Bürgi's Kunstweg is a set of algorithms developed by Jost Bürgi in the late 16th century. They are used to calculate sines to arbitrary precision.. Bürgi used these algorithms to calculate a Canon Sinuum, a sine table in increments of 2 arc seconds. It is believed that the table featured values accurate to eight sexagesimal places. Some authors have speculated that the table only covered the range from 0° to 45°, although there is no evidence supporting this claim. Such tables were crucial for maritime navigation. Johannes Kepler described the Canon Sinuum as the most precise sine table known at the time. Bürgi explained his algorithms in his work Fundamentum Astronomiae, which he presented to Emperor Rudolf II in 1592. The Kunstweg algorithm calculates sine values iteratively. In each step, the value of a cell is the sum of the two preceding cells in the same column. The final cell's value is halved before beginning the next iteration. Ultimately, the values in the last column are normalized. Accurate sine approximations are achieved after only a few iterations. In 2015, Menso Folkerts and coworkers demonstrated that this iterative process does indeed converge toward the true sine values. According to them this was the first step towards differential calculus.
Version space learning
Version space learning is a logical approach to machine learning, specifically binary classification. Version space learning algorithms search a predefined space of hypotheses, viewed as a set of logical sentences. Formally, the hypothesis space is a disjunction H 1 ∨ H 2 ∨ . . . ∨ H n {\displaystyle H_{1}\lor H_{2}\lor ...\lor H_{n}} (i.e., one or more of hypotheses 1 through n are true). A version space learning algorithm is presented with examples, which it will use to restrict its hypothesis space; for each example x, the hypotheses that are inconsistent with x are removed from the space. This iterative refining of the hypothesis space is called the candidate elimination algorithm, the hypothesis space maintained inside the algorithm, its version space. == The version space algorithm == In settings where there is a generality-ordering on hypotheses, it is possible to represent the version space by two sets of hypotheses: (1) the most specific consistent hypotheses, and (2) the most general consistent hypotheses, where "consistent" indicates agreement with observed data. The most specific hypotheses (i.e., the specific boundary SB) cover the observed positive training examples, and as little of the remaining feature space as possible. These hypotheses, if reduced any further, exclude a positive training example, and hence become inconsistent. These minimal hypotheses essentially constitute a (pessimistic) claim that the true concept is defined just by the positive data already observed: Thus, if a novel (never-before-seen) data point is observed, it should be assumed to be negative. (I.e., if data has not previously been ruled in, then it's ruled out.) The most general hypotheses (i.e., the general boundary GB) cover the observed positive training examples, but also cover as much of the remaining feature space without including any negative training examples. These, if enlarged any further, include a negative training example, and hence become inconsistent. These maximal hypotheses essentially constitute a (optimistic) claim that the true concept is defined just by the negative data already observed: Thus, if a novel (never-before-seen) data point is observed, it should be assumed to be positive. (I.e., if data has not previously been ruled out, then it's ruled in.) Thus, during learning, the version space (which itself is a set – possibly infinite – containing all consistent hypotheses) can be represented by just its lower and upper bounds (maximally general and maximally specific hypothesis sets), and learning operations can be performed just on these representative sets. After learning, classification can be performed on unseen examples by testing the hypothesis learned by the algorithm. If the example is consistent with multiple hypotheses, a majority vote rule can be applied. == Historical background == The notion of version spaces was introduced by Mitchell in the early 1980s as a framework for understanding the basic problem of supervised learning within the context of solution search. Although the basic "candidate elimination" search method that accompanies the version space framework is not a popular learning algorithm, there are some practical implementations that have been developed (e.g., Sverdlik & Reynolds 1992, Hong & Tsang 1997, Dubois & Quafafou 2002). A major drawback of version space learning is its inability to deal with noise: any pair of inconsistent examples can cause the version space to collapse, i.e., become empty, so that classification becomes impossible. One solution of this problem is proposed by Dubois and Quafafou that proposed the Rough Version Space, where rough sets based approximations are used to learn certain and possible hypothesis in the presence of inconsistent data.
