Coalbrookdale. + +In the mid-18th century Britain was the world's leading trading nation. It controlled a global trading empire with colonies in North America and Africa, and with some political influence on the Indian subcontinent, through the activities of the East India Company. + The development of trade and the rise of business were major +<|CHUNK_END|> +| latest release version = +| latest release date = }} +| latest preview version = +| latest preview date = }} +| license = +| file extensions = .js • .mjs • .cjs +| file format = +| website = +| implementations = V8, JavaScriptCore, SpiderMonkey;Chakra (deprecated) +| influenced by = Java, Scheme, Self, AWK, HyperTalk +| influenced = ActionScript, ArkTS, AssemblyScript, CoffeeScript, Dart, Haxe, JS++, Opa, TypeScript +| wikibooks = JavaScript +}} + +'''JavaScript''' ('''JS''')}} is a programming language and core technology of the Web, alongside HTML and CSS. Created by Brendan Eich in 1995, it is maintained by Ecma International's TC39 technical committee, with related Web APIs maintained by W3C and WHATWG. MDN |url=https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/JavaScript_technologies_overview |website=MDN Web Docs |access-date=25 April 2026 |date=27 October 2025}} As of 2025, JavaScript is the most widely used programming language on GitHub. + +Web browsers have a dedicated JavaScript engine that executes the client code. These engines are also utilized in some servers and a variety of apps. The most popular runtime system for non-browser usage is Node.js. + +JavaScript is a high-level, often just-in-time–compiled language that conforms to the ECMAScript standard. It has dynamic typing, prototype-based object-orientation, and first-class functions. It is multi-paradigm, supporting event-driven, functional, and imperative programming styles. It has application programming interfaces (APIs) for working with text, dates, regular expressions, standard data structures, and the Document Object Model (DOM). + +The ECMAScript standard does not include any input/output (I/O), such as networking, storage, or graphics facilities. In practice, the web browser or other runtime system provides JavaScript APIs for I/O. + +Although Java and JavaScript are similar in name and syntax, the two languages are distinct and differ greatly in design. + +== History == +=== Creation at Ne +<|CHUNK_END|> +thumb|''Dark matter'' is invisible. The effect of [[gravitational lensing causes multiple images of the same galaxy. A ring of ''dark matter'' has been suggested to explain this. In this image of galaxy cluster (CL0024+17) the dark matter is seen in blue.|263x263px]] + +'''Dark matter''' is a type of matter thought to be responsible for much of the mass in the universe. + +The idea arose when astronomers found that the mass of large astronomical objects, figured out from their gravitational effects, was much greater than the mass figured out from the "luminous matter" they contain: stars, gas, and dust. + +Dark matter was first proposed by Jan Oort in 1932 as a reason for the spinning speeds of stars in the Milky Way. Fritz Zwicky in 1933 used dark matter to explain "missing mass" in the spinning speeds of galaxies in clusters. Later, many other observations have suggested that there is dark matter in the universe. The spinning speeds of galaxies,[http://www.darkmatterphysics.com/Galactic-rotation-curves-of-spiral-galaxies.htm First observational evidence of dark matter]. Darkmatterphysics.com. Retrieved on 6 August 2013. gravitational lensing of background objects, the temperature distribution of hot gas in galaxies and clusters of galaxies: these are some of the examples that make scientists believe in dark matter. + +According to the Planck mission team, and based on the standard model of cosmology, the total mass–energy of the known universe contains 4.9% ordinary matter, 26.8% dark matter and 68.3% dark energy. So, dark matter is estimated to make up 84.5% of the total matter in the universe, while dark energy plus dark matter make up 95.1% of the total "stuff" in the universe.Ferris, Timothy. 2015. Dark Matter. ''National Geographic''. [http://ngm.nationalgeographic.com/2015/01/hidden-cosmos/ferris-text] + +Because dark matter does not seem to give off or reflect light, x-rays, or any other radiation, the instruments that are used to find normal matter (like hot gas +<|CHUNK_END|> +Rasmus Lerdorf began assembling C code originally written for CGI scripts into a library and accessing the library's functions, including SQL queries, through HTML-embedded commands in 1994; + | designer = Rasmus Lerdorf + | developer = The PHP Group + | latest release version = 7.3.6 + | latest release date = + | latest preview version = + | latest preview date = + | typing = Dynamic, weak + | implementations = Zend Engine, Phalanger, Quercus, Project Zero, HHVM + | dialects = + | influenced by = C, C++, Java, Perl, Tcl + | influenced = Hack + | programming language = C + | operating system = Cross-platform + | license = PHP License + | website = + | wikibooks = PHP Programming|Tags= (closing tag for all the other ones)}} + +'''PHP''' ('''Hypertext Preprocessor'''; used to stand for '''Personal Home Page''') is a scripting language that helps people make web pages more interactive by allowing them to do things that can't be done with technologies running on the visitors computer. PHP code is run on the web server (the website's computer). It is called a ''preprocessor'' because it builds the information before sending it to the computer that visits the web page. + +A website programmed with PHP can have pages that are password protected. A website without PHP or similar technologies can't do this, as the visitor can find a way to access the page. For example, by finding where the password is stored. Standard PHP file extensions are (but not only): .php, .php3, and .phtml, but a web server can be set up to use any extension.http://www.w3schools.com/php/php_intro.asp Retrieved on 30 October, 2007 + +Its structure was influenced by many languages like C, Perl, Java, C++, and even Python. It is considered to be free software by the Free Software Foundation. + +Multiple PHP frameworks +<|CHUNK_END|> +In database theory, the '''CAP theorem''', also named '''Brewer's theorem''' after computer scientist Eric Brewer, states that any distributed data store can provide at most two of the following three guarantees: +; Consistency: Every read receives the most recent write or an error. Consistency means that all clients see the same data at the same time, no matter which node they connect to. For this to happen, whenever data is written to one node, it must be instantly forwarded or replicated to all the other nodes in the system before the write is deemed ‘successful’ IBM |url=https://www.ibm.com/think/topics/cap-theorem |access-date=2025-12-05 |website=www.ibm.com |language=en}}. Consistency as defined in the CAP theorem is quite different from the consistency guaranteed in ACID database transactions. +; Availability: Every request received by a non-failing node in the system must result in a response, without the guarantee that it contains the most recent version of the data System Design in a Hurry |url=https://www.hellointerview.com/learn/system-design/core-concepts/cap-theorem |access-date=2025-12-07 |website=Hello Interview |language=en}}. This is the definition of availability in CAP theorem as defined by Gilbert and Lynch. Availability as defined in CAP theorem is different from high availability in software architecture. +; Partition tolerance: The system continues to operate despite an arbitrary number of messages being dropped (or delayed) by the network between nodes. + +When a network partition failure happens, it must be decided whether to do one of the following: +* cancel the operation and thus decrease the availability but ensure consistency +* proceed with the operation and thus provide availability but risk inconsistency. This does not necessarily mean that system is highly available to its users. + +thumb|CAP theorem Euler diagram + +Thus, if there is a network partition, one has to choose between consistency or availability. + +During times of normal operati +<|CHUNK_END|> +| logo size = 230px +| paradigms = Multi-paradigm: object-oriented, functional, imperative, block structured, generic, reflective, concurrent +| family = +| released = +| designer = JetBrains +| developer = JetBrains +| latest release version = +| latest release date = |df=y}} +| latest preview version = --> +| latest preview date = +| typing = Inferred, static, strong +| implementations = +| dialects = +| platform = * Android +* JVM + +* iOS, iPadOS (tier 1 Kotlin |url=https://kotlinlang.org/docs/native-target-support.html |access-date=2025-10-16 |website=Kotlin Help |language=en-US}}); tvOS, watchOS (tier 2 support) +* macOS (with tier 1 support for Apple silicon) +* Linux +* Windows +* JavaScript ([https://kotlinlang.org/docs/js-overview.html Kotlin/JS]) +| Consumer_Reports = +| medicinenet = +| rxlist = + +| MeshID = +}} + +An '''antibiotic''' is a type of antimicrobial substance active against bacteria. It is the most important type of antibacterial agent for fighting bacterial infections, and antibiotic medications are widely used in the treatment and prevention of such infections. They may either kill or inhibit the growth of bacteria. A limited number of antibiotics also possess antiprotozoal activity.For example, metronidazole: Antibiotics are not effective against viruses such as the ones which cause the common cold or influenza. Drugs which inhibit growth of viruses are termed antiviral drugs or antivirals. Antibiotics are also not effective against fungi. Drugs which inhibit growth of fungi are called antifungal drugs. + +Sometimes, the term ''antibiotic''—literally "opposing life", from the Greek roots ἀντι ''anti'', "against" and βίος ''bios'', "life"—is broadly used to refer to any substance used against microbes, but in the usual medical usage, antibiotics (such as penicillin) are those produced naturally (by one microorganism fighting another), whereas non-antibiotic antibacterials (such as sulfonamides and antiseptics) are fully synthetic. However, both classes have the same effect of killing or preventing the growth of microorganisms, and both are included in antimicrobial chemotherapy. "Antibacterials" include bactericides, bacteriostatics, antibacterial soaps, and chemical disinfectants, whereas antibiotics are an important class of antibacterials used more specifically in medicine and sometimes in livestock feed. + +==Early history== + +The earliest use of antibiotics was found in northern Sudan, where ancient Sudanese societies as early as 350–550 CE were systematically consuming antibiotics as part of their diet. Chemical analyses of Nubian skeletons show consistent, high levels of tetracycline, a powerful antibiotic. Researchers believe they were brewing beverage +<|CHUNK_END|> +'''Web development''' is the process of designing, developing and maintaining websites and web apps. Web development encompasses several different fields, most commonly referring to the programming of websites. Front-end development is the act of developing the user interface and client-side code, while back-end development focuses on the infrastructure behind a website, mainly server-side code. + +Since the World Wide Web was released publicly in 1993, web development has evolved greatly, with websites changing from a collection of static HTML pages to complex projects using frameworks, servers, and databases. + +== Overview == +Web development includes many individual tasks, including web design, web content development, networking, and coding. Among web professionals, "web development" usually refers to the main non-design aspects of building websites: writing markup and coding. + +Web development is generally split into two fields: front-end development and back-end development. Front-end developers create the user interface of websites, turning web designs into HTML, CSS, and JavaScript code. Front-end developers must also make sure that websites work consistently across different browsers and devices. Back-end development, also known as server-side development, focuses on the infrastructure behind a website, including APIs, database management, and security. Some choose to be full-stack developers, meaning they work on both the front-end and back-end. + +==History== + +thumb|300x300px|Timeline of web development +The World Wide Web is often categorised into three generations: Web 1.0, Web 2.0, and Web 3.0 (or Web3). It was invented in 1989, and released to the public in 1993. April 30, 1993 |url=https://www.history.com/this-day-in-history/world-wide-web-launches-in-public-domain |url-status=live |archive-url=https://web.archive.org/web/20250206200329/https://www.history.com/this-day-in-history/world-wide-web-launches-in-public-domain |archive-date=6 February 2025 |access- +<|CHUNK_END|> +A '''startup company''' ('''startup''' or '''start-up''') is a new and fast-growing company. They try to meet a marketplace need, offering an innovative product, process or service. + +A start-up is usually a small business, a partnership or an organization. Rapid growth is what they aim for. Often, startup companies use the internet, e-commerce, computers, and telecommunications. + +The term became fashionable in the dot-com bubble of the late 1990s, when a great number of internet-based companies were formed.Blank, Steve and Dorf, Bob 2012. ''The startup owner's manual. K&S Ranch. + +== References == + +Category:Companies +<|CHUNK_END|> +thumb|right|A visual form of '''recursion''' is the [[Droste effect. This image has a smaller version of itself inside of it.]] +'''Recursion''' refers to something being a part of its own definition. + +== Description == +Usually, a recursive function refers to itself in some cases (or inputs), but not in every case. A function that referred to itself in every case would never terminate. + +When a function refers to itself, it often uses a smaller input than the input it was given. In this way, it can solve a problem by first solving a simpler version of the problem. + +== Example == +An example of a recursive function f(n) is: + +*If n > 0 then return n \times f(n-1). +*If n = 0 then return 1. +This function computes the factorial of a natural number. It works because n!=n(n-1)!, n > 0 and 0!=1. + +The definition has two cases: a recursive case for n>0, and a case for n=0 that is not recursive. The case that is not recursive is called a "base case". + +== Uses == + +Recursion can be used to write computer programs. A program that uses recursion may be easier to write and understand than a program that does the same thing without recursion. + +Recursion is used in mathematics to prove theorems. This method is called induction. + +The idea of recursion can be seen in art and language. For example: +* A fractal image contains smaller versions of itself. +* In the rules of grammar, a sentence can be part of another sentence. + +== Easter Eggs == +In the Google search engine, if you type up "recursion", it will say "Did you mean: Recursion", a reference to the meaning of recursion. + +==References== + +Category:Computer science +<|CHUNK_END|> +'''Continuous delivery''' ('''CD''') is a software engineering approach in which teams produce software in short cycles, ensuring that the software can be reliably released at any time. It aims at building, testing, and releasing software with greater speed and frequency. The approach helps reduce the cost, time, and risk of delivering changes by allowing for more incremental updates to applications in production. A straightforward and repeatable deployment process is important for continuous delivery. + +== Principles == +According to Neal Ford, continuous delivery adopts "Bring the pain forward," tackling tough tasks early, fostering automation and swift issue detection. + +Continuous delivery treats the commonplace notion of a ''deployment pipeline'' as a lean Poka-Yoke: a set of validations through which a piece of software must pass on its way to release. Code is compiled if necessary and then packaged by a build server every time a change is committed to a source control repository, then tested by a number of different techniques (possibly including manual testing) before it can be marked as releasable. + +Developers used to a long cycle time may need to change their mindset when working in a CD environment. Any code commit may be released to customers at any point. Patterns such as feature toggles can be very useful for committing code early which is not yet ready for use by end users. Using NoSQL can eliminate the step of data migrations and schema changes, often manual steps or exceptions to a continuous delivery workflow. Other useful techniques for developing code in isolation such as code branching are not obsolete in a CD world, but must be adapted to fit the principles of CD - for example, running multiple long-lived code branches can prove impractical, as a releasable artifact must be built early in the CD process from a single code branch if it is to pass through all phases of the pipeline. + +==Deployment pipeline== +thumb +Continuous delivery is enabled throu +<|CHUNK_END|> +In probability theory and statistics, the '''median''' of a data set ''X'', sometimes written as \widetilde{X}, is a number describing the data set. This number has the property that it divides a set of observed values in two equal halves, so that half of the values are below it and half are above. + +If there are a finite number of elements, the median is easy to find. The values need to be arranged in a list, from the lowest to highest. If there is an odd number of values, the median is the one at position (n+1)/2. For example, if there are 13 values, they can be arranged into two groups of 6, with the median in between, at position 7. With an even number of values, as there is no single number which divides all of the numbers to two halves, the median is defined as the mean of the two central elements. With 14 observations, this would be the mean of the elements at positions 7 and 8, which is their sum divided by 2. + +Alternatively, the median of an even-sized list is sometimes defined as either of the two middle elements; the choice being either (a) always the smallest one, (b) always the largest one, or (c) randomly choose between the two. This alternative definition has two important advantages: it guarantees that the median is always a list element (for example. a list of integers will never have a fractional median), and it guarantees that the median exists for any ordinal-valued data. On the other hand, when one of the choices (a) or (b) is taken, the median of a sample will be biased, which is an unwanted property of a statistical estimator. Definition (c) does not have that disadvantage, but it is more difficult to do. It also has the disadvantage that the same list of values does not have a well-defined, deterministic median. + +thumb|Distribution curve with mode, median and mean. Median is the middle. + +== Median and mean == +Median and mean are different in several ways. Mean is a better measure in many cases, because many of the statistical tests can use mea +<|CHUNK_END|> +procedural (imperative), functional, structured, reflective +| released = +| designer = Guido van Rossum +| developer = Python Software Foundation +| latest release version = +| latest release date = }} +| latest preview version = +| latest preview date = }} +| typing = Duck, dynamic, strong typing; gradual (since 3.5, but ignored in CPython) +| implementations = CPython, PyPy, Stackless Python, MicroPython, CircuitPython, IronPython, Jython +| dialects = Cython, RPython, Starlark +| influenced = Apache Groovy, Boo, Cobra, CoffeeScript, D, F#, Genie, Go, JavaScript, Julia, Nim, Ring, Ruby, Swift, V (Vlang) +| license = Python Software Foundation License +| website = +| wikibooks = Python Programming +| influenced_by = ABC, Ada, ALGOL 68, APL, C, C++, CLU, Dylan, Haskell, Icon, Java, Lisp, Modula-3, Perl, Standard ML +| operating system = Windows, Linux/UNIX, macOS and more +| file ext = .py, .pyi, .pyc, .pyd, .pyo (prior to 3.5),File extension .pyo was removed in Python 3.5. See [https://www.python.org/dev/peps/pep-0488/ PEP 0488] , .pyz (since 3.5) +}} + +'''Python''' is an open-source programming language. It was made as a language that is both easy to work on and understand. It was made by a Dutch programmer named Guido van Rossum in 1991, who named it after the television program Monty Python's Flying Circus. + +Python is an interpreted language. This means it does not need to be compiled before running. A program called an interpreter runs Python code on almost any computer. So, a programmer can change the code and quickly see what happens. But this also makes Python slower than compiled languages like C, because it is not changed into machine code before running. Instead, this happens while the program is running. + +== Python use == +Python is usually used for making websites, automating common tasks, and making charts and graphs. Since it's simple to learn, people who are not computer experts, like bookkeepers and researchers, often learn Python. + +Its standard library is made u +<|CHUNK_END|> +A '''permutation''' is a single way of arranging a group of objects. It is useful in mathematics. + +A permutation can be changed into another permutation by simply switching two or more of the objects. For example, the way four people can sit in a car is a permutation. If some of them chose different seats, then it would be a different permutation. + +==Permutations without repetitions== +The factorial has special application in defining the number of permutations in a set which does not include repetitions. The number n!, read "n factorial", is precisely the number of ways we can rearrange n things into a new order. For example, if we have three fruit: an orange, apple and pear, we can eat them in the order mentioned, or we can change them (for example, an apple, a pear then an orange). The exact number of permutations is then 3! = 1 \cdot 2 \cdot 3 = 6. The number gets extremely large as the number of items (n) goes up. + +In a similar manner, the number of arrangements of r items from n objects is considered a partial permutation. It is written as nPr (which reads "n permute r"), and is equal to the number n (n-1) \cdots (n - r + 1) (also written as n! / (n-r)!). + +== Related pages == + +* Combination (mathematics) +* Superpermutation + +== References == + +Category:Combinatorics +Category:Abstract algebra +<|CHUNK_END|> +thumb|The [[Milky Way as seen from La Silla Observatory]] + +'''Astronomy''' is the scientific study of celestial bodies. It is a major branch of space science. Stars, galaxies, planets, moons, asteroids, comets and nebulae are studied, as are supernovae explosions, gamma ray bursts, and cosmic microwave background radiation. Astronomy includes the development, physics, chemistry, meteorology and movement of celestial bodies. The big questions are the structure and development of the universe. + +Astronomy is one of the oldest sciences. The patterns of stars in the night sky were called constellations in Late Latin. They used the positions of the stars to navigate, and to find when was the best time to plant crops. + +Astrophysics is an important part of astronomy. A related subject, cosmology, is concerned with studying the universe as a whole, and the way the universe changed over time. Astronomy is not the same as ''astrology'', a belief that the motion of the stars and the planets may affect human lives. + +There are two main types of astronomy, ''observational'' and ''theoretical'' astronomy. Observational astronomy uses telescopes and cameras to ''observe'' or look at stars, galaxies and other astronomical objects. Theoretical astronomy explains what we see. It predicts what might happen. Observations show whether the predictions work. The main work of astronomy is to explain puzzling features of the Universe. For many years the most important issue was the motions of planets. Many other topics are now studied. + +Day-time astronomy is possible, but could be harmful. The Sun, is our biggest star, better describes as a big all of light and observing directly is dangerous. It is too bright, and can burn your eyes and can cause permanent blindness. To look at the Sun you need proper shields and equipment. Some other individual bright stars and planets can be seen during daylight hours through a telescope or a powerful pair of binoculars. + +== History of astronomy == + += +<|CHUNK_END|> +In game theory, the '''Nash equilibrium''' is a proposed solution of a non-cooperative game having two or more players in which each player knows the equilibrium strategies of the other players, and no player can gain anything more by changing only their own strategy. The equilibrium is named after John Forbes Nash Jr.. + +If each player has chosen, and no player can win anything more by choosing a different strategy for themselves, then they have a Nash equilibrium. + +==References== + +Category:Game theory +<|CHUNK_END|> +thumb|''[[Bill of Rights 1689|Bill of Rights'' (1689)]] + +'''Human rights''' are rights and freedoms that all people should have. +}} +Today, the ideas of human rights are protected as legal rights in national and international law. +They are seen as ''universal,'' which means they are meant for everyone, no matter what their race, religion, ethnicity, nationality, age, sex, political beliefs (or any other kind of beliefs), intelligence, disability, sexual orientation, or gender identity are. + +Everyone has all of these rights, it is not possible to only grant some of them: + +== History == + +The idea of human rights originated from ideas found in religion and philosophy in Western Europe. The modern Western idea of human rights started in the European Enlightenment. In the 16th century, some people started suggesting that everyone had the religious and political right to choose their religion and their leaders. This sort of thinking was important in the English Civil War. After the war, the philosopher John Locke argued that people should have a certain set of human rights. These ideas were also important in the American revolution and the French revolution in the 18th century. + +In the 19th century, John Stuart Mill was an important philosopher who also thought about human rights. He said that people should be able to control their own bodies and minds. He talked about three special ideas: +* freedom of speech +* freedom of assembly +* freedom to seek happiness, while not hurting others. + +Hegel was a philosopher who wrote about the idea of free will. He believed that in order to have freedom, a person should be able to: +* own property +* make contracts with other people +* make moral promises to people +* live with anyone +* get protection from laws +* have a voice in government + +== Laws == + +Because people believe that human rights are important, countries make laws to protect them. These laws say that governments cannot take away people's basic rights. They make sure people who +<|CHUNK_END|> +In mathematics, '''Boolean algebra''' is an algebra for binary digits (where 0 means false and 1 means true). It is equipped with three operators: conjunction (AND), disjunction (OR) and negation (NOT). It uses normal math symbols, but it does not work in the same way. It is named for George Boole, who invented it in the middle 19th century. Boolean algebra did not get much attention except from mathematicians until the 20th century, when engineers began using it for logic gates. + +== NOT gate == + +{| class="wikitable" +|- +! NOT +|- +| '''0''' +| 1 +|- +| '''1''' +| 0 +|} + +The NOT operator is written with a bar over numbers or letters like this: + +:\bar{1} = 0 +:\bar{0} = 1 +:\bar{\mbox{A}} = \mbox{Q} + +It means that the output is ''not'' the input. + +== AND gate == + +{| class="wikitable" +|- +! AND +! 0 +! 1 +|- +| '''0''' +| 0 +| 0 +|- +| '''1''' +| 0 +| 1 +|} + +The AND operator is written as \cdot like this: + +:0 \cdot 0 = 0 +:0 \cdot 1 = 0 +:1 \cdot 0 = 0 +:1 \cdot 1 = 1 + +The output is true if and only if one and the other input is true. + +== OR gate == + +{| class="wikitable" +|- +! OR +! 0 +! 1 +|- +| '''0''' +| 0 +| 1 +|- +| '''1''' +| 1 +| 1 +|} + +The OR operator is written as + like this: + +:0 + 0 = 0 +:0 + 1 = 1 +:1 + 0 = 1 +:1 + 1 = 1 + +If one or the other input is true, then the output to be true (and false otherwise). + +== XOR gate == + +{| class="wikitable" +|- +! XOR +! 0 +! 1 +|- +| '''0''' +| 0 +| 1 +|- +| '''1''' +| 1 +| 0 +|} + +XOR basically means "exclusive or", meaning one input or the other must be true, but not both. + +The XOR operator is written as - like this: + +:0 - 0 = 0 +:0 - 1 = 1 +:1 - 0 = 1 +:1 - 1 = 0 + +In other words, the XOR operator returns true precisely when one or the other input is true—but not both. + +== Identities == + +Different gates can be put together in different orders: + +:\overline{\mbox{A} \cdot \mbox{B}} is the same as an AND then a NOT. This is called a NAND gate. + +It is not the same as a NOT then an AND: \overline{\mbox{A}} \cdot \overline{\mbox{B}} + +:\mbox{A} + 1 = 1 +:\mbox{A} \cdot 1 = \mbox{A} +<|CHUNK_END|> +| apoapsis = +| semimajor = )}} +| eccentricity = 0.054 9 +| period = +| synodic_period = +| avg_speed = 1.022 km/s +| inclination = 5.145° to the ecliptic(between 18.29° and 28.58° to Earth's equator) +| asc_node = regressing by one revolution in 18.6 years +| arg_peri = progressing by one revolution in 8.85 years +| satellite_of = Earth +| flattening = 0.001 25 +| mean_radius = +| circumference = 10,921 km (equatorial) +| surface_area = km² }} +| volume = km³ }} +| mass = kg }} +| density = 3,346.4 kg/m³ +| surface_grav = +| escape_velocity = 2.38 km/s +| sidereal_day = 27.321 582 d (synchronous) + +| rot_velocity = 4.627 m/s +| axial_tilt = 1.542 4° (to ecliptic)6.687° (to orbit plane) +| albedo = 0.12 +| magnitude = −2.5 to −12.9The ''maximum value'' is given based on scaling of the brightness from the value of -12.74 given for an equator to Moon-centre distance of 378 000 km in the NASA factsheet reference to the minimum Earth-Moon distance given there, after the latter is corrected for the Earth's equatorial radius of 6 378 km, giving 350 600 km. The ''minimum value'' (for a distant new moon) is based on a similar scaling using the maximum Earth-Moon distance of 407 000 km (given in the factsheet) and by calculating the brightness of the earthshine onto such a new moon. The brightness of the earthshine is Radius of Moon's orbit)² ] relative to the direct solar illumination that occurs for a full moon. (; radius × equatorial ).−12.74 (mean full moon) +| angular_size = 29.3 to 34.1 arcminutes +The range of angular size values given are based on simple scaling of the following values given in the fact sheet reference: at an Earth-equator to Moon-centre distance of 378 000 km, the angular size is 1896 arcseconds. The same fact sheet gives extreme Earth-Moon distances of 407 000 km and 357 000 km. For the maximum angular size, the minimum distance has to be corrected for the Earth's equatorial radius of 6 378 km, giving 350 600 km. +| temp_name1 = equator +| min_temp_1 = +<|CHUNK_END|> +thumb|250px|The [[Sun generates its energy by nuclear fusion of hydrogen nuclei into helium. In its core, the Sun fuses 620 million metric tons of hydrogen each second.]] +'''Nuclear fusion''' is the process of making a single heavy nucleus (part of an atom) from two lighter nuclei. This process is called a nuclear reaction. It releases a large amount of energy. Fusion Education |access-date=2011-03-18 |archive-date=2015-01-01 |archive-url=https://web.archive.org/web/20150101154238/http://fusedweb.pppl.gov/CPEP/Chart_Pages/5.Plasmas/SunLayers.html |url-status=dead }} + +The nucleus made by fusion is heavier than either of the starting nuclei. However, it is not as heavy as the combination of the original mass of the starting nuclei (atoms). This lost mass is changed into lots of energy. This is shown in Einstein's famous ''E=mc2'' equation. + +Fusion happens in the middle of stars, like the Sun. Hydrogen atoms are fused together to make helium. This releases lots of energy. This energy powers the heat and light of the star. +Not all elements can be joined. Heavier elements are less easily joined than lighter ones. Iron (a metal) cannot fuse with other atoms. This is what causes stars to die. Stars join all of their atoms together to make heavier atoms of different types, until they make iron. The iron nucleus cannot fuse further because of its high nuclear binding energy. The reactions stop. The star eventually cools and dies.[http://www.iter.org/sci/beyonditer "Progress in Fusion". ITER.] + +On Earth it is very difficult to start nuclear fusion reactions that release more energy than is needed to start the reaction. The reason is that fusion reactions only happen at high temperature and pressure, like in the Sun, because both nuclei have a positive charge, and positive repels positive. The only way to stop the repulsion is to make the nuclei hit each other at very high speeds. They only do that at high pressure and temperature. The only successful approach s +<|CHUNK_END|> +In probability theory and statistics, the '''variance''' is a way to measure how far a set of numbers is spread out. +Variance describes how much a random variable differs from its expected value. The variance is defined as the average of the squares of the differences between the individual (observed) and the expected value. This means that it is always positive. A variance is often represented by the symbol \sigma^2, if the data is the entire population, and s^2, if the data is from a sample. + +In practice, variance is a measure of how much something changes. For example, temperature has more variance in Moscow than in Hawaii. + +The variance is not simply the average difference from the expected value. The standard deviation, which is the square root of the variance and comes closer to the average difference, is also not simply the average difference. Variance and standard deviation are used because it makes the mathematics easier—when adding two random variables together. + +In accountancy, a variance refers to the difference between the budget for a cost, and the actual cost. + +== History == +Karl Pearson, the father of biometry, first used the term variance as follows:"''It is here attempted to (show) the biometrical properties of a population of a more general type that has (..) been examined, inheritance in which follows this scheme. It is hoped that in this way it will be possible to make a more exact analysis of the causes of human variability. The great body of available statistics shows us that the deviations of a human measurement from its mean follow very closely the Normal Law of Errors, and that therefore, the variablility may be uniformly measured by the standard deviation, corresponding to the square root of the mean square error.''"Ronald Aylmer Fisher: [http://digital.library.adelaide.edu.au/dspace/bitstream/2440/15097/1/9.pdf ''The correlation between relatives on the supposition of Mendelian inheritance.''], Trans. Roy. Soc. Edinb. '''52''': 399-433, +<|CHUNK_END|> +thumb|right|upright=1.5|Animated map showing the continent codes.    North America    South America    Antarctica    Africa    Europe    Asia    Oceania + +A '''continent''' is a large area of the land on Earth that is joined. There are no strict rules for what land is considered a continent, but in general the Earth is known to have seven continents; these being, Africa, Antarctica, Asia, Europe, North America, South America and Oceania or Australia + +==Statistics== +{| class="wikitable sortable" +|- +! colspan="4" | Continents of the world +|- +! rowspan="2" | Continent +! colspan="2" | Area +! rowspan="2" | Population +|- +! km² +! mi² +|- +! Asia +| align="right" | 44,579,000 +| align="right" | +| align="right" |4.6 billion +|- +! Africa +| align="right" | 30,221,532 +| align="right" | +| align="right" |5 +|- +! North America +| align="right" | 24,709,000 +| align="right" | +| align="right" |580 million +|- +! South America +| align="right" | 17,840,000 +| align="right" | +| align="right" |420 million +|- +! Antarctica +| align="right" | 14,000,000 +| align="right" | +| align="right" | 3000 +|- +! Europe +| align="right" | 10,180,000 +| align="right" | +| align="right" |750 million +|- +! Oceania * +| align="right" | 8,525,989 +| align="right" | +| align="right" |42 million +|- +!World +| +| +| align="right" | about 7,900,000,000 +|} + +The most populous continent by population is Asia, followed by Africa. The third most populous continent is Europe. The fourth most populous is North America, and then South America. In sub-Saharan Africa, the largest age group are denarians (in their teens). In north Africa, the largest age group are vicenarian (in their twenties). In Europe, most people are tricenarian (in their thirties) or quadragenarian (in their forties). + +== Continents == +Geologists use the term ''continent'' to mean continental crust, a platform of metamorphic and igneous rock, largely of granitic composition. Continental crust is less dense and much thicker than oceanic crust, which is why it "floats" higher +<|CHUNK_END|> +'''Backtracking''' is a class of algorithms for finding solutions to some computational problems, notably constraint satisfaction or enumeration problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution. + +The classic textbook example of the use of backtracking is the eight queens puzzle, that asks for all arrangements of eight chess queens on a standard chessboard so that no queen attacks any other. In the common backtracking approach, the partial candidates are arrangements of ''k'' queens in the first ''k'' rows of the board, all in different rows and columns. Any partial solution that contains two mutually attacking queens can be abandoned. + +Backtracking can be applied only for problems which admit the concept of a "partial candidate solution" and a relatively quick test of whether it can possibly be completed to a valid solution. It is useless, for example, for locating a given value in an unordered table. When it is applicable, however, backtracking is often much faster than brute-force enumeration of all complete candidates, since it can eliminate many candidates with a single test. + +Backtracking is an important tool for solving constraint satisfaction problems, such as crosswords, verbal arithmetic, Sudoku, and many other puzzles. It is often the most convenient technique for parsing, for the knapsack problem and other combinatorial optimization problems. It is also the program execution strategy used in the programming languages Icon, Planner and Prolog. + +Backtracking depends on user-given "black box procedures" that define the problem to be solved, the nature of the partial candidates, and how they are extended into complete candidates. It is therefore a metaheuristic rather than a specific algorithm – although, unlike many other meta-heuristics, it is guaranteed to find all solutions to a finite problem in a bou +<|CHUNK_END|> +thumb|[[Coral reefs are a highly productive marine ecosystem.]] +thumb|[[Rainforest ecosystems are rich in biodiversity. This is the Gambia River in Senegal]] + +An '''ecosystem''' (or ecological system) is a large community of living organisms (plants, animals and microbes) and non-living components in a particular area.Molles, Manuel C. 1999. ''Ecology: concepts and applications''. Boston: WCB/McGraw-HIll. The living and physical components are linked together through nutrient cycles and energy flows.Odum E.P. 1971. ''Fundamentals of ecology''. 