AI Grammar Tagalog

AI Grammar Tagalog — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Double descent

  Double descent in statistics and machine learning is the phenomenon where a model's error rate on the test set initially decreases with the number of parameters, then peaks, then decreases again. This phenomenon has been considered surprising, as it contradicts assumptions about overfitting in classical machine learning. The increase usually occurs near the interpolation threshold, where the number of parameters is the same as the number of training data points (the model is just large enough to fit the training data). Or, more precisely, it is the maximum number of samples on which the model/training procedure achieves approximately on average 0 training error. == History == Early observations of what would later be called double descent in specific models date back to 1989. The term "double descent" was coined by Belkin et. al. in 2019, when the phenomenon gained popularity as a broader concept exhibited by many models. The latter development was prompted by a perceived contradiction between the conventional wisdom that too many parameters in the model result in a significant overfitting error (an extrapolation of the bias–variance tradeoff), and the empirical observations in the 2010s that some modern machine learning techniques tend to perform better with larger models. == Theoretical models == Double descent occurs in linear regression with isotropic Gaussian covariates and isotropic Gaussian noise. A model of double descent at the thermodynamic limit has been analyzed using the replica trick, and the result has been confirmed numerically. A number of works have suggested that double descent can be explained using the concept of effective dimension: While a network may have a large number of parameters, in practice only a subset of those parameters are relevant for generalization performance, as measured by the local Hessian curvature. This explanation is formalized through PAC-Bayes compression-based generalization bounds, which show that less complex models are expected to generalize better under a Solomonoff prior.

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  WebCrow

  The WebCrow is a research project carried out at the Information Engineering Department of the University of Siena with the purpose of automatically solving crosswords. == The Project == The scientific relevance of the project can be understood considering that cracking crosswords requires human-level knowledge. Unlike chess and related games and there is no closed world configuration space. A first nucleus of technology, such as search engines, information retrieval, and machine learning techniques enable computers to enfold with semantics real-life concepts. The project is based on a software system whose major assumption is to attack crosswords making use of the Web as its primary source of knowledge. WebCrow is very fast and often thrashes human challengers in competitions, especially on multi language crossword schemes. A distinct feature of the WebCrow software system is to combine properly natural language processing (NLP) techniques, the Google web search engine, and constraint satisfaction algorithms from artificial intelligence to acquire knowledge and to fill the schema. The most important component of WebCrow is the Web Search Module (WSM), which implements a domain specific web based question answering algorithm. The way WebCrow approaches crosswords solving is quite different with respect to humans: Whereas we tend to first answer clues we are sure of and then proceed filling the schema by exploiting the already answered clues as hints, WebCrow uses two clearly distinct stages. In the first one, it processes all the clues and tries to answer them all: For each clue it finds many possible candidates and sorts them according to complex ranking models mainly based on a probability criteria. In the second stage, WebCrow uses constraint satisfaction algorithms to fill the grid with the overall most likely combination of clue answers. In order to interact with Google, first of all, WebCrow needs to compose queries on the basis of the given clues. This is done by query expansion, whose purpose is to convert the clue into a query expressed by a simplified and more appropriate language for Google. The retrieved documents are parsed so as to extract a list of word candidates that are congruent with the crossword length constraints. Crosswords can hardly be faced by using encyclopedic knowledge only, since many clues are wordplays or are otherwise purposefully very ambiguous. This enigmatic component of crosswords is faced by a massive use of database of solved crosswords, and by automatic reasoning on a properly organized knowledge base of wired rules. Last but not the least, the final constraint satisfaction step is very effective to fill the correct candidate, even though, unlike humans, the system can not rely on very high confidence on the correctness of the answer. == Competitions == WebCrow speed and effectiveness has been tested many times in man-machine competitions on Italian, English and multi-language crosswords The outcome of the tests is that WebCrow can successfully compete with average human players on single language schemes and reaches expert level performance in multi-language crosswords. However, WebCrow has not reached expert level in single-language crosswords, yet. === ECAI-06 Competition === On August 30, 2006, at the European Conference on Artificial Intelligence (ECAI2006), 25 conference attendees and 53 internet connected crosswords lovers, competed with WebCrow in an official challenge organized within the conference program. The challenge consisted in 5 different crosswords (2 in Italian, 2 in English and one multi-language in Italian and English) and 15 minutes were assigned for each crossword. WebCrow ranked 21 out of 74 participants in the Italian competition, and won both the bilingual and English competitions. === Other Competitions === Several competitions have been held in Florence, Italy within the Creativity Festival in December 2006, and another official conference competition took place in Hyderabad, India in January 2007, within the International Conference of Artificial Intelligence, where it ranked second out of 25 participants.