Komodo (chess)
Komodo and Dragon by Komodo Chess (also known as Dragon or Komodo Dragon) are UCI chess engines developed by Komodo Chess, which is a part of Chess.com. The engines were originally authored by Don Dailey and GM Larry Kaufman. Dragon is a commercial chess engine, but Komodo is free for non-commercial use. Dragon is consistently ranked near the top of most major chess engine rating lists, along with Stockfish and Leela Chess Zero. == History == === Komodo === Komodo was derived from Don Dailey's former engine Doch in January 2010. The first multiprocessor version of Komodo was released in June 2013 as Komodo 5.1 MP. This version was a major rewrite and a port of Komodo to C++11. A single-processor version of Komodo (which won the CCT15 tournament in February earlier that year) was released as a stand-alone product shortly before the 5.1 MP release. This version, named Komodo CCT, was still based on the older C code, and was approximately 30 Elo stronger than the 5.1 MP version, as the latter was still undergoing massive code-cleanup work. With the release of Komodo 6 on October 4, 2013, Don Dailey announced that he was suffering from an acute form of leukaemia, and would no longer contribute to the future development of Komodo. On October 8, Don made an announcement on the Talkchess forum that Mark Lefler would be joining the Komodo team and would continue its development. Komodo TCEC was released on December 4, 2013. This was the same version that had won TCEC Season 5, and was the last with input from Don Dailey, to whom it was dedicated. Komodo 7 was released on May 21, 2014, adding Syzygy tablebase support. On May 24, 2018, Chess.com announced that it has acquired Komodo and that the Komodo team have joined Chess.com. The Komodo team is now called Komodo Chess. On December 17, 2018, Komodo Chess released Komodo 12.3 MCTS, a version of the Komodo 12.3 engine that uses Monte Carlo tree search instead of alpha–beta pruning/minimax. The last version, Komodo 14.3, was released on October 4, 2023. === Dragon === On November 9, 2020, Komodo Chess released Dragon by Komodo Chess 1.0, which features the use of efficiently updatable neural networks in its evaluation function. Dragon is derived from Komodo in the same way that Komodo was derived from Doch. Dragon is also called Komodo Dragon in certain tournaments such as the Top Chess Engine Championship and the World Computer Chess Championship (WCCC) but not in the Chess.com Computer Chess Championship (CCC). A Chess.com staff member named Dmitry Pervov joined the Dragon development team to write the NNUE code for Dragon, and Dietrich Kappe joined the Dragon development team to help Larry Kaufman and Mark Lefter train Dragon's neural networks. On March 17, 2023, Larry Kaufman announced that he and Mark Lefter have stepped down from Dragon development and from ownership of Komodo Chess, and that Chess.com have taken full control of Komodo Chess. As of March 17, 2023, Dietrich Kappe is the only person responsible for the development of Dragon, but Chess.com are looking for more programmers to help with Dragon development. The final version, Dragon 3.3, was released on October 4, 2023. == Competition results == === Komodo === Komodo has played in the ICT 2010 in Leiden, and further in the CCT12 and CCT14. Komodo had its first tournament success in 1999, when it won the CCT15 with a score of 6½/7. Komodo won both the World Computer Chess Championship and World Computer Software Championship in 2016. Komodo once again won the World Computer Chess Championship and World Blitz in 2017. In TCEC competition, Komodo was historically one of the strongest engines. In Season 4, it lost only eight out of its 53 games and managed to reach Stage 4 (Quarterfinals), against very strong competition which were running on eight cores (Komodo was running on a single processor). The next season, Komodo won the superfinal against Stockfish. The two engines jockeyed for the championship over the next few seasons: Stockfish won in Season 6, while Komodo won Seasons 7 and 8. Komodo failed to make the superfinal in Season 9, losing out to Houdini; but after Houdini was later disqualified for containing code plagiarized from Stockfish, Komodo was promoted to the runner-up. Komodo retrospectively won Season 10 in the same way. Starting from Season 11 however, Stockfish improved at a rate that left its rivals behind, crushing Komodo in Season 12 and 13. The advent of the neural network engine Leela Chess Zero meant Komodo has largely failed to qualify for the superfinal since, with a single exception in Season 22, when it lost to Stockfish. Although Komodo has not qualified for the superfinal, it has cemented itself as the third-strongest engine in the competition, finishing in that position for five of the last six seasons. ==== Chess.com Computer Chess Championship ==== === Dragon === ==== Chess.com Computer Chess Championship ==== ==== Top Chess Engine Championship ==== == Notable games == Komodo vs Hannibal, nTCEC - Stage 2b - Season 1, Round 4.1, ECO: A10, 1–0 Archived 2016-03-04 at the Wayback Machine Komodo sacrifices an exchange for positional gain. Gull vs Komodo, nTCEC - Stage 3 - Season 2, Round 2.2, ECO: E10, 0–1 Archived March 4, 2016, at the Wayback Machine Archived 2016-03-04 at the Wayback Machine