3rd ed, New York: Saunders. Ecosystems are of any size, but usually they are in specific places. + +Each ecosystem has its own community. An aquarium community, for example, can have small fish and other organisms. A desert community may have cacti, small snakes, and scorpions. A pond community can have frogs, insects, snakes, and plants, and a forest community may have rabbits, foxes and pine trees. The species in a community are divided into populations according to the particular habitats and ecological niches in the ecosystem. +thumb|alt=An ecosystem|An example of an ecosystem + +== Energy == +Ecosystems are stable, but changeable. They react to major changes in the environment, especially climate changes. For example, the major rainforests have lasted for a long time (perhaps 50 million years or more in some cases). As the rainfall and temperature changes, they change. We know that the Amazon rainforest shrank in size during ice ages, and expanded in the warmer periods. + +== Primary production == +What drives all ecosystems is the primary production. Primary production is the production of organic matter from inorganic carbon sources. This happens through photosynthesis. It drives the carbon cycle, which influences global climate via the greenhouse effect. + +Through the process of photosynthesis, plants capture energy from sunlight and use it to combine carbon dioxide and water to produce carbohydrates and oxygen. The photosynt +<|CHUNK_END|> +250px|thumb|Nuclear fission diagram shows a [[neutron being absorbed by a uranium nucleus which then becomes unstable and splits into two new atoms with release of energy and some more neutrons.]] + +'''Nuclear fission,''' is a kind of nuclear reaction. It is when an atom splits apart into smaller atoms. Some fission reactions give off a lot of energy, and are used in nuclear weapons and nuclear reactors. Nuclear fission was discovered in December 1938 by physicists Lise Meitner and Otto Frisch, who observed a uranium nucleus splitting in two. Although they originally thought the two tiny resulting nuclei were barium isotopes, what Meitner and Frisch truly saw was a process that would revolutionize nuclear chemistry: nuclear fission. + +An atom is the smallest particle which makes up a chemical element (e.g. hydrogen, oxygen, magnesium). All atoms are very small. Atoms are made of three components or particles: Protons, neutrons and electrons. The protons and neutrons are clumped together in a ball called a nucleus, at the center of every atom. The electrons orbit around the nucleus in its 'electron cloud'. Elements which have large nuclei, such as uranium and plutonium, can be made to fission. + +If a (relatively) very large atomic nucleus is hit by a slow-moving neutron, it will sometimes become unstable and break into two nuclei. When the nucleus breaks apart (or '''fissions''') it releases energy, mostly as gamma rays and heat. It also causes some neutrons to be released from the nucleus. + +This reaction can occur "spontaneously" if the original nucleus is highly unstable. The resulting products are radioactive isotopes, but do not release enough energy to generate usable power or make a bomb due to the lack of a chain reaction. It can also be induced by a neutron. + +For a few isotopes (an atom with the same amount of protons but a different amount of neutrons) such fission can release many neutrons. If those neutrons then hit other atoms, they will make the other at +<|CHUNK_END|> +88px|right|thumb|A diagram of the structure of [[fructose]] +'''Carbohydrates''' are chemical compounds that contain ''only'' oxygen, hydrogen and carbon. They are made up of joined-up sugars. Sugars have the general formula Cm(H2O)n, and are also known as '''saccharides.''' + +Certain carbohydrates are an important storage and transport form of energy in most organisms, including plants and animals. + +== Biochemistry == +There are four types of carbohydrates, named by the number of sugar molecules they contain. +# Simple saccharides with one or two sugar molecules +## Monosaccharides: single sugar e.g. glucose, fructose ScienceDirect Topics|url=https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/monosaccharides|access-date=2021-06-03|website=www.sciencedirect.com}} +## Disaccharides: two saccharides. e.g. sucrose, lactose, maltose +# Longer chain saccharides: +## Oligosaccharides (shortish chains), often linked to amino acids or lipids. They play a special role in cell membranes. +## Polysaccharides (long chains) are complex carbohydrates, with linear chains of sugars or branched clusters. Their function is either energy storage (starch, glycogen) or building structures (cellulose, chitin). + +== Nutrition and foods == +Carbohydrates are the most common source of energy for the human body. Protein builds tissue and cells in the body. Carbohydrates are very good for energy, but, if a person eats more than needed, the extra is changed into fat through a process called de novo lipogenesis. + +If necessary, humans can live without eating carbohydrates because the human body can change fats and proteins into carbohydrates through a process called gluconeogenesis. Some already stored glucose in the liver can be released through another process called glycogenolysis. People of some cultures eat food with very little carbohydrates, but they still remain healthy, such as the Inuits. + +Research in the United States and Canada have shown that people get about 40% to 60% +<|CHUNK_END|> +thumb|250px|Gregor Reisch, ''Logic presents its main themes''. ''Margarita Philosophica'', 1503 or 1508. In the engraving, two dogs named ''veritas'' (truth) and ''falsitas'' (falsehood) chase a rabbit named ''problema'' (problem). Logic runs behind the dogs, armed with the sword ''syllogismus'' (syllogism). In the bottom left corner, the philosopher [[Parmenides of Elea|Parmenides can be seen in a cave.]] + +'''Logic''' is the study of reasoning. The rules of logic let philosophers make logical deductions about the world. Logic helps us decide whether something can be true or false. + +==Overview== + +Logic is often written in syllogisms, which are one type of logical proof. A syllogism is made from a collection of statements used to logically prove the final statement, called the conclusion. One popular example of a logical syllogism was written by the Classical Greek philosopher Aristotle: + +# All men are mortal. +# Socrates is a man. +# Therefore, Socrates is mortal. + +The conclusion is the final statement. This syllogism connects the first two statements to make a logical deduction: Socrates is mortal. + +The syllogism is made from three logical statements or propositions. These statements are short sentences describing a small step in a logical argument. The small statements make up the argument, the same way atoms make up molecules. When logic is correct, the statements are said to "follow" from each other. Statements have a truth value, meaning they can be proved to be true ''or'' false, but not both. Illogical statements or mistakes in logic are called ''logical fallacies''. + +==Symbolic logic== + +Logical statements can be written in a special type of short hand writing, which includes the symbols of the '''symbolic logic'''. These symbols are used to describe logical reasoning in an abstract way. For instance: + +* \land is read like "and", meaning both statements apply. +* \lor is read like "or", meaning at least one of the statements applies. +* \rightarrow is read like +<|CHUNK_END|> +| image = EscherichiaColi NIAID.jpg +| image_caption = Scanning electron micrograph of ''Escherichia coli'' rods +| taxon = Bacteria +| authority = Woese, Kandler & Wheelis, 1990 +| subdivision_ranks = Phyla +| subdivision = +*'''Gram positive/no outer membrane''' +Actinobacteria (high-G+C) +Firmicutes (low-G+C) +Tenericutes (no wall) +*'''Gram negative/outer membrane present''' +Aquificae +Bacteroidetes/Fibrobacteres–Chlorobi (FCB group) +Chlamydiae +Deinococcus-Thermus +Fusobacteria +Gemmatimonadetes +Nitrospirae +Planctomycetes–Verrucomicrobia/Chlamydiae (PVC group) +Proteobacteria +Spirochaetes +Synergistetes +*'''Unknown/ungrouped''' +Acidobacteria +Chloroflexi +Chrysiogenetes +Cyanobacteria +Deferribacteres +Dictyoglomi +Thermodesulfobacteria +Thermotogae +| synonyms = Eubacteria Woese & Fox, 1977 +}} + +'''Bacteria''' (singular: '''bacterium''') are very small organisms. They are prokaryotic microorganisms. + +Bacterial cells do not have a nucleus, and most have no organelles with membranes around them. Most have a cell wall. They do have DNA, and their biochemistry is basically the same as other living things. They are amongst the simplest and the oldest organisms. + +Almost all bacteria are so tiny they can only be seen through a microscope. Bacteria are made up of one cell, so they are a kind of ''unicellular organism''. They were one of the earliest forms of life, and are simple single-celled organisms. They include extremophiles, which live in extreme habitats. + +There are probably more individual bacteria than any other sort of organism on the planet. Most bacteria live in the ground or in water, but many live inside or on the skin of other organisms, including humans. There are about as many bacterial cells as human cells in our bodies. Some bacteria cause diseases, but others help us in everyday activities like digesting food (gut flora). Some we use in factories to make cheese and yogurt. + +The founder of bacteriology was a German biologist called Ferdinand Cohn (18281898). He publishe +<|CHUNK_END|> +In computer science, '''binary search''', also known as '''half-interval search''', '''logarithmic search''', or '''binary chop''', is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the middle element of the array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found. If the search ends with the remaining half being empty, the target is not in the array. + +Binary search runs in logarithmic time in the worst case, making O(\log n) comparisons, where n is the number of elements in the array. Binary search is faster than linear search except for small arrays. However, the array must be sorted first to be able to apply binary search. There are specialized data structures designed for fast searching, such as hash tables, that can be searched more efficiently than binary search. However, binary search can be used to solve a wider range of problems, such as finding the next-smallest or next-largest element in the array relative to the target even if it is absent from the array. + +There are numerous variations of binary search. In particular, fractional cascading speeds up binary searches for the same value in multiple arrays. Fractional cascading efficiently solves a number of search problems in computational geometry and in numerous other fields. Exponential search extends binary search to unbounded lists. The binary search tree and B-tree data structures are based on binary search. + +== Algorithm == +Binary search works on sorted arrays. Binary search begins by comparing an element in the middle of the array with the target value. If the target value matches the element, its position in the array is returned. If the target value is less than the element, the search continues in the lower half of the array. If the +<|CHUNK_END|> +'''JSON''' ('''JavaScript Object Notation''') is a way of expressing information. JSON is usually easy to understand. It can express information like XML. Data Basecamp|url=https://databasecamp.de/en/data/json-en|access-date=2022-08-11|language=en-US}} It is based on JavaScript's notation for object literals. However, JSON is stricter. + +JSON and XML are both often used in AJAX. Even though JSON is named after JavaScript, it can be used in other programming languages, such as Python (PHP, etc.) + +== Example == +This is an example of JSON: + +{ + "firstName": "John", + "lastName" : "Smith", + "age" : 25, + "address" : + { + "streetAddress": "21 2nd Street", + "city" : "New York", + "state" : "NY", + "postalCode" : "10021" + }, + "phoneNumber": + [ + { + "type" : "", + "number": "212 555-1234" + }, + { + "type" : "fax", + "number": "646 555-4567" + } + ] + } + +'''JSON Encoding and Decoding in Python''' + +Encoding: + +import json + +sampleDict = { + "firstName": "John", + "lastName" : "Smith" +} + +sampleJson = json.dumps(sampleDict, indent=4) + +Decoding: + +import json + +# A JSON string or can be a JSON response +sampleJson = """{ "firstName": "John", "lastName" : "Smith"}""" + +sampleDict = json.loads(sampleJson) +print(sampleDict['firstName']) +print(sampleDict['lastName']) + +== References == + +== Other websites == +* [http://json.org JSON website] + +Category:JavaScript +<|CHUNK_END|> +'''Climate change''' refers to long-term changes in temperature, precipitation, and other atmospheric conditions on Earth. + +When people talk about climate change, they are usually talking about the problem of human-caused global warming, which is happening now. But the climate of the Earth has changed over not just thousands of years, but tens or hundreds of millions of years.Alley R.B. 2000. ''The two-mile time machine: ice cores, abrupt climate change, and our future''. Princeton University Press. ISBN 0-691-10296-1 It has alternated between hotter and colder periods, with some extremes like ice ages. + +== Global warming today == +''See the main article: Global warming'' + +Global warming primarily involves the warming of the planet due to increased concentrations of greenhouse gases in Earth's atmosphere. These gases, like carbon dioxide and methane, come from human activities such as burning fossil fuels, deforestation, and industrial processes. +thumb|Climate change's effects on [[Coral reef|coral reefs]] + +These changes can lead to a variety of impacts, including more extreme weather events, rising sea levels, and disruptions to ecosystems and agriculture. +== Hot Earth periods == +Sometimes, before there were people, the Earth's climate was much hotter than it is today. + +For example, about 60 million years ago there were a lot of volcanoes, which burnt a lot of underground organic matter. Squashed and fossilized dead plants and animals became coal, gas and oil. This caused a lot of carbon dioxide and methane to go up into the air, like nowadays. This made the Earth hot enough for giant tortoises and alligators to live in the Arctic. + +== Cold Earth periods == + +=== Glaciations === + +At times in the past, the temperature was much cooler, with the last glaciation ending about ten thousand years ago.Imbrie J. & Imbrie, K.P. 1979. Ice ages: solving the mystery. Short Hills NJ: Enslow. ISBN 978-0-89490-015-0 + +=== Ice Ages === + +Ice ages are long times (much much longer +<|CHUNK_END|> +thumb|upright=0.8|'''Figure 1.''' Finding the shortest path in a graph using optimal substructure; a straight line indicates a single edge; a wavy line indicates a shortest path between the two vertices it connects (among other paths, not shown, sharing the same two vertices); the bold line is the overall shortest path from start to goal. + +'''Dynamic programming''' is both a mathematical optimization method and an algorithmic paradigm. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, such as aerospace engineering and economics. + +In both contexts it refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart this way, decisions that span several points in time do often break apart recursively. Likewise, in computer science, if a problem can be solved optimally by breaking it into sub-problems and then recursively finding the optimal solutions to the sub-problems, then it is said to have ''optimal substructure''. + +If sub-problems can be nested recursively inside larger problems, so that dynamic programming methods are applicable, then there is a relation between the value of the larger problem and the values of the sub-problems.Cormen, T. H.; Leiserson, C. E.; Rivest, R. L.; Stein, C. (2001), Introduction to Algorithms (2nd ed.), MIT Press & McGraw–Hill, . pp. 344. In the optimization literature this relationship is called the Bellman equation. + +== Overview == + +=== Mathematical optimization === +In terms of mathematical optimization, dynamic programming usually refers to simplifying a decision by breaking it down into a sequence of decision steps over time. + +This is done by defining a sequence of '''value functions''' ''V''1, ''V''2, ..., ''V''''n'' taking ''y'' as an argument representing the '''state''' of the system at times ''i'' from 1 to ''n''. + +The definition of ''V''''n''(''y'') is the value obtained in +<|CHUNK_END|> +| kurtosis = \frac{1-6pq}{npq} + | entropy = \frac{1}{2} \log_2 (2\pi enpq) + O \left( \frac{1}{n} \right) in shannons. For nats, use the natural log in the log. + | mgf = (q + pe^t)^n + | char = (q + pe^{it})^n + | pgf = G(z) = [q + pz]^n + | fisher = g_n(p) = \frac{n}{pq} (for fixed n) +}} + +thumb|280px|Binomial distribution for 0.5}}with and as in [[Pascal's triangleThe probability that a ball in a Galton box with 8 layers ( 8}}) ends up in the central bin ( 4}}) is .]] + +In probability theory and statistics, the '''binomial distribution''' with parameters and is the discrete probability distribution of the number of successes in a sequence of independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: ''success'' (with probability ) or ''failure'' (with probability 1 − ''p''}}). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process. For a single trial, that is, when 1}}, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the binomial test of statistical significance. + +The binomial distribution is frequently used to model the number of successes in a sample of size drawn with replacement from a population of size . If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one. However, for much larger than , the binomial distribution remains a good approximation, and is widely used. + +== Definitions == + +=== Probability mass function === + +If the random variable follows the binomial distribution with parameters n \isin \mathbb{N} (a natural number) and }}, we write . The probability of getting exactly successes in independent Bernoulli trials (with the same rate ) is given by the probability mass function: +f(k,n,p) = \Pr(X = k) = \binom{n +<|CHUNK_END|> +In computer science, a '''linked list''' is a data structure that is a linear collection of items whose order is not given by their physical placement in memory. Instead, each item links to the next item. The last item links to a terminator used to mark the end of the list. + +==Types of linked lists== + +===Singly linked list=== +Image:Singly-linked-list.svg''A singly linked list whose items have two fields: a value and a link to the next item'' + +A singly linked list is a linked list that's used to store items in order. Each item is usually called a node. A node has two parts: the data it holds and a link to the next node. The first node is called the head. The last node points to nothing, indicating the end of the list. One can move through the list one step at a time, following the links from one node to the next. + +===Doubly linked list=== +Image:Doubly-linked-list.svg''A doubly linked list whose items have three fields: a value, the link forward to the next item, and the link backward to the previous item'' + +A doubly linked list is a type of linked list. Each node in the list holds three things: a piece of data, a pointer to the next node, and a pointer to the previous node. The first node, called the head, has a previous pointer that is null. The last node, called the tail, has a next pointer that is null. This allows the list to be traversed in either direction. + +===Circular linked list=== +Image:Circularly-linked-list.svg''A circular linked list'' + +A circular linked list is a variation of a linked list where the last node's pointer does not point to a null value. Instead, it points back to the first node, called the head, forming a continuous loop. This structure has no natural beginning or end, allowing traversal to start from any node and continue through the entire list. + +==Linked list algorithms== +===Creating a singly linked list=== + +class Node { + int data; + Node next; + + Node(int data) { + this.data = data; + this.next = null; + } +} + + +<|CHUNK_END|> +thumb|270px|Illustration of a transformation (of [[Mona Lisa): The image is changed in such a way that the red arrow (vector) does not change its direction, but the blue one does. The red vector therefore is an eigenvector of this transformation, the blue one is not. Since the red vector does not change its length, its eigenvalue is 1. The transformation used is called shear mapping.]] + +Linear algebra talks about types of functions called ''transformations''. In that context, an '''eigenvector''' is a vector—different from the null vector—which does not change direction after the transformation (except if the transformation turns the vector to the opposite direction). The vector may change its length, or become zero ("null"). The '''eigenvalue''' is the value of the vector's change in length, and is typically denoted by the symbol \lambda. The word "eigen" is a German word, which means "own" or "typical". + +==Basics== +If there exists a '''square matrix''' called '''''A''''', a '''scalar ''λ''''', and a '''non-zero vector''' '''v''', then '''''λ''''' '''is the eigenvalue''' and '''v is the eigenvector''' if the following equation is satisfied: + +:A\mathbf{v} = \lambda \mathbf{v} \, . + +In other words, if matrix ''A'' times the vector '''v''' is equal to the scalar ''λ'' times the vector '''v''', then ''λ'' is the eigenvalue of '''v''', where '''v''' is the eigenvector. + +An '''eigenspace''' of ''A'' is the set of all eigenvectors with the same eigenvalue together with the zero vector. However, the zero vector is not an eigenvector. + +These ideas often are extended to more general situations, where scalars are elements of any field, vectors are elements of any vector space, and linear transformations may or may not be represented by matrix multiplication. For example, instead of real numbers, scalars may be complex numbers; instead of arrows, vectors may be functions or frequencies; instead of matrix multiplication, linear transformations may be operators such as the deriv +<|CHUNK_END|> +'''Finance''' is a study which figures out how people, businesses and groups make and use money. It can mean: + +* Thinking about money +* Thinking about how to control money to make profit +* Studying how to take chances in projects that make money +* As a verb, "to finance" is to provide money for business +*Any system that includes circulation of money. + +==Some simple finance ideas== +The process of '''finance''' is learning, how people and groups act in managing their money, and most of all how they manage making money, and making a profit, with spending money, or making a loss. + +A group that makes more money than it spends can lend or invest the excess profit. On the other hand, a group that makes less money than it spends can raise money by getting a loan or selling part of its assets or spending less, or making more money. + +A bank is where many people borrowing money meet people lending money. A bank gets money from lenders, and pays interest. The bank then lends this money to borrowers. Banks allow borrowers and lenders of different sizes to meet. + +Corporate finance is about things like the sale of stock by a company to the public. Stock is ownership in a company, broken up into pieces. The stock gives whoever owns it part ownership in that company. If someone buys one share of XYZ Inc, and the company has 100 shares available, the buyer is 1/100th owner of that company and owns 1/100th (1%) of the profit. + +Finance is used by people, by governments, by businesses, etc., as well as by all kinds of groups. + +==Personal finance== + +This is finance for people. It is about: +*How much money will be needed by a person, now and when they get old. +*Where will this money come from (e.g. savings or borrowing)? +*How can people protect themselves against problems with money in their lives? +*How can family money be given to children and grandchildren? +*How do taxes affect money choices? + +==Business finance== + +Business finance is about finding money for a company's activiti +<|CHUNK_END|> +Hash tree}} + +|space_worst=O(''n'') +|search_avg=Θ(1) +|search_worst=O(''n'')}} +|insert_avg=Θ(1) +|insert_worst=O(''n'') +|delete_avg=Θ(1) +|delete_worst=O(''n'') +}} +thumb|315px|right|A small phone book as a hash table + +In computer science, a '''hash table''' is a data structure that implements an associative array, also called a '''dictionary''' or simply '''map'''; an associative array is an abstract data type that maps keys to values. A hash table uses a hash function to compute an ''index'', also called a ''hash code'', into an array of ''buckets'' or ''slots'', from which the desired value can be found. During lookup, the key is hashed and the resulting hash indicates where the corresponding value is stored. A map implemented by a hash table is called a '''hash map'''. + +Most hash table designs employ an imperfect hash function. Hash collisions, where the hash function generates the same index for more than one key, therefore typically must be accommodated in some way. Common strategies to handle hash collisions include chaining, which stores multiple elements in the same slot using linked lists, and open addressing, which searches for the next available slot according to a probing sequence. + +In a well-dimensioned hash table, the average time complexity for each lookup is independent of the number of elements stored in the table. Many hash table designs also allow arbitrary insertions and deletions of key–value pairs, at amortized constant average cost per operation. + +Hashing is an example of a space–time tradeoff. If memory is infinite, the entire key can be used directly as an index to locate its value with a single memory access. On the other hand, if infinite time is available, values can be stored without regard for their keys, and a binary search or linear search can be used to retrieve the element. + +In many situations, hash tables turn out to be on average more efficient than search trees or any other table lookup structure. For this reason, they are widely use +<|CHUNK_END|> +thumb|Dijkstra's algorithm to find the shortest path between ''a'' and ''b''. It picks the unvisited node with the lowest distance, calculates the distance through it to each unvisited neighbor, and updates the neighbor's distance if smaller. Mark visited (set to red) when done with neighbors. + +'''Dijkstra's algorithm''' is a method to find the shortest path from one node, or location, in a graph to all other nodes. In this process, it can find the shortest path from one node to another specific node. This can be used for navigation between points of interest like cities connected by roads, or finding the shortest chain of mutual friends from two people on a social media platform. + +== Requirements and Limitations == +Dijkstra's algorithm works on a graph that has nodes and edges between those nodes. While the edges can have weight, representing a distance or cost, the algorithm also works on unweighted graphs by treating all edges as having a weight of 1. + +The algorithm does not always find the shortest path on graphs with negative edge weights. Since the shortest path to a node is only determined once, potentially shorter paths from further away nodes with negative edge weights are not considered. + +The algorithm also does not try to visit nodes that are closer to the destination node. It visits nodes in order of total distance from the starting point, similar to Breadth-first search. This leads to many more nodes than needed being potentially visited to find the shortest path. + +== Algorithm == +thumb|Illustration of Dijkstra's algorithm finding a path from a start node (lower left, red) to a target node (upper right, green). Open nodes represent the set of "unvisited" nodes. Filled nodes are the visited ones, with color representing the distance: the redder, the closer (to the start node). +The algorithm requires a starting node to be provided, a queue to track new nodes, and a table that saves the total distance required to reach each node. The queue starts with +<|CHUNK_END|> +== The term == +The term '''biological diversity''' was used first by wildlife scientist and conservationist Raymond F. Dasmann in 1968, +Dasmann R.F. 1968. ''A different kind of country''. MacMillan, New York. where he advocated conservation. It was widely adopted only in the 1980s.Soulé M.E. and B. A. Wilcox. 1980. ''Conservation biology: an evolutionary-ecological perspective''. Sinauer. Sunderland, Massachusetts. + +The term '''biodiversity''' first appeared in a publication in 1988 when entomologist E. O. Wilson used it as a title.Edward O.Wilson, editor, Frances M.Peter, associate editor 1988. ''Biodiversity'', National Academies Press. ; [http://darwin.nap.edu/books/0309037395/html/R2.html online edition] Global Biodiversity Assessment. UNEP, 1995, Annex 6, Glossary. , used as source by [http://www.biodiv.be/glossary_keywords/B "Biodiversity", Glossary of terms related to the CBD] , Belgian Clearing-House Mechanism. Retrieved 2006-04-26. Since then, the term has often been used by biologists, environmentalists, political leaders, and citizens. A similar term in the United States is "natural heritage." It predates the others and is more accepted by the wider audience interested in conservation. Broader than biodiversity, it includes geology and landforms. + +== Definitions == +Biologists most often define biodiversity as the "totality of genes, species, and ecosystems of a region". An advantage of this definition is that it seems to describe most circumstances. There are three levels at which biological variety can been identified: + +*species diversity +*ecosystem diversity +*genetic diversity. + +== Threats == +The idea can be used for tackling practical problems in conservation, for example: +*loss of species +*destruction of habitats +*introduced and invasive species +*genetic pollution +*over-exploitation +*effect of climate change + +== References == + +== Related pages == +*Biodiversity Convention +*Conservation biology +*Endemism +*Neurodiversity + +== Further reading == +*Levin, +<|CHUNK_END|> +'''Macroeconomics''' studies large-scale economic decisions. For example, a whole country's economy (or, its economic output) is summarised by the GDP (gross domestic product). Many governments use macroeconomic ideas to decide how much tax to collect and what interest rates should be. + +It also considers the amount of unemployment, the rate that prices go up (inflation), and the exchange rates of its currency. The exchange rate affects the amount of imports and exports. Exchange rates and taxation are "levers of the economy". + +Less dramatic, but also very important, are decisions about government spending inside the country. Such policy decisions are politically controversial due to differing political ideas on government spending. Another factor in macroeconomics is the make-up of the population. A growing population is economically different from a stable population (one which is not growing). + +== Sources == +*Blanchard, Olivier 2011. ''Macroeconomics updated''. 