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  2024 Abu Dhabi Autonomous Racing League

  On 27 April 2024, the inaugural race of the Abu Dhabi Autonomous Racing League was held at the Yas Marina Circuit in Abu Dhabi. The race, originally scheduled to last eight laps, was ultimately shortened to six laps due to various complications, including subpar performance. It involved four self-driving race cars, only two of which – German cars Hailey and Constructor AI – finished the race; the other two did not finish. == Background == === Abu Dhabi Autonomous Racing League (A2RL) === The A2RL is an autonomous racing championship based in Abu Dhabi and organized by ASPIRE, part of the Advanced Technology Research Council. It is one of two active autonomous car racing championships, the second being the US-based Indy Autonomous Challenge. Unlike the IAC, which primarily focuses on time trials, simulated races, and challenges for teams, the A2RL's car races are closer to a standard grand prix formula race format. Both use Dallara-supplied racecars; the IAC uses the AV-24 chassis derived from Indy NXT's IL-15, while the A2RL chassis is designated EAV-24 and is derived from the SF-23 chassis used in Japanese Super Formula races. === Entrants === In total, eight teams were part of the A2RL in 2024, but only four would compete in the race proper. The list of teams in 2024 is: Fly Eagle (China/UAE) Code19 Racing (United States) Constructor University (Germany) Kinetiz (Singapore/UAE) Humda Lab (Hungary) PoliMove (Italy) Unimore (Italy) Technical University of Munich (Germany) Most teams come from universities and many, such as PoliMove and TUM, already have experience with autonomous racing, primarily from competing in the IAC. All teams had two months to code and test their AIs. Unlike most international open-wheel racing tournaments, such as Formula 1 or Formula E, no free practice sessions were undertaken. === TII Pre-race demonstration === Prior to the race itself, a mock 1v1 duel between former F1 driver Danill Kvyat and a self-driving car from the non-competing TII Racing team took place; the autonomous car was green and had number 01, while Kvyat's car was red and had number 00. Kvyat spent most of the duel in the pits. Kvyat himself said: "I'm not racing autonomous cars here. It won't be a flat-out race". == Qualifying == === Qualifying report === As only four of the eight entrants would compete in the main event, qualifying time trials were held to determine the four main race competitors, as well as their positions in the grid. Only the cars with the four best lap times over three time trial sessions held on Friday and Saturday would qualify. Multiple errors and setbacks occurred during qualifying. In the first session, Maveric AI, Code19's car, left the track and stopped just after turn 14 due to connectivity issues. Fly Eagle's car, Feiying, had multiple upsets; at one point, Feiying ran into localization issues and began swerving left and right before stopping just before turn 10. Later, Feiying swerved again and nearly hit the wall at the back straight, near the support pits, due to further localization issues. Sparkz, the Kinetiz team's car, swerved and crashed into the wall near yacht berths 51-56 after turn 11, damaging the front right wheel's axle and partially detaching the forward wings. Sparkz would be the only car to not have a set time at the end of the time trials. PoliMove car Eva braked hard without warning at the straight, the LED status indicator turning off, suggesting the AI computer had a system crash or shut itself down. After the sun went down, during the second session, Hailey, the car from the TUM team, went off-track after turn 9 and stopped, its status indicator flashing red, meaning Hailey's AI disengaged itself. Eva had further issues, once again braking hard and spinning out into turn 1. Later, the same thing happened to Feiying; it later swerved left and right and stopped due to further localization issues. The morning after, during the third and final session, Hailey went off-track after turn 5, and were unable to regain the pole position. === Qualifying classification === == Attack/Defend challenge == === Attack/Defend challenge report === In this part of the event, cars would be put on a series of 1v1 duels to see how well they could defend their position or attack to gain one higher. During one such duel, an incident occurred where Hailey rear-ended Eva, sending both off the track and prematurely ending the duel. The challenge was otherwise uneventful. === Attack/Defend challenge results === == Main race == === Race report === Eventually, at around 20:30 Gulf Standard Time on the night of 27 April, the main event (termed the "Grand Final" on-stream) would begin. The starting order was Eva first, Gianna second, Hailey third, and Constructor AI last. The race began with a rolling start. As a safety measure, the first two laps were conducted under virtual safety car (VSC) to make sure the cars stayed together, making them de facto formation laps, even if they counted towards race distance. However, Hailey ended up stopping at the final turn and strayed too far from the cars ahead, and as a result, the VSC conditions were extended for another lap. According to the livestream's on-screen graphics, Hailey was upwards of one minute and 22.3 seconds behind Gianna after the former started moving again. On lap 4, halfway through the planned race, and with Hailey more than 30 seconds behind Gianna, the VSC was lifted, and the green flag finally dropped. At first, the two Italian cars were leading the pack, Eva was the race leader with Gianna 3.2 seconds behind, however, as it entered the chicane, Eva hit the brakes and spun out, with Gianna briefly stopping as it passed Eva. Eva's spin automatically triggered a full-course yellow flag. Normally, under yellow flag conditions, overtaking is not permitted, but with Eva stopped and being moved off the track, it was theoretically permitted to overtake Eva. However, presumably due to an oversight in the AI's code, the cars assumed overtaking Eva, despite being off the track, was not permitted. As a result, both Gianna and Constructor AI stopped as they did not want to overtake Eva due to the yellow flag, with Hailey following suit as it approached. Constructor AI's status indicator was solid red, suggesting the AI had disengaged; however, Gianna's status indicator remained solid purple, showing the AI was still in control. Eva's status indicator was also solid purple, but was soon flashing green, suggesting the AI had disengaged but was ready to take control again. With all cars stalled, and Eva being off the track, the race was effectively red-flagged and suspended. Hailey, Gianna, and Constructor AI drove themselves back to their team's pits; Eva did not, it was towed to the main pits on a flatbed truck. Constructor was the first to arrive at the pits, followed by Gianna and Hailey, in that order. This incident, combined with loss of internet connection, led to Eva retiring - it did not finish the race. Eventually, it was decided to resume the race. With Eva retired, the restart order was Gianna first, Hailey second, and Constructor AI third. The race was also shortened - from eight laps to six. With lap 5 under full-course yellow, this meant all three remaining teams would effectively restart the race on the sixth and final lap. The trio left the pits at 22:25 Gulf Standard Time, and the race resumed two minutes later. At first, Gianna was winning with Hailey 2.6 seconds behind, but then Gianna stopped on turn 5, giving Hailey the lead. Constructor AI also overtook Gianna, but not without briefly stopping. Gianna remained stopped, its status indicator solid red - it did not finish either. With both Italian teams out of the picture, Hailey finished first and won A2RL 2024, with Constructor AI finishing second, 27.2 seconds behind. === Final race classification ===