Karen Hao
Karen Hao (born in the United States c. 1993) is an American journalist and author. Currently a freelancer for publications like The Atlantic and previously a foreign correspondent based in Hong Kong for The Wall Street Journal and senior artificial intelligence editor at the MIT Technology Review, she is best known for her coverage on AI research, technology ethics and the social impact of AI. Hao also co-produced the podcast In Machines We Trust and wrote the newsletter The Algorithm. Previously, she worked at Quartz as a tech reporter and data scientist and was an application engineer at the first startup to spin out of X Development. Hao's writing has also appeared in Mother Jones, Sierra Magazine, The New Republic, and other publications. == Early life and education == Hao is the daughter of Chinese immigrant parents, and grew up in New Jersey. She is a native speaker of both English and Mandarin Chinese. She graduated from The Lawrenceville School in 2011. She then studied at the Massachusetts Institute of Technology (MIT), graduating with a B.S. in mechanical engineering and a minor in energy studies in 2015. == Career == Hao is known in the technology world for her coverage of new AI research findings and their societal and ethical impacts. Her writing has spanned research and issues regarding big tech data privacy, misinformation, deepfakes, facial recognition, and AI healthcare tools. In March 2021, Hao published a piece that uncovered previously unknown information about how attempts to combat misinformation by different teams at Facebook using machine learning were impeded and constantly at odds with Facebook's drive to grow user engagement. Upon its release, leaders at Facebook including Mike Schroepfer and Yann LeCun immediately criticized the piece through Twitter responses. AI researchers and AI ethics experts Timnit Gebru and Margaret Mitchell responded in support of Hao's writing and advocated for more change and improvement for all. Hao also co-produced the podcast In Machines We Trust, which discusses the rise of AI with people developing, researching, and using AI technologies. The podcast won the 2020 Front Page Award in investigative reporting. Hao has occasionally created data visualizations that have been featured in her work at the MIT Technology Review and elsewhere. In 2018, her "What is AI?" flowchart visualization was exhibited as an installation at the Museum of Applied Arts in Vienna. She has been an invited speaker at TEDxGateway, the United Nations Foundation, EmTech, WNPR, and many other conferences and podcasts. Her TEDx talk discussed the importance of democratizing how AI is built. In March 2022, she was hired by The Wall Street Journal to cover China technology and society, while being based in Hong Kong. She left the WSJ in 2023. In May 2025, Hao released the book Empire of AI: Dreams and Nightmares in Sam Altman's OpenAI. The book became a New York Times Bestseller and was named a Book of the Year by the Financial Times. In December 2025, after criticism from readers, Hao issued a correction to her book where she had previously overestimated the water consumption of a data center in Chile compared to the community's water consumption by factor of 1,000, due to an error in a government document. In April 2026 the book won the New York Public Library's Helen Bernstein Book Award for Excellence in Journalism. === Selected awards and honors === 2019 Webby Award nominee for best newsletter, as a writer of The Algorithm 2021 Front Page Award in investigative reporting, as a co-producer for In Machines We Trust 2021 Ambies Award nominee for best knowledge and science podcast, as a co-producer for In Machines We Trust 2021 Webby Award nominee for best technology podcast, as a co-producer for In Machines We Trust 2024 American Humanist Media Award 2025 TIME100 AI, named by TIME magazine as one of the 100 most influential people in artificial intelligence 2026 New York Public Library's Helen Bernstein Book Award for Excellence in Journalism 2026 Whiting Award in Non-fiction
Shane Legg
Shane Legg (born 1973 or 1974) is a machine learning researcher and entrepreneur. With Demis Hassabis and Mustafa Suleyman, he cofounded DeepMind Technologies (later bought by Google and now called Google DeepMind), and works there as the chief AGI scientist. He is also known for his academic work on artificial general intelligence, including his thesis supervised by Marcus Hutter. == Early life and education == Legg attended Rotorua Lakes High School in Rotorua, on New Zealand's North Island. He completed his undergraduate studies at Waikato University in 1996. Also in 1996, he obtained his MSc degree with a thesis entitled "Solomonoff Induction", with Cristian S. Calude at the University of Auckland. == Research interests == In the early 2000s, Legg re-introduced and popularized with Ben Goertzel the term "artificial general