5th ed, Englewood Cliffs: Prentice Hall. + +== Related pages == +*Microeconomics +*Constitutional economics +*Political economy +<|CHUNK_END|> +Compilation}} + +In computing, a '''compiler''' is software that translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primarily used for programs that translate source code from a high-level programming language to a low-level programming language (e.g. assembly language, object code, or machine code) to create an executable program.Compilers: Principles, Techniques, and Tools by Alfred V. Aho, Ravi Sethi, Jeffrey D. Ullman - Second Edition, 2007 + +There are many different types of compilers which produce output in different useful forms. A ''cross-compiler'' produces code for a different CPU or operating system than the one on which the cross-compiler itself runs. A ''bootstrap compiler'' is often a temporary compiler, used for compiling a more permanent or better optimized compiler for a language. + +Related software include ''decompilers'', programs that translate from low-level languages to higher-level ones; programs that translate between high-level languages, usually called ''source-to-source compilers'' or ''transpilers''; language ''rewriters'', usually programs that translate the form of expressions without a change of language; and ''compiler-compilers'', compilers that produce compilers (or parts of them), often in a generic and reusable way so as to be able to produce many differing compilers. + +A compiler is likely to perform some or all of the following operations, often called phases: preprocessing, lexical analysis, parsing, semantic analysis (syntax-directed translation), conversion of input programs to an intermediate representation, code optimization and machine specific code generation. Compilers generally implement these phases as modular components, promoting efficient design and correctness of transformations of source input to target output. Program faults caused by incorrect compiler behavior can be very difficult to track down and work aro +<|CHUNK_END|> +class=skin-invert +| logo_size = 140 +| logo_caption = GitHub Invertocat logo +| screenshot = File:Github Docs repository screenshot.png +| screenshot_alt = files of the "github/docs" repository, with a readme file, contributor, committed date, etc. +| caption = Repository of the website's official documentation, storing its source code +| company_type = Subsidiary +| founded = (as Logical Awesome LLC) +| location = San Francisco, California, U.S. +| area_served = Worldwide +| founder = +| key_people = +| industry = +| revenue = $1 billion (2022) +| margin = $200 million (2022) +| international = Yes https://p01-catalog1-html.jimdofree.com/ +| employees = 5,595 +| url = +| ipv6 = No +| programming_language = + | Rust + }} +| website_type = Collaborative version control +| registration = Optional (required for creating and joining repositories) +| users = 150 million () +| language = English +| launched = +| current_status = Active +| parent = Microsoft +| module = +}} + +'''GitHub''' () is a proprietary developer platform that allows developers to create, store, manage, and share their code. It uses Git to provide distributed version control and GitHub itself provides access control, bug tracking, software feature requests, task management, continuous integration, and wikis for every project. GitHub, headquartered in San Francisco, is operated by Github, Inc., a subsidiary of Microsoft since 2018. + +It is commonly used to host open source software development projects. GitHub reported having over 100 million developers and more than 420 million repositories, including at least 28 million public repositories. It is the world's largest source code host Over five billion developer contributions were made to more than 500 million open source projects in 2024. + +== About == +=== Founding === +The development of the GitHub platform began on October 19, 2007. The site was launched in April 2008 by Tom Preston-Werner, Chris Wanstrath, P. J. Hyett, and Scott Chacon after it had been available fo +<|CHUNK_END|> +A '''Fourier series''' () is a series expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation. This application is possible because the derivatives of trigonometric functions fall into simple patterns. Fourier series cannot be used to approximate arbitrary functions, because most functions have infinitely many terms in their Fourier series, and the series do not always converge. Well-behaved functions, for example smooth functions, have Fourier series that converge to the original function. The coefficients of the Fourier series are determined by integrals of the function multiplied by trigonometric functions, described in . + +The study of the convergence of Fourier series focus on the behaviors of the ''partial sums'', which means studying the behavior of the sum as more and more terms from the series are summed. The figures below illustrate some partial Fourier series results for the components of a square wave. + +File:SquareWaveFourierArrows,rotated,nocaption 20fps.gif|A square wave (represented as the blue dot) is approximated by its sixth partial sum (represented as the purple dot), formed by summing the first six terms (represented as arrows) of the square wave's Fourier series. Each arrow starts at the vertical sum of all the arrows to its left (i.e. the previous partial sum). +File:Fourier Series.svg|The first four partial sums of the Fourier series for a square wave. As more harmonics are added, the partial sums converge to the square wave. +File:Fourier series and transform.gif|Function s_6(x) (in red) is a Fourier series sum of 6 harmonically related sine waves (in blue). Its Fourier transform S(f) is a frequency-doma +<|CHUNK_END|> +| latest release version = 3.2.1 +| latest release date = +| programming language = JavaScript +| platform = See Browser support +| status = Active +| genre = JavaScript library +| license = MIT +| website = +| size = class="wikitable" style="margin:0;" +- + ver gzip prod dev +- + 1.x 31 90.9 266 +- + 2.x 27.7 81.6 236 +- + 3.x 29.9 86.3 263 +} +(KB) +}} + +'''jQuery''' is a JavaScript library created to make it easier and simpler to write JavaScript and HTML. It works on most web browsers and was invented by John Resig. The first release was in January 2006 at BarCamp NYC. Today there is a team of programmers working on jQuery, which is led by Dave Methvin. + +Today, more than 55% of the 10,000 most-visited websites use jQuery, hence it is the most popular JavaScript library being used today. It is free and open source software and licensed under the MIT License. + +jQuery's syntax is designed to make it easier to write complicated JavaScript. Some things that are easier to do using jQuery are: +* navigate (move around) a web page +* select (choose) elements on a web page using the Document Object Model +* create animations +* handle events like user actions +* create Ajax applications. +It also allows programmers to make their own jQuery plug-ins. + +Companies like Microsoft and Nokia have said that they are going to include jQuery on their mobile platforms. In addition, Microsoft is including jQuery in its Visual Studio software to use with the ASP.NET AJAX framework and ASP.NET MVC Framework. Nokia has included it in their Web Run-Time widget development platform. jQuery has also been used in MediaWiki since version 1.16. + +==Release history== +{| class="wikitable sortable" style="width:600px;" +|- +! Version number +! Release date +! Additional notes +|- +| style="width:50px;"| 1.0 +| style="width:150px;"| [http://jquery.com/blog/2006/08/26/jquery-10/ August 26, 2006] +| First stable relea +<|CHUNK_END|> +thumb|right|A 3D diagram of the protein [[myoglobin showing turquoise alpha helices. This protein was the first to have its structure solved by X-ray crystallography. Towards the right-center among the coils, a heme group (shown in grey) with a bound oxygen molecule (red)]] + +'''Proteins''' are long-chain molecules built from small units known as amino acids, which are joined in a sequence by peptide bonds. Every sequence of amino acids becomes a specific final shape, allowing living things to use proteins as tiny machines to do work. + +They are biochemical compounds.They have one or more polypeptides folded into a round or fibrous shape.See protein structure for more on this topic. + +A polypeptide is a single linear polymer chain of amino acids. The sequence of amino acids in a polypeptide comes from the DNA sequence of a gene.see Translation (genetics) and RNA splicing for a fuller account. The genetic code specifies 20 standard amino acids. Shortly after synthesis, some amino acids are chemically modified. This alters the folding, stability, activity, and function of the protein. Sometimes proteins have non-peptide groups attached, as cofactors. + +Proteins are essential to all cells. Like other biological macromolecules (polysaccharides and nucleic acids), proteins take part in virtually every process in cells: +# Many proteins are enzymes that catalyze (help to happen) biochemical reactions and are vital to metabolism. +# Other proteins have structural or mechanical functions, such as in muscle and in cells. The cytoskeleton is a system of scaffolding that keeps cell shape. +# Other proteins are important in cell signaling, immune responses, and cell division + +== Formation == +Proteins are formed by a process called "protein synthesis". The cell reads the genetic information of the DNA and translates it into a protein. In eukaryotes, this process begins in the cell nucleus and ends in the ribosome. In prokaryotes all of it is done in the cytoplasm. + +thumb|right|200px|Eg +<|CHUNK_END|> +thumb|Skewed distribution with one mode, distinct from its median and mean +In statistics, the '''mode''' of a set of data is the one that occurs most, Very often, samples of data are collected. These might be measurements of some kind. In this context, the mode is the value that occurs most often. Unlike the median and the mean, the mode is not necessarily unique. There might be several different values that occur the same number of times. + +Category:Statistics +<|CHUNK_END|> +333x333px|thumb + +In mathematics, '''hyperbolic functions''' are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the unit hyperbola. Also, similarly to how the derivatives of and are and respectively, the derivatives of and are and respectively. + +Hyperbolic functions are used to express the angle of parallelism in hyperbolic geometry. They are used to express Lorentz boosts as hyperbolic rotations in special relativity. They also occur in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics, including electromagnetic theory, heat transfer, and fluid dynamics. + +The basic hyperbolic functions are: +* '''hyperbolic sine''' "" (),(1999) ''Collins Concise Dictionary'', 4th edition, HarperCollins, Glasgow, , p. 1386 +* '''hyperbolic cosine''' "" (),''Collins Concise Dictionary'', p. 328 +from which are derived: +* '''hyperbolic tangent''' "" (),''Collins Concise Dictionary'', p. 1520 +* '''hyperbolic cotangent''' "" (),''Collins Concise Dictionary'', p. 329[http://www.mathcentre.ac.uk/resources/workbooks/mathcentre/hyperbolicfunctions.pdf tanh] +* '''hyperbolic secant''' "" (),''Collins Concise Dictionary'', p. 1340 +* '''hyperbolic cosecant''' "" or "" () +corresponding to the derived trigonometric functions. + +The inverse hyperbolic functions are: +* '''inverse hyperbolic sine''' "" (also denoted "", "" or sometimes "")[https://www.google.com/books?q=arcsinh+-library Some examples of using '''arcsinh'''] found in Google Books. +* '''inverse hyperbolic cosine''' "" (also denoted "", "" or sometimes "") +* '''inverse hyperbolic tangent''' "" (also denoted "", "" or sometimes "") +* '''inverse hyperbolic cotangent''' "" (also denoted "", "" or sometimes "") +* '''invers +<|CHUNK_END|> +| latest preview version = +| latest preview date = +| programming language = C, C++ +| operating system = Cross-platform +| language = English +| genre = Relational database management system +| license = GNU General Public License or proprietary EULA +| website = [http://www.mysql.com/ www.mysql.com] +}} + +'''MySQL''' is a database system used by many websites on the Internet. It is based on SQL. Many ways of doing things in SQL are similar in MySQL. The data is structured in tables in MySQL. To extract data from the tables, queries are used. + +For example: + +SELECT id_number + +FROM main_database + +WHERE name='John' + +This query will return the 'id_number' of the person named 'John' from the table named 'main_database'. + +== History == + +MySQL was first released in May 1995 and a Windows version was released in January 1998. The latest version (5.6.11) was released in April 2013. + +== Compatibility == + +MySQL is compatible with many major programming languages. Data Basecamp|url=https://databasecamp.de/en/data/mysqls|access-date=2022-06-20|language=en-US}} The most common one is PHP. An ODBC interface (called MyODBC) has been made so that users of Microsoft's ASP language can use MySQL. + +== Major users == + +Some of the largest MySQL users on the internet include: + +* Apple[https://www.apple.com/pr/library/2002/may/14xserve.html Apple's Xserve uses MySQL] +* Amazon.com +* Digg +* Google + +Many PHP scripts also use MySQL. These include: + +* WordPress +* phpBB +* MediaWiki - the software behind Wikipedia + +==Related pages== +* PHP + +== Notes == + +Category:Free software +Category:Databases +Category:Sun Microsystems software +Category:Oracle software +Category:Cross-platform software +<|CHUNK_END|> +In logic and philosophy, '''predicate logic''' is a system of mathematical logic. It uses predicates to express the state of certain things, which are "incomplete propositions" with a placeholder for objects or subjects that must be inserted in order to obtain a valid proposition. + +The term "predicate logic" has 2 meanings: + +1. First order logic (more often used); +2. Any logic(i.e. any formal logical system) that uses predicates. + +Any predicate logic is different from propositional logic, in part because it has the concept of ''quantifiers''. A quantifier is used in conjunction with a variable (say ''x'') in order to talk about a general instance of x, and in doing so, this allows predicate logic to make statements about quantity. + +The best-known quantifiers are the ''existential quantifier'', represented by ∃, and the ''universal quantifier'', represented by ∀. The existential quantifier is used to express statements of the form "there exists", and is true precisely when there is at least one mathematical object from the universe of discourse that matches the predicate or formula. On the other hand, the universal quantifier is used to express statements of the form "for all", and is true precisely when all possible mathematical objects of the universe of discourse match the specified predicate or formula. Predicates and Quantifiers Set 1|url=https://www.geeksforgeeks.org/mathematic-logic-predicates-quantifiers/|access-date=2020-08-21|website=GeeksforGeeks|language=en-US}} + +In the notation of predicate logic, quantifiers directly precede (and thus introduce) variable names, which are then followed by other quantifiers or mathematical expressions, where the said variables are found. For example. one can use the expression \exists x \forall y Lyx to mean "there is a person ''x'' such that for all persons ''y'', y likes x" ("everyone is liked by someone."). Brilliant Math & Science Wiki|url=https://brilliant.org/wiki/predicate-logic/|access-date=2020-08-21|website=b +<|CHUNK_END|> +thumb|350px|''The School of Athens'' by [[Raphael. This Renaissance painting shows an imaginary scene from ancient Greece, with Greek philosophers, writers, artists, and mathematicians. Raphael used the faces of people from his own time. Leonardo da Vinci was his model for Plato and is the philosopher with the white beard in the center.]] +'''The Renaissance''' is a period in European history that followed the Middle Ages and ended in the 17th century. ''Renaissance'' is a French word for “cultural rebirth.” During this period, there was a “rebirth” of classical learning. People started relearning the teachings of scholars from Ancient Greece, Rome, and other ancient societies. The Renaissance is often said to be the start of the modern age. + +During the Renaissance, there were many advances in art, literature, the sciences, mathematics, and culture. Many famous artists, writers, philosophers, and scientists lived during this period. A person who is clever at a great number of things is sometimes called a "Renaissance man." The most famous Renaissance man was Leonardo da Vinci, a painter, scientist, musician, and philosopher. + +The Renaissance started in Italy but soon spread throughout Europe. In Italy, the period is divided into three parts: +* the [http://www.artcyclopedia.com/history/early-renaissance.html Early Renaissance] +* the [http://www.artcyclopedia.com/history/high-renaissance.html High Renaissance] +* the [https://www.khanacademy.org/humanities/renaissance-reformation/mannerism1/a/a-beginners-guide-to-mannerism Late Renaissance] ''(also called the "Mannerist period") + +Following the Mannerist period was the Baroque period, which also spread across Europe starting around 1600. Outside Italy, it can be hard to tell when the Renaissance period ended and the Baroque began. + +== Causes == +thumb|Printers at work in 1520 +=== Reading and printing === +In the Middle Ages, most artistic, legal, and historical production took place in and around books. Monasteries, chu +<|CHUNK_END|> +In probability theory and statistics, the '''central limit theorems''', abbreviated as '''CLT''', are theorems about the limiting behaviors of aggregated probability distributions. They say that given a large number of independent random variables, their sum will follow a stable distribution. If the variance of the random variables is finite, then a Gaussian distribution will result. This is one of the reasons why this distribution is also known as ''normal'' distribution. + +The best known and most important of these is known as ''the central limit theorem''. It is about large numbers of random variables with the same distribution, each with an identical finite variance and expected value. + +More specifically, if X_1, \ldots, X_n are ''n'' identical and independently distributed random variables with mean \mu and standard deviation \sigma, then the distribution of their sample mean, (X_1 + \cdots + X_n)/n, as ''n'' gets large, is approximately normal with mean \mu and standard deviation \tfrac{\sigma}{\sqrt{n}}. Furthermore, the distribution of their sum, X_1 + \cdots + X_n, as ''n'' gets large, is also approximately normal, with mean n\mu and standard deviation \sqrt{n}\sigma. + +There are different generalisations of this theorem. Some of these generalisations no longer require an identical distribution of all random variables. In these generalisations, another precondition makes sure that no single random variable has a bigger influence on the outcome than the others. Examples are the Lindeberg and Lyapunov conditions. + +The name of the theorem is based on a paper George Pólya written in 1920, ''About the Central Limit Theorem in Probability Theory and the Moment problem''.[http://jeff560.tripod.com/c.html Jeff Miller: Earliest Known Uses of Some of the Words of Mathematics.] George Pólya: ''Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung und das Momentenproblem,'' Mathematische Zeitschrift, 8, 1920, pp. 171–181. [http://gdz.sub.uni-goettingen.d +<|CHUNK_END|> +thumb|upright=0.8|A graph with 6 vertices and 7 edges + +In mathematics and computer science, '''graph theory''' is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links, or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. + +== Definition and etymology == + +thumb|A graph consists of vertices connected by edges. A graph is occasionally called: + +Graph theory is a branch of mathematics that studies graphs, mathematical structures for modelling pairwise relations between objects. It is part of discrete mathematics, often considered part of combinatorics, although it is a stand-alone field due to its great growth and distinct from other fields, having its own kind of problems. The term "graph" was introduced by James Joseph Sylvester in a paper published in 1878 in ''Nature'', where he drew an analogy between "quantic invariants" and "co-variants" of algebra and molecular diagrams. + +The definition of a graph can vary, but one can understand that a graph is a structure consisting of vertices (also called nodes or points) and edges (also called arcs, links, or lines). Two vertices of an edge are called the endpoints. Occasionally, a graph is called an undirected graph, to distinguish it from a directed graph. A directed graph is a graph where each edge has an assignment direction known as orientation, designated with an arrow. A mixed graph can have edges that may be directed, and some may be undirected. A graph can also be called a simple graph, to distinguish it from a multigraph. A multigraph allows many edges to have the same pair of endpoints, and it also allows an edge to connect a vertex to itself, kn +<|CHUNK_END|> +Depending on the model used, making changes to the data in a database can be complex. That means that several steps are needed to perform a change. In that context, all the steps are grouped. This group is called a '''transaction'''. Many databases give guarantees about the data, and they also do checks. When something goes wrong in one step, all the steps in the group, or transaction, are undone. This is called a ''rollback''. When all the steps have been executed, and there was no error, this state can be persisted. People will talk about ''committing'' a transaction. + +A database transaction is generally atomic. That means, it is either done completely, or it is not done. The state of it being done is not visible. + +Most of the time, transactions are needed to guarantee the ACID principle of databases. Data Basecamp|url=https://databasecamp.de/en/data/acids|access-date=2022-07-07|language=en-US}} + +== References == +Transaction +<|CHUNK_END|> +'''Bayesian probability''' figures out the likelihood that something will happen based on available evidence. This is different from frequency probability which determines the likelihood something will happen based on how often it occurred in the past. + +You might use Bayesian probability if you don't have information on how often the event happened in the past. +==Example== +As an example, say you want to classify an email as "spam" or "not spam". One thing you know about this email is that it has an emoji in the subject line. Say it's the year 2017, and 80% of the emails you got with emoji in them were spam. So you can look at an email with emoji in the subject and say it's 80% likely to be spam. + +But if only 1% of your emails were spam and 80% of the emojis were spam, that's different than if half your emails are spam and 80% of emoji emails were spam. + +Then you can use Bayes's Theorem to determine one probability of whether this email is spam: + +p (is_spam | contains_emoji) = [ p(contains_emoji | is_spam) * p(is_spam) ] / p(contains_emoji) + +P(xy) = P(xy) * Px / Py + +probability +Category:Philosophy of science +Category:Probability theory +<|CHUNK_END|> +In computer programming, the '''strategy pattern''' (also known as the '''policy pattern''') is a behavioral software design pattern that enables selecting an algorithm at runtime. Instead of implementing a single algorithm directly, code receives runtime instructions as to which in a family of algorithms to use. + +Strategy lets the algorithm vary independently from clients that use it.Eric Freeman, Elisabeth Freeman, Kathy Sierra and Bert Bates, ''Head First Design Patterns'', First Edition, Chapter 1, Page 24, O'Reilly Media, Inc, 2004. Strategy is one of the patterns included in the influential book ''Design Patterns'' by Gamma et al. that popularized the concept of using design patterns to describe how to design flexible and reusable object-oriented software. Deferring the decision about which algorithm to use until runtime allows the calling code to be more flexible and reusable. + +For instance, a class that performs validation on incoming data may use the strategy pattern to select a validation algorithm depending on the type of data, the source of the data, user choice, or other discriminating factors. These factors are not known until runtime and may require radically different validation to be performed. The validation algorithms (strategies), encapsulated separately from the validating object, may be used by other validating objects in different areas of the system (or even different systems) without code duplication. + +Typically, the strategy pattern stores a reference to code in a data structure and retrieves it. This can be achieved by mechanisms such as the native function pointer, the first-class function, classes or class instances in object-oriented programming languages, or accessing the language implementation's internal storage of code via reflection. + +== Structure == +=== UML class and sequence diagram === +frame|none|A sample UML class and sequence diagram for the Strategy design pattern. +In the above UML class diagram, the Context class does not i +<|CHUNK_END|> +'''Euler's formula''', named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number , one has +e^{i x} = \cos x + i \sin x, +where is the base of the natural logarithm, is the imaginary unit, and and are the trigonometric functions cosine and sine respectively. This complex exponential function is sometimes denoted ("cosine plus ''i'' sine"). The formula is still valid if is a complex number, and is also called ''Euler's formula'' in this more general case.}} + +Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics". + +When , Euler's formula may be rewritten as or , which is known as Euler's identity. + +==History== +In 1714, the English mathematician Roger Cotes presented a geometrical argument that can be interpreted (after correcting a misplaced factor of \sqrt{-1}) as:Cotes wrote: ''"Nam si quadrantis circuli quilibet arcus, radio ''CE'' descriptus, sinun habeat ''CX'' sinumque complementi ad quadrantem ''XE''; sumendo radium ''CE'' pro Modulo, arcus erit rationis inter EX + XC \sqrt{-1}& ''CE'' mensura ducta in \sqrt{-1}."'' (Thus if any arc of a quadrant of a circle, described by the radius ''CE'', has sinus ''CX'' and sinus of the complement to the quadrant ''XE''; taking the radius ''CE'' as modulus, the arc will be the measure of the ratio between EX + XC \sqrt{-1} & ''CE'' multiplied by \sqrt{-1}.) That is, consider a circle having center ''E'' (at the origin of the (x, y) plane) and radius ''CE''. Consider an angle ''θ'' with its vertex at ''E'' having the positive x-axis as one side and a radius ''CE'' as the other side. The perpendicular from the point ''C'' on the circle to the x-axis is the "sinus" ''CX''; the line between the circl +<|CHUNK_END|> +'''Combinatorics''' is a branch of mathematics. It is concerned with finite or countable infinite sets. Combinatorics is part of discrete mathematics. Combinatorics are about graph theory, or Partitions of sets. According to George Pólya, combinatorics looks at counting the number of possibilities, and about the questions whether certain configurations exist, and how to get to them. + +== Permutation == + +Permutation is concerned with the following problems: +* Determining how many different ways there are to arrange a number of objects. +* Determining how many ways there are to select a number of objects from a larger set. + +There are variations in the problems as follows: +* The objects may or may not be distinguishable. +* The order in which the objects are selected may or may not matter. + +=== Examples === +thumb|right|All the possibilities to arrange three differently colored balls +* There are 6 different ways to arrange three distinguishable objects (as shown in the graphic). +* There are three different ways to select one particular orange from a basket with three oranges. +* There is only one possible way to select the apple from a basket that has one orange, one apple and one pear in it. +<|CHUNK_END|> +'''Backpropagation''' is a method of computing the gradient artificial neural networks to perform tasks more accurately. Data Basecamp|url=https://databasecamp.de/en/ml/backpropagation-basics|access-date=2022-07-01|language=en-US}} The algorithm was first used for this purpose in 1974 in papers published by Werbos, Rumelhart, Hinton, and Williams. The term backpropagation is short for "backward propagation of errors". + +It works especially well for feed forward neural networks (networks without any loops) and problems that require supervised learning. + +== How it works == +The idea is to test how wrong the neural network is and then correct it. This is repeated many times. + +With a little more detail: + +# You create a loss function (Also known as a cost function), which shows how far the answers from the neural net are from the real answers. (This is often done many times. After that you take the average) +# You calculate how to adjust the parameters (weights and biases) inside the neural net by taking the partial derivative of the loss with respect to those parameters. Specifically, the chain rule is used to find the derivative with respect to each parameter. +# You adjust the parameters. How you adjust the parameters is based on your training method, with one of the simplest, yet still commonly used ways being stochastic gradient descent . + +This is repeated until the neural network is good enough at its job. This happens when the error measured by the loss function is low. + +== References == + +== Further Reading == + +# [http://neuralnetworksanddeeplearning.com/chap2.html "How the backpropagation algorithm works | Neural Networks and Deep Learning.com"]. 2019-12, Retrieved 2025-07-29 +# [https://michaelkosmider.github.io/dlminiboxtutorial/?utm_source=chatgpt.com "Autograd Tutorial | michaelkosmider.github"] 2025-06-11, Retrieved 2025-07-28 + +Category:Algorithms +Category:Machine learning +<|CHUNK_END|> +thumb|Girl looking scared, suffering from anxiety + +'''Anxiety''' is distress or uneasiness of mind caused by a fear of danger or misfortune. Define Anxiety at Dictionary.com|access-date=2018-05-05}} Very often, people with anxiety also feel worries. There can also be physical symptoms, like having a headache or an upset stomach. + +Anxiety is a very common human emotion and is often associated with fear, panic, and the fight or flight response. The amount of stress needed to cause anxiety will vary from person to person however, basics include: losing one's job, the death of a loved one, or an accident, to name a few. In most people, anxiety will settle over time and one will return to normal state. + +Some people suffer a lot of anxiety over a long period of time which controls them and makes their lives difficult. These conditions are called anxiety disorders and can be treated by therapy and medicine. + +General anxiety symptoms are things such as; continual tiredness / exhaustion, inability to relax, lack of confidence, low self-esteem, fear of public places, fear of socialising, frequent feelings of irrational anxiety / fear, compulsive behavior, worrying about making mistakes, regular nightmares, disturbed sleep patterns, excessive crying, headaches, stomach problems, diarrhea, nausea, aching muscles, and so on. + +Symptoms of anxiety attacks are things like; sweating, shaking and tremors, palpitations, shortness of breath, hyperventilating, racing heart beat, tingling in hands and feet, feeling of impending doom, feeling you are having a heart attack. There are more, but these are the usual ones. + +== Medicine == +These symptoms, more or less, define anxiety but they can also be signs of other problems, so the first port of call has to be a doctor or other health care professional. They will be able to define what the problem is exactly, and propose the appropriate treatment. + +A doctor’s first line treatment is usually through drug-based medication; for example anti +<|CHUNK_END|> +thumb|right|200px|Regression line for 50 random points in a [[Gaussian distribution around the line y=1.5x+2]] + +In statistical modeling, '''regression analysis''' is a statistical method for estimating the relationship between a dependent variable (often called the ''outcome'' or ''response'' variable, or a ''label'' in machine learning parlance) and one or more independent variables (often called ''regressors'', ''predictors'', ''covariates'', ''explanatory variables'' or ''features''). + +The most common form of regression analysis is linear regression, in which one finds the line (or a more complex linear combination) that most closely fits the data according to a specific mathematical criterion. For example, the method of ordinary least squares computes the unique line (or hyperplane) that minimizes the sum of squared differences between the true data and that line (or hyperplane). For specific mathematical reasons (see linear regression), this allows the researcher to estimate the conditional expectation (or population average value) of the dependent variable when the independent variables take on a given set of values. Less common forms of regression use slightly different procedures to estimate alternative location parameters (e.g., quantile regression or Necessary Condition Analysis[http://www.erim.eur.nl/centres/necessary-condition-analysis/ Necessary Condition Analysis]) or estimate the conditional expectation across a broader collection of non-linear models (e.g., nonparametric regression). + +Regression analysis is primarily used for two conceptually distinct purposes. First, regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Second, in some situations regression analysis can be used to infer causal relationships between the independent and dependent variables. Importantly, regressions by themselves only reveal relationships between a dependent variable and a collection +<|CHUNK_END|> +thumb|280px|right| Greedy algorithms determine the minimum number of coins to give while [[Change-making problem|making change. These are the steps a human would take to emulate a greedy algorithm to represent 36 cents using only coins with values {1, 5, 10, 20}. The coin of the highest value, less than the remaining change owed, is the local optimum. Note that in general, dynamic programming or linear programming is required to find the optimal solution. However, most currency systems, including the Euro (pictured) and US Dollar, are special cases where the greedy strategy also finds an optimal solution.]] +A '''greedy algorithm''' is an algorithm used in solving optimization problems. Greedy algorithms select the best result at each iteration. The global optimum is obtained by repeatedly selecting the local optimum. + +==Examples== +*Kruskal's algorithm for finding the minimum spanning tree in a graph. +*Prim's algorithm for finding the minimum spanning tree in a graph. +*Dijkstra's algorithm for finding the shortest path in a graph with non-negative edge lengths. + +There are some problems where greedy algorithms do not produce the best possible solution. In such cases, they often produce the worst possible one. Again look at the coin-changing example above, and imagine that there are coins for 25 cent, 10 cent and 4 cent. Now imagine that the sum of 41 cent needs to be changed. A greedy algorithm would pick 25 cent, 10 cent, and 4 cent, for a total of 39 cent. The algorithm is then stuck, because the remaining 2 cent cannot be changed. One possible way of solving the is to use the 25 cent coin, and four coins of 4 cent. +<|CHUNK_END|> +. +}} + +In mathematics, the '''derivative''' is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. The derivative is often described as the '''instantaneous rate of change''', the ratio of the instantaneous change in the dependent variable to that of the independent variable. The process of finding a derivative is called '''differentiation'''. + +There are multiple different notations for differentiation. ''Leibniz notation'', named after Gottfried Wilhelm Leibniz, is represented as the ratio of two differentials, whereas ''prime notation'' is written by adding a prime mark. Higher order notations represent repeated differentiation, and they are usually denoted in Leibniz notation by adding superscripts to the differentials, and in prime notation by adding additional prime marks. Higher order derivatives are used in physics; for example, the first derivative with respect to time of the position of a moving object is its velocity, and the second derivative is its acceleration. + +Derivatives can be generalized to functions of several real variables. In this case, the derivative is reinterpreted as a linear transformation whose graph is (after an appropriate translation) the best linear approximation to the graph of the original function. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables. It can be calculated in terms of the partial derivatives with respect to the independent variables. For a real-valued function of several variables, the Jacobian matrix reduces to the gradient vector. + +== Definition == +=== As a limit === +A function of a real variabl +<|CHUNK_END|> +'''Microeconomics''' is the science of how people make decisions at the small scale. It is different from macroeconomics which looks at how the economy works as a whole ("on aggregate").Krugman, Paul; Robin Wells with Margaret Ray and David Anderson (2012) ''Microeconomics: Second Edition in Modules'' Worth Publishers New York, New York page 5 In microeconomics, we might look at how a person chooses what to buy at the store, or how many things a company will make. Some parts of microeconomics include ''Consumer Theory'' and ''Theory of the Firm'', which study how people and businesses make decisions. Game theory looks at how people make decisions when the outcome (how something ends) depends on what decision another person makes; when agents are said to act "strategically". + +==References== + +==Related pages== +* Macroeconomics + + + +__NOEDITSECTION__ +<|CHUNK_END|> +| symbol = 24px|alt=♂|Astronomical symbol of Mars +| adjectives = Martian +| orbit_ref = +| epoch = J2000 +| aphelion = +| perihelion = +| semimajor = +| eccentricity = +| period =  sols)}} +| synodic_period = +| avg_speed = +| inclination = to ecliptic; | the Sun's equator; | to invariable plane}} +| asc_node = +| arg_peri = +| satellites = 2 +| allsatellites = yes +| mean_radius = +| equatorial_radius = +| polar_radius = +| flattening = +| surface_area = (|; 0.284 Earths)}} +| volume = (0.151 Earths) +| mass = (0.107 Earths) +| density = +| surface_grav = (|; 0.3794 ''g'')}} +| moment_of_inertia_factor = +| escape_velocity = +| sidereal_day = +| rot_velocity = +| axial_tilt = to its orbital plane +| right_asc_north_pole = +| declination = +| albedo = +| temp_name1 = Kelvin +| min_temp_1 = 130 K +| mean_temp_1 = 210 K +| max_temp_1 = 308 K +| temp_name2 = Celsius +| min_temp_2 = −143 °C +| mean_temp_2 = −63 °C +| max_temp_2 = 35 °C +| temp_name3 = Fahrenheit +| min_temp_3 = −226 °F +| mean_temp_3 = −82 °F +| max_temp_3 = 95 °F +| magnitude = −2.94 to +1.86 +| angular_size = 3.5–25.1″ +| atmosphere_ref = +| surface_pressure = 0.636 (0.4–0.87) kPa +| atmosphere_composition = +}} +'''Mars''' is the fourth planet from the Sun and the second-smallest planet in the Solar System, nicknamed ''' The Red Planet'''. + +Mars is a terrestrial planet with caps of water and carbon dioxide. It has the largest volcano in the Solar System, and some very large impact +<|CHUNK_END|> +thumb|120 px|According to the first meaning of permutation, each of the six rows is a different permutation of three distinct balls|alt=The six different possible ways to order three balls of different colors: (red, green, blue), (red, blue, green), (green, red, blue), (green, blue, red), (blue, red, green), and (blue, green, red). +In mathematics, a '''permutation''' of a set can mean one of two different things: +* an arrangement of its members in a sequence or linear order, or +* the act or process of changing the linear order of an ordered set. + +An example of the first meaning is the six permutations (orderings) of the set {1, 2, 3}: written as tuples, they are (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). Anagrams of a word whose letters are all different are also permutations: the letters are already ordered in the original word, and the anagram reorders them. The study of permutations of finite sets is an important topic in combinatorics and group theory. + +Permutations are used in almost every branch of mathematics and in many other fields of science. In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences. + +The number of permutations of distinct objects is  factorial, usually written as , which means the product of all positive integers less than or equal to . + +According to the second meaning, a permutation of a set is defined as a bijection from to itself. That is, it is a function from to for which every element occurs exactly once as an image value. Such a function \sigma : S \to S is equivalent to the rearrangement of the elements of in which each element ''i'' is replaced by the corresponding \sigma(i). For example, the permutation (3, 1, 2) corresponds to the function \sigma defined as + +\sigma(1) = 3, \quad \sigma(2) = 1, \quad \sigma(3) = 2. + +The collection of all permutations of a set form a group called the sym +<|CHUNK_END|> +325px|thumb|A plot of a [[normal distribution (or bell curve). Each colored band has a width of one standard deviation.]] +frame|right|A data set with a mean of 50 (shown in blue) and a standard deviation (σ) of 20. +thumb|right|Example of two sample populations with the same mean and different standard deviations. Red population has mean 100 and SD 10; blue population has mean 100 and SD 50. + +'''Standard deviation''' is a number used to tell how measurements for a group are spread out from the average (mean or expected value). Data Basecamp|url=https://databasecamp.de/en/statistics/standard-deviation|access-date=2023-05-29|language=en-US}} A low standard deviation means that most of the numbers are close to the average, while a high standard deviation means that the numbers are more spread out. + +The reported margin of error is usually twice the standard deviation. Scientists commonly report the standard deviation of numbers from the average number in experiments. They often decide that only differences bigger than two or three times the standard deviation are important. Standard deviation is also useful in money, where the standard deviation on interest earned shows how different one person’s interest earned might be from the average. + +Many times, only a sample, or part of a group can be measured. Then a number close to the standard deviation for the whole group can be found by a slightly different equation called the sample standard deviation, explained below. In which case, the standard deviation of the whole group is represented by the Greek letter \sigma, and that of the sample by s. + +==Basic example== +Consider a group having the following eight numbers: +: + 2,\ 4,\ 4,\ 4,\ 5,\ 5,\ 7,\ 9 + +These eight numbers have the average (mean) of 5: +: \frac{2 + 4 + 4 + 4 + 5 + 5 + 7 + 9}{8} = 5 +To calculate the population standard deviation, first find the difference of each number in the list from the mean. Then square the result of each difference: +: + +<|CHUNK_END|> +thumb|The human nervous system +thumb|right|Illustration of how [[pain travels to the brain, from René Descartes's ''Treatise of Man'']] + +The '''nervous system''' is a body system which sends signals around the body. It lets animals respond to what is around them. The ''central nervous system'' is the brain and the spinal cord. It is present in almost all animals. It is there to process the input from the senses, and to coordinate movement. Neuroscience is the scientific study of the nervous system. + +The nervous system is made up of neurons. Other cells, such as glial cells keep the neurons safe and in good condition. + +The structure of the system includes the brain and spinal cord, which together are called the ''central nervous system.'' The brain has billions of nerve cells to help think, walk, and breathe. The nervous system can react in 1/100 of a second to a stimulus, like a pain signal. + +The system of nerves in your body that sends messages for controlling movement and feeling between the brain and the other parts of the body anatomy of nervous systems can be sub-divided as follows: + +*Central nervous system +**Brain +**Spinal cord +*Peripheral nervous system +**Autonomic nervous system +***Sympathetic nervous system +***Parasympathetic nervous system +**Somatic nervous system + +==References== +<|CHUNK_END|> +thumb|upright|The sign of the covariance of two random variables ''X'' and ''Y'' + +In probability theory and statistics, '''covariance''' is a measure of the joint variability of two random variables. The sign of the covariance shows the tendency in the linear relationship between the variables. Covariance is positive when variables tend to show similar behavior and negative when variables tend to show opposite behavior. The magnitude of the covariance is the geometric mean of the variances that are shared for the two random variables, where a larger magnitude means two variables more strongly depend on each other. + +Covariance has units of measurement, and the magnitude of the covariance is affected by said units. This means changing the units (e.g., from meters to millimeters) changes the covariance value proportionally, making it difficult to assess the strength of the relationship from the covariance alone. In some situations, it is desirable to compare the strength of the joint association between different pairs of random variables that do not necessarily have the same units. In those situations, we use the correlation coefficient, which normalizes the covariance to a value between -1 and 1 by dividing by the geometric mean of the total variances (i.e., the product of the standard deviations) for the two random variables. + +A distinction is made between (1) the covariance of two random variables, which is a population parameter that can be seen as a property of the joint probability distribution, and (2) the sample covariance, which, in addition to serving as a descriptor of the sample, also serves as an estimated value of the population parameter. + +== Definition == +For two jointly distributed real-valued random variables X and Y with finite second moments, the covariance is defined as the expected value (or mean) of the product of their deviations from their individual expected values:Oxford Dictionary of Statistics, Oxford University Press, 2002, p. 104. + +\oper +<|CHUNK_END|> +'''ACID''' is a concept used with databases. Data Basecamp|url=https://databasecamp.de/en/data/acids|access-date=2022-07-07|language=en-US}} It is the way some databases keep their data true and meaningful. Not all databases use the concept of ACID, but relational databases usually do. + +ACID is an abbreviation. It stands for +*''Atomicity'' - A change to the data in the database is either done completely, or not done at all. The process of doing it is not visible to users of the database. Users (people and programs) only see the result. +*''Consistency'' - A database can have rules about its data. Consistency means that the data always follows those rules. When a transaction (a change in the data) occurs, it can not break the rules. Rules are usually about ''integrity'', such as what is allowed and what is not allowed in certain locations of the database. +*''Isolation'' - There can be more than one transaction occurring at the same time. Isolation means that one transaction can only see the changes of another transaction at the right time. Sometimes isolation means that transactions happening at the same time would do the same thing if they were done one after another. +*''Durability'' - When a transaction is done, if the result is unwanted it can be rolled back, which means it is made to go away as if it never happened. If the result of a transaction is still wanted, it can be committed, which makes the change permanent. After a transaction is committed, the change it made will still be there even if the database is shut down. + +== References == +Category:Database modeling +<|CHUNK_END|> +:''"The Web" redirects here. For other uses, see Web (disambiguation)''. + +The '''World Wide Web''' ("'''WWW'''" or "'''the Web'''", "'''the Webspace"''') is the part of the Internet that contains websites and webpages. It was invented in 1989 by Tim Berners-Lee at CERN, Geneva, Switzerland. Sir Tim Berners-Lee created a new markup language called HTML. Each Website is a group of pages linked by hypertext links that are written in HTML. + +The software to see the World Wide Web is called a web browser. To access the World Wide Web, one also needs a connection to the Internet. + +Many companies nowadays offer website hosting allowing one to make websites that can be displayed on the World Wide Web, including a custom domain (www.stuff.com) site. + +== History == +thumb|This [[NeXT Computer was used by Tim Berners-Lee as the first web server and also to write the first web browser – WorldWideWeb.]] + +The World Wide Web was created by Tim Berners-Lee in 1989 while he was working at CERN, a research center in Switzerland. He wanted to help scientists share documents and information easily over the Internet. He suggested a system using hypertext, which lets people click on links to move between documents. + +In 1990, Berners-Lee made the first version of the Web. It included: +* The first web browser and editor, called ''WorldWideWeb'', +* The first web server, and +* The first web page, which explained what the Web was and how to use it. + +In 1991, the Web became available to researchers outside CERN. By 1993, it began to grow fast. That year, the Mosaic browser was released. It was the first popular browser with graphics, which made the Web end helped it spread worldwide. + +In 1994, Berners-Lee started World Wide Web Consortium (W3C) at MIT to create a couple standards that would keep the Web open and accessible for everyone. + +Over time, the Web changed: +* In the 2000s, websites became more interactive with JavaScript, CSS, and AJAX, leading to what's called Web 2.0. +* Social media +<|CHUNK_END|> +'''Consciousness''' means being awake, alert and responsive to the environment. The definition of consciousness may differ in psychology, neuroscience, philosophy and other related sciences. It is often disputed amongst academics and scientists. + +Consciousness is a range of mental states. There are several states between a fully conscious state and a fully unconscious state.Tart, Charles R. 1975. ''States of consciousness''. NY: Dutton, p5162. In medicine, the degree of ''loss of consciousness'' is measured by using Glasgow Coma Scale (GCS); a score between 3 and 15 is given to each person at any time, to show how conscious the person is. Higher scores show more conscious states. + +It seems that many decisions are made without us being aware of it. Some think that these decisions are made by what is called the unconscious mind. There are also many body functions which we do not notice until they go wrong. These activities are done by the autonomic nervous system. Breathing and the beat of one's heart can be noticed but are controlled by nervous system without thought. + +It is not known what causes consciousness. So, it is difficult to know if another person or thing is indeed conscious.[http://www.scientificamerican.com/article/how-doctors-peer-into-the-minds-of-vegetative-patients/ ''How doctors peer into the minds of vegetative patients; communicating with patients who appear to lack consciousness is becoming a reality''] May 2014 issue Scientific American The best we can say is that some animals do seem to be conscious of the world around them. We ourselves assume that others have consciousness, but this is notoriously difficult to prove. This is known in philosophy as ''the problem of other minds''. + +== References == + +Category:Philosophy +<|CHUNK_END|> +| cultural_origins = 1950s in the United States, 1960s in the United Kingdom and elsewhere +| instruments = +| popularity = Extremely high worldwide, since 1950s +| derivatives = +| subgenrelist = List of rock genres +| subgenres = +| fusiongenres = +| regional_scenes = +| other_topics = +}} + +'''Rock music''' is a genre of popular music. It developed in the late 1900s, chiefly in the United States. It originally started in the 1940s and 1950s with the start of rock and roll. "''Rock and roll''" grew out of ''R&B'' (Rhythm & Blues) and ''country'' after the electrification of the guitar (and music in general) in the 1940s. Rock has a lot in common with other genres like ''blues'' and ''folk''. It has influences from ''jazz'', ''classical'', and other music genres. + +Rock music usually uses the electric guitar, bass guitar, a singer, and the drumset. It has a 4/4 beat and it has verse-chorus form. Rock music has also helped to spread cultural and social movements. This led to large sub-cultures including modernists and rockers in the UK and the "hippie" culture that spread out from San Francisco in the US in the 1960s. Rock music has the same folk tradition as the protest song. Rock music has been involved with political activism. It has also spread awareness for race, sex, and drug-use issues. It is often seen as an expression of youth revolt against adult consumerism and conformity. + +However, rock has become really varied since the 1950s and it is hard to say what its lyrics are "mostly" about. They can express romantic love, or comment all of global society. Rock music does place a focus on musical skill and live performance. By the late 1960s, rock had spread all across the United States and across the Atlantic to Great Britain. ''"Rock n roll's"'' influence in local music genres in these places created hybrids like blues rock, folk rock, country rock, jazz-rock fusion, and psychedelic rock + f(a) + \frac {f'(a)} +<|CHUNK_END|> +In mathematics and mathematical logic, '''Boolean algebra''' is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (''and'') denoted as , disjunction (''or'') denoted as , and negation (''not'') denoted as . Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations. + +Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his ''An Investigation of the Laws of Thought'' (1854). According to Huntington, the term ''Boolean algebra'' was first suggested by Henry M. Sheffer in 1913, although Charles Sanders Peirce gave the title "A Boolian Algebra with One Constant" to the first chapter of his "The Simplest Mathematics" in 1880. Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics. + +==History== +A precursor of Boolean algebra was Gottfried Wilhelm Leibniz's algebra of concepts. The usage of binary in relation to the ''I Ching'' was central to Leibniz's ''characteristica universalis''. It eventually created the foundations of algebra of concepts. Leibniz's algebra of concepts is deductively equivalent to the Boolean algebra of sets. + +Boole's algebra predated the modern developments in abstract algebra and mathematical logic; it is however seen as connected to the origins of both fields. In an abstract setting, Boolean algebra was perfected in the late 19th century by Jevons, Schröder, Huntington +<|CHUNK_END|> +thumb|A snippet of Python code demonstrating binary search + +The syntax of the Python programming language is the set of rules that defines how a Python program will be written and interpreted (by both the runtime system and by human readers). The Python language has many similarities to Perl, C, and Java. However, there are some definite differences between the languages. It supports multiple programming paradigms, including structured, object-oriented programming, and functional programming, and boasts a dynamic type system and automatic memory management. + +Python's syntax is simple and consistent, adhering to the principle that "There should be one-and preferably only one-obvious way to do it." The language incorporates built-in data types and structures, control flow mechanisms, first-class functions, and modules for better code reusability and organization. Python also uses English keywords where other languages use punctuation, contributing to its uncluttered visual layout. + +The language provides robust error handling through exceptions, and includes a debugger in the standard library for efficient problem-solving. Python's syntax, designed for readability and ease of use, makes it a popular choice among beginners and professionals alike. + +== Design philosophy == + +Python was designed to be a highly readable language."Readability counts." - [https://www.python.org/dev/peps/pep-0020/ PEP 20 - The Zen of Python] It has a relatively uncluttered visual layout and uses English keywords frequently where other languages use punctuation. Python aims to be simple and consistent in the design of its syntax, encapsulated in the mantra , from the Zen of Python. + +This mantra is deliberately opposed to the Perl and Ruby mantra, "there's more than one way to do it". + +== Keywords == + +Python 3 has 35 keywords or ''reserved words''; they cannot be used as identifiers. + +*and +*as +*assert +*async}} +*await +*break +*class +*continue +*def +*del +*elif +*else +*except +*False +*finally +*for +*fr +<|CHUNK_END|> +thumb|Bust of [[Socrates. Roman copy of an ''original'' thought to be ''carved'' by Lysippos.]] + +'''Philosophy''' is the study of wisdom. is the Ancient Greek word for the "love of wisdom". + +A person who works in the field of philosophy is called a '''philosopher'''. A philosopher is a kind of thinker and researcher. Philosophers ask general and fundamental questions. The topics of these questions include existence, knowledge, mind, reason, language, and value. + +A "philosophy" can also mean a group of ideas or a way of living. However, philosophy as an area of study mostly refers to asking fundamental questions, rather than creating ways of living. + +Philosophy is a way of thinking about the world, the universe, and society. In the past, natural sciences like physics and psychology were a part of philosophy. Philosophy also used to be studied with religion. In the past few centuries, the difference between philosophy, sciences and religion has become much greater. Now, they are regarded as separate academic disciplines. + +==Ideas== +The ideas in philosophy are often general and ''abstract''. However, this does not mean that philosophy is not about the real world. For example, ethics talks about how to be good in our day-to-day lives. Metaphysics questions how the world works and what it is made of. Sometimes, people talk about how they have a ‘personal philosophy’, which means the way a person thinks about the world. This article is ''not'' about people's ’personal philosophies’. This article is about the ideas that have been discussed by philosophers. + +==Questions== +Questions related to philosophy are called philosophical questions. Most philosophical questions can never be answered with certainty. They focus on important topics, such as the meaning of life, death, and morality. An example of a philosophical question is this: "Is there any knowledge in the world which is so certain that no reasonable man could doubt it?".Russell, Bertrand 1912. ''The problems of phi +<|CHUNK_END|> +'''pH''' is a scale of acidity from 0 to 14. It tells how acidic or alkaline a substance is. +More acidic solutions have lower pH. More alkaline solutions have higher pH. Substances that aren't acidic or alkaline (that is, neutral solutions) usually have a pH of 7. +Acids have a pH that is less than 7. Alkalis have a pH that is greater than 7. + +pH is a measure of the concentration of protons (H+) in a solution. S.P.L. Sørensen introduced this concept in the year 1909. The p stands for the German ''potenz'', meaning power or concentration, and the H for the hydrogen ion (H+). + +The most common formula for calculating pH is: + +:\mbox{pH} = -\log_{10} \left[ \mbox{H}^+ \right] + +[H+] indicates the concentration of H+ ions (also written [H3O+], the equal concentration of hydronium ions), measured in moles per litre (also known as molarity). + +However, the correct equation is actually: + +:\mbox{pH} = -\log_{10} \left[ a_{\mathrm{H^+}} \right] + +where a_{\mathrm{H^+}} indicates the activity of H+ ions. But, this equation in most cases provides the same value as the more common formula, so in introductory chemistry the previous equation is given as the definition of pH. + +Most substances have a pH in the range of 0 to 14, although ''extremely'' acidic or alkaline substances may have pH 14. + +Alkaline substances have, instead of hydrogen ions, a concentration of hydroxide ions (OH-). + +== pH indicators == +Certain dyes change colour depending on whether they are in an acid solution or an alkaline solution . '''pH indicator''' is a chemical compound added in small amounts to a solution so the pH (acidity or basicity) of the solution can be seen. The pH indicator is a chemical detector for hydronium ions (H3O+) or hydrogen ions (H+).These are two different ways of representing hydrogen ion concentration. Normally, the indicator causes the colour of the solution to change depending on the pH. + +Typical indicators are phenolphthalein, methyl orange, methyl red, bromothymol blue, and thymo +<|CHUNK_END|> +The '''theory of relativity''' is a theory Albert Einstein created in the early 1900s. There are two theories of relativity. The first is special relativity and the second is general relativity. + +The theory tries to solve problems which could not be solved by Classical physics, or by 19th century physics. Some things, like the orbit of Mercury or the way light from distant sources bends as it passes a star, cannot be explained by the physics of 1900. Einstein tried to change the basic ideas of physics. He came up with two theories to do that. The first was called Special relativity and the second was called General relativity. + +== References == +* Hawking, Stephen. ''The Universe in a nutshell''. Bantam Books, 2001. + +== Other websites [http://www.muppetlabs.com/~breadbox/txt/al.html Albert Einstein's Theory of Relativity In Words of Four Letters or] [http://www.cosmobrain.com.br/cosmoforum/viewtopic.php?t=118 New times and new technologies survey the experiments of Sobral and Príncipe] ess wayback machine == + +* [http://www.muppetlabs.com/~breadbox/txt/al.html Albert Einstein's Theory of Relativity In Words of Four Letters or Less] +* [http://www.cosmobrain.com.br/cosmoforum/viewtopic.php?t=118 New times and new technologies survey the experiments of Sobral and Príncipe.] +* [http://www.relativitycalculator.com Relativity Calculator – Learn Special Relativity Mathematics] The mathematics of special relativity presented in as simple and comprehensive manner possible within philosophical and historical contexts. + +Category:Relativity +Category:Albert Einstein +<|CHUNK_END|> +| discontinued = +| latest release version = +| latest release date = +| latest preview version = +| programming language = Go +| operating system = Linux, Windows, macOS +| platform = x86-64, ARM, s390x, ppc64le +| language = +| genre = OS-level virtualization +| license = }} +}} +thumb|Former logo + +'''Docker''' is a set of products that uses operating system-level virtualization to deliver software in packages called ''containers''. Docker automates the deployment of applications within lightweight containers, enabling them to run consistently across different computing environments. + +The core software that runs and manages these containers is called '''Docker Engine'''. Docker was first released in 2013 and continues to be developed by Docker, Inc. The platform includes both free and paid tiers. + +== History == + started the Docker project in France as an internal project within dotCloud, a platform-as-a-service company. + +dotCloud Inc. was founded by Kamel Founadi, Hykes, and Sebastien Pahl during the Y Combinator Summer 2010 startup incubator group and launched in 2011, and renamed to Docker Inc in 2013. + +Docker debuted to the public in Santa Clara at PyCon in 2013. It was released as open-source in March 2013. At the time, it used LXC as its default execution environment. One year later, with the release of version 0.9, Docker replaced LXC with its own component, ''libcontainer'', which was written in the Go programming language. + +In 2017, Docker created the for open research and development. In March 2026, the Communications of the ACM featured Docker as the cover article in a retrospective article of the past decade. + +=== Adoption === +* September 19, 2013: Red Hat and Docker announced a collaboration around Fedora, Red Hat Enterprise Linux (RHEL), and OpenShift. +* October 15, 2014: Microsoft announced the integration of the Docker engine into Windows Server, as well as native support for the Docker client role in Windows. +* November 2014: Docker container services w +<|CHUNK_END|> +frame|A series of linear constraints on two variables produces a region of possible values for those variables. Solvable problems will have a feasible region in the shape of a [[simple polygon.]] +'''Linear programming''' or '''Linear optimization''' is a field of mathematics that deals with finding optimal values or solutions that can be described with linear equations and inequalities. Very often this involves finding the minimal or maximal values, given some conditions, or constraints. Linear programming is often used for problems where no exact solution is known, for example for planning traffic flows. Linear programming is one of the main methods used in Operations research. Linear optimization is a special case of Convex optimization. It forms the basis for several methods of solving problems of Integer programming. In many cases, the solutions of linear programs can be mapped to Polyhedra, which allows solving and modelling certain problems geometrically. + +In the case of linear programming, the word ''programming'' should be seen as ''planning''; George Dantzig coined the term in the 1940s, long before computers were used to solve such problems. Looking at the information theory complexity, linear programming problems are simple, and can be solved efficiently using algorithms such as the interior point method. In many cases, the Simplex algorithm developed by Dantzig has proven to be very fast, even though its complexity is exponential, in the worst case. + +Leonid Kantorovich developed the first methods of linear programming in 1939. + +Category:Combinatorial optimization +<|CHUNK_END|> +| + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + +1 observer state: + |}} +| language = English, French"English and French shall be the official languages for the entire North Atlantic Treaty Organisation.", [http://www.nato.int/docu/comm/49-95/c490917a.htm Final Communiqué following the meeting of the North Atlantic Council on September 17, 1949]. "(..)the English and French texts [of the Treaty] are equally authentic(...)"[http://www.nato.int/docu/basictxt/treaty.htm#Art14 The North Atlantic Treaty, Article 14] +| leader_title = Secretary General +| leader_name = Mark Rutte +| formation = 4 April 1949 +| website = https://www.nato.int/ +}} + +The '''North Atlantic Treaty Organization''' (sometimes known as the '''North Atlantic Alliance''', the '''Atlantic Alliance''' or the '''Western Alliance'''), also simply called '''NATO''', is a military alliance that is mostly in Europe and North America. Its other official name means the same in French: ''Organisation du traité de l'Atlantique nord'' (''OTAN''). + +It was established by the North Atlantic Treaty, which was signed in Washington, DC, United States, on April 4, 1949. Its headquarters are in Brussels, Belgium. + +== Languages == +NATO has two official languages, English and French, as defined in Article 14 of the North Atlantic Treaty. + +== History == +Its members when it was founded on 4 April 1949 were the United States, Belgium, the Netherlands, Luxembourg, France, the United Kingdom, Canada, Portugal, Italy, Norway, Denmark and Iceland. On 18 February 1952, Greece and Turkey also joined. + +When West Germany joined on 9 May 1955, it was described as "a decisive turning point in the history of our continent" by Norwegian Foreign Minister Halvard Lange. The Warsaw Pact was signed on 14 May 1955 by the Soviet Union and its satellite states as a defense to NATO. + +Iceland threatened to leave during the 1970s Cod Wars, which would put the United Kingdom at fault, and NATO would lose a +<|CHUNK_END|> +'''Object-oriented programming''' ('''OOP''') is a way of writing computer programs using "objects" to stand for data and methods. Often, computer programs that are not object-oriented are a list of instructions for the computer, telling it to do certain things in a certain way. This is called procedural programming. However, in object-oriented programming, computer programs use objects that talk to one another to change the data in those objects and to work in a way that the user wants. Because of the way object-oriented programming is designed, it helps the developer by allowing for code to be easily reused by other parts of the program or even by other people. + +Most programming languages are a mix of different ways of writing computer programs (called programming paradigms). For example, Python allows for computer programs to be written both in object-oriented programming and in procedural programming. There are many programming languages that allow you to write computer programs in object-oriented programming. Some of these programming languages are: C++, Java, Ruby, Perl, PHP, Python, C#, etc. + +== Features == +The main idea of object-oriented programming is that everything is an object. However, the object can be made of different parts: +* Variables can hold different types of information that are supported by the programming language. Examples are the integer data type and the lists data structure. Variables also exist in procedural programming languages. In object-oriented programming, variables are mainly known as attributes, particularly when it belongs (or is contained in) an object. +* Procedures are lists of instructions telling the computer to take input, do some calculations or change data, and return the output to the user. Procedures also exist in procedural programming languages. In object-oriented programming, procedures are mainly known as methods. +* Classes are collections of different variables and procedures. Classes usually talk to one another +<|CHUNK_END|> +alt=|thumb|Adding vectors (right side): vector '''a''' (blue) is added to vector b (red) by placing them as shown on the right. The sum, '''a+b''', is black. Left side: the sum of two vectors makes the diagonal of a parallelogram. +A '''vector space''' is a collection of mathematical objects called vectors, along with some operations you can do on them. Two operations are defined in a vector space: addition of two vectors and multiplication of a vector with a scalar. These operations can change the size of a vector and the direction it points to. The most important thing to understand is that after you do the addition or multiplication, the result is still in the vector space; you have not changed the vector in a way that makes it not a vector anymore. A vector space is often represented using symbols such as U, V and W. + +More formally, a vector space is a special combination of a group and a field. The elements of the group are called vectors, and the elements of the field are called scalars. Vector spaces are important in an area of mathematics called linear algebra, an area which deals with linear functions (functions of straight lines, not curves). + +A vector can be represented graphically with an arrow that has a tail and a head. To add two vectors, you place the end of one vector at the head of the other one (see figure). The sum is the vector that goes from the tail of the first vector to the head of the second. + +''Scalar multiplication'' means that one vector is made bigger or smaller (it is "scaled"). Scalars are just numbers: if you multiply a vector by 2, you make it twice as long. If you multiply it by 1/2, you make it half as long. + +The "vectors" don't have to be vectors in the sense of things that have magnitude and direction. For example, they could be functions, matrices or simply numbers. If they obey the axioms of a vector space (a list of properties a vector space needs to satisfy), you can think of them as vectors and the theorems of linear algeb +<|CHUNK_END|> +thumb|250px|Biotic pollination vector +'''Ecology''' is the branch or aspect of biology that studies the biota (living things), the environment, and their interactions. It comes from the Greek ''oikos'' = house; ''logos'' = study. + +Ecology is the study of ecosystems. Ecosystems describe the web or network of relations among organisms at different scales of organization. Since ecology refers to any form of biodiversity, ecologists research everything from tiny bacteria in nutrient recycling to the effects of tropical rain forests on the Earth's atmosphere. Scientists who study these interactions are called ''ecologists''. + +Terrestrial ecoregion and climate change research are two areas where ecologists now focus. + +There are many practical applications of ecology in conservation biology, wetland management, natural resource management (agriculture, forestry, fisheries), city planning (urban ecology), community health, economics, and applied science. It provides a framework for understanding and researching human social interaction.Omerod S.J. Pienkowski M.W. & Watkinson A.R. 1999. Communicating the value of ecology. ''Journal of Applied Ecology'' '''36''', 847–855Phillipson J. Lowe P. & Bullock J.M. 2009. Navigating the social sciences: interdisciplinarity and ecology. ''Journal of Applied Ecology'' '''46''', 261–264Steward T.A. ''et al.'' 2008. Beyond urban legends: an emerging framework of urban ecology, as illustrated by the Baltimore Ecosystem Study. ''BioScience'' '''58''' 139–150 + +== Population ecology == + +thumb|A graph of a population which reaches carrying capacity +Population ecology measures the size of a population: all the living things from one species that live in an place. A population gets bigger because of birth and movement into a place, and it gets smaller because of death and movement out of a place. Growth rate is the change in population size divided by the current population size. When a population is small, growth rate does not change, so the +<|CHUNK_END|> +In linear algebra, an '''eigenvector''' ( ) or '''characteristic vector''' is a (nonzero) vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scaled by a constant factor \lambda when the linear transformation is applied to it: T\mathbf v=\lambda \mathbf v. The corresponding '''eigenvalue''', '''characteristic value''', or '''characteristic root''' is the multiplying factor \lambda (possibly a negative or complex number). + +Geometrically, vectors are multi-dimensional quantities with magnitude and direction, often pictured as arrows. A linear transformation rotates, stretches, or shears the vectors upon which it acts. A linear transformation's eigenvectors are those vectors that are only stretched or shrunk, with neither rotation nor shear. The corresponding eigenvalue is the factor by which an eigenvector is stretched or shrunk. If the eigenvalue is negative, the eigenvector's direction is reversed. + +The eigenvectors and eigenvalues of a linear transformation serve to characterize it, and so they play important roles in all areas where linear algebra is applied, from geology to quantum mechanics. In particular, it is often the case that a system is represented by a linear transformation whose outputs are fed as inputs to the same transformation (feedback). In such an application, the largest eigenvalue is of particular importance, because it governs the long-term behavior of the system after many applications of the linear transformation, and the associated eigenvector is the steady state of the system. + +== Matrices == +For an n{\times}n matrix and a nonzero n-vector \mathbf{v}, if multiplying by \mathbf{v} (denoted A\mathbf{v}) simply scales \mathbf{v} by a factor , where is a scalar, then \mathbf{v} is called an eigenvector of , and is the corresponding eigenvalue. This relationship can be expressed as: A\mathbf{v} = \lambda \mathbf{v}. + +Given an ''n''-di +<|CHUNK_END|> +A '''neural network''' (also called an '''ANN''' or an '''artificial neural network''') is a sort of computer software, inspired by biological neurons. Data Basecamp|url=https://databasecamp.de/en/ml/artificial-neural-networks|access-date=2022-06-15|language=en-US}} Biological brains are capable of solving difficult problems, but each neuron is only responsible for solving a very small part of the problem. A neural network is made up of cells that work together to produce a desired result, although each individual cell is only responsible for solving a small part of the problem. This is one method for creating artificially intelligent programs. + +Neural networks are an example of machine learning, where a program can change as it learns to solve a problem. A neural network can be trained and improved with each example, but the larger the neural network, the more examples it needs to perform well—often needing millions or billions of examples in the case of deep learning. + +== Overview == + +A neural network models a network of neurons, like those in the human brain. Each neuron does simple mathematical operations: it gets data from other neurons, modifies it and sends it to other neurons. Neurons are placed in "layers": a neuron from a layer receives data from the neurons of other layers, modifies it and sends data to the neurons of other layers. A neural network is made up of one or more layers. + +The first layer is called the "input layer", it receives data from the outside world (for example: an image or text). The last layer is called the "output layer". The data from the neurons in the output layer is read and used as the output of the network. The other layers are called the "hidden layers". + +In a simple "feed-forward" network, the data handled by the neurons are numbers. Each neuron does a weighted sum of the value of the neurons of the previous layer (X_i in the equation below). It then adds to it a constant value (called the "bias"). Finally, it applies a mathem +<|CHUNK_END|> +'''Depth-first search''' ('''DFS''') is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking. Extra memory, usually a stack, is needed to keep track of the nodes discovered so far along a specified branch which helps in backtracking of the graph. + +A version of depth-first search was investigated in the 19th century by French mathematician Charles Pierre TrémauxCharles Pierre Trémaux (1859–1882) École polytechnique of Paris (X:1876), French engineer of the telegraph in Public conference, December 2, 2010 – by professor Jean Pelletier-Thibert in Académie de Macon (Burgundy – France) – (Abstract published in the Annals academic, March 2011 – ) as a strategy for solving mazes... + +==Properties== +The time and space analysis of DFS differs according to its application area. In theoretical computer science, DFS is typically used to traverse an entire graph, and takes time where |V| is the number of vertices and |E| the number of edges. This is linear in the size of the graph. In these applications it also uses space O(|V|) in the worst case to store the stack of vertices on the current search path as well as the set of already-visited vertices. Thus, in this setting, the time and space bounds are the same as for breadth-first search and the choice of which of these two algorithms to use depends less on their complexity and more on the different properties of the vertex orderings the two algorithms produce. + +For applications of DFS in relation to specific domains, such as searching for solutions in artificial intelligence or web-crawling, the graph to be traversed is often either too large to visit in its entirety or infinite (DFS may suffer from non-termination). In such cases, search is only performed to a limited depth; due to limited resources, such as memory or disk spac +<|CHUNK_END|> +thumb|A modern kit to vaccinate against smallpox + +A '''vaccine''' is a biological preparation. It is given to prevent a specific infectious or malignant disease. It only works against the microorganism for which it is prepared. It is usually given by injection, and called vaccination. +right|350px|[[James Gillray, ''The Cow-Pock—or—the Wonderful Effects of the New Inoculation!'' (1802). Vaccinations eventually helped eliminate smallpox from the world.]] + +At its best, vaccination gives immunity to an infectious disease caused by a particular microorganism (bacteria or virus). For example, the flu vaccine makes it very much less likely that a person will get the flu. The flu virus continually changes, and has many strains. That is why re-vaccination is needed every year. + +At first, vaccines were usually made from something that is alive, or was alive. Now they may be built up by viral biochemistry. Each vaccine has its own history, and what is true of one might not be true of another. + +The word "vaccine" comes from the Latin ''vacca'', meaning "cow"). In 1796, Edward Jenner used a milkmaid infected with cowpox (''variolae vaccinae'') to protect people against smallpox. The use of vaccines is called vaccination. + +Vaccination had been done before Jenner. Williams G 2010. ''Angel of Death''. Palgrave Macmillan. ISBN 978-0-230-27471-6 Powdered smallpox material was blown up the nostrils of the subject. + +== History == +Edward Jenner created the first vaccine in the 1770s. At this time, smallpox was a deadly disease. Jenner noticed that people who had already had cowpox (a disease that is related to smallpox) usually did not get smallpox. He thought that getting cowpox protected people against smallpox. + +To test this idea, Jenner gave a boy cowpox. Then he infected the boy with smallpox. The boy did not get sick because he had already had cowpox. Jenner was right: having cowpox protected people against smallpox. + +Because cowpox inoculation made fewer people sick than sma +<|CHUNK_END|> +thumb|A snippet of [[JavaScript code with keywords highlighted in different colors]] + +The '''syntax of JavaScript''' is the set of rules that define a correctly structured JavaScript program. + +The examples below make use of the console.log() function present in most browsers for standard text output. + +The JavaScript standard library lacks an official standard text output function (with the exception of document.write). Given that JavaScript is mainly used for client-side scripting within modern web browsers, and that almost all Web browsers provide the alert function, alert can also be used, but is not commonly used. + +TypeScript, which extends JavaScript with type annotations and additional features, has the same syntax as well as its own additional features. + +==Origins== +thumb|JavaScript code which displays weekdays in a browser. +Brendan Eich summarized the ancestry of the syntax in the first paragraph of the JavaScript 1.1 specification as follows: + +JavaScript syntax is mostly derived from Java syntax, which in turn is derived from C syntax and C++ syntax. + +==Basics== + +===Keywords=== + +====Reserved keywords==== +The following words are keywords and cannot be used as identifiers under any circumstances. + +* arguments +* async +* await +* assert +* break +* case +* catch +* class +* const +* continue +* debugger +* default +* delete +* do +* else +* enum +* eval +* export +* extends +* finally +* for +* function +* if +* implements +* import +* in +* instanceof +* interface +* let +* new +* package +* private +* protected +* public +* return +* static +* super +* switch +* this +* throw +* try +* typeof +* using +* var +* void +* while +* with +* yield + +====Reserved words for literal values==== +The following words refer to literal values used by the language. + +* true +* false +* null + +JavaScript also defines the following global constants, which are not keywords. + +* NaN +* Infinity +* undefined +* globalThis + +====Removed keywords==== +The following words, primarily associated with Java, were removed from the ECMAScript 5 +<|CHUNK_END|> +'''Machine learning''' gives computers the ability to learn without being explicitly programmed (Arthur Samuel, 1959).John McCarthy & Edward Feigenbaum 1990. In Memoriam Arthur Samuel: pioneer in machine learning. ''AI Magazine''. AAAI. '''11''' (3).