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  Evolutionary computation

  Evolutionary computation (EC) from computer science is a family of algorithms for global optimization inspired by biological evolution, and a subfield of computational intelligence and soft computing studying these algorithms. In technical terms, they are a family of population-based trial and error problem solvers with a metaheuristic or stochastic optimization character. In evolutionary computation, an initial set of candidate solutions is generated and iteratively updated. Each new generation is produced by stochastically removing less desired solutions, and introducing small random changes as well as, depending on the method, mixing parental information. In biological terminology, a population of solutions is subjected to natural selection (or artificial selection), mutation and possibly recombination. These biological functions serve as role models for the genetic operators - mutation, crossover, and selection - used in the EC procedures. As a result, the population will gradually evolve to increase in fitness, in this case the chosen fitness function of the algorithm. Evolutionary computation techniques can produce highly optimized solutions in a wide range of problem settings, making them popular in computer science. Many variants and extensions exist, suited to more specific families of problems and data structures. Evolutionary computation is also sometimes used in evolutionary biology as an in silico experimental procedure to study common aspects of general evolutionary processes. == History == The concept of mimicking evolutionary processes to solve problems originates before the advent of computers, such as when Alan Turing proposed a method of genetic search in 1948 . Turing's B-type u-machines resemble primitive neural networks, and connections between neurons were learnt via a sort of genetic algorithm. His P-type u-machines resemble a method for reinforcement learning, where pleasure and pain signals direct the machine to learn certain behaviors. However, Turing's paper went unpublished until 1968, and he died in 1954, so this early work had little to no effect on the field of evolutionary computation that was to develop. Evolutionary computing as a field began in earnest in the 1950s and 1960s. There were several independent attempts to use the process of evolution in computing at this time, which developed separately for roughly 15 years. Three branches emerged in different places to attain this goal: evolution strategies, evolutionary programming, and genetic algorithms. A fourth branch, genetic programming, eventually emerged in the early 1990s. These approaches differ in the method of selection, the permitted mutations, and the representation of genetic data. By the 1990s, the distinctions between the historic branches had begun to blur, and the term 'evolutionary computing' was coined in 1991 to denote a field that exists over all four paradigms. In 1962, Lawrence J. Fogel initiated the research of Evolutionary Programming in the United States, which was considered an artificial intelligence endeavor. In this system, finite state machines are used to solve a prediction problem: these machines would be mutated (adding or deleting states, or changing the state transition rules), and the best of these mutated machines would be evolved further in future generations. The final finite state machine may be used to generate predictions when needed. The evolutionary programming method was successfully applied to prediction problems, system identification, and automatic control. It was eventually extended to handle time series data and to model the evolution of gaming strategies. In 1964, Ingo Rechenberg and Hans-Paul Schwefel introduce the paradigm of evolution strategies in Germany. Since traditional gradient descent techniques produce results that may get stuck in local minima, Rechenberg and Schwefel proposed that random mutations (applied to all parameters of some solution vector) may be used to escape these minima. Child solutions were generated from parent solutions, and the more successful of the two was kept for future generations. This technique was first used by the two to successfully solve optimization problems in fluid dynamics. Initially, this optimization technique was performed without computers, instead relying on dice to determine random mutations. By 1965, the calculations were performed wholly by machine. John Henry Holland introduced genetic algorithms in the 1960s, and it was further developed at the University of Michigan in the 1970s. While the other approaches were focused on solving problems, Holland primarily aimed to use genetic algorithms to study adaptation and determine how it may be simulated. Populations of chromosomes, represented as bit strings, were transformed by an artificial selection process, selecting for specific 'allele' bits in the bit string. Among other mutation methods, interactions between chromosomes were used to simulate the recombination of DNA between different organisms. While previous methods only tracked a single optimal organism at a time (having children compete with parents), Holland's genetic algorithms tracked large populations (having many organisms compete each generation). By the 1990s, a new approach to evolutionary computation that came to be called genetic programming emerged, advocated for by John Koza among others. In this class of algorithms, the subject of evolution was itself a program written in a high-level programming language (there had been some previous attempts as early as 1958 to use machine code, but they met with little success). For Koza, the programs were Lisp S-expressions, which can be thought of as trees of sub-expressions. This representation permits programs to swap subtrees, representing a sort of genetic mixing. Programs are scored based on how well they complete a certain task, and the score is used for artificial selection. Sequence induction, pattern recognition, and planning were all successful applications of the genetic programming paradigm. Many other figures played a role in the history of evolutionary computing, although their work did not always fit into one of the major historical branches of the field. The earliest computational simulations of evolution using evolutionary algorithms and artificial life techniques were performed by Nils Aall Barricelli in 1953, with first results published in 1954. Another pioneer in the 1950s was Alex Fraser, who published a series of papers on simulation of artificial selection. As academic interest grew, dramatic increases in the power of computers allowed practical applications, including the automatic evolution of computer programs. Evolutionary algorithms are now used to solve multi-dimensional problems more efficiently than software produced by human designers, and also to optimize the design of systems. == Techniques == Evolutionary computing techniques mostly involve metaheuristic optimization algorithms. Broadly speaking, the field includes: Agent-based modeling Ant colony optimization Particle swarm optimization Swarm intelligence Artificial immune systems Artificial life Digital organism Cultural algorithms Differential evolution Dual-phase evolution Estimation of distribution algorithm Evolutionary algorithm Genetic algorithm Evolutionary programming Genetic programming Gene expression programming Grammatical evolution Evolution strategy Learnable evolution model Learning classifier system Memetic algorithms Neuroevolution Self-organization such as self-organizing maps, competitive learning Over recent years many dubious algorithms have been proposed, that are often just copies of existing algorithms (frequently Particle Swarm Optimization), where only the metaphor changed, but the algorithm itself is not new at all. A thorough catalogue with many of these dubious algorithms has been published in the Evolutionary Computation Bestiary. It is also important to note that many of these dubiously 'novel' algorithms have poor experimental validation. == Evolutionary algorithms == Evolutionary algorithms form a subset of evolutionary computation in that they generally only involve techniques implementing mechanisms inspired by biological evolution such as reproduction, mutation, recombination and natural selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the cost function determines the environment within which the solutions "live" (see also fitness function). Evolution of the population then takes place after the repeated application of the above operators. In this process, there are two main forces that form the basis of evolutionary systems: Recombination (e.g. crossover) and mutation create the necessary diversity and thereby facilitate novelty, while selection acts as a force increasing quality. Many aspects of such an evolutionary process are stochastic. Changed pieces of information due to recombination and mutati