intelligence" (AGI), to describe an AI that can do practically any cognitive task a human can do. At that time, talking about AGI "would put you on the lunatic fringe". Legg is known for his concern of existential risk from AI, highlighted in 2011 in an interview on LessWrong and in 2023 he signed the statement on AI risk of extinction. == Career == Before his PhD and before cofounding DeepMind, Shane Legg worked at "a number of software development positions at private companies", including the "big data firm Adaptive Intelligence" and the startup WebMind founded by Ben Goertzel. === Research === Legg later obtained a PhD at the Dalle Molle Institute for Artificial Intelligence Research (IDSIA), a joint research institute of USI Università della Svizzera italiana and SUPSI. He worked on theoretical models of super intelligent machines (AIXI) with Marcus Hutter, and completed in 2008 his doctoral thesis entitled "Machine Super Intelligence". He then went on to complete a postdoctoral fellowship in finance at USI, and began a further fellowship at University College London's Gatsby Computational Neuroscience Unit. === DeepMind === Demis Hassabis and Shane Legg first met in 2009 at University College London, where Legg was a postdoctoral researcher. In 2010, Legg cofounded the start-up DeepMind Technologies along with Demis Hassabis and Mustafa Suleyman. DeepMind Technologies was bought in 2014 by Google. After the merge with Google Brain in 2023, the company is now known as Google DeepMind. According to a 2017 article, a significant part of his job as the chief scientist was to supervise recruitment, to decide where DeepMind should focus its efforts, and to lead DeepMind's AI safety work. As of July 2023, Legg works at Google DeepMind as the Chief AGI Scientist. == Awards and honors == Legg was awarded the $10,000 prize of the Singularity Institute for Artificial Intelligence for his PhD done in 2008. Legg was appointed Commander of the Order of the British Empire (CBE) in the 2019 Birthday Honours for services to the science and technology sector and to investment.
Adobe After Effects
Adobe After Effects is a digital effects, motion graphics, and compositing application developed by Adobe Inc.; it is used for animation and in the post-production process of film making, video games and television production. Among other things, After Effects can be used for keying, tracking, compositing, and animation. It also functions as a very basic non-linear editor, audio editor, and media transcoder. In 2019, the program won an Academy Award for scientific and technical achievement. == History == After Effects was originally created by David Herbstman, David Simons, Daniel Wilk, David M. Cotter, and Russell Belfer at the Company of Science and Art in Providence, Rhode Island. The first two versions of the software, 1.0 (January 1993) and 1.1, were released there by the company. CoSA with After Effects was acquired by Aldus Corporation in July 1993, which in turn was acquired by Adobe in 1994. Adobe acquired PageMaker as well. Adobe's first new release of After Effects was version 3.0. == Third-party integrations == After Effects functionality can be extended through a variety of third-party integrations. The most common integrations are: plug-ins, scripts, and extensions. === Plug-ins === Plug-ins are predominantly written in C or C++ and extend the functionality of After Effects, allowing for more advanced features such as particle systems, physics engines, 3D effects, and the ability to bridge the gap between After Effects and another. === Scripts === After Effects Scripts are a series of commands written in both JavaScript and the ExtendScript language. After Effects Scripts, unlike plug-ins, can only access the core functionality of After Effects. Scripts are often developed to automate repetitive tasks, to simplify complex After Effects features, or to perform complex calculations that would otherwise take a long time to complete. Scripts can also use some functionality not directly exposed through the graphical user interface. === Extensions === After Effects Extensions offer the ability to extend After Effects functionality through modern web development technologies like HTML5, and Node.js, without the need for C++. After Effects Extensions make use of Adobe's Common Extensibility Platform or CEP Panels, which means they can be built to interact with other Adobe CC apps.
Composite Capability/Preference Profiles
Composite Capability/Preference Profiles (CC/PP) is a specification for defining capabilities and preferences of user agents (also known as "delivery context"). The delivery context can be used to guide the process of tailoring content for a user agent. CC/PP is a vocabulary extension of the Resource Description Framework (RDF). The CC/PP specification is maintained by the W3C's Ubiquitous Web Applications Working Group (UWAWG) Working Group. == History == Composite Capability/Preference Profiles (CC/PP): Structure and Vocabularies 1.0 became a W3C recommendation on 15 January 2004. A "Last-Call Working-Draft" of CC/PP 2.0 was issued in April 2007