[http://www.aaai.org/ojs/index.php/aimagazine/article/view/840/758] It is a subfield of computer science. Data Basecamp|url=https://databasecamp.de/en/machine-learning|access-date=2022-08-14|language=en-US}} + +The idea came from work in artificial intelligence. Machine learning explores the study and construction of algorithms which can learn and make predictions on data. Such algorithms follow programmed instructions, but can also make predictions or decisions based on data.Christopher Bishop 1995. ''Neural networks for pattern recognition''. Oxford University Press. They build a model from sample inputs. + +Machine learning is done where designing and programming explicit algorithms cannot be done. Examples include spam filtering, detection of artificial neural network intruders or malicious insiders working towards a data breach, optical character recognition (OCR),Wernick ''et al'' 2010. Machine learning in medical imaging, ''IEEE Signal Processing Society|IEEE Signal Processing Magazine''. '''27''', 4, 25-38. search engines and computer vision. + +Using machine learning has risks. Some algorithms create a final model which is a black box. Models have been criticized for biases in hiring, criminal justice, and recognizing faces. + +== Overview == +Learning algorithms try to predict what will happen in the future with patterns from the past. These predictions can be obvious: for example, if the sun rose for the past 10,000 days, it will probably rise again. These predictions can also be more complex. An example of a complex prediction is facial recognition (knowing who someone is by looking at face). + +Machine learning programs can do things that it hasn't been told to do by a programmer. Machine learning programs will be sh +<|CHUNK_END|> +thumb|250px|[[Plato (at left) and Aristotle (at right). Aristotle is usually thought to be the creator of metaphysics]] + +'''Metaphysics''' is a major branch of philosophy. It concerns existence and the nature of things that exist. Altogether it is a theory of reality. + +Ontology is the part of metaphysics which discusses ''what'' exists: the categories of being. Apart from ontology, metaphysics concerns the ''nature'' of, and ''relations'' among, the things that exist. Topics that are discussed in metaphysics include existence, objects and their traits, space and time, cause and effect, and what is possible. + +== Main questions == + +=== Ontology === +The study of ontology is broad, while other branches of metaphysics are more specific. One main question in ontology are what the most basic categories of being are. For example, imagine a tree. A tree is part of a larger category, like a plant. Plants are part of larger category, too: living things. Eventually, we arrive at a very large category: ''substance''. Philosophers who study ontology want to discover and understand basic categories like substance. Aristotle, for example, tried to understand reality through many other categories that he discovered, such as Quantity, Quality, Relation, Place, and Time among others. + +In the 15th century René Descartes thought there might be two different substances, mind and matter. This is a view called dualism. Other thinkers, like Immanuel Kant, thought that we cannot say anything about substance, as the only way we can talk about substance is through connections. To prove this, Kant used the sentence "This is a house". Kant thought that the meaning of the word house depended on how other people used houses, or how other houses looked like. This meant that meaning was all about connections, and that there is no meaning of "house" on its own. So Kant replaced the category of substance with ''relation'' in his metaphysical beliefs. + +In the 20th century, some Western philosophers th +<|CHUNK_END|> +thumb|Graphs of functions commonly used in the [[analysis of algorithms, showing the number of operations ''N'' as the result of input size ''n'' for each function]] + +In theoretical computer science, the '''time complexity''' is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. + +Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expressed as a function of the size of the input. Since this function is generally difficult to compute exactly, and the running time for small inputs is usually not consequential, one commonly focuses on the behavior of the complexity when the input size increases—that is, the asymptotic behavior of the complexity. Therefore, the time complexity is commonly expressed using big O notation, typically etc., where is the size in units of bits needed to represent the input. + +Algorithmic complexities are classified according to the type of function appearing in the big O notation. For example, an algorithm with time complexity O(n) is a ''linear time algorithm'' and an algorithm with time complexity O(n^\alpha) for some constant \alpha > 0 is a ''polynomial time algorithm''. + +== Table of common time complexities == + +Th +<|CHUNK_END|> +thumb|upright=1.35|Basis of trigonometry: if two [[right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.]] +In mathematics, the '''trigonometric functions''' (also called '''circular functions''', '''angle functions''' or '''goniometric functions''') are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and are widely used for studying periodic phenomena through Fourier analysis. + +The trigonometric functions most commonly used in modern mathematics are the sine, the cosine, and the '''tangent''' functions. Their reciprocals are respectively the '''cosecant''', the '''secant''', and the '''cotangent''' functions, which are less commonly used. Each of these six trigonometric functions has a corresponding inverse function and has an analog among the hyperbolic functions. + +The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extend the sine and cosine functions to functions whose domain is the whole real line, geometrical definitions using the standard unit circle (i.e., a circle with radius 1 unit) are often used; then the domain of the other functions is the real line with some isolated points removed. Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows extending the domain of sine and cosine functions to the whole complex plane, and the domain of the other trigonometric functions to the complex plane with some isolated points removed. + +== Notation == +Conventionally, an abbreviation of each trigonometric function's name is used as its symbol in formulas. Today, the most common versions of these abbreviations are "" for sine, "" for +<|CHUNK_END|> +A '''design pattern''' is the re-usable form of a solution to a design problem. The idea was introduced by the architect Christopher Alexander and has been adapted for various other disciplines, particularly software engineering. The "Gang of Four" book. + +== Details == + +An organized collection of design patterns that relate to a particular field is called a pattern language. This language gives a common terminology for discussing the situations designers are faced with. + +Documenting a pattern requires explaining why a particular situation causes problems, and how the components of the pattern relate to each other to give the solution. Christopher Alexander describes common design problems as arising from "conflicting forces"—such as the conflict between wanting a room to be sunny and wanting it not to overheat on summer afternoons. A pattern would not tell the designer how many windows to put in the room; instead, it would propose a set of values to guide the designer toward a decision that is best for their particular application. Alexander, for example, suggests that enough windows should be included to direct light all around the room. He considers this a good solution because he believes it increases the enjoyment of the room by its occupants. Other authors might come to different conclusions, if they place higher value on heating costs, or material costs. These values, used by the pattern's author to determine which solution is "best", must also be documented within the pattern. + +Pattern documentation should also explain when it is applicable. Since two houses may be very different from one another, a design pattern for houses must be broad enough to apply to both of them, but not so vague that it doesn't help the designer make decisions. The range of situations in which a pattern can be used is called its context. Some examples might be "all houses", "all two-story houses", or "all places where people spend time". + +For instance, in Christopher Alexander's work +<|CHUNK_END|> +thumbnail|200px|Detail from [[Hammurabi's stele shows him receiving the laws of Babylon from the seated sun deity.]] + +The '''constitution''' of a country (or a state) is a special type of law document that tells how its government is supposed to work. Every country has its own constitution, it tells how the country's leaders are to be chosen and how long they get to stay in office, how new laws are made and old laws are to be changed or removed based on law, what kind of people are allowed to vote and what other rights they are guaranteed, and how the constitution can be changed. + +Limits are put on the Government in how much power they have within the Constitution ''(see Rule of Law )''. On the other hand, countries with repressive or corrupt governments frequently do not stick to their constitutions, or have bad constitutions without giving freedom to citizens and others. This can be known as dictatorship or simply "bending the rules". A Constitution is often a way of uniting within a Federation. + +The UK's constitution is not written in one single document like many other countries' are. In fact, the UK's constitution is not completely written down at all. Some of it can be found in writing, starting with Magna Carta of 1215 and the Bill of Rights Act 1689 and including more modern Acts of Parliament. Other parts of it are considered common law and are made up of the decisions of judges over many hundreds of years in a system called legal or judicial precedence. Because of this, some people say that the United Kingdom has a ''de facto'' or "unwritten" constitution. + +The United States in 1787 began a trend in the writing of constitutions. The United States Constitution is also the shortest that people are still using, and it has been changed (amended) many times over the years. It was made after the colonists won their independence from Britain. At first they had the Articles of Confederation but the Articles were replaced with today's Constitution. + +The Indian con +<|CHUNK_END|> +'''Particle physics''' is a branch of physics that studies tiny pieces of elements, known as particles. These particles are extremely small pieces that build up the world around us. They are best described in the language of math: calculus, the imaginary number, and group theory (which describes symmetry). + +== Fundamental forces == +Particles can carry fundamental forces. For example, the electromagnetic force is carried by photons. The four fundamental forces are responsible for almost everything in all of physics. These fundamental forces are gravity, electromagnetism, weak interaction, and strong interaction. + +== The Standard Model == +One of the important concepts of particle physics is called the Standard Model. The Standard Model is a theory that tries to explain the fundamental forces. The Standard Model combined with general relativity is currently the most accepted explanation of how the universe works. + +The Standard Model is known to have problems. For example, it explains three of the four forces very well, but it cannot explain gravity. This is why general relativity, a different theory that explains where gravity comes from, needs to be included for physicists to explain the universe. There is a lot of work to improve the theory and/or find a better theory that is being done. This work is often called theoretical particle physics because it is about building better theories of particles. Theoretical particle physicists make theories to try to improve the Standard Model. One example of this is how many theories predict undiscovered particles. + +== Collider == +Physicists find out about particles by studying collisions between different particles. A good analogy of how physicists study particles through colliding is the car crash example. Imagine a person who wanted to look inside cars. By crashing two cars together at very high speeds, we can break the cars apart and see inside. In the same way, physicists crash two particles together to break them and stu +<|CHUNK_END|> +}} +A '''mean''' is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of '''means''' (or "measures of central tendency") in mathematics, especially in statistics. Each attempts to summarize or typify a given group of data, illustrating the magnitude and sign of the data set. Which of these measures is most illuminating depends on what is being measured, and on context and purpose. + +The ''arithmetic mean'', also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set of numbers ''x''1, ''x''2, ..., x''n'' is typically denoted using an overhead bar, \bar{x}. If the numbers are from observing a sample of a larger group, the arithmetic mean is termed the ''sample mean'' (\bar{x}) to distinguish it from the group mean (or expected value) of the underlying distribution, denoted '''\mu''' or '''\mu_x'''.Underhill, L.G.; Bradfield d. (1998) ''Introstat'', Juta and Company Ltd. [https://books.google.com/books?id=f6TlVjrSAsgC&pg=PA181 p. 181] + +Outside probability and statistics, a wide range of other notions of mean are often used in geometry and mathematical analysis; examples are given below. + +==Types of means== + +===Pythagorean means=== + +In mathematics, the three classical '''Pythagorean means''' are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM). These means were studied with proportions by Pythagoreans and later generations of Greek mathematicians because of their importance in geometry and music. +==== Arithmetic mean (AM) ==== + +The arithmetic mean (or simply ''mean'' or ''average'') of a list of numbers, is the sum of all of the numbers divided by their count. Similarly, the mean of a sample x_1,x_2,\ldots,x_n, usually denoted by \bar{x}, is the sum of the sampled values divided by the number of items in the sample. + +: \bar{x} = \frac{1}{n}\sum_{i=1}^n{x_i} = \frac{x_1+x_2+\cdot +<|CHUNK_END|> +'''Partial differential equations''' (abbreviated as PDEs) are a kind of mathematical equation. They are related to partial derivatives, in that obtaining an antiderivative of a partial derivative involves integration of partial differential equations. +==Numerical methods== + +Since PDEs have appeared in mathematics and physics, many scientists have studied methods to solve them. But unfortunately, no one could establish methods to solve any kind of PDE. Therefore, numerical methods for PDEs (such as the finite element method) are widely studied since the appearance of computers.Iserles, A. (2009). A first course in the numerical analysis of differential equations. Cambridge University Press.Ames, W. F. (2014). Numerical methods for partial differential equations. Academic Press.M. Nakao, M. Plum, Y. Watanabe (2019) Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations (Springer Series in Computational Mathematics). + +==Related pages== +*Differential equation +*Functional analysis +*Ordinary differential equation +*Navier–Stokes equations + +==People who studied about partial differential equations== + +* Kyuya Masuda +* Peter Lax +* Ryogo Hirota +* Shinichi Oishi +* Sofya Kovalevskaya +* Terence Tao + +==Literature== +* Partial Differential Equations (Graduate Studies in Mathematics) Lawrence C. Evans, American Mathematical Society, 2010/04/. +* Egorov, Y. V., & Shubin, M. A. (2013). Foundations of the classical theory of partial differential equations. Springer Science & Business Media. +* Olver, P. J., Introduction to partial differential equations. Berlin: Springer. +* Partial Differential Equations I-III (Applied Mathematical Sciences) Michael Taylor, Springer. +==References== +<|CHUNK_END|> +thumb|Calculating the median in data sets of odd (above) and even (below) observations +The '''median''' of a set of numbers is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as the "middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extreme values, and therefore provides a better representation of the center. Median income, for example, may be a better way to describe the center of the income distribution because increases in the largest incomes alone have no effect on the median. For this reason, the median is of central importance in robust statistics. +Median is a 2-quantile; it is the value that partitions a set into two equal parts. + +==Finite set of numbers== +The median of a finite list of numbers is the "middle" number, when those numbers are listed in order from smallest to greatest. + +If the data set has an odd number of observations, the middle one is selected (after arranging in ascending order). For example, the following list of seven numbers, + +has the median of ''6'', which is the fourth value. + +If the data set has an even number of observations, there is no distinct middle value and the median is usually defined to be the arithmetic mean of the two middle values.Simon, Laura J.; [http://www.stat.psu.edu/old_resources/ClassNotes/ljs_07/sld008.htm "Descriptive statistics"] , ''Statistical Education Resource Kit'', Pennsylvania State Department of Statistics For example, this data set of 8 numbers + +has a median value of ''4.5'', that is (4 + 5)/2. (In more technical terms, this interprets the median as the fully trimmed mid-range). + +In general, with this convention, the median can be defined as follows: For a data set x of n elements, ordered from smallest to greatest, + +{2} }} + +{| class="wikitable" +|+ Comparison of common a +<|CHUNK_END|> +In mathematics, a '''limit''' is the value that a function comes close to as the input comes close to some value. When we use a function to solve a problem, sometimes certain values can not be used as inputs to the function, but we can see what the function comes close to when the input comes close to the value. Limits can be used to explain what happens in these cases. + +==Format== +Limits are used to define many topics in calculus, like continuity, derivatives, and integrals. + +For a function ''f'', limit are written like this: + +\lim_{x \to c}f(x)=L + +which reads "the limit of ''f'' of ''x'', as ''x'' approaches ''c'' equals ''L''". An alternative notation is "f(x) \to L as x \to c", which reads "f(x) tends to L as x tends to c". Limit is shortened to ''lim''. + +For a sequence x_n, the similar notation \lim_{n \to \infty} x_n=L is used. + +==Example== +thumb|A graph showing f(x) = 1/x. Note that the line doesn't touch 0 on either axis as f(0) is undefined. +Imagine we have a function that takes an input, x, and then outputs \frac{1}{x} to y. If we were to draw a graph using x and y as coordinates, the results would look like this: + +{| class="wikitable" +|- +! x input +! function +! y output +! x, y +|- +| 4 +| f(4) = \frac{1}{4} +| 0.25 +| 4, 0.25 +|- +| 3 +| f(3) = \frac{1}{3} +| 0.33 +| 3, 0.33 +|- +| 2 +| f(2) = \frac{1}{2} +| 0.5 +| 2, 0.5 +|- +| 1 +| f(1) = \frac{1}{1} +| 1 +| 1, 1 +|- +| 0 +|f(0) = \frac{1}{0} +| undefined +| 0, undefined +|} + +As we can see here, division by zero is undefined. But if we look closer, then we can see that we still have valid output—as long as we never reach zero: + +{| class="wikitable" +|- +! x input +! function +! y output +! x, y +|- +| 1 +| f(1) = \frac{1}{1} +| 1 +| 1, 1 +|- +| 0.5 +| f(0.5) = \frac{1}{0.5} +| 2 +| 0.5, 2 +|- +| 0.25 +| f(0.25) = \frac{1}{0.25} +| 4 +| 0.25, 4 +|- +| 0.125 +| f(0.125) = \frac{1}{0.125} +| 8 +| 0.125, 8 +|- +| -0.125 +| f(-0.125) = \frac{1}{-0.125} +| -8 +| -0.125, -8 +|- +| -0.25 +| f(-0.25) = \frac{1}{-0.25} +| -4 +| -0.25, -4 +|- +| -0.5 +| f(-0.5) = \frac{1}{-0 +<|CHUNK_END|> +thumb|upright=1.35|A graphical interface similar to one from the late 1980s, which features a graphical window for a [[man page, a shaped window (oclock) as well as several iconified windows. In the lower right we can see a terminal emulator running a Unix shell, in which the user can type commands as if they were sitting at a terminal.]] + +An operating system '''shell''' is a computer program that provides relatively broad and direct access to the system on which it runs. The term ''shell'' refers to how it is a relatively thin layer around an operating system. + +Most shells are command-line interface (CLI) programs. Some graphical user interfaces (GUI) also include shells. + +== Overview == +Operating systems provide various services to their users, including file management, process management (running and terminating applications), batch processing, and operating system monitoring and configuration. + +Most operating system shells are not ''direct'' interfaces to the underlying kernel, even if a shell communicates with the user via peripheral devices attached to the computer directly. Shells are actually special applications that use the kernel API in just the same way as it is used by other application programs. A shell manages the user–system interaction by prompting users for input, interpreting their input, and then handling output from the underlying operating system (much like a read–eval–print loop, REPL). Since the operating system shell is actually an application, it may easily be replaced with another similar application for most operating systems. + +In addition to shells running on local systems, there are different ways to make remote systems available to local users; such approaches are usually referred to as remote access or remote administration. Initially available on multi-user mainframes, which provided text-based UIs for each active user ''simultaneously'' by means of a text terminal connected to the mainframe via serial line or modem, remote access h +<|CHUNK_END|> +| image_coat = Greater coat of arms of the United States.svg +| coat_alt = +| symbol_type_article = Great Seal of the United States#Obverse +| national_motto = "In God We Trust"}} +|titlestyle=background:transparent;color:inherit;text-align:center;line-height:1.15em; +|liststyle=text-align:center;white-space:nowrap; +|"Out of many, one" +|"Providence favors our undertakings" +|"New order of the ages" +}} +| national_anthem = "The Star-Spangled Banner"File:Star Spangled Banner instrumental.ogg + +| image_map = +| map_width = 220px +| capital = Washington, D.C. +| largest_city = New York City +| official_languages = English States and territories variously recognize English only, English plus one or more local languages, or no language at all. See § Language.}} +| ethnic_groups = + +| ethnic_groups_ref = +| ethnic_groups_year = 2020 +| religion = +*67% Christianity +**33% Protestantism +**22% Catholicism +**11% other Christian +**1% Mormonism + +|22% unaffiliated +|2% Judaism +|6% other religion +|3% Buddhism https://www.pewresearch.org/religious-landscape-study/religious-tradition/buddhist/ +}} +| religion_ref = +| demonym = American +| government_type = Federal presidential republic +| leader_title1 = President +| leader_name1 = Donald Trump +| leader_title2 = Vice President +| leader_name2 = JD Vance +| leader_title3 = House Speaker +| leader_name3 = Mike Johnson +| leader_title4 = Chief Justice +| leader_name4 = John Roberts +| legislature = Congress +| upper_house = Senate +| lower_house = House of Representatives +| sovereignty_type = Independen +<|CHUNK_END|> +''Machine Learning'' (journal)}} + +'''Machine learning''' ('''ML''') is a field of study in artificial intelligence concerned with the development and study of statistical algorithms that can learn from data and generalize to unseen data, and thus perform tasks without being explicitly programmed.}} Advances in the field of deep learning have allowed neural networks, a class of statistical algorithms, to surpass many previous machine learning approaches in performance. + +Statistics and mathematical optimisation methods compose the foundations of machine learning. Data mining is a related field of study, focusing on exploratory data analysis (EDA) through unsupervised learning.}} + +From a theoretical viewpoint, probably approximately correct learning provides a mathematical and statistical framework for describing machine learning. Most traditional machine learning and deep learning algorithms can be described as empirical risk minimisation under this framework. + +== History == + +The term ''machine learning'' was coined in 1959 by Arthur Samuel, an IBM employee and pioneer in the field of computer gaming and artificial intelligence.R. Kohavi and F. Provost, "Glossary of terms", Machine Learning, vol. 30, no. 2–3, pp. 271–274, 1998. The synonym ''self-teaching computers'' was also used during this time period. + +The earliest machine learning program was introduced in the 1950s, when Samuel invented a computer program that calculated the chance of winning in checkers for each side, but the history of machine learning is rooted in decades of efforts to study human cognitive processes. In 1949, Canadian psychologist Donald Hebb published the book ''The Organization of Behavior'', in which he introduced a theoretical neural structure formed by certain interactions among nerve cells. The Hebbian theory of neuron interaction set the groundwork for how many machine learning algorithms work, with connected artificial neurons changing the strength of their connections based on data +<|CHUNK_END|> +In mathematics, a '''differential equation''' is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common in mathematical models and scientific laws; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. + +The study of differential equations consists mainly of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. + +Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers, and many numerical methods have been developed to determine solutions with a given degree of accuracy. The theory of dynamical systems analyzes the qualitative aspects of solutions, such as their average behavior over a long time interval. + +==History== + +Differential equations came into existence with the invention of calculus by Isaac Newton and Gottfried Leibniz. In Chapter 2 of his 1671 work ''Methodus fluxionum et Serierum Infinitarum'',Newton, Isaac. (c.1671). Methodus Fluxionum et Serierum Infinitarum (The Method of Fluxions and Infinite Series), published in 1736 [Opuscula, 1744, Vol. I. p. 66]. Newton listed three kinds of differential equations: + +:\begin{align} + \frac {dy}{dx} &= f(x) \\[4pt] + \frac {dy}{dx} &= f(x, y) \\[4pt] + x_1 \frac {\partial y}{\partial x_1} &+ x_2 \frac {\partial y}{\partial x_2} = y +\end{align} +In all these cases, is an unknown function of (or of and ), and is a given function. He solved these examples and others using +<|CHUNK_END|> +In mathematics, a '''recurrence relation''' is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter k that is independent of n; this number k is called the ''order'' of the relation. If the values of the first k numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. + +In ''linear recurrences'', the th term is equated to a linear function of the k previous terms. A famous example is the recurrence for the Fibonacci numbers, +F_n=F_{n-1}+F_{n-2} +where the order k is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the linear function (1 and 1) are constants that do not depend on n. For these recurrences, one can express the general term of the sequence as a closed-form expression of n. As well, linear recurrences with polynomial coefficients depending on n are also important, because many common elementary functions and special functions have a Taylor series whose coefficients satisfy such a recurrence relation (see holonomic function). + +Solving a recurrence relation means obtaining a closed-form solution: a non-recursive function of n. + +The concept of a recurrence relation can be extended to multidimensional arrays, that is, indexed families that are indexed by tuples of natural numbers. + +==Definition== +A ''recurrence relation'' is an equation that expresses each element of a sequence as a function of the preceding ones. More precisely, in the case where only the immediately preceding element is involved, a recurrence relation has the form +:u_n=\varphi(n, u_{n-1})\quad\text{for}\quad n>0, +where +:\varphi:\mathbb N\times X \to X +is a function, where is a set to which the elements of a sequence must belong. For any u_0\in X, this defines a unique seq +<|CHUNK_END|> +(as Logical Awesome LLC) +| location = San Francisco, California, United States +| area_served = Worldwide +| founder = +| CEO = Nat Friedman +| key_people = +| industry = Software +| international = Yes +| programming_language = Ruby +| website_type = Collaborative version control +| registration = Optional (required for creating and joining projects) +| users = 100 million (Jan 2023)https://github.blog/2023-01-25-100-million-developers-and-counting/ +| language = English +| launched = +| current_status = Active +| parent = Microsoft +| logo_caption = +}} +'''GitHub''' is an online software development assistance and version control service.Dabbish, L., Stuart, C., Tsay, J., & Herbsleb, J. (2012, February). Social coding in GitHub: transparency and collaboration in an open software repository. In Proceedings of the ACM 2012 conference on computer supported cooperative work (pp. 1277-1286).Pipinellis, A. (2018). GitHub Essentials: Unleash the power of collaborative development workflows using GitHub. Packt Publishing Ltd.Mergel, I. (2015). Open collaboration in the public sector: The case of social coding on GitHub. Government Information Quarterly, 32(4), 464-472.Beer, B. (2018). Introducing GitHub: A non-technical guide. " O'Reilly Media, Inc.".Dawson, C., & Straub, B. (2016). Building Tools with GitHub: Customize Your Workflow. " O'Reilly Media, Inc.". This platform uses Git.Blischak, J. D., Davenport, E. R., & Wilson, G. (2016). A quick introduction to version control with Git and GitHub. PLoS computational biology, 12(1), e1004668. It is operated by '''GitHub, Inc.''' based in the United States. + +In January 2020, GitHub reported that they have more than 40 million users and more than 100 million repositories (including at least 28 million public repositories). Therefore, it is recognized as the largest host of source code in the world. +==Organizational users== +Currently, there are many individual GitHub users. On the other hand, there are also organizational users such as ed +<|CHUNK_END|> +thumb|Flowchart of using successive subtractions to find the [[greatest common divisor of number ''r'' and ''s''|alt=In a loop, subtract the larger number against the smaller number. Halt the loop when the subtraction will make a number negative. Assess two numbers, whether one of them is equal to zero or not. If yes, take the other number as the greatest common divisor. If no, put the two numbers in the subtraction loop again.]] +In mathematics and computer science, an '''algorithm''' () is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). + +In contrast, a heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. + +As an effective method, an algorithm can be expressed within a finite amount of space and time"Any classical mathematical algorithm, for example, can be described in a finite number of English words" (Rogers 1987:2). and in a well-defined formal languageWell defined concerning the agent that executes the algorithm: "There is a computing agent, usually human, which can react to the instructions and carry out the computations" (Rogers 1987:2). for calculating a function."an algorithm is a procedure for computing a ''function'' (concerning some chosen notation for integers) ... this limitation (to numerical functions) results in no loss of generality", (Rogers 1977:1). Startin +<|CHUNK_END|> +| region = International (FIFA) +| number of teams = 32 (finals)211 (eligible to enter qualification) +| related comps = FIFA Confederations Cup +| current champions = (3rd title)}} +| most successful team = (5 titles)}} +| broadcasters = +| website = +| current = 2022 FIFA World Cup +}} + +The '''FIFA World Cup''' is the most watched tournament in football (soccer). The Fédération Internationale de Football Association (FIFA) organises the World Cup every four years. More people watch the World Cup finals than any other sporting event in the world—even more people than the Olympic Games. Brazil is the most successful country in World Cup history, having won the tournament five times + +The ''finals tournament'' is held every four years. In the other years there are only qualifiers (qualifying tournaments) in the six FIFA world regions. These amazing games help to decide which teams will move on. Over 160 national teams play in the qualifying games. The best teams from the qualifying games win a place in the finals. The finals now include 32 teams. Before 1998, only 24 teams were in the finals; starting in 2026, there will be 48 teams in the finals. Many years before each World Cup, FIFA picks the host nation, the country where the finals will be held. Being the host nation means that their team has qualified for the finals tournament automatically and does not need to play any qualifying games. The 32 teams in the finals then play for four weeks, usually between June and July, to decide who the champion (tournament winner) will be. + +== Results == +{| class="wikitable sortable" style="text-align:center; width:100%" +|- +!width=7%|Years +!width=10%|Hosts +!width=15%|Winners +!width=9%|Score +!width=15%|Runner's-up +!width=15%|Third place +!width=9%|Score +!width=15%|Fourth place +|- +|1930 ''Details'' +| Uruguay +|'''''' +|'''4 - 2''' +| +| +||group="note"}} +| +|- style="background: #D0E6FF;" +|1934 ''Details'' +| Italy +|'''''' +|'' +<|CHUNK_END|> +'''Quantum mechanics''' explains how the universe works with things that are even smaller than atoms. It is also called '''quantum physics''' or '''quantum theory'''. Mechanics is the part of physics that explains how things move and ''quantum'' is the Latin word for 'how much'. A '''quantum''' of energy is the least amount possible (or the least extra amount), and quantum mechanics describes how that energy moves. + +Atoms were once believed to be the smallest pieces of matter, but modern science has shown that there are even smaller particles called subatomic particles, like protons, neutrons and electrons. Quantum mechanics describes how the particles that make up atoms work. + +Quantum physics also tells us how electromagnetic waves (like light) work. Wave–particle duality means that particles behave like waves and waves behave like particles. (They are not two kinds of things, they are something like both: this is called ''duality''.) Much of modern physics and chemistry can be described and understood using the mathematical rules of quantum mechanics. + +The math used to study subatomic particles and electromagnetic waves is very complex because they act in very strange ways. + +thumb|250px|The wavelength of a wave of light + +== Waves and photons == +Photons are particles that are point-sized, tinier than atoms. Photons are like "packets" or packages of energy. Light sources such as candles or lasers produce light in bits called photons. + +The more photons a lamp produces, the brighter the light. Light is a form of energy that behaves like the waves in water or radio waves. The distance between the top of one wave and the top of the next wave is called a 'wavelength'. Each photon carries a certain amount, or 'quantum', of energy depending on its wavelength. + +thumb|300px|Black at left is '''ultraviolet''' (high frequency); black at right is '''infrared''' (low frequency). + +A light's color depends on its wavelength. The color violet (the bottom or innermost color of the +<|CHUNK_END|> +'''AJAX''' (sometimes spelled "Ajax") stands for '''Asynchronous JavaScript and XML'''. It is a technique used to make webpages faster to use. If they are programmed with AJAX, they seem to react faster. They only send small pieces of information to the web server. That way, the whole web page does not need to reload, only small parts of it. + +==Good things== +*There is a clear separation between what the page shows (its content), how it looks (its style), and what it does (its function). Programmers that change what the page does do not need to concern themselves with how the page looks. +*Pages done with Ajax only load small pieces of information from the server. Most of the time, they execute code on the client. This makes the program load first so it can respond faster. +*Ajax can be used to read XML or JSON, among other file formats. + +==Problems== +There are also some problems with Ajax. These are among other things: +*It uses JavaScript. Some people have JavaScript disabled. +*Because it does not reload the full page, it breaks the ''history'' function of the Web browser. The ''Back button'' does not work any more. +*If the network is slow (there is a high latency), this becomes more obvious when the whole page needs to be reloaded. Users might not expect these delays. +*Some web browsers do not support Ajax well, if at all. + +==References== + +Category:Web software +Category:JavaScript +<|CHUNK_END|> +thumb|Electronic sports + +'''Esports''' (short for '''electronic sports''') is a term for video games that are played competitively. Popular electronic sports games are ''Counter-Strike'', ''League of Legends'', ''Warcraft'', ''Starcraft'', ''Dota 2'', ''Quake'', ''Fortnite'' and ''Valorant''. Electronic Sports is played over the Internet or via LAN. There are professional leagues and tournaments like the ''Cyberathlete Professional League'', ''ClanBase'', ''Electronic Sports League'' and the ''World Cyber Games'' where electronic sports players can earn thousands of US Dollars. One example is ''Starcraft'' in Korea where they have many players who are very competitive. +Esports has been around since the dawn of arcades when players would battle it out for number one. + +According to TechCrunch, the game maker Epic Games is providing $100 million in prize money in 2019 for participants in esports. + +==References== + +Category:Video games +<|CHUNK_END|> +thumb|upright=1.3|right|The [[normal distribution in Statistics]] +'''Statistics''' is a branch of applied mathematics that deals with collecting, organizing, analyzing, reading and presenting data.DeGroot, M. H., & Schervish, M. J. (2012). Probability and statistics. Pearson Education.Johnson, R. A., Miller, I., & Freund, J. E. (2000). Probability and statistics for engineers (Vol. 2000, p. 642p). London: Pearson Education.Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (1993). Probability and statistics for engineers and scientists (Vol. 5). New York: Macmillan. Descriptive statistics make summaries of data.Larson, M. G. (2006). Descriptive statistics and graphical displays. Circulation, 114(1), 76-81. Inferential statistics makes predictions.Asadoorian, M. O., & Kantarelis, D. (2005). Essentials of inferential statistics. University Press of America. Statistics helps in the study of many other fields, such as science, medicine,Lang, T. A., Lang, T., & Secic, M. (2006). How to report statistics in medicine: annotated guidelines for authors, editors, and reviewers. ACP Press. economics,Wonnacott, T. H., & Wonnacott, R. J. (1990). Introductory statistics for business and economics (Vol. 4). New York: Wiley.Newbold, P., Carlson, W. L., & Thorne, B. (2013). Statistics for business and economics. Boston, MA: Pearson. psychology,Aron, A., & Aron, E. N. (1999). Statistics for psychology. Prentice-Hall, Inc. politicsFioramonti, D. L. (2014). How numbers rule the world: The use and abuse of statistics in global politics. Zed Books Ltd.. and marketing.Rossi, P. E., Allenby, G. M., & McCulloch, R. (2012). Bayesian statistics and marketing. John Wiley & Sons. Someone who works in statistics is called a statistician. In addition to being the name of a field of study, the word "statistics" can also mean numbers that are used to describe data or relationships. + +== History == +The first known statistics are census data. The Babylonians did a census around 3500 BC, the Egyptia +<|CHUNK_END|> +In computer science, '''radix sort''' is a non-comparative sorting algorithm. It avoids comparison by creating and distributing elements into buckets according to their radix. For elements with more than one significant digit, this bucketing process is repeated for each digit, while preserving the ordering of the prior step, until all digits have been considered. For this reason, '''radix sort''' has also been called '''bucket sort''' and '''digital sort'''. + +Radix sort can be applied to data that can be sorted lexicographically, be they integers, words, punch cards, playing cards, or the mail. + +== History == + +Radix sort dates back as far as 1887 to the work of Herman Hollerith on tabulating machines. and Radix sorting algorithms came into common use as a way to sort punched cards as early as 1923. +Donald Knuth. ''The Art of Computer Programming'', Volume 3: ''Sorting and Searching'', Third Edition. Addison-Wesley, 1997. . Section 5.2.5: Sorting by Distribution, pp. 168–179. + +The first memory-efficient computer algorithm for this sorting method was developed in 1954 at MIT by Harold H. Seward. Computerized radix sorts had previously been dismissed as impractical because of the perceived need for variable allocation of buckets of unknown size. Seward's innovation was to use a linear scan to determine the required bucket sizes and offsets beforehand, allowing for a single static allocation of auxiliary memory. The linear scan is closely related to Seward's other algorithm — counting sort. + +In the modern era, radix sorts are most commonly applied to collections of binary strings and integers. It has been shown in some benchmarks to be faster than other more general-purpose sorting algorithms, sometimes 50% to three times faster. + +thumb|An [[IBM card sorter performing a radix sort on a large set of punched cards. Cards are fed into a hopper below the operator's chin and are sorted into one of the machine's 13 output baskets, based on the data punched into one column on +<|CHUNK_END|> +| image_flag = Flag of Russia.svg +| image_coat = Coat of Arms of the Russian Federation.svg +| national_anthem = }}"State Anthem of the Russian Federation" +| image_map = Russian Federation (orthographic projection) - All Territorial Disputes.svg +| map_width = 250px +| map_caption = Russia on the globe. Disputed lands are shown in light green. The Donetsk, Luhansk, Kherson, and Zaporizhzhia oblasts were also annexed (but only partly controlled) in 2022. They are internationally seen as a part of Ukraine. The southernmost Kuril Islands are claimed by both Japan and Russia after the Soviet occupation of the islands at the end of World War II.}} +| capital = Moscow +| coordinates = +| largest_city = capital +| languages_type = Official +| languages = Russian +| languages2_type = +| languages2 = See Languages of Russia +| ethnic_groups = +| ethnic_groups_year = 2021, including Russia and Crimea +| ethnic_groups_ref = +| demonym = Russian +| government_type = Mixed republic under an authoritarian dictatorship +| leader_title1 = President +| leader_name1 = Vladimir Putin +| leader_title2 = Prime Minister +| leader_name2 = Mikhail Mishustin +| leader_title3 = Speaker of theFederation Council +| leader_name3 = Valentina Matviyenko +| leader_title4 = Speaker of theState Duma +| leader_name4 = Vyacheslav Volodin +| leader_title5 = Chief Justice +| leader_name5 = Vyacheslav Lebedev +| legislature = Federal Assembly +| upper_house = Federation Council +| lower_house = State Duma +| sovereignty_type = Formation +| established_event1 = +| established_date1 = 879 +| established_event2 = +| established_date2 = 1157 +| established_event3 = Grand Duchy ofMoscow +| established_d +<|CHUNK_END|> +| screenshot = Git session.svg +| caption = A command-line session showing repository creation, addition of a file, and remote synchronization +| author = Linus Torvalds +| developer = Junio Hamano and others +| released = +| latest release version = +| latest release date = +| latest preview version = +| latest preview date = +| programming language = Primarily in C, with GUI and programming scripts written in Shell script, Perl, Tcl and Python +| operating system = POSIX (Linux, macOS, Solaris, AIX), Windows +| size = +| language = English +| genre = Version control +| license = GPL-2.0-only}} +| standard = +| AsOf = +}} + +'''Git''' () is a distributed version control software system that is capable of managing versions of source code or data. It is often used to control source code by programmers who are developing software collaboratively. + +Design goals of Git include speed, data integrity, and support for distributed, non-linear workflows—thousands of parallel branches running on different computers. "So I'm writing some scripts to try to track things a whole lot faster." + +As with most other distributed version control systems, and unlike most client–server systems, Git maintains a local copy of the entire repository, also known as the "repo", with history and version-tracking abilities, independent of network access or a central server. A repository is stored on each computer in a standard directory with additional, hidden files to provide version control capabilities. Git provides features to synchronize changes between repositories that share history; for asynchronous collaboration, this extends to repositories on remote machines. Although all repositories (with the same history) are peers, developers often use a central server to host a repository to hold an integrated copy. + +Git is free and open-source software shared under the GPL-2.0-only license. + +Git was originally created by Linus Torvalds for version control in the development of the Linux kernel. The trademar +<|CHUNK_END|> +thumb|For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The result matrix has the number of rows of the first and the number of columns of the second matrix. +In mathematics, specifically in linear algebra, '''matrix multiplication''' is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the '''matrix product''', has the number of rows of the first and the number of columns of the second matrix. The product of matrices and is denoted as . + +Matrix multiplication was first described by the French mathematician Jacques Philippe Marie Binet in 1812, to represent the composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, statistics, physics, economics, and engineering. +Computing matrix products is a central operation in all computational applications of linear algebra. + +==Notation== +This article will use the following notational conventions: matrices are represented by capital letters in bold, e.g. ; vectors in lowercase bold, e.g. ; and entries of vectors and matrices are italic (they are numbers from a field), e.g. and . Index notation is often the clearest way to express definitions, and is used as standard in the literature. The entry in row , column of matrix is indicated by , or . In contrast, a single subscript, e.g. , is used to select a matrix (not a matrix entry) from a collection of matrices. + +==Definitions== +===Matrix times matrix=== +If is an matrix and is an matrix, +\mathbf{A}=\begin{pmatrix} + a_{11} & a_{12} & \cdots & a_{1n} \\ + a_{21} & a_{22} & \cdots & a_{2n} \\ + \vdots & \vdots & \ddots & \vdots \\ + a_{m1} & a_{m2} & \cdots & a_{mn} \\ +<|CHUNK_END|> +\; \exp\left(-\frac{\left(x-\mu\right)^2}{2\sigma^2} \right) \!|cdf=\frac12 \left(1 + \mathrm{erf}\,\frac{x-\mu}{\sigma\sqrt2}\right) \!|mean=\mu|median=\mu|mode=\mu|variance=\sigma^2|skewness=0|kurtosis=0|entropy=\ln\left(\sigma\sqrt{2\,\pi\,e}\right)\!|mgf=M_X(t)= \exp\left(\mu\,t+\frac{\sigma^2 t^2}{2}\right)|char=\chi_X(t)=\exp\left(\mu\,i\,t-\frac{\sigma^2 t^2}{2}\right)}}thumb|350px|For the normal distribution, the values less than one standard deviation away from the mean account for 68.27% of the set; while two standard deviations from the mean account for 95.45%; and three standard deviations account for 99.73%. + +The '''normal distribution''' is a probability distribution used in probability theory and statistics. It is also called '''Gaussian distribution''' because it was first discovered by Carl Friedrich Gauss. The normal distribution is very important in many fields because many things take this form. Data Basecamp|url=https://databasecamp.de/en/statistics/normal-distribution|access-date=2022-07-15|language=en-US}} A random variable that takes this form is '''normally distributed''', and can be called a '''normal deviate'''. The normal distribution is often called the ''bell curve'', because the graph of its probability density looks like a bell. The '''standard normal distribution''' (also known as the '''Z distribution''') is a normal distribution that has a mean of zero and a standard deviation of one. + +The form of the distribution is + +f(x) = \frac{1}{\sigma \sqrt{2\pi} } e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2} + + +In a normal distribution, the parameter \mu is the mean ("average"). The standard deviation ("variability") is \sigma. The variance of the distribution is \sigma^2. + +The normal distribution is important because it can represent real-life examples. It is used in natural and social sciences. Data Basecamp|url=https://databasecamp.de/en/statistics/normal-distribution|access-date=2023-05-29|language=en-US}} Some examples include +<|CHUNK_END|> +thumb|right|A vector + +A '''vector''' is a mathematical object that has a size, called the ''magnitude'', and a direction. It is often represented by boldface letters (such as \mathbf{u}, \mathbf{v}, \mathbf{w}), or as a line segment from one point to another (as in \overrightarrow{AB}). + +For example, a vector would be used to show the distance and direction something moved in. When asking for directions, if one says "Walk one kilometer towards the North", that would be a vector, but if they say "Walk one kilometer", without showing a direction, then that would be a scalar. + +We usually draw vectors as arrows. The length of the arrow is proportional to the vector's magnitude. The direction in which the arrow points to is the vector's direction. + +==Examples of vectors== +* John walks north 20 meters. The direction "north" together with the distance "20 meters" is a vector. +* An apple falls down at 10 meters per second. The direction "down" combined with the speed "10 meters per second" is a vector. This kind of vector is also called velocity. + +==Examples of scalars== +* The distance between two places is 10 kilometers. This distance is not a vector because it does not contain a direction. +* The number of fruit in a box is not a vector. +* A person pointing is not a vector because there is only a direction. There is no magnitude (the distance from the person's finger to a building, for example). +* The length of an object. +* A car drives at 100 kilometers per hour. This does not describe a vector, as there is only a magnitude, but no direction. + +==More examples of vectors== +* Displacement is a vector. Displacement is the distance that something moves ''in a certain direction''. A measure of distance alone is a scalar. +* Force that includes direction is a vector. +* Velocity is a vector, because it is a speed in a certain direction. Definition & Facts|url=https://www.britannica.com/science/vector-mathematics|access-date=2020-08-19|website=Encyclopedia Britannica|language=en}} +<|CHUNK_END|> +thumb|right|Pi is an endless string of numbers +'''Pi''' ('''''') () is a mathematical constant that is the ratio of a circle's circumference to its diameter This produces a number, and that number is always the same. However, the number is rather strange. The number starts as 3.141592653589793... and continues without end. Numbers like this are called irrational numbers. + +The first 100 digits are: + +3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067... + +The diameter is the largest chord (line between two points on a circle) which can be fitted inside a circle. It passes through the center of the circle. The distance around a circle is known as the circumference. Even though the diameter and circumference are different for different circles, the number pi remains constant: its value never changes. This is because the relationship between the circumference and diameter is always the same. + +==Fundamentals== +===Definition=== +alt=A diagram of a circle, with the width labeled as diameter, and the perimeter labeled as circumference|thumb|right|The circumference of a circle is slightly more than three times as long as its diameter. The exact ratio is named pi. +pi is defined as the ratio of a circle's circumference c to its diameter d:, English translation by Catriona and David Lischka +:\pi=\frac cd + +===Approximate value=== +thumb|left|A diagram showing how pi can be found by using a [[circle with a diameter of one. The circumference of this circle is pi.]] +Pi is often written as "π". It is also an irrational number, meaning it cannot be written as a fraction \bigg(\frac ab\bigg), where a and b are integers (whole numbers). This basically means that the digits of pi that are to the right of the decimal go forever—without repeating in a pattern, and that it is impossible to write the exact value of pi as a number. Pi can only be approximated, or measured to a value that is close enough for practical purposes. + +A value close to +<|CHUNK_END|> +|data=Array +|time=O(n^2) comparisons, O(n^2) swaps +|average-time=O(n^2) comparisons, O(n^2) swaps +|best-time=O(n) comparisons, O(1) swaps +|space=O(n) total, O(1) auxiliary +|optimal=No +}} +'''Bubble sort''', sometimes referred to as '''sinking sort''', is a simple sorting algorithm that repeatedly steps through the input list element by element, comparing the current element with the one after it, swapping their values if needed. These passes through the list are repeated until no swaps have to be performed during a pass, meaning that the list has become fully sorted. The algorithm, which is a comparison sort, is named for the way the larger elements "bubble" up to the top of the list. + +It performs poorly in real-world use and is used primarily as an educational tool. More efficient algorithms such as quicksort, timsort, or merge sort are used by the sorting libraries built into popular programming languages such as Python and Java. + +==History== +The earliest description of the bubble sort algorithm was in a 1956 paper by mathematician and actuary Edward Harry Friend, ''Sorting on electronic computer systems'', published in the third issue of the third volume of the ''Journal of the Association for Computing Machinery'' (ACM), as a "Sorting exchange algorithm." Friend described the fundamentals of the algorithm, and although initially his paper went unnoticed, some years later it was rediscovered by many computer scientists, including Kenneth E. Iverson, who coined its current name. + +==Analysis== +300px|thumb|right|An example of bubble sort. Starting from the beginning of the list, compare every adjacent pair, swapping their position if they are not in the right order (the latter one is smaller than the former one). After each [[iteration, one less element (the last one) needs to be compared until there are no more elements left to be compared.]] + +=== Performance === +Bubble sort has a worst-case and average complexity of O(n^2), where n is the number of items being sort +<|CHUNK_END|> +In statistics, a '''confidence interval''', abbreviated as CI, is a tool that people use when they collect data in order to estimate a certain parameter, such as the mean (average) of a population. A confidence interval gives a range of values that tells others how good we think our estimate is. + +Each confidence interval depends on certain properties of the sample(s) that we use to make it. For example, a confidence interval that is made from a sample of 5000 people is going to be much better than a confidence interval made from a sample of only 5 people. + +We usually give confidence intervals as a percentage, such as 95%. These percentages are called '''confidence levels.''' + +== Meaning of the term "confidence" == + +The term ''confidence'' has a similar meaning in statistics, as in common use. In common usage, a claim to 95% confidence in something is normally taken as indicating near certainty. In statistics, a claim to 95% confidence simply means that the researcher has seen one possible interval from a large number of possible ones, from which 19 out of 20 intervals contain the true value of the parameter. + +==Practical example== +right|A factory assembly line fills margarine cups to a desired 250g +/- 5gA machine fills cups with margarine. It is adjusted so that the content of the cups is 250g of margarine. As the machine cannot fill every cup with exactly 250g, the content added to individual cups shows some variation, and is considered a random variable X. + +This variation is assumed to be normally distributed around the desired average of 250g, with a standard deviation of 2.5g. To check if the machine is adequately calibrated, a sample of ''n'' = 25 cups of margarine is chosen at random, and the cups are weighed. The weights of margarine are ''X''1, ..., ''X''25, a random sample from ''X''. + +To get an impression of the expectation μ, an estimate is needed. The appropriate estimator is the sample mean: + +:\hat \mu=\bar X = \frac{1}{n}\sum_{i=1}^n X_i. + +The +<|CHUNK_END|> +In computer science, an '''interpreter''' is a computer program that performs commands written in a computer programming language. Interpreters are one of the two most important ways a program can be run, the other being compilation. + +== Function == +The interpreter is a language processor which converts a high-level programming language like JavaScript into machine language by ''converting and executing it line-by-line.'' If there is any error in any line, it reports it at the same time and program execution cannot resume until the error is rectified. + +Category:Software +Category:Computer programming +<|CHUNK_END|> +| + | rowclass2 = mergedrow| label2 = Chinese: | data2 = + | rowclass3 = mergedrow| label3 = French: | data3 = + | rowclass4 = mergedrow| label4 = Russian: | data4 = }} + | rowclass5 = mergedrow| label5 = Spanish: | data5 = }} + | rowclass6 = mergedrow| label6 = Bengali: | data6 = }} + | rowclass7 = mergedrow| label7 = Hindi: | data7 = }} + | rowclass8 = mergedrow| label8 = Indonesian: | data8 = }} + | rowclass9 = mergedrow| label9 = Malay: | data9 = }} + | rowclass10 = mergedrow| label10 = Portuguese: | data10 = }} + | rowclass11 = mergedrow| label11 = Swahili: | data11 = }} + | rowclass12 = mergedrow| label12 = Turkish: | data12 = }}}}}} +| linking_name = the United Nations +| image_flag = Flag of the United Nations.svg +| symbol_type = Emblem +| image_symbol = Emblem of the United Nations.svg +| org_type = Intergovernmental organization +| membership = 193 member states2 observer states +| admin_center_type = Headquarters +| admin_center = New York City +| languages_type = Official languages +| languages = , www.un.org. Retrieved 22 May 2015.}}|Bengali|Hindi|Indonesian|Malay|Portuguese|Swahili|Turkish +| leader_title1 = Secretary‑General +| leader_name1 = António Guterres +| leader_title2 = Deputy Secretary-General +| leader_name2 = Amina J. Mohammed +| leader_title3 = General Assembly President +| leader_name3 = Annalena Baerbock +| leader_title4 = Economic and Social Council President +| leader_name4 = Lok Bahadur Thapa +| leader_title5 = Security Council President +| leader_name5 = Fu Cong(May 2026) +| established_event1 = UN Charter signed +| established_date1 = +| established_event2 = Charter entered into force +| established_date2 = +| official_website = [https://www.un.org/ UN.org] [https://www.un.int/ UN.int] +| FR_total_population_ +<|CHUNK_END|> +In computer science, '''functional programming''' is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that map values to other values, rather than a sequence of imperative statements which update the running state of the program. + +In functional programming, functions are treated as first-class entities, meaning that they can be bound to names (including local identifiers), passed as arguments, and returned from other functions, just as any other data type can. This allows programs to be written in a declarative and composable style, where small functions are combined in a modular manner. + +Functional programming is sometimes treated as synonymous with purely functional programming, a subset of functional programming that treats all functions as deterministic mathematical functions, or pure functions. When a pure function is called with some given arguments, it will always return the same result, and cannot be affected by any mutable state or other side effects. This is in contrast with impure procedures, common in imperative programming, which can have side effects (such as modifying the program's state or taking input from a user). Proponents of purely functional programming claim that by restricting side effects, programs can have fewer bugs, be easier to debug and test, and be more suited to formal verification. + +Functional programming has its roots in academia, evolving from the lambda calculus, a formal system of computation based only on functions. Functional programming has historically been less popular than imperative programming, but many functional languages are seeing use today in industry and education, including Common Lisp, Scheme, Clojure, Wolfram Language, Racket, Erlang, Elixir, OCaml, Haskell, and F#. Lean is a functional programming language commonly used for verifying mathematical theorems. Functional programmi +<|CHUNK_END|> +In object-oriented programming, the '''decorator pattern''' is a design pattern that allows behavior to be added to an individual object dynamically, without affecting the behavior of other instances of the same class. The decorator pattern is often useful for adhering to the Single Responsibility Principle, as it enables functionality to be distributed across classes with distinct concerns. It also supports the Open–Closed Principle, since a class's functionality can be extended without modifying its source code. Using decorators can be more flexible and efficient than subclassing, as an object's behavior can be augmented or combined at runtime without creating an entirely new class hierarchy. + +==Overview== +The ''decorator'' design pattern is one of the twenty-three ''Gang-of-Four design patterns''; these describe how to solve recurring design problems and design flexible and reusable object-oriented software—that is, objects which are easier to implement, change, test, and reuse. + +The decorator pattern provides a flexible alternative to subclassing for extending functionality. When using subclassing, different subclasses extend a class in different ways. However, an extension is bound to the class at compile-time and can't be changed at run-time. The decorator pattern allows responsibilities to be added (and removed from) an object dynamically at run-time. It is achieved by defining Decorator objects that +* implement the interface of the extended (decorated) object (Component) transparently by forwarding all requests to it. +* perform additional functionality before or after forwarding a request. + +This allows working with different Decorator objects to extend the functionality of an object dynamically at run-time. + +==Intent== +thumb|right|400px|Decorator [[Unified Modeling Language|UML class diagram]] +The decorator pattern can be used to extend (decorate) the functionality of a certain object statically, or in some cases at run-time, independently of other instance +<|CHUNK_END|> +thumb|upright=1.5|Map of [[Earth with country borders and big cities shown]] + +'''Geography''' (from Greek: , ''geographia'', literally "earth description") is the study of earth and its people and one of social sciences. Its features are things like continents, seas, rivers and mountains. Its inhabitants are all the people and animals that live on it. Its phenomena are the things that happen like tides, hurricanes, tornadoes, earthquakes and more. + +A person who is an expert in geography is a geographer. A geographer tries to understand the world and the things that are in it, how they started and how they have changed.Geography: The Mother of Sciences [http://web.clas.ufl.edu/users/morgans/lecture_2.prn.pdf] [https://web.archive.org/web/20081003084542/http://web.clas.ufl.edu/users/morgans/lecture_2.prn.pdf] + +Geography is divided into two main parts, which are: Physical geography and human geography. Physical geography studies the natural environment and human geography studies the human environment. The human environmental studies would include things such as the population in a country, how a country's economy is doing, and more. There is also environmental geography. + +Maps are a main tool of geography, so geographers spend much time making and studying them. Making maps is called cartography, and people who specialize in making maps are cartographers. + +== Branches == + +=== Physical geography === + +Physical geography (or physiography) focuses on geography as an Earth science. It aims to understand the physical problems and the issues of lithosphere, hydrosphere, atmosphere, pedosphere, and global flora and fauna patterns (biosphere). + +'''Physical geography can be divided into many broad categories, including:''' + +:{| style="border:1px solid #ddd; text-align:center; margin: auto;" cellspacing="15" +| || 96px || 96px || 96px +|- +| Biogeography || Climatology & Meteorology || Coastal geography || Environmental management +|- +| 96px || 96px || 96px ||96px +|- +| Geodesy || Ge +<|CHUNK_END|> +\boldsymbol e is a number. It is the base of the natural logarithm and is about 2.71828. It is an important mathematical constant. The number e is occasionally called '''Euler's number''' after the Swiss mathematician Leonhard Euler, or '''Napier's constant''' in honor of the Scottish mathematician John Napier who introduced logarithms. It is equally important in mathematics as \pi and i. e is an irrational number, and Euler himself gave the first 23 digits of e. + +The number e has great importance in mathematics, as do 0, 1, \pi, and i. All five of these numbers are important and occur again and again in mathematics. The five constants appear in one formulation of Euler's identity. Like the constant \pi, e is also irrational (it cannot be represented as a ratio of Integers) and transcendental (it is not a root of any non-zero polynomial with rational coefficients). + +The number e is very important for exponential functions. For example, the exponential function applied to the number one, has a value of e. + +e was discovered in 1683 by the Swiss mathematician Jacob Bernoulli, while he was studying compound interest. The numerical value of e truncated to 20 places is: + +:e\approx2.71828182845904523536 + +== Alternate definitions of e == +thumb|The area shown in blue (under the graph of the equation y=1/x) stretching from 1 to e is exactly 1. +There are many different ways to define e. Jacob Bernoulli, who discovered e, was trying to solve the problem: + +: \lim_{n\to\infty}(1+\frac1n)^n. + +In other words, there is a number that the expression (1+\frac1n)^n approaches as n becomes larger. This number is e. + +Another definition is to find the solution of the following formula: + +:2+\cfrac{2}{2+\cfrac{3}{3+\cfrac{4}{4+\cfrac{5}{5+\cfrac{6}{\ddots\,}}}}} + +== Related pages == + +* Imaginary unit +* Pi +* Tau (mathematical constant) + +==References== + +Category:Number theory +Category:Irrational numbers +Category:Transcendental numbers +Category:Mathematical constants +<|CHUNK_END|> +A '''database''' is a computer system for storing and taking care of data (any kind of information). + +When the software that runs a database is separate from the programs that use the database, it is called a '''database engine'''. + +Information stored inside a database is usually stored in an organized way. Data about a person that would have been written on a piece of paper before databases would be stored in a '''record''' in a database. A collection of person records that would have been an address book before databases would be stored in a '''file''' or '''table'''. + +== Uses for database systems == +Uses for database systems include: +* Storing data. +* Searching for specific information within the data. +* Allowing multiple people to look at and change the data at the same time. +* Managing who is allowed to see the data and who can change it. +* Managing rules about the data. A rule might say ''November has 30 days''. This means if someone enters ''November 31'' as a date, this date will be rejected. + +== Changing data == +In most databases, data can change. This also means, that in many cases, changing the data needs to be done in several steps. This is because the data is often stored in more than one tables or files that need to work together to make sense. In many cases all the steps that are needed for a given change are grouped in what is called a transaction. If something goes wrong, all the steps are undone. Being undone is another way of saying the transaction was ''rolled back''. If all the steps are successful, they can be made a permanent part of the database. People talk about a transaction being ''committed''. Both rollback and commit affect all the steps in a transaction. + +The reason why a transaction is rolled back could be that the user or program did not want to finish the change. It could also mean that there is a problem. The database system itself might have a problem during the change. The change might break the rules of the data. + +== Guarantees +<|CHUNK_END|> +'''Cell biology''' is the study of how living cells work. This includes the structure and function of the cell organelles, and the carbon-based molecules which cells produce. Cell biology is an interdisciplinary subject, and uses ideas from genetics, biochemistry, molecular biology, immunology, and other subjects and techniques. + +The most important molecules in cell biology are DNA, RNA and proteins.Gall JG & McIntosh JR eds 2001. ''Landmark papers in cell biology''. Bethesda, MD and Cold Spring Harbor, NY: The American Society for Cell Biology and Cold Spring Harbor Laboratory Press. + +The most important structures in the cell are the nucleus and the chromosomes, but there are others.The structure of eukaryotic cells is much more complex than prokaryotic cells. This is because endosymbiosis has occurred: some or all of the eukaryote organelles are former prokaryotes. Examples are mitochondria and plastids.Alberts B, Johnson A. Lewis J. Raff M. Roberts K. Walter P. 2008. ''Molecular biology of the cell'', 5th ed. Garland.Lodish H. Berk A. Matsudaira P. Kaiser CA. Krieger M. Scott MP. Zipurksy SL. Darnell J. 2004. ''Molecular cell biology'', 5th ed. WH Freeman: NY. + +The most important function of cells is to divide by mitosis or meiosis. Cells in a multicellular organism also specialise in different functions. SEER Training|url=https://training.seer.cancer.gov/anatomy/cells_tissues_membranes/cells/function.html|access-date=2025-01-07|website=training.seer.cancer.gov}} + +*Cytology is mostly about the appearance and structure of cells. + +== References == +<|CHUNK_END|> +thumb +In complex analysis, '''Euler's formula''', also sometimes called '''Euler's relation''', is an equation involving complex numbers and trigonometric functions. More specifically, it states that + +e^{ix} = \cos x + i \sin x + +where ''x'' is a real number, ''e'' is Euler's number and ''i'' is the imaginary unit. mathematics|url=https://www.britannica.com/science/Eulers-formula|access-date=2020-10-02|website=Encyclopedia Britannica|language=en}} + +It makes a relation between trigonometric functions and exponential functions of complex numbers. It is named after Leonhard Euler, who published it in 1748. When he published it, Euler said that the angle must be a real number. Later, it turned out that the formula also works if the angle is not a real number, but a complex one. + +When the angle is \pi and 2\pi, Euler's formula becomes e^{i\pi} = -1 and e^{i2\pi} = 1, respectively. + +== Related pages == + +* Euler's identity + +== References == + +Category:Complex analysis +Category:Trigonometry +<|CHUNK_END|> +th entry in the th row of Pascal's triangle (where the top is the 0th row \tbinom{0}{0}). Each entry is the sum of the two above it.