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  Smart data capture

  Smart data capture (SDC), also known as 'intelligent data capture' or 'automated data capture', describes the branch of technology concerned with using computer vision techniques like optical character recognition (OCR), barcode scanning, object recognition and other similar technologies to extract and process information from semi-structured and unstructured data sources. IDC characterize smart data capture as an integrated hardware, software, and connectivity strategy to help organizations enable the capture of data in an efficient, repeatable, scalable, and future-proof way. Data is captured visually from barcodes, text, IDs and other objects - often from many sources simultaneously - before being converted and prepared for digital use, typically by artificial intelligence-powered software. An important feature of SDC is that it focuses not just on capturing data more efficiently but serving up easy-to-access, actionable insights at the instant of data collection to both frontline and desk-based workers, aiding decision-making and making it a two-way process. Smart data capture automates and accelerates capture, applying insights in real time and automating processes based on extracted input. Smart data capture is designed to be repeatable and scalable to reduce low-level manual tasks and eliminate human error. To achieve this goal, smart data capture solutions are often made available using specialist software installed on commodity hardware such as smartphones. However, some solutions may rely on specialized hardware such as dedicated scanning devices, wearables or shop floor robots. == Differences from OCR == Optical character recognition applications are typically concerned with the actual data capture process; they are intended to faithfully reproduce text, words, letters and symbols from a printed document. Smart data capture is multimodal, capable of extracting data from a wider range of semi-structured and unstructured sources, going beyond basic text recognition to offer a wider scope of applications. By extending functionality to provide actionable insights at the point of capture, SDC is also a two-way process (capture-display), while OCR is more commonly one-way (capture only), primarily used for data input. Smart data capture solutions typically have two parts: Data capture (which includes OCR, barcode scanning, object recognition) Functionality that then uses this data to provide actionable insights at the point of capture. == Applications == Smart data capture can be applied to almost any industry and application that requires visual information capture and interpretation. This may include: Retail Warehouse inventory control Logistics, handling and shipping Manufacturing Field service Healthcare Transport and travel Fraud detection

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  Paranoia (role-playing game)

  Paranoia is a dystopian science-fiction tabletop role-playing game originally designed and written by Greg Costikyan, Dan Gelber, and Eric Goldberg, and first published in 1984 by West End Games. Since 2004 the game has been published under license by Mongoose Publishing. The game won the Origins Award for Best Roleplaying Rules of 1984 and was inducted into the Origins Awards Hall of Fame in 2007. Paranoia is notable among tabletop games for being more competitive than co-operative, with players encouraged to betray one another for their own interests, as well as for keeping a light-hearted, tongue in cheek tone despite its dystopian setting. Several editions of the game have been published since the original version, and the franchise has spawned several spin-offs, novels and comic books based on the game. == Premise == The game is set in a dystopian future city controlled by the Computer (also known as "Friend Computer"), and where information (including the game rules) are restricted by color-coded "security clearance". Player characters are initially enforcers of the Computer's authority known as Troubleshooters, and are given missions to seek out and eliminate threats to the Computer's control. They are also part of prohibited underground movements, and have secret objectives including theft from and murder of other player characters. == Tone == Paranoia is a humorous role-playing game set in a dystopian future along the lines of Nineteen Eighty-Four, Brave New World, Logan's Run, and THX 1138; however, the tone of the game is rife with black humor, frequently tongue-in-cheek rather than dark and heavy. Most of the game's humor is derived from the players' (usually futile) attempts to complete their assignment while simultaneously adhering to the Computer's arbitrary, contradictory and often nonsensical security directives. The Paranoia rulebook is unusual in a number of ways; demonstrating any knowledge of the rules is forbidden, and most of the rulebook is written in an easy, conversational tone that often makes fun of the players and their characters, while occasionally taking digs at other notable role-playing games. === Setting === The game's main setting is an immense, futuristic city called Alpha Complex. Alpha Complex is controlled by the Computer, a civil service AI construct (a literal realization of the "Influencing Machine" that some schizophrenics fear). The Computer serves as the game's principal antagonist, and fears a number of threats to its 'perfect' society, such as the Outdoors, mutants, and secret societies (especially Communists). To deal with these threats, the Computer employs Troubleshooters, whose job is to go out, find trouble, and shoot it. Player characters are usually Troubleshooters, although later game supplements have allowed the players to take on other roles, such as High-Programmers of Alpha Complex. The player characters frequently receive mission instructions from the Computer that are incomprehensible, self-contradictory, or obviously fatal if adhered to, and side-missions (such as Mandatory Bonus Duties) that conflict with the main mission. Failing a mission generally results in termination of the player character, but succeeding can just as often result in the same fate, after being rewarded for successfully concluding the mission. They are issued equipment that is uniformly dangerous, faulty, or "experimental" (i.e., almost certainly dangerous and faulty). Additionally, each player character is generally an unregistered mutant and a secret society member (which are both termination offenses in Alpha Complex), and has a hidden agenda separate from the group's goals, often involving stealing from or killing teammates. Thus, missions often turn into a comedy of errors, as everyone on the team seeks to double-cross everyone else while keeping their own secrets. The game's manual encourages suspicion between players, offering several tips on how to make the gameplay as paranoid as possible. Every player's character is assigned six clones, known as a six-pack, which are used to replace the preceding clone upon his or her death. The game lacks a conventional health system; most wounds the player characters can suffer are assumed to be fatal. As a result, Paranoia allows characters to be routinely killed, yet the player can continue instead of leaving the game. This easy spending of clones tends to lead to frequent firefights, gruesome slapstick, and the horrible yet humorous