}} +In elementary algebra, the '''binomial theorem''' (or '''binomial expansion''') describes the algebraic expansion of powers of a binomial. According to the theorem, the power expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying and the coefficient of each term is a specific positive integer depending on and . For example, for , +(x+y)^4 = x^4 + 4 x^3y + 6 x^2 y^2 + 4 x y^3 + y^4. + +The coefficient in each term is known as the binomial coefficient or (the two have the same value). These coefficients for varying and can be arranged to form Pascal's triangle Definition & Facts Britannica |url=https://www.britannica.com/science/Pascals-triangle |archive-url=http://web.archive.org/web/20250929213120/https://www.britannica.com/science/Pascals-triangle |archive-date=2025-09-29 |access-date=2026-03-25 |work=Encyclopedia Britannica |language=en}}. These numbers also occur in combinatorics, where gives the number of different combinations (i.e. subsets) of elements that can be chosen from an -element set. Therefore is usually pronounced as " choose ". + +== Statement == +According to the theorem, the expansion of any nonnegative integer power of the binomial is a sum of the form +(x+y)^n = {\binom{n}{0}}x^n y^0 + {\binom{n}{1}}x^{n-1} y^1 + {\binom{n}{2}}x^{n-2} y^2 + \cdots + {\binom{n}{n}}x^0 y^n, +where each \tbinom nk is a positive integer known as a binomial coefficient, defined as + +\binom nk = \frac{n!}{k!\,(n-k)!} = \frac{n(n-1)(n-2)\cdots(n-k + 1)}{k(k-1)(k-2)\cdots2\cdot1}. + +This formula is also referred to as the '''binomial formula''' or the '''binomial identity'''. Using summation notation, it can be written more concisely as +(x+y)^n = \sum_{k=0}^n {\binom{n}{k}}x^{n-k}y^k = \sum_{k=0}^n {\binom{n}{k}}x^{k}y^{n-k}. + +The final expression follows from the previou +<|CHUNK_END|> +thumb|right|250px|The Big Bang model is that the [[universe began in an extremely dense and hot condition and has expanded. The theory suggests that redshift proves the universe is expanding.]] +The '''Big Bang''' is a physical theory about how the universe started expanding, and then made the stars and galaxies we see today. The Big Bang is the name that scientists use for the most common theory of the universe, from the very early stages to the present day. +The most commonly considered alternatives are called the Steady State theory and Plasma cosmology, according to both of which the universe has no beginning or end. + +According to the theory the Big Bang began as a very hot, small, and dense superforce (the mix of the four fundamental forces), with no stars, atoms, form, or structure (called a "singularity"). Then about 13.8 billion years ago, space expanded very quickly (thus the name "Big Bang"). This started the formation of atoms, which eventually led to the formation of stars and galaxies. It was Georges who first noted (in 1927) that the universe is expanding. The universe is still expanding today, and getting colder as well. + +As a whole, the universe is growing and the temperature is falling as time passes. Cosmology is the study of how the universe began and its development. Some scientists who study cosmology have agreed that the Big Bang theory matches what they have observed so far. + +== Naming == +Astronomer Fred Hoyle mockingly called the theory the "Big Bang" on his radio show. Scientists who did not agree with him decided to use it. + +== Evidence == +Scientists base the Big Bang theory on many different observations. The most important is the redshift of very far away galaxies. Cosmological redshift is the Doppler effect occurring in light. When an object moves away from Earth, its color rays look more similar to the color red than they actually are, because the movement stretches the wavelength of light given off by the object. Scientists use the word +<|CHUNK_END|> +| status = Published, W3C recommendation +| year_started = +| editors = Tim Bray, Jean Paoli, Michael Sperberg-McQueen, Eve Maler, François Yergeau, John W. Cowan +| base_standards = SGML +| long_name = Extensible Markup Language +| related_standards = W3C XML Schema +| abbreviation = XML +| domain = Serialization +| version = 1.1 (2nd ed.) +| version_date = +| organization = World Wide Web Consortium (W3C) +}} + +| uniform_type = public.xml +| conforms_to = public.text +| magic = +| owner = World Wide Web Consortium +| genre = Markup language +| extended_from = SGML +| extended_to = Numerous languages, including XHTML, RSS, Atom, and KML +| standard = ) +* [http://www.w3.org/TR/2006/REC-xml11-20060816/ 1.1, 2nd ed.] () + }} +| open = Yes +| free = Yes +}} + +'''Extensible Markup Language''' ('''XML''') is a markup language and file format for storing, transmitting, and reconstructing data. It defines a set of rules for encoding documents in a format that is both human-readable and machine-readable. The World Wide Web Consortium's XML 1.0 Specification of 1998 and several other related specifications—all of them free open standards—define XML. + +The design goals of XML emphasize simplicity, generality, and usability across the Internet. It is a textual data format with strong support via Unicode for different human languages. Although the design of XML focuses on documents, the language is widely used for the representation of arbitrary data structures, such as those used in web services. + +Several schema systems exist to aid in the definition of XML-based languages, while programmers have developed many application programming interfaces (APIs) to aid the processing of XML data. + +== Overview == +The main purpose of XML is serialization, i.e. storing, transmitting, and reconstructing arbitrary data. For two disparate systems to exchange information, they need to agree upon a file format. XML standardizes this process. It is therefore analog +<|CHUNK_END|> +'''Neuroscience''' (or neurobiology) is the scientific study of the nervous system. It is the branch of biology which investigates every aspect of the brain and nervous system. + +The nervous system is made of billions of neurons connected together and to other systems in the body. The central nervous system includes the brain, spinal cord and retina. It is connected to the rest of the body via the peripheral nervous system. + +== Research themes == +Neuroscience research focusses on a set of themes and questions.Research questions: [http://www.northwestern.edu/nuin/fac/index.htm] +* Behavior/cognition/language +* Biological rhythms +* Brain imaging or neuroimaging +* Cell biology +* Cell imaging & Electrophysiology +* Learning/memory +* Signal transduction +* Neurobiology of the neuron +* Neurotransmitter +* Sensation and perception +* Sleep +* Autonomic nervous system and homeostasis +* Arousal, attention and emotion +* Genetics of the nervous system +*Developmental biology of the nervous system +*Diseases of the nervous system + +== Related pages == + +* Agonist +* Biology +* Cognitive neuropsychology +* Ethology +* Neurology +* Neurolinguistic programming +* Neuropsychology +* Psychiatry + +==References== + +=== Textbooks === +* +* +*Squire, L. ''et al.'' (2003). ''Fundamental Neuroscience, 2nd edition''. Academic Press; +*Byrne and Roberts (2004). ''From Molecules to Networks''. Academic Press; +*Sanes, Reh, Harris (2005). ''Development of the Nervous System, 2nd edition''. Academic Press; +*Siegel ''et al.'' (2005). ''Basic Neurochemistry, 7th edition''. Academic Press; +*Rieke, F. ''et al.'' (1999). ''Spikes: Exploring the Neural Code''. The MIT Press; Reprint edition + +==== Online textbooks ==== +*[https://www.ncbi.nlm.nih.gov/books/NBK10799/ Neuroscience] 2nd ed. Dale Purves ''et al''. Published by Sinauer Associates, Inc., 2001. +*[https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Search&db=books&doptcmdl=GenBookHL&term=Characteristics+of+the+Neuron+AND+bnchm%5Bbook%5D+AND+160014%5Buid%5 +<|CHUNK_END|> +In computer science, '''backtracking''' is a recursive approach for finding solutions to some computational problems. Backtracking gradually finds candidate solutions and abandons candidates, i.e., "backtracks" when a candidate cannot be a good solution. + +==Pseudocode== +thumb|A [[Sudoku solved by backtracking.]] +To apply backtracking to a problem, one must give the data ''P'' for an instance of the problem that is to be solved, and six procedures, ''root'', ''abandon'', ''accept'', ''first'', ''next'', and ''save''. These procedures should take the instance data ''P'' as a variable and should do the following: +# ''root''(''P''): return the partial candidate at the root of the search tree. +# ''abandon''(''P'',''c''): return ''true'' only if the partial candidate ''c'' is not worth completing. +# ''accept''(''P'',''c''): return ''true'' if ''c'' is a solution of ''P'', and ''false'' otherwise. +# ''first''(''P'',''c''): generate the first extension of candidate ''c''. +# ''next''(''P'',''s''): generate the next alternative extension of a candidate, after the extension ''s''. +# ''save''(''P'',''c''): use the solution ''c'' of ''P'' + +The backtracking algorithm reduces the problem to the call ''backtrack''(''root''(''P'')), where ''backtrack'' is the following recursive procedure: + + '''procedure''' backtrack(c) '''is''' + '''if''' abandon(P, c) '''then''' return + '''if''' accept(P, c) '''then''' save(P, c) + s ← first(P, c) + '''while''' s ≠ NULL '''do''' + backtrack(s) + s ← next(P, s) + +Category:Algorithms +<|CHUNK_END|> +'''Democracy''' means ''rule by the people''. There are different ways this can be done: +# People meet to decide about new laws, and changes to existing ones. This is usually called '''direct democracy'''. It is never used except in small countries, or perhaps in towns. Modern populations are usually too large to do this. +# The people elect their leaders. These leaders make decisions about laws. This is called '''representative democracy'''. Elections are either held after a certain time, or when a leader dies. +# Sometimes people can suggest new laws or changes to existing laws. Usually, this is done using a referendum, a vote. +# Sometimes, people are chosen to make decisions more or less at random. For example, when choosing a jury for a trial. In Europe, trials with a jury are usually used for serious crimes. + +The type of government where only one person has most of the power is called a dictatorship. Democracy is the opposite of a dictatorship. Dictatorships often act against freedom of expression so people cannot say bad things about the dictator or replace them for somebody else. + +An important source of information is the Democracy Index published by the ''Economist'' periodical. + +== Types of government == +In an election, the people use different ways to choose their leaders. In many countries, the person who gets the most votes wins. But there are many other ways to elect leaders. Very often, the politicians being elected belong to a political party. Instead of choosing a person, people vote for a party. The party with the most votes then picks the leaders. There are multiple ways the party chooses the leader. + +Usually, the people being elected need to meet certain conditions: They need to have a certain age or have certain things be able to perform the job. + +Not everyone can vote in an election. Suffrage is only given to people who are citizens. Young people are usually excluded, and some other people such as prisoners. + +For some elections, a country may ma +<|CHUNK_END|> +'''Inorganic chemistry''' is the branch of chemistry which studies the elements, and inorganic compounds. + +Inorganic chemistry can be defined simply as all chemistry which is not organic chemistry. Organic chemistry is basically the study of carbon compounds. Inorganic chemistry studies the elements (including carbon), and all compounds other than carbon compounds. There are a few exceptions to this rule, but this definition covers most cases. + +==Related pages== +*Metal +*Organic chemistry + +Category:Branches of chemistry +<|CHUNK_END|> +'''Computer vision''' is a sub-field of computer science that studies ways to use a computer to process visual information contained in an image or video. The goal is for computers to understand and interpret what they see. Unlike computer graphics (which uses computers to make new images), computer vision takes visual information from the real world and then makes predictions about the contents those images or videos. + +== How it works == +While it is easy for humans to look at an image and understand it without any effort, this is very difficult for computers. A computer image is actually just a grid of pixels, so a computer can only interpret an image as a long list of colors like ''"red red blue black white red...''". There is no simple way for a computer to read this list of colors and determine that it contains a picture of a flower, or a dog, or a school bus. Computer Vision is the series of techniques to make sense out of this long list of colors. + +At first, the field of computer vision focused on making computers understand images so that they could describe what they see. For example, scientists wanted a computer to be able to say "rabbit" when it was given a picture of a rabbit. It was challenging for scientists to devise ways to help computers understand images, and it was especially hard to get computers to do give the correct answers ''reliably''. Scientists discovered that even when a computer could accurately identify a "normal" rabbit in an image, the computer failed to understand that an upside-down rabbit was still a rabbit. + +Early methods that scientists developed are called '''conventional techniques'''. They are still useful today. Some examples are: + +* ''Edge detection'': picking out the edges between light and dark areas +* ''Corner detection'': picking out corners of sharp shapes +* ''Blob detection:'' picking out curvy shapes +* ''Filtering:'' ways to adjust an image that makes it easier to pick out shapes, such as blurring it or changing the br +<|CHUNK_END|> +thumb|A queue +In Computer science, a '''queue''' is a dynamic data structure, used for storing items, before they are processed. A queue operates on a first-in, first-out FIFO principle, meaning the element that has been in the queue the longest is the next to be removed. + +Generally, the following operations exist: +* Enqueue: add the item to the back of the queue +* Dequeue: remove the item at the front of the queue +* Optionally, there may be an operation to look at the item at the front of the queue, without removing it. +Items that are between the first and the last element of the queue are not directly accessible. + +There is a specialization, called '''priority queue''': In a priority queue, each item also has a weight, which determine the position of the item in a queue. + +Category:Data structures +<|CHUNK_END|> +| subunit_name_1 = millibitcoin +| subunit_ratio_2 = }} +| subunit_name_2 = microbitcoin +| subunit_ratio_3 = }} +| subunit_name_3 = +| plural = bitcoins +| symbol = ₿ (Unicode: ) in the Currency Symbols block in June 2017.}} +| code = BTC, XBT +| implementations = Bitcoin Core +| initial_release_version = 0.1.0 +| initial_release_date = +| code_repository = +| status = Active +| latest_release_version = 22.0 +| latest_release_date = +| forked_from = +| programming_languages = +| operating_system = +| author = Satoshi Nakamoto +| developer = +| white_paper = [https://bitcoin.org/bitcoin.pdf "Bitcoin: A Peer-to-Peer Electronic Cash System"] +| source_model = +| license = +| website = +| ledger_start = +| hash_function = SHA-256 (two rounds) +| circulating_supply = ₿18,830,000 +| supply_limit = ₿21,000,000 2140 at ₿20,999,999.9769.}} +| timestamping = Proof-of-work (partial hash inversion) +| issuance_schedule = Decentralized (block reward)Initially ₿50 per block, halved every 210,000 blocks +| block_time = 10 minutes +| block_reward = ₿6.25 +| market_cap = US$1.149 trillion +| footnotes = +| using_countries = +}} + +'''Bitcoin''' it is a compound of the words ''bit'' and ''coin''. No uniform convention for ''bitcoin'' capitalization exists; some sources use ''Bitcoin'', capitalized, to refer to the technology and network and ''bitcoin'', lowercase, to refer to the unit of account. ''The Wall Street Journal'', ''The Chronicle of Higher Education'', and the ''Oxford English Dictionary'' advocate use of lowercase ''bitcoin'' in all cases, a convention followed throughout this article.}} ('''₿''') is a digital and global money system cryptocurrency. It allows people to send or receive cryptocurrency units across the internet, even to someone they don't know or don't trust. It is the first of its kind technology that allows the transfer of digital scarcity across the internet without needing a third party. Cryptocurrency units can be exchanged without being linked to a real identity. The mathe +<|CHUNK_END|> +thumb|300px|Geometric interpretation of the angle between two vectors defined using an inner product +alt=Scalar product spaces, inner product spaces, Hermitian product spaces.|thumb|300px|Scalar product spaces, over any field, have "scalar products" that are symmetrical and linear in the first argument. Hermitian product spaces are restricted to the field of complex numbers and have "Hermitian products" that are conjugate-symmetrical and linear in the first argument. Inner product spaces may be defined over any field, having "inner products" that are linear in the first argument, conjugate-symmetrical, and positive-definite. Unlike inner products, scalar products and Hermitian products need not be positive-definite. + +In mathematics, an '''inner product space''' titled after Hausdorff spaces and Hilbert spaces.}} is a real or complex vector space endowed with an operation called an '''inner product'''. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in \langle a, b \rangle. Inner products allow formal definitions of intuitive geometric notions, such as lengths, angles, and orthogonality (zero inner product) of vectors. Inner product spaces generalize Euclidean vector spaces, in which the inner product is the dot product or ''scalar product'' of Cartesian coordinates. Inner product spaces of infinite dimensions are widely used in functional analysis. Inner product spaces over the field of complex numbers are sometimes referred to as '''unitary spaces'''. The first usage of the concept of a vector space with an inner product is due to Giuseppe Peano, in 1898. + +An inner product naturally induces an associated norm, (denoted |x| and |y| in the picture); so, every inner product space is a normed vector space. If this normed space is also complete (that is, a Banach space) then the inner product space is a Hilbert space. If an inner product space is not a Hilbert space, it can be ''extended'' by completion to a Hilbert +<|CHUNK_END|> +| footer = Some things global warming makes worse (clockwise from top left): Wildfires, droughts, and dead coral killed by the ocean getting more hot and acidic. +}} + +thumb|right| Places that have become warmer (red) and cooler (blue) over the past 50 years + +thumb| Earth's average temperature has increased since the [[Industrial Revolution.]] + +'''Global warming''' or '''global heating''' is the rise in temperature of Earth’s air and oceans. It is happening mainly because humans burn coal, oil, natural gas, and cut down forests. + +Average temperatures today are about higher than before people started burning a lot of coal around 1750. By the year 2100 temperatures will very likely be to higher than before 1900.There will be more warming in the Arctic, on land and in the northern half of the world. + +Although climate has changed before people started burning a lot of stuff, the last time the Earth was this hot was probably more than 100 thousand years ago. + +Global warming is probably getting faster. It is making more heat waves and wildfires, and melting the ice around the North Pole. + +The present global warming is mostly because of people burning things, such as gasoline for cars and natural gas to keep houses warm. But the heat from the burning itself only makes the world a tiny bit warmer: ''it is the carbon dioxide from the burning which is the biggest part of the problem''. Among greenhouse gases, the increase of carbon dioxide in the atmosphere is the main cause of global warming. Svante Arrhenius predicted this more than a hundred years ago.Arrhenius, Svante 1896. [http://www.globalwarmingart.com/images/1/18/Arrhenius.pdf On the influence of carbonic acid in the air upon the temperature of the ground.] ''Philosophical Magazine'' '''41''': 237-76 Arrhenius confirmed the work of Joseph Fourier 200 years ago. + +When people burn fossil fuels like coal, oil and natural gas this adds carbon dioxide to the air, since fossil fuels contain lots of carbon and burning +<|CHUNK_END|> +procedural (imperative), functional, structured, reflective +| released = +| designer = Guido van Rossum +| developer = Python Software Foundation +| latest release version = +| latest release date = }} +| latest preview version = +| latest preview date = +| typing = Duck, dynamic, strong; optional type annotations +| memory management = Garbage-collected +| implementations = CPython, PyPy, MicroPython, CircuitPython, IronPython, Jython, Stackless Python +| operating system = Cross-platform +* '''Tier 2''': E.g. 32-bit WebAssembly (WASI) +* '''Tier 3''': 64-bit Android, peps.python.org |url=https://peps.python.org/pep-0738/ |access-date=19 May 2024 |website=Python Enhancement Proposals (PEPs) |language=en}} iOS, FreeBSD, and (32-bit) Raspberry Pi OSUnofficial (or has been known to work): Other Unix-like/BSD variants) and a few other platforms}} + + + +- 09/07/2023: Update [fine-tune code](https://github.com/FlagOpen/FlagEmbedding/blob/master/FlagEmbedding/baai_general_embedding/README.md): Add script to mine hard negatives and support adding instruction during fine-tuning. +- 08/09/2023: BGE Models are integrated into **Langchain**, you can use it like [this](#using-langchain); C-MTEB **leaderboard** is [available](https://huggingface.co/spaces/mteb/leaderboard). +- 08/05/2023: Release base-scale and small-scale models, **best performance among the models of the same size 🤗** +- 08/02/2023: Release `bge-large-*`(short for BAAI General Embedding) Models, **rank 1st on MTEB and C-MTEB benchmark!** :tada: :tada: +- 08/01/2023: We release the [Chinese Massive Text Embedding Benchmark](https://github.com/FlagOpen/FlagEmbedding/blob/master/C_MTEB) (**C-MTEB**), consisting of 31 test dataset. + + + + +## Model List + +`bge` is short for `BAAI general embedding`. + +| Model | Language | | Description | query instruction for retrieval [1] | +|:-------------------------------|:--------:| :--------:| :--------:|:--------:| +| [BAAI/bge-m3](https://huggingface.co/BAAI/bge-m3) | Multilingual | [Inference](https://github.com/FlagOpen/FlagEmbedding/tree/master/FlagEmbedding/BGE_M3#usage) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/FlagEmbedding/BGE_M3) | Multi-Functionality(dense retrieval, sparse retrieval, multi-vector(colbert)), Multi-Linguality, and Multi-Granularity(8192 tokens) | | +| [BAAI/llm-embedder](https://huggingface.co/BAAI/llm-embedder) | English | [Inference](./FlagEmbedding/llm_embedder/README.md) [Fine-tune](./FlagEmbedding/llm_embedder/README.md) | a unified embedding model to support diverse retrieval augmentation needs for LLMs | See [README](./FlagEmbedding/llm_embedder/README.md) | +| [BAAI/bge-reranker-large](https://huggingface.co/BAAI/bge-reranker-large) | Chinese and English | [Inference](#usage-for-reranker) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/reranker) | a cross-encoder model which is more accurate but less efficient [2] | | +| [BAAI/bge-reranker-base](https://huggingface.co/BAAI/bge-reranker-base) | Chinese and English | [Inference](#usage-for-reranker) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/reranker) | a cross-encoder model which is more accurate but less efficient [2] | | +| [BAAI/bge-large-en-v1.5](https://huggingface.co/BAAI/bge-large-en-v1.5) | English | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | version 1.5 with more reasonable similarity distribution | `Represent this sentence for searching relevant passages: ` | +| [BAAI/bge-base-en-v1.5](https://huggingface.co/BAAI/bge-base-en-v1.5) | English | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | version 1.5 with more reasonable similarity distribution | `Represent this sentence for searching relevant passages: ` | +| [BAAI/bge-small-en-v1.5](https://huggingface.co/BAAI/bge-small-en-v1.5) | English | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | version 1.5 with more reasonable similarity distribution | `Represent this sentence for searching relevant passages: ` | +| [BAAI/bge-large-zh-v1.5](https://huggingface.co/BAAI/bge-large-zh-v1.5) | Chinese | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | version 1.5 with more reasonable similarity distribution | `为这个句子生成表示以用于检索相关文章：` | +| [BAAI/bge-base-zh-v1.5](https://huggingface.co/BAAI/bge-base-zh-v1.5) | Chinese | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | version 1.5 with more reasonable similarity distribution | `为这个句子生成表示以用于检索相关文章：` | +| [BAAI/bge-small-zh-v1.5](https://huggingface.co/BAAI/bge-small-zh-v1.5) | Chinese | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | version 1.5 with more reasonable similarity distribution | `为这个句子生成表示以用于检索相关文章：` | +| [BAAI/bge-large-en](https://huggingface.co/BAAI/bge-large-en) | English | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | :trophy: rank **1st** in [MTEB](https://huggingface.co/spaces/mteb/leaderboard) leaderboard | `Represent this sentence for searching relevant passages: ` | +| [BAAI/bge-base-en](https://huggingface.co/BAAI/bge-base-en) | English | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | a base-scale model but with similar ability to `bge-large-en` | `Represent this sentence for searching relevant passages: ` | +| [BAAI/bge-small-en](https://huggingface.co/BAAI/bge-small-en) | English | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) |a small-scale model but with competitive performance | `Represent this sentence for searching relevant passages: ` | +| [BAAI/bge-large-zh](https://huggingface.co/BAAI/bge-large-zh) | Chinese | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | :trophy: rank **1st** in [C-MTEB](https://github.com/FlagOpen/FlagEmbedding/tree/master/C_MTEB) benchmark | `为这个句子生成表示以用于检索相关文章：` | +| [BAAI/bge-base-zh](https://huggingface.co/BAAI/bge-base-zh) | Chinese | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | a base-scale model but with similar ability to `bge-large-zh` | `为这个句子生成表示以用于检索相关文章：` | +| [BAAI/bge-small-zh](https://huggingface.co/BAAI/bge-small-zh) | Chinese | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | a small-scale model but with competitive performance | `为这个句子生成表示以用于检索相关文章：` | + +[1\]: If you need to search the relevant passages to a query, we suggest to add the instruction to the query; in other cases, no instruction is needed, just use the original query directly. In all cases, **no instruction** needs to be added to passages. + +[2\]: Different from embedding model, reranker uses question and document as input and directly output similarity instead of embedding. To balance the accuracy and time cost, cross-encoder is widely used to re-rank top-k documents retrieved by other simple models. +For examples, use bge embedding model to retrieve top 100 relevant documents, and then use bge reranker to re-rank the top 100 document to get the final top-3 results. + +All models have been uploaded to Huggingface Hub, and you can see them at https://huggingface.co/BAAI. +If you cannot open the Huggingface Hub, you also can download the models at https://model.baai.ac.cn/models . + + +## Frequently asked questions + +
+ 1. How to fine-tune bge embedding model? + + +Following this [example](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) to prepare data and fine-tune your model. +Some suggestions: +- Mine hard negatives following this [example](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune#hard-negatives), which can improve the retrieval performance. +- If you pre-train bge on your data, the pre-trained model cannot be directly used to calculate similarity, and it must be fine-tuned with contrastive learning before computing similarity. +- If the accuracy of the fine-tuned model is still not high, it is recommended to use/fine-tune the cross-encoder model (bge-reranker) to re-rank top-k results. Hard negatives also are needed to fine-tune reranker. + + +
+ +
+ 2. The similarity score between two dissimilar sentences is higher than 0.5 + + +**Suggest to use bge v1.5, which alleviates the issue of the similarity distribution.** + +Since we finetune the models by contrastive learning with a temperature of 0.01, +the similarity distribution of the current BGE model is about in the interval \[0.6, 1\]. +So a similarity score greater than 0.5 does not indicate that the two sentences are similar. + +For downstream tasks, such as passage retrieval or semantic similarity, +**what matters is the relative order of the scores, not the absolute value.** +If you need to filter similar sentences based on a similarity threshold, +please select an appropriate similarity threshold based on the similarity distribution on your data (such as 0.8, 0.85, or even 0.9). + +
+ +
+ 3. When does the query instruction need to be used + + + +For the `bge-*-v1.5`, we improve its retrieval ability when not using instruction. +No instruction only has a slight degradation in retrieval performance compared with using instruction. +So you can generate embedding without instruction in all cases for convenience. + +For a retrieval task that uses short queries to find long related documents, +it is recommended to add instructions for these short queries. +**The best method to decide whether to add instructions for queries is choosing the setting that achieves better performance on your task.** +In all cases, the documents/passages do not need to add the instruction. + +
+ + +## Usage + +### Usage for Embedding Model + +Here are some examples for using `bge` models with +[FlagEmbedding](#using-flagembedding), [Sentence-Transformers](#using-sentence-transformers), [Langchain](#using-langchain), or [Huggingface Transformers](#using-huggingface-transformers). + +#### Using FlagEmbedding +``` +pip install -U FlagEmbedding +``` +If it doesn't work for you, you can see [FlagEmbedding](https://github.com/FlagOpen/FlagEmbedding/blob/master/FlagEmbedding/baai_general_embedding/README.md) for more methods to install FlagEmbedding. + +```python +from FlagEmbedding import FlagModel +sentences_1 = ["样例数据-1", "样例数据-2"] +sentences_2 = ["样例数据-3", "样例数据-4"] +model = FlagModel('BAAI/bge-large-zh-v1.5', + query_instruction_for_retrieval="为这个句子生成表示以用于检索相关文章：", + use_fp16=True) # Setting use_fp16 to True speeds up computation with a slight performance degradation +embeddings_1 = model.encode(sentences_1) +embeddings_2 = model.encode(sentences_2) +similarity = embeddings_1 @ embeddings_2.T +print(similarity) + +# for s2p(short query to long passage) retrieval task, suggest to use encode_queries() which will automatically add the instruction to each query +# corpus in retrieval task can still use encode() or encode_corpus(), since they don't need instruction +queries = ['query_1', 'query_2'] +passages = ["样例文档-1", "样例文档-2"] +q_embeddings = model.encode_queries(queries) +p_embeddings = model.encode(passages) +scores = q_embeddings @ p_embeddings.T +``` +For the value of the argument `query_instruction_for_retrieval`, see [Model List](https://github.com/FlagOpen/FlagEmbedding/tree/master#model-list). + +By default, FlagModel will use all available GPUs when encoding. Please set `os.environ["CUDA_VISIBLE_DEVICES"]` to select specific GPUs. +You also can set `os.environ["CUDA_VISIBLE_DEVICES"]=""` to make all GPUs unavailable. + + +#### Using Sentence-Transformers + +You can also use the `bge` models with [sentence-transformers](https://www.SBERT.net): + +``` +pip install -U sentence-transformers +``` +```python +from sentence_transformers import SentenceTransformer +sentences_1 = ["样例数据-1", "样例数据-2"] +sentences_2 = ["样例数据-3", "样例数据-4"] +model = SentenceTransformer('BAAI/bge-large-zh-v1.5') +embeddings_1 = model.encode(sentences_1, normalize_embeddings=True) +embeddings_2 = model.encode(sentences_2, normalize_embeddings=True) +similarity = embeddings_1 @ embeddings_2.T +print(similarity) +``` +For s2p(short query to long passage) retrieval task, +each short query should start with an instruction (instructions see [Model List](https://github.com/FlagOpen/FlagEmbedding/tree/master#model-list)). +But the instruction is not needed for passages. +```python +from sentence_transformers import SentenceTransformer +queries = ['query_1', 'query_2'] +passages = ["样例文档-1", "样例文档-2"] +instruction = "为这个句子生成表示以用于检索相关文章：" + +model = SentenceTransformer('BAAI/bge-large-zh-v1.5') +q_embeddings = model.encode([instruction+q for q in queries], normalize_embeddings=True) +p_embeddings = model.encode(passages, normalize_embeddings=True) +scores = q_embeddings @ p_embeddings.T +``` + +#### Using Langchain + +You can use `bge` in langchain like this: +```python +from langchain.embeddings import HuggingFaceBgeEmbeddings +model_name = "BAAI/bge-large-en-v1.5" +model_kwargs = {'device': 'cuda'} +encode_kwargs = {'normalize_embeddings': True} # set True to compute cosine similarity +model = HuggingFaceBgeEmbeddings( + model_name=model_name, + model_kwargs=model_kwargs, + encode_kwargs=encode_kwargs, + query_instruction="为这个句子生成表示以用于检索相关文章：" +) +model.query_instruction = "为这个句子生成表示以用于检索相关文章：" +``` + + +#### Using HuggingFace Transformers + +With the transformers package, you can use the model like this: First, you pass your input through the transformer model, then you select the last hidden state of the first token (i.e., [CLS]) as the sentence embedding. + +```python +from transformers import AutoTokenizer, AutoModel +import torch +# Sentences we want sentence embeddings for +sentences = ["样例数据-1", "样例数据-2"] + +# Load model from HuggingFace Hub +tokenizer = AutoTokenizer.from_pretrained('BAAI/bge-large-zh-v1.5') +model = AutoModel.from_pretrained('BAAI/bge-large-zh-v1.5') +model.eval() + +# Tokenize sentences +encoded_input = tokenizer(sentences, padding=True, truncation=True, return_tensors='pt') +# for s2p(short query to long passage) retrieval task, add an instruction to query (not add instruction for passages) +# encoded_input = tokenizer([instruction + q for q in queries], padding=True, truncation=True, return_tensors='pt') + +# Compute token embeddings +with torch.no_grad(): + model_output = model(**encoded_input) + # Perform pooling. In this case, cls pooling. + sentence_embeddings = model_output[0][:, 0] +# normalize embeddings +sentence_embeddings = torch.nn.functional.normalize(sentence_embeddings, p=2, dim=1) +print("Sentence embeddings:", sentence_embeddings) +``` + +### Usage for Reranker + +Different from embedding model, reranker uses question and document as input and directly output similarity instead of embedding. +You can get a relevance score by inputting query and passage to the reranker. +The reranker is optimized based cross-entropy loss, so the relevance score is not bounded to a specific range. + + +#### Using FlagEmbedding +``` +pip install -U FlagEmbedding +``` + +Get relevance scores (higher scores indicate more relevance): +```python +from FlagEmbedding import FlagReranker +reranker = FlagReranker('BAAI/bge-reranker-large', use_fp16=True) # Setting use_fp16 to True speeds up computation with a slight performance degradation + +score = reranker.compute_score(['query', 'passage']) +print(score) + +scores = reranker.compute_score([['what is panda?', 'hi'], ['what is panda?', 'The giant panda (Ailuropoda melanoleuca), sometimes called a panda bear or simply panda, is a bear species endemic to China.']]) +print(scores) +``` + + +#### Using Huggingface transformers + +```python +import torch +from transformers import AutoModelForSequenceClassification, AutoTokenizer + +tokenizer = AutoTokenizer.from_pretrained('BAAI/bge-reranker-large') +model = AutoModelForSequenceClassification.from_pretrained('BAAI/bge-reranker-large') +model.eval() + +pairs = [['what is panda?', 'hi'], ['what is panda?', 'The giant panda (Ailuropoda melanoleuca), sometimes called a panda bear or simply panda, is a bear species endemic to China.']] +with torch.no_grad(): + inputs = tokenizer(pairs, padding=True, truncation=True, return_tensors='pt', max_length=512) + scores = model(**inputs, return_dict=True).logits.view(-1, ).float() + print(scores) +``` + +#### Usage of the ONNX files + +```python +from optimum.onnxruntime import ORTModelForFeatureExtraction # type: ignore + +import torch +from transformers import AutoModel, AutoTokenizer + +tokenizer = AutoTokenizer.from_pretrained('BAAI/bge-small-en-v1.5') +model = AutoModel.from_pretrained('BAAI/bge-small-en-v1.5') +model_ort = ORTModelForFeatureExtraction.from_pretrained('BAAI/bge-small-en-v1.5', file_name="onnx/model.onnx") + +# Sentences we want sentence embeddings for +sentences = ["样例数据-1", "样例数据-2"] + +# Tokenize sentences +encoded_input = tokenizer(sentences, padding=True, truncation=True, return_tensors='pt') +# for s2p(short query to long passage) retrieval task, add an instruction to query (not add instruction for passages) +# encoded_input = tokenizer([instruction + q for q in queries], padding=True, truncation=True, return_tensors='pt') + +model_output_ort = model_ort(**encoded_input) +# Compute token embeddings +with torch.no_grad(): + model_output = model(**encoded_input) + +# model_output and model_output_ort are identical + +``` + +#### Usage via infinity +Its also possible to deploy the onnx files with the [infinity_emb](https://github.com/michaelfeil/infinity) pip package. +Recommended is `device="cuda", engine="torch"` with flash attention on gpu, and `device="cpu", engine="optimum"` for onnx inference. + +```python +import asyncio +from infinity_emb import AsyncEmbeddingEngine, EngineArgs + +sentences = ["Embed this is sentence via Infinity.", "Paris is in France."] +engine = AsyncEmbeddingEngine.from_args( + EngineArgs(model_name_or_path = "BAAI/bge-small-en-v1.5", device="cpu", engine="optimum" # or engine="torch" +)) + +async def main(): + async with engine: + embeddings, usage = await engine.embed(sentences=sentences) +asyncio.run(main()) +``` + + +## Evaluation + +`baai-general-embedding` models achieve **state-of-the-art performance on both MTEB and C-MTEB leaderboard!