demise of most if not all of the player character's clone family. Additional clones can be purchased if one gains sufficient favour with the Computer. === Security clearances === Paranoia features a security clearance system based on colors of the visible spectrum which heavily restricts what the players can and cannot legally do; everything from corridors to food and equipment have security restrictions. The lowest rating is Infrared, but the lowest playable security clearance is Red; the game usually begins with the characters having just been promoted to Red grade. Interfering with anything which is above that player's clearance carries significant risk. The full order of clearances from lowest to highest is Infrared (visually represented by black), Red, Orange, Yellow, Green, Blue, Indigo, Violet, and Ultraviolet (visually represented by white). Within the game, Infrared-clearance citizens live dull lives of mindless drudgery and are heavily medicated, while higher clearance characters may be allowed to demote or even summarily execute those of a lower rank and those with Ultraviolet clearance are almost completely unrestricted and have a great deal of access to the Computer; they are the only citizens that may (legally) access and modify the Computer's programming, and thus Ultraviolet citizens are also referred to as "High Programmers". Security clearance is not related to competence but is instead the result of the Computer's often insane and unjustified calculus of trust concerning a citizen. It is suggested that it may in fact be the High Programmers' meddling with The Computer's programming that resulted in its insanity. === Secret societies === In the game, secret societies tend to be based on sketchy and spurious knowledge of historical matters. For example, previous editions included societies such as the "Seal Club" that idolizes the Outdoors but is unsure what plants and animals actually look like. Other societies include the Knights of the Circular Object (based on the Knights of the Round Table), the Trekkies, and the First Church of Christ Computer Programmer. In keeping with the theme of paranoia, many secret societies have spies or double agents in each other's organizations. The first edition also included secret societies such as Programs Groups (the personal agents and spies of the High Programmers at the apex of Alpha Complex society) and Spy For Another Alpha Complex. The actual societies which would be encountered in a game depends on the play style; some societies are more suited for more light-hearted games (Zap-style, or the lighter end of Classic), whereas others represent a more serious threat to Alpha Complex and are therefore more suitable for Straight or the more dark sort of Classic games. == Publication history == Six editions have been published. Three of these were published by West End Games — the first, second, and fifth editions — whereas the later three editions (Paranoia XP, the 25th Anniversary edition and the "Red Clearance" edition) were published by Mongoose Publishing. In addition to these six published editions, it is known that West End Games were working on a third edition — to replace the poorly received fifth edition — in the late 1990s, but their financial issues would prevent this edition from being published, except for being included in one tournament adventure. === First edition === The first edition, was written by Greg Costikyan, Dan Gelber, and Eric Goldberg, and published in 1984 by West End Games. In 1985, this edition of Paranoia won the Origins Award for Best Roleplaying Rules of 1984. This edition, while encouraging dark humour in-game, took a fairly serious dystopian tone; the supplements and adventures released to accompany it emphasised the lighter side, however, establishing the freewheeling mix of slapstick, intra-team backstabbing and satire that is classically associated with a game of Paranoia. === Second edition === The second edition, is credited to Costikyan, Gelber, Goldberg, Ken Rolston, and Paul Murphy, was published in 1987 by West End Games. This edition can be seen as a response to the natural development of the line towards a rules-light, fast and entertaining play style. Here, the humorous possibilities of life in a paranoid dystopia are emphasised, and the rules are simplified. ==== Metaplot and the second edition ==== Many of the supplements released for the second edition fall into a story arc set up by new writers and line editors

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  Ghost in the Shell

  Ghost in the Shell is a Japanese cyberpunk military science fiction media franchise that began with the eponymous manga series, written and illustrated by Masamune Shirow. The manga, first serialized from 1989 to 1991, is set in the mid-21st-century and follows the fictional counter-cyberterrorist organization Public Security Section 9, led by protagonist Major Motoko Kusanagi. Animation studio Production I.G has produced several anime adaptations of the series. These include the 1995 film of the same name and its 2004 sequel, Ghost in the Shell 2: Innocence; the 2002 television series Ghost in the Shell: Stand Alone Complex and its 2020 follow-up, Ghost in the Shell: SAC_2045; and the Ghost in the Shell: Arise original video animation series. In addition, an American-produced live-action film was released in March 2017. == Overview == === Title === The original editor Koichi Yuri says: At first, Ghost in the Shell came from Shirow, but when Yuri asked for "something more flashy", Shirow came up with "攻殻機動隊 Koukaku Kidou Tai (Shell Squad)" for Yuri. But Shirow was attached to including "Ghost in the Shell" as well even if in smaller type. === Setting === Primarily set in the mid-twenty-first century in the fictional Japanese city of Niihama, Niihama Prefecture (新浜県新浜市, Niihama-ken Niihama-shi), otherwise known as New Port City (ニューポートシティ, Nyū Pōto Shiti), the manga and the many anime adaptations follow the members of Public Security Section 9, a task-force consisting of various professionals skilled at solving and preventing crime, mostly with some sort of police background. Political intrigue and counter-terrorism operations are standard fare for Section 9, but the various actions of corrupt officials, companies, and cyber-criminals in each scenario are unique and require the diverse skills of Section 9's staff to prevent a series of incidents from escalating. In this post-cyberpunk iteration of a possible future, computer technology has advanced to the point that many members of the public possess cyberbrains, technology that allows them to interface their biological brain with various networks. The level of cyberization varies from simple minimal interfaces to almost complete replacement of the brain with cybernetic parts, in cases of severe trauma. This can also be combined with various levels of prostheses, with a fully prosthetic body enabling a person to become a cyborg. The main character of Ghost in the Shell, Major Motoko Kusanagi, is such a cyborg, having had a terrible accident befall her as a child that ultimately required her to use a full-body prosthesis to house her cyberbrain. This high level of cyberization, however, opens the brain up to attacks from highly skilled hackers, with the most dangerous being those who will hack a person to bend to their whims. == Media == === Literature === ==== Original manga ==== The original Ghost in the Shell manga ran in Japan from April 1989 to November 1990 in Kodansha's manga anthology Young Magazine, and was released in a tankōbon volume on October 2, 1991. Ghost in the Shell 2: Man-Machine Interface followed in 1997 for nine issues in Young Magazine, and was collected in the Ghost in the Shell: Solid Box on December 1, 2000. Then a standard version with modifications and new pages was published on June 26, 2001. Four stories from Man-Machine Interface that were not released in tankobon format from previous releases were later collected in Ghost in the Shell 1.5: Human-Error Processor, and published by Kodansha on July 17, 2003. Several art books have also been published for the manga. === Films === ==== Animated films ==== Two animated films based on the original manga have been released, both directed by Mamoru Oshii and animated by Production I.G. Ghost in the Shell was released in 1995 and follows the "Puppet Master" storyline from the manga. It was re-released in 2008 as Ghost in the Shell 2.0 with new audio and updated 3D computer graphics in certain scenes. Innocence, otherwise known as Ghost in the Shell 2: Innocence, was released in 2004, with its story based on a chapter from the first manga. ==== Live-action film ==== In 2008, DreamWorks and producer Steven Spielberg acquired the rights to a live-action film adaptation of the original Ghost in the Shell manga. On January 24, 2014, Rupert Sanders was announced as director, with a screenplay by William Wheeler. In April 2016, the full cast was announced, which included Juliette Binoche, Chin Han, Lasarus Ratuere and Kaori Momoi, and Scarlett Johansson in the lead role; the casting of Johansson drew accusations of whitewashing. Principal photography on the film began on location in Wellington, New Zealand, on February 1, 2016. Filming wrapped in June 2016. Ghost in the Shell premiered in Tokyo on March 16, 2017, and was released in the United States on March 31, 2017, in 2D, 3D and IMAX 3D. It received mixed reviews, with praise for its visuals and Johansson's performance but criticism for its script. === Television === ==== Stand