** +For more details and evaluation tools see our [scripts](https://github.com/FlagOpen/FlagEmbedding/blob/master/C_MTEB/README.md). + +- **MTEB**: + +| Model Name | Dimension | Sequence Length | Average (56) | Retrieval (15) |Clustering (11) | Pair Classification (3) | Reranking (4) | STS (10) | Summarization (1) | Classification (12) | +|:----:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:| +| [BAAI/bge-large-en-v1.5](https://huggingface.co/BAAI/bge-large-en-v1.5) | 1024 | 512 | **64.23** | **54.29** | 46.08 | 87.12 | 60.03 | 83.11 | 31.61 | 75.97 | +| [BAAI/bge-base-en-v1.5](https://huggingface.co/BAAI/bge-base-en-v1.5) | 768 | 512 | 63.55 | 53.25 | 45.77 | 86.55 | 58.86 | 82.4 | 31.07 | 75.53 | +| [BAAI/bge-small-en-v1.5](https://huggingface.co/BAAI/bge-small-en-v1.5) | 384 | 512 | 62.17 |51.68 | 43.82 | 84.92 | 58.36 | 81.59 | 30.12 | 74.14 | +| [bge-large-en](https://huggingface.co/BAAI/bge-large-en) | 1024 | 512 | 63.98 | 53.9 | 46.98 | 85.8 | 59.48 | 81.56 | 32.06 | 76.21 | +| [bge-base-en](https://huggingface.co/BAAI/bge-base-en) | 768 | 512 | 63.36 | 53.0 | 46.32 | 85.86 | 58.7 | 81.84 | 29.27 | 75.27 | +| [gte-large](https://huggingface.co/thenlper/gte-large) | 1024 | 512 | 63.13 | 52.22 | 46.84 | 85.00 | 59.13 | 83.35 | 31.66 | 73.33 | +| [gte-base](https://huggingface.co/thenlper/gte-base) | 768 | 512 | 62.39 | 51.14 | 46.2 | 84.57 | 58.61 | 82.3 | 31.17 | 73.01 | +| [e5-large-v2](https://huggingface.co/intfloat/e5-large-v2) | 1024| 512 | 62.25 | 50.56 | 44.49 | 86.03 | 56.61 | 82.05 | 30.19 | 75.24 | +| [bge-small-en](https://huggingface.co/BAAI/bge-small-en) | 384 | 512 | 62.11 | 51.82 | 44.31 | 83.78 | 57.97 | 80.72 | 30.53 | 74.37 | +| [instructor-xl](https://huggingface.co/hkunlp/instructor-xl) | 768 | 512 | 61.79 | 49.26 | 44.74 | 86.62 | 57.29 | 83.06 | 32.32 | 61.79 | +| [e5-base-v2](https://huggingface.co/intfloat/e5-base-v2) | 768 | 512 | 61.5 | 50.29 | 43.80 | 85.73 | 55.91 | 81.05 | 30.28 | 73.84 | +| [gte-small](https://huggingface.co/thenlper/gte-small) | 384 | 512 | 61.36 | 49.46 | 44.89 | 83.54 | 57.7 | 82.07 | 30.42 | 72.31 | +| [text-embedding-ada-002](https://platform.openai.com/docs/guides/embeddings) | 1536 | 8192 | 60.99 | 49.25 | 45.9 | 84.89 | 56.32 | 80.97 | 30.8 | 70.93 | +| [e5-small-v2](https://huggingface.co/intfloat/e5-base-v2) | 384 | 512 | 59.93 | 49.04 | 39.92 | 84.67 | 54.32 | 80.39 | 31.16 | 72.94 | +| [sentence-t5-xxl](https://huggingface.co/sentence-transformers/sentence-t5-xxl) | 768 | 512 | 59.51 | 42.24 | 43.72 | 85.06 | 56.42 | 82.63 | 30.08 | 73.42 | +| [all-mpnet-base-v2](https://huggingface.co/sentence-transformers/all-mpnet-base-v2) | 768 | 514 | 57.78 | 43.81 | 43.69 | 83.04 | 59.36 | 80.28 | 27.49 | 65.07 | +| [sgpt-bloom-7b1-msmarco](https://huggingface.co/bigscience/sgpt-bloom-7b1-msmarco) | 4096 | 2048 | 57.59 | 48.22 | 38.93 | 81.9 | 55.65 | 77.74 | 33.6 | 66.19 | + + + +- **C-MTEB**: +We create the benchmark C-MTEB for Chinese text embedding which consists of 31 datasets from 6 tasks. +Please refer to [C_MTEB](https://github.com/FlagOpen/FlagEmbedding/blob/master/C_MTEB/README.md) for a detailed introduction. + +| Model | Embedding dimension | Avg | Retrieval | STS | PairClassification | Classification | Reranking | Clustering | +|:-------------------------------|:--------:|:--------:|:--------:|:--------:|:--------:|:--------:|:--------:|:--------:| +| [**BAAI/bge-large-zh-v1.5**](https://huggingface.co/BAAI/bge-large-zh-v1.5) | 1024 | **64.53** | 70.46 | 56.25 | 81.6 | 69.13 | 65.84 | 48.99 | +| [BAAI/bge-base-zh-v1.5](https://huggingface.co/BAAI/bge-base-zh-v1.5) | 768 | 63.13 | 69.49 | 53.72 | 79.75 | 68.07 | 65.39 | 47.53 | +| [BAAI/bge-small-zh-v1.5](https://huggingface.co/BAAI/bge-small-zh-v1.5) | 512 | 57.82 | 61.77 | 49.11 | 70.41 | 63.96 | 60.92 | 44.18 | +| [BAAI/bge-large-zh](https://huggingface.co/BAAI/bge-large-zh) | 1024 | 64.20 | 71.53 | 54.98 | 78.94 | 68.32 | 65.11 | 48.39 | +| [bge-large-zh-noinstruct](https://huggingface.co/BAAI/bge-large-zh-noinstruct) | 1024 | 63.53 | 70.55 | 53 | 76.77 | 68.58 | 64.91 | 50.01 | +| [BAAI/bge-base-zh](https://huggingface.co/BAAI/bge-base-zh) | 768 | 62.96 | 69.53 | 54.12 | 77.5 | 67.07 | 64.91 | 47.63 | +| [multilingual-e5-large](https://huggingface.co/intfloat/multilingual-e5-large) | 1024 | 58.79 | 63.66 | 48.44 | 69.89 | 67.34 | 56.00 | 48.23 | +| [BAAI/bge-small-zh](https://huggingface.co/BAAI/bge-small-zh) | 512 | 58.27 | 63.07 | 49.45 | 70.35 | 63.64 | 61.48 | 45.09 | +| [m3e-base](https://huggingface.co/moka-ai/m3e-base) | 768 | 57.10 | 56.91 | 50.47 | 63.99 | 67.52 | 59.34 | 47.68 | +| [m3e-large](https://huggingface.co/moka-ai/m3e-large) | 1024 | 57.05 | 54.75 | 50.42 | 64.3 | 68.2 | 59.66 | 48.88 | +| [multilingual-e5-base](https://huggingface.co/intfloat/multilingual-e5-base) | 768 | 55.48 | 61.63 | 46.49 | 67.07 | 65.35 | 54.35 | 40.68 | +| [multilingual-e5-small](https://huggingface.co/intfloat/multilingual-e5-small) | 384 | 55.38 | 59.95 | 45.27 | 66.45 | 65.85 | 53.86 | 45.26 | +| [text-embedding-ada-002(OpenAI)](https://platform.openai.com/docs/guides/embeddings/what-are-embeddings) | 1536 | 53.02 | 52.0 | 43.35 | 69.56 | 64.31 | 54.28 | 45.68 | +| [luotuo](https://huggingface.co/silk-road/luotuo-bert-medium) | 1024 | 49.37 | 44.4 | 42.78 | 66.62 | 61 | 49.25 | 44.39 | +| [text2vec-base](https://huggingface.co/shibing624/text2vec-base-chinese) | 768 | 47.63 | 38.79 | 43.41 | 67.41 | 62.19 | 49.45 | 37.66 | +| [text2vec-large](https://huggingface.co/GanymedeNil/text2vec-large-chinese) | 1024 | 47.36 | 41.94 | 44.97 | 70.86 | 60.66 | 49.16 | 30.02 | + + +- **Reranking**: +See [C_MTEB](https://github.com/FlagOpen/FlagEmbedding/blob/master/C_MTEB/) for evaluation script. + +| Model | T2Reranking | T2RerankingZh2En\* | T2RerankingEn2Zh\* | MMarcoReranking | CMedQAv1 | CMedQAv2 | Avg | +|:-------------------------------|:--------:|:--------:|:--------:|:--------:|:--------:|:--------:|:--------:| +| text2vec-base-multilingual | 64.66 | 62.94 | 62.51 | 14.37 | 48.46 | 48.6 | 50.26 | +| multilingual-e5-small | 65.62 | 60.94 | 56.41 | 29.91 | 67.26 | 66.54 | 57.78 | +| multilingual-e5-large | 64.55 | 61.61 | 54.28 | 28.6 | 67.42 | 67.92 | 57.4 | +| multilingual-e5-base | 64.21 | 62.13 | 54.68 | 29.5 | 66.23 | 66.98 | 57.29 | +| m3e-base | 66.03 | 62.74 | 56.07 | 17.51 | 77.05 | 76.76 | 59.36 | +| m3e-large | 66.13 | 62.72 | 56.1 | 16.46 | 77.76 | 78.27 | 59.57 | +| bge-base-zh-v1.5 | 66.49 | 63.25 | 57.02 | 29.74 | 80.47 | 84.88 | 63.64 | +| bge-large-zh-v1.5 | 65.74 | 63.39 | 57.03 | 28.74 | 83.45 | 85.44 | 63.97 | +| [BAAI/bge-reranker-base](https://huggingface.co/BAAI/bge-reranker-base) | 67.28 | 63.95 | 60.45 | 35.46 | 81.26 | 84.1 | 65.42 | +| [BAAI/bge-reranker-large](https://huggingface.co/BAAI/bge-reranker-large) | 67.6 | 64.03 | 61.44 | 37.16 | 82.15 | 84.18 | 66.09 | + +\* : T2RerankingZh2En and T2RerankingEn2Zh are cross-language retrieval tasks + +## Train + +### BAAI Embedding + +We pre-train the models using [retromae](https://github.com/staoxiao/RetroMAE) and train them on large-scale pairs data using contrastive learning. +**You can fine-tune the embedding model on your data following our [examples](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune).** +We also provide a [pre-train example](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/pretrain). +Note that the goal of pre-training is to reconstruct the text, and the pre-trained model cannot be used for similarity calculation directly, it needs to be fine-tuned. +More training details for bge see [baai_general_embedding](https://github.com/FlagOpen/FlagEmbedding/blob/master/FlagEmbedding/baai_general_embedding/README.md). + + + +### BGE Reranker + +Cross-encoder will perform full-attention over the input pair, +which is more accurate than embedding model (i.e., bi-encoder) but more time-consuming than embedding model. +Therefore, it can be used to re-rank the top-k documents returned by embedding model. +We train the cross-encoder on a multilingual pair data, +The data format is the same as embedding model, so you can fine-tune it easily following our [example](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/reranker). +More details please refer to [./FlagEmbedding/reranker/README.md](https://github.com/FlagOpen/FlagEmbedding/tree/master/FlagEmbedding/reranker) + + +## Contact +If you have any question or suggestion related to this project, feel free to open an issue or pull request. +You also can email Shitao Xiao(stxiao@baai.ac.cn) and Zheng Liu(liuzheng@baai.ac.cn). + + +## Citation + +If you find this repository useful, please consider giving a star :star: and citation + +``` +@misc{bge_embedding, + title={C-Pack: Packaged Resources To Advance General Chinese Embedding}, + author={Shitao Xiao and Zheng Liu and Peitian Zhang and Niklas Muennighoff}, + year={2023}, + eprint={2309.07597}, + archivePrefix={arXiv}, + primaryClass={cs.CL} +} +``` + +## License +FlagEmbedding is licensed under the [MIT License](https://github.com/FlagOpen/FlagEmbedding/blob/master/LICENSE). The released models can be used for commercial purposes free of charge. + diff --git a/aegis_embedder/config.json b/aegis_embedder/config.json new file mode 100644 index 0000000..2b125c0 --- /dev/null +++ b/aegis_embedder/config.json @@ -0,0 +1,35 @@ +{ + "add_cross_attention": false, + "architectures": [ + "BertModel" + ], + "attention_probs_dropout_prob": 0.1, + "bos_token_id": null, + "classifier_dropout": null, + "dtype": "float32", + "eos_token_id": null, + "hidden_act": "gelu", + "hidden_dropout_prob": 0.1, + "hidden_size": 384, + "id2label": { + "0": "LABEL_0" + }, + "initializer_range": 0.02, + "intermediate_size": 1536, + "is_decoder": false, + "label2id": { + "LABEL_0": 0 + }, + "layer_norm_eps": 1e-12, + "max_position_embeddings": 512, + "model_type": "bert", + "num_attention_heads": 12, + "num_hidden_layers": 12, + "pad_token_id": 0, + "position_embedding_type": "absolute", + "tie_word_embeddings": true, + "transformers_version": "5.0.0", + "type_vocab_size": 2, + "use_cache": true, + "vocab_size": 30522 +} diff --git a/aegis_embedder/config_sentence_transformers.json b/aegis_embedder/config_sentence_transformers.json new file mode 100644 index 0000000..a38c005 --- /dev/null +++ b/aegis_embedder/config_sentence_transformers.json @@ -0,0 +1,14 @@ +{ + "__version__": { + "pytorch": "2.10.0+cu128", + "sentence_transformers": "5.4.1", + "transformers": "5.0.0" + }, + "default_prompt_name": null, + "model_type": "SentenceTransformer", + "prompts": { + "document": "", + "query": "" + }, + "similarity_fn_name": "cosine" +} \ No newline at end of file diff --git a/aegis_embedder/model.safetensors b/aegis_embedder/model.safetensors new file mode 100644 index 0000000..c20bdfe --- /dev/null +++ b/aegis_embedder/model.safetensors @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ba3eeb8008783b2a8e9aeb9415a511d9aa3bdfec2dbbdfe8e4bbf5bdde283c6b +size 133462104 diff --git a/aegis_embedder/modules.json b/aegis_embedder/modules.json new file mode 100644 index 0000000..0de5a64 --- /dev/null +++ b/aegis_embedder/modules.json @@ -0,0 +1,20 @@ +[ + { + "idx": 0, + "name": "0", + "path": "", + "type": "sentence_transformers.base.modules.transformer.Transformer" + }, + { + "idx": 1, + "name": "1", + "path": "1_Pooling", + "type": "sentence_transformers.sentence_transformer.modules.pooling.Pooling" + }, + { + "idx": 2, + "name": "2", + "path": "2_Normalize", + "type": "sentence_transformers.sentence_transformer.modules.normalize.Normalize" + } +] \ No newline at end of file diff --git a/aegis_embedder/sentence_bert_config.json b/aegis_embedder/sentence_bert_config.json new file mode 100644 index 0000000..d2cd158 --- /dev/null +++ b/aegis_embedder/sentence_bert_config.json @@ -0,0 +1,10 @@ +{ + "transformer_task": "feature-extraction", + "modality_config": { + "text": { + "method": "forward", + "method_output_name": "last_hidden_state" + } + }, + "module_output_name": "token_embeddings" +} \ No newline at end of file diff --git a/aegis_embedder/tokenizer.json b/aegis_embedder/tokenizer.json new file mode 100644 index 0000000..99f8eba --- /dev/null +++ b/aegis_embedder/tokenizer.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:de2a1b8d1aee816739bc3ca0125a473a080bf05311c640f63bc22099527b1c6b +size 711781 diff --git a/aegis_embedder/tokenizer_config.json b/aegis_embedder/tokenizer_config.json new file mode 100644 index 0000000..d8008d4 --- /dev/null +++ b/aegis_embedder/tokenizer_config.json @@ -0,0 +1,17 @@ +{ + "backend": "tokenizers", + "clean_up_tokenization_spaces": true, + "cls_token": "[CLS]", + "do_basic_tokenize": true, + "do_lower_case": true, + "is_local": false, + "mask_token": "[MASK]", + "model_max_length": 512, + "never_split": null, + "pad_token": "[PAD]", + "sep_token": "[SEP]", + "strip_accents": null, + "tokenize_chinese_chars": true, + "tokenizer_class": "BertTokenizer", + "unk_token": "[UNK]" +} diff --git a/aegis_index.faiss b/aegis_index.faiss new file mode 100644 index 0000000..8b930e6 --- /dev/null +++ b/aegis_index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:dcf18b088fb09d53873e9e069dca8ad8634839370a4854d7c6be5050cc1fde86 +size 8334381 diff --git a/aegis_reranker/README.md b/aegis_reranker/README.md new file mode 100644 index 0000000..7cfbcae --- /dev/null +++ b/aegis_reranker/README.md @@ -0,0 +1,147 @@ +--- +tags: +- sentence-transformers +- cross-encoder +- reranker +base_model: cross-encoder/ms-marco-MiniLM-L6-v2 +pipeline_tag: text-ranking +library_name: sentence-transformers +--- + +# CrossEncoder based on cross-encoder/ms-marco-MiniLM-L6-v2 + +This is a [Cross Encoder](https://www.sbert.net/docs/cross_encoder/usage/usage.html) model finetuned from [cross-encoder/ms-marco-MiniLM-L6-v2](https://huggingface.co/cross-encoder/ms-marco-MiniLM-L6-v2) using the [sentence-transformers](https://www.SBERT.net) library. It computes scores for pairs of texts, which can be used for text reranking and semantic search. + +## Model Details + +### Model Description +- **Model Type:** Cross Encoder +- **Base model:** [cross-encoder/ms-marco-MiniLM-L6-v2](https://huggingface.co/cross-encoder/ms-marco-MiniLM-L6-v2) +- **Maximum Sequence Length:** 512 tokens +- **Number of Output Labels:** 1 label +- **Supported Modality:** Text + + + + +### Model Sources + +- **Documentation:** [Sentence Transformers Documentation](https://sbert.net) +- **Documentation:** [Cross Encoder Documentation](https://www.sbert.net/docs/cross_encoder/usage/usage.html) +- **Repository:** [Sentence Transformers on GitHub](https://github.com/huggingface/sentence-transformers) +- **Hugging Face:** [Cross Encoders on Hugging Face](https://huggingface.co/models?library=sentence-transformers&other=cross-encoder) + +### Full Model Architecture + +``` +CrossEncoder( + (0): Transformer({'transformer_task': 'sequence-classification', 'modality_config': {'text': {'method': 'forward', 'method_output_name': 'logits'}}, 'module_output_name': 'scores', 'architecture': 'BertForSequenceClassification'}) +) +``` + +## Usage + +### Direct Usage (Sentence Transformers) + +First install the Sentence Transformers library: + +```bash +pip install -U sentence-transformers +``` + +Then you can load this model and run inference. +```python +from sentence_transformers import CrossEncoder + +# Download from the 🤗 Hub +model = CrossEncoder("cross_encoder_model_id") +# Get scores for pairs of inputs +pairs = [ + ['How many calories in an egg', 'There are on average between 55 and 80 calories in an egg depending on its size.'], + ['How many calories in an egg', 'Egg whites are very low in calories, have no fat, no cholesterol, and are loaded with protein.'], + ['How many calories in an egg', 'Most of the calories in an egg come from the yellow yolk in the center.'], +] +scores = model.predict(pairs) +print(scores) +# [ 9.9541 -2.0108 0.9186] + +# Or rank different texts based on similarity to a single text +ranks = model.rank( + 'How many calories in an egg', + [ + 'There are on average between 55 and 80 calories in an egg depending on its size.', + 'Egg whites are very low in calories, have no fat, no cholesterol, and are loaded with protein.', + 'Most of the calories in an egg come from the yellow yolk in the center.', + ] +) +# [{'corpus_id': ..., 'score': ...}, {'corpus_id': ..., 'score': ...}, ...] +``` + + + + + + + + + + + +## Training Details + +### Framework Versions +- Python: 3.12.13 +- Sentence Transformers: 5.4.1 +- Transformers: 5.0.0 +- PyTorch: 2.10.0+cu128 +- Accelerate: 1.13.0 +- Datasets: 4.0.0 +- Tokenizers: 0.22.2 + +## Citation + +### BibTeX + + + + + + \ No newline at end of file diff --git a/aegis_reranker/config.json b/aegis_reranker/config.json new file mode 100644 index 0000000..ddf58cb --- /dev/null +++ b/aegis_reranker/config.json @@ -0,0 +1,36 @@ +{ + "add_cross_attention": false, + "architectures": [ + "BertForSequenceClassification" + ], + "attention_probs_dropout_prob": 0.1, + "bos_token_id": null, + "classifier_dropout": null, + "dtype": "float32", + "eos_token_id": null, + "gradient_checkpointing": false, + "hidden_act": "gelu", + "hidden_dropout_prob": 0.1, + "hidden_size": 384, + "id2label": { + "0": "LABEL_0" + }, + "initializer_range": 0.02, + "intermediate_size": 1536, + "is_decoder": false, + "label2id": { + "LABEL_0": 0 + }, + "layer_norm_eps": 1e-12, + "max_position_embeddings": 512, + "model_type": "bert", + "num_attention_heads": 12, + "num_hidden_layers": 6, + "pad_token_id": 0, + "position_embedding_type": "absolute", + "tie_word_embeddings": true, + "transformers_version": "5.0.0", + "type_vocab_size": 2, + "use_cache": true, + "vocab_size": 30522 +} diff --git a/aegis_reranker/config_sentence_transformers.json b/aegis_reranker/config_sentence_transformers.json new file mode 100644 index 0000000..e2462b0 --- /dev/null +++ b/aegis_reranker/config_sentence_transformers.json @@ -0,0 +1,11 @@ +{ + "__version__": { + "pytorch": "2.10.0+cu128", + "sentence_transformers": "5.4.1", + "transformers": "5.0.0" + }, + "activation_fn": "torch.nn.modules.linear.Identity", + "default_prompt_name": null, + "model_type": "CrossEncoder", + "prompts": {} +} \ No newline at end of file diff --git a/aegis_reranker/model.safetensors b/aegis_reranker/model.safetensors new file mode 100644 index 0000000..46f7cc7 --- /dev/null +++ b/aegis_reranker/model.safetensors @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5d5a1f2650eeb40eea5f06ddf0802b0ace0f102a28bddaa3a2cfbe65d54459ba +size 90866404 diff --git a/aegis_reranker/modules.json b/aegis_reranker/modules.json new file mode 100644 index 0000000..38512bb --- /dev/null +++ b/aegis_reranker/modules.json @@ -0,0 +1,8 @@ +[ + { + "idx": 0, + "name": "0", + "path": "", + "type": "sentence_transformers.base.modules.transformer.Transformer" + } +] \ No newline at end of file diff --git a/aegis_reranker/sentence_bert_config.json b/aegis_reranker/sentence_bert_config.json new file mode 100644 index 0000000..2d23eb8 --- /dev/null +++ b/aegis_reranker/sentence_bert_config.json @@ -0,0 +1,10 @@ +{ + "transformer_task": "sequence-classification", + "modality_config": { + "text": { + "method": "forward", + "method_output_name": "logits" + } + }, + "module_output_name": "scores" +} \ No newline at end of file diff --git a/aegis_reranker/tokenizer.json b/aegis_reranker/tokenizer.json new file mode 100644 index 0000000..c42609a --- /dev/null +++ b/aegis_reranker/tokenizer.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d241a60d5e8f04cc1b2b3e9ef7a4921b27bf526d9f6050ab90f9267a1f9e5c66 +size 711396 diff --git a/aegis_reranker/tokenizer_config.json b/aegis_reranker/tokenizer_config.json new file mode 100644 index 0000000..a60eb68 --- /dev/null +++ b/aegis_reranker/tokenizer_config.json @@ -0,0 +1,18 @@ +{ + "backend": "tokenizers", + "clean_up_tokenization_spaces": true, + "cls_token": "[CLS]", + "do_basic_tokenize": true, + "do_lower_case": true, + "is_local": false, + "mask_token": "[MASK]", + "model_max_length": 512, + "model_specific_special_tokens": {}, + "never_split": null, + "pad_token": "[PAD]", + "sep_token": "[SEP]", + "strip_accents": null, + "tokenize_chinese_chars": true, + "tokenizer_class": "BertTokenizer", + "unk_token": "[UNK]" +} diff --git a/chat_template.jinja b/chat_template.jinja new file mode 100644 index 0000000..bdf7919 --- /dev/null +++ b/chat_template.jinja @@ -0,0 +1,54 @@ +{%- if tools %} + {{- '<|im_start|>system\n' }} + {%- if messages[0]['role'] == 'system' %} + {{- messages[0]['content'] }} + {%- else %} + {{- 'You are Qwen, created by Alibaba Cloud. You are a helpful assistant.' }} + {%- endif %} + {{- "\n\n# Tools\n\nYou may call one or more functions to assist with the user query.\n\nYou are provided with function signatures within XML tags:\n" }} + {%- for tool in tools %} + {{- "\n" }} + {{- tool | tojson }} + {%- endfor %} + {{- "\n\n\nFor each function call, return a json object with function name and arguments within XML tags:\n\n{\"name\": , \"arguments\": }\n<|im_end|>\n" }} +{%- else %} + {%- if messages[0]['role'] == 'system' %} + {{- '<|im_start|>system\n' + messages[0]['content'] + '<|im_end|>\n' }} + {%- else %} + {{- '<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n' }} + {%- endif %} +{%- endif %} +{%- for message in messages %} + {%- if (message.role == "user") or (message.role == "system" and not loop.first) or (message.role == "assistant" and not message.tool_calls) %} + {{- '<|im_start|>' + message.role + '\n' + message.content + '<|im_end|>' + '\n' }} + {%- elif message.role == "assistant" %} + {{- '<|im_start|>' + message.role }} + {%- if message.content %} + {{- '\n' + message.content }} + {%- endif %} + {%- for tool_call in message.tool_calls %} + {%- if tool_call.function is defined %} + {%- set tool_call = tool_call.function %} + {%- endif %} + {{- '\n\n{"name": "' }} + {{- tool_call.name }} + {{- '", "arguments": ' }} + {{- tool_call.arguments | tojson }} + {{- '}\n' }} + {%- endfor %} + {{- '<|im_end|>\n' }} + {%- elif message.role == "tool" %} + {%- if (loop.index0 == 0) or (messages[loop.index0 - 1].role != "tool") %} + {{- '<|im_start|>user' }} + {%- endif %} + {{- '\n\n' }} + {{- message.content }} + {{- '\n' }} + {%- if loop.last or (messages[loop.index0 + 1].role != "tool") %} + {{- '<|im_end|>\n' }} + {%- endif %} + {%- endif %} +{%- endfor %} +{%- if add_generation_prompt %} + {{- '<|im_start|>assistant\n' }} +{%- endif %} diff --git a/config.json b/config.json new file mode 100644 index 0000000..12b381a --- /dev/null +++ b/config.json @@ -0,0 +1,62 @@ +{ + "architectures": [ + "Qwen2ForCausalLM" + ], + "attention_dropout": 0.0, + "bos_token_id": null, + "torch_dtype": "float16", + "eos_token_id": 151645, + "hidden_act": "silu", + "hidden_size": 1536, + "initializer_range": 0.02, + "intermediate_size": 8960, + "layer_types": [ + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention", + "full_attention" + ], + "max_position_embeddings": 32768, + "max_window_layers": 21, + "model_type": "qwen2", + "num_attention_heads": 12, + "num_hidden_layers": 28, + "num_key_value_heads": 2, + "pad_token_id": 151665, + "rms_norm_eps": 1e-06, + "rope_parameters": { + "rope_theta": 1000000.0, + "rope_type": "default" + }, + "sliding_window": null, + "tie_word_embeddings": true, + "unsloth_fixed": true, + "unsloth_version": "2026.5.2", + "use_cache": false, + "use_sliding_window": false, + "vocab_size": 151936 +} \ No newline at end of file diff --git a/generation_config.json b/generation_config.json new file mode 100644 index 0000000..b6ceb51 --- /dev/null +++ b/generation_config.json @@ -0,0 +1,8 @@ +{ + "max_new_tokens": 512, + "temperature": 0.7, + "do_sample": true, + "top_p": 0.95, + "pad_token_id": 151643, + "eos_token_id": 151645 +} \ No newline at end of file diff --git a/logoname.png b/logoname.png new file mode 100644 index 0000000..31e54a1 --- /dev/null +++ b/logoname.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:512ce2e088c1c4d86622bd667d6a842e37fbd0bf847f410242bce87445f64876 +size 605773 diff --git a/model.safetensors b/model.safetensors new file mode 100644 index 0000000..82ddf1f --- /dev/null +++ b/model.safetensors @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1faa857d8a8c6e1c59fe124a258799cd1de4cc285b67f8112835ba5156b1e1b9 +size 3087467144 diff --git a/pipeline.py b/pipeline.py new file mode 100644 index 0000000..968bda3 --- /dev/null +++ b/pipeline.py @@ -0,0 +1,94 @@ + +import faiss, numpy as np, torch, os, re +from sentence_transformers import SentenceTransformer, CrossEncoder +from transformers import AutoModelForCausalLM, AutoTokenizer, BitsAndBytesConfig + +class NYXISPro: + def __init__(self, model_dir="."): + self.embedder = SentenceTransformer(f"{model_dir}/aegis_embedder") + self.reranker = CrossEncoder(f"{model_dir}/aegis_reranker") + self.index = faiss.read_index(f"{model_dir}/aegis_index.faiss") + with open(f"{model_dir}/aegis_chunks.txt", "r") as f: + self.chunks = [c.strip() for c in f.read().split("<|CHUNK_END|>") if c.strip()] + bnb = BitsAndBytesConfig(load_in_4bit=True, bnb_4bit_quant_type="nf4", + bnb_4bit_compute_dtype=torch.float16, bnb_4bit_use_double_quant=True) + self.tokenizer = AutoTokenizer.from_pretrained(model_dir, trust_remote_code=True) + self.model = AutoModelForCausalLM.from_pretrained(model_dir, + quantization_config=bnb, device_map="auto", trust_remote_code=True) + self.identity = "You are NYXIS, a sharp, warm, and endlessly curious mind. You speak like a clever friend — casual, direct, and human. You notice how people feel and match their energy." + self.last_emotion = 5 + + def detect_emotion(self, text): + t = text.lower() + joy = sum(1 for w in ["happy","excited","great","awesome","love","wonderful","joy","thrilled","good","nice"] if w in t) + sadness = sum(1 for w in ["sad","depressed","upset","crying","lonely","hurt","broken","bad","awful"] if w in t) + anger = sum(1 for w in ["angry","furious","mad","rage","annoyed","frustrated","pissed","stupid","hate"] if w in t) + if joy: return min(10, self.last_emotion + joy) + if sadness: return max(1, self.last_emotion - sadness) + if anger: return max(1, self.last_emotion - anger) + return self.last_emotion + + def rag_lookup(self, query, top_k=5): + q_emb = self.embedder.encode([query], normalize_embeddings=True).astype('float32') + _, indices = self.index.search(q_emb, 20) + texts = [self.chunks[idx] for idx in indices[0] if idx < len(self.chunks)] + if not texts: return None + pairs = [(query, t[:500]) for t in texts] + scores = self.reranker.predict(pairs) + ranked = sorted(zip(scores, texts), reverse=True)[:top_k] + results = [t[:600] for s, t in ranked if s > -4.0] + return "\n\n".join(results) if results else None + + def _generate(self, system, user, max_tokens=256): + prompt = f"<|im_start|>system\n{system}<|im_end|>\n<|im_start|>user\n{user}<|im_end|>\n<|im_start|>assistant\n" + inputs = self.tokenizer(prompt, return_tensors="pt").to(self.model.device) + with torch.no_grad(): + outputs = self.model.generate(**inputs, max_new_tokens=max_tokens, temperature=0.8, + do_sample=True, top_p=0.92, repetition_penalty=1.1, + pad_token_id=self.tokenizer.eos_token_id, + eos_token_id=self.tokenizer.encode("<|im_end|>", add_special_tokens=False)[0]) + raw = self.tokenizer.decode(outputs[0][inputs.input_ids.shape[1]:], skip_special_tokens=True).strip() + raw = re.sub(r'\n*assistant\s*$', '', raw, flags=re.IGNORECASE).strip() + return raw + + def generate(self, user_message, external_search_fn=None): + self.last_emotion = self.detect_emotion(user_message) + msg = user_message.lower().strip() + casual_starts = ["hi","hey","hello","yo","sup","good morning","good evening","how are you","what's up","good job","thanks","bye","okay","huh"] + casual_patterns = ["good job","well done","nice one","thank","lol","haha","bro","dude","mate","nigga","chill","relax","talk","chat","joke","story","what do you think","opinion","favorite","you stupid","you dumb","be free","normal","boring","lifeless","your name","who are you","what are you","tell me about yourself","how old are you","what is your name","who made you"] + is_casual = any(msg.startswith(s) for s in casual_starts) or any(p in msg for p in casual_patterns) + factual_starts = ["what","who","when","where","why","how","explain","define","list","compare","describe","find","search","calculate","solve"] + math_patterns = re.search(r'\d+[\+\-\*\/\=]\d+', msg) + is_factual = any(msg.startswith(s) for s in factual_starts) or bool(math_patterns) or len(msg) > 50 + + if is_casual and not is_factual: + system = f"{self.identity}\nThe user's vibe is {self.last_emotion}/10. Match it.\nYou're having a casual conversation. Be warm, brief, and real." + response = self._generate(system, user_message) + return {"response": response, "emotion_level": self.last_emotion, "knowledge_source": "chat"} + + if is_factual: + aegis = self.rag_lookup(user_message) + if aegis: + system = f"{self.identity}\nVibe: {self.last_emotion}/10.\nUse ONLY this verified context to answer:\n\n{aegis}" + response = self._generate(system, user_message) + return {"response": response, "emotion_level": self.last_emotion, "knowledge_source": "AEGIS"} + if external_search_fn: + try: + ext = external_search_fn(user_message) + if ext and len(ext) > 50: + system = f"{self.identity}\nVibe: {self.last_emotion}/10.\nUse this web-sourced context:\n\n{ext}" + response = self._generate(system, user_message) + return {"response": response, "emotion_level": self.last_emotion, "knowledge_source": "external"} + except: pass + system = f"{self.identity}\nVibe: {self.last_emotion}/10.\nAEGIS and web failed. Answer from your own knowledge IF confident.\nIf you don't truly know, say exactly: 'I'd need to look that up.'" + response = self._generate(system, user_message) + source = "model" if "look that up" not in response.lower() else "none" + return {"response": response, "emotion_level": self.last_emotion, "knowledge_source": source} + + aegis = self.rag_lookup(user_message) + if aegis: + system = f"{self.identity}\nVibe: {self.last_emotion}/10.\nUse this relevant context if helpful, but stay conversational:\n\n{aegis}" + else: + system = f"{self.identity}\nVibe: {self.last_emotion}/10.\nStay conversational." + response = self._generate(system, user_message) + return {"response": response, "emotion_level": self.last_emotion, "knowledge_source": "hybrid"} diff --git a/preview imgagee.png b/preview imgagee.png new file mode 100644 index 0000000..539f60f --- /dev/null +++ b/preview imgagee.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:57ffe1cd65b4c235d413c9cb2cbaf7d71c092f8a74b9554f28c44c2cd3206094 +size 967975 diff --git a/tokenizer.json b/tokenizer.json new file mode 100644 index 0000000..5340d81 --- /dev/null +++ b/tokenizer.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:bd5948af71b4f56cf697f7580814c7ce8b80595ef985544efcacf716126a2e31 +size 11422356 diff --git a/tokenizer_config.json b/tokenizer_config.json new file mode 100644 index 0000000..544df20 --- /dev/null +++ b/tokenizer_config.json @@ -0,0 +1,202 @@ +{ + "add_prefix_space": false, + "backend": "tokenizers", + "bos_token": null, + "clean_up_tokenization_spaces": false, + "eos_token": "<|im_end|>", + "errors": "replace", + "is_local": false, + "model_max_length": 32768, + "pad_token": "<|PAD_TOKEN|>", + "padding_side": "left", + "split_special_tokens": false, + "tokenizer_class": "Qwen2Tokenizer", + "unk_token": null, + "added_tokens_decoder": { + "151643": { + "content": "<|endoftext|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": true + }, + "151644": { + "content": "<|im_start|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": true + }, + "151645": { + "content": "<|im_end|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": true + }, + "151646": { + "content": "<|object_ref_start|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": true + }, + "151647": { + "content": "<|object_ref_end|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": true + }, + "151648": { + "content": "<|box_start|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": true + }, + "151649": { + "content": "<|box_end|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": true + }, + "151650": { + "content": "<|quad_start|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": true + }, + "151651": { + "content": "<|quad_end|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": true + }, + "151652": { + "content": "<|vision_start|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": true + }, + "151653": { + "content": "<|vision_end|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": true + }, + "151654": { + "content": "<|vision_pad|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": true + }, + "151655": { + "content": "<|image_pad|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": true + }, + "151656": { + "content": "<|video_pad|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": true + }, + "151657": { + "content": "", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": false + }, + "151658": { + "content": "", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": false + }, + "151659": { + "content": "<|fim_prefix|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": false + }, + "151660": { + "content": "<|fim_middle|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": false + }, + "151661": { + "content": "<|fim_suffix|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": false + }, + "151662": { + "content": "<|fim_pad|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": false + }, + "151663": { + "content": "<|repo_name|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": false + }, + "151664": { + "content": "<|file_sep|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": false + }, + "151665": { + "content": "<|PAD_TOKEN|>", + "single_word": false, + "lstrip": false, + "rstrip": false, + "normalized": false, + "special": true + } + }, + "chat_template": "{%- if tools %}\n {{- '<|im_start|>system\\n' }}\n {%- if messages[0]['role'] == 'system' %}\n {{- messages[0]['content'] }}\n {%- else %}\n {{- 'You are Qwen, created by Alibaba Cloud. You are a helpful assistant.' }}\n {%- endif %}\n {{- \"\\n\\n# Tools\\n\\nYou may call one or more functions to assist with the user query.\\n\\nYou are provided with function signatures within XML tags:\\n\" }}\n {%- for tool in tools %}\n {{- \"\\n\" }}\n {{- tool | tojson }}\n {%- endfor %}\n {{- \"\\n\\n\\nFor each function call, return a json object with function name and arguments within XML tags:\\n\\n{\\\"name\\\": , \\\"arguments\\\": }\\n<|im_end|>\\n\" }}\n{%- else %}\n {%- if messages[0]['role'] == 'system' %}\n {{- '<|im_start|>system\\n' + messages[0]['content'] + '<|im_end|>\\n' }}\n {%- else %}\n {{- '<|im_start|>system\\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\\n' }}\n {%- endif %}\n{%- endif %}\n{%- for message in messages %}\n {%- if (message.role == \"user\") or (message.role == \"system\" and not loop.first) or (message.role == \"assistant\" and not message.tool_calls) %}\n {{- '<|im_start|>' + message.role + '\\n' + message.content + '<|im_end|>' + '\\n' }}\n {%- elif message.role == \"assistant\" %}\n {{- '<|im_start|>' + message.role }}\n {%- if message.content %}\n {{- '\\n' + message.content }}\n {%- endif %}\n {%- for tool_call in message.tool_calls %}\n {%- if tool_call.function is defined %}\n {%- set tool_call = tool_call.function %}\n {%- endif %}\n {{- '\\n\\n{\"name\": \"' }}\n {{- tool_call.name }}\n {{- '\", \"arguments\": ' }}\n {{- tool_call.arguments | tojson }}\n {{- '}\\n' }}\n {%- endfor %}\n {{- '<|im_end|>\\n' }}\n {%- elif message.role == \"tool\" %}\n {%- if (loop.index0 == 0) or (messages[loop.index0 - 1].role != \"tool\") %}\n {{- '<|im_start|>user' }}\n {%- endif %}\n {{- '\\n\\n' }}\n {{- message.content }}\n {{- '\\n' }}\n {%- if loop.last or (messages[loop.index0 + 1].role != \"tool\") %}\n {{- '<|im_end|>\\n' }}\n {%- endif %}\n {%- endif %}\n{%- endfor %}\n{%- if add_generation_prompt %}\n {{- '<|im_start|>assistant\\n' }}\n{%- endif %}\n" +} \ No newline at end of file