Alone Complex TV series, film and ONA ==== In 2002, Ghost in the Shell: Stand Alone Complex premiered on Animax, presenting a new telling of Ghost in the Shell independent from the original manga, focusing on Section 9's investigation of the Laughing Man hacker. It was followed in 2004 by a second season titled Ghost in the Shell: S.A.C. 2nd GIG, which focused on the Individual Eleven terrorist group. The primary storylines of both seasons were compressed into OVAs broadcast as Ghost in the Shell: Stand Alone Complex The Laughing Man in 2005 and Ghost in the Shell: Stand Alone Complex Individual Eleven in 2006. Also in 2006, Ghost in the Shell: Stand Alone Complex - Solid State Society, featuring Section 9's confrontation with a hacker known as the Puppeteer, was broadcast, serving as a finale to the anime series. The extensive score for the series and its films was composed by Yoko Kanno. On April 7, 2017, Kodansha and Production I.G announced that Kenji Kamiyama and Shinji Aramaki would be co-directing a new Kōkaku Kidōtai anime production. On December 7, 2018, it was reported by Netflix that they had acquired the worldwide streaming rights to the original net animation (ONA) anime series, titled Ghost in the Shell: SAC_2045, and that it would premiere on April 23, 2020. The series is in 3DCG and Sola Digital Arts collaborated with Production I.G on the project. Ilya Kuvshinov handled character designs. The series had two seasons of 12 episodes each. In addition to the anime, a series of published books, two separate manga adaptations, and several video games for consoles and mobile phones have been released for Stand Alone Complex. ==== Arise OVA, TV series and film ==== In 2013, a new iteration of the series titled Ghost in the Shell: Arise premiered, taking an original look at the Ghost in the Shell world, set before the original manga. It was released as a series of four original video animation (OVA) episodes (with limited theatrical releases) from 2013 to 2014, then recompiled as a 10-episode television series under the title of Kōkaku Kidōtai: Arise - Alternative Architecture. An additional fifth OVA titled Pyrophoric Cult, originally premiering in the Alternative Architecture broadcast as two original episodes, was released on August 26, 2015. Kazuchika Kise served as the chief director of the series, with Tow Ubukata as head writer. Cornelius was brought onto the project to compose the score for the series, with the Major's new voice actress Maaya Sakamoto also providing vocals for certain tracks. Ghost in the Shell: The New Movie, also known as Ghost in the Shell: Arise − The Movie or New Ghost in the Shell, is a 2015 film directed by Kazuya Nomura that serves as a finale to the Ghost in the Shell: Arise story arc. The film is a continuation to the plot of the Pyrophoric Cult episode of Arise, and ties up loose ends from that arc. A manga adaptation was serialized in Kodansha's Young Magazine, which started on March 13 and ended on August 26, 2013. ==== 2026 anime ==== On May 25, 2024, it was announced that a new anime television series adaptation will be produced by Science Saru for a July 2026 premiere. Saru will be in a production committee with Bandai Namco Filmworks, Kodansha and Production I.G. The series will be directed by Monkochan, with a script by EnJoe Toh. === Video games === Ghost in the Shell was developed by Exact and released for the PlayStation on July 17, 1997, in Japan by Sony Computer Entertainment. It is a third-person shooter featuring an original storyline where the character plays a rookie member of Section 9. The video game's soundtrack Megatech Body features various techno artists, such as Takkyu Ishino, Scan X and Mijk Van Dijk. Several video games were also developed to tie into the Stand Alone Complex television series, in addition to a first-person shooter by Nexon and Neople titled Ghost in the Shell: Stand Alone Complex - First Assault Online,

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  Sourcegraph

  Sourcegraph Inc. is a company developing code search and code intelligence tools that semantically index and analyze large codebases so that they can be searched across commercial, open-source, local, and cloud-based repositories. The company has two core products: Code Search and Amp. A previous core product, Cody, retains limited legacy support for existing customers. Code Search was initially released in 2013 under the name Sourcegraph, but was rebranded to Code Search when the company unveiled Cody in 2023. As of 2021, the platform has around 800,000 developers and has indexed around 54 billion lines of code. In July 2025, new accounts for Cody were discontinued, and a new AI coding project, Amp, was released. In December 2025, Amp was spun-off to become a separate company. == History == Sourcegraph Inc. was founded by Stanford graduates Quinn Slack and Beyang Liu to drive the development of a code search and code intelligence tool, formerly called Sourcegraph. It was first released in 2013 but was rebranded to Code Search in 2023. It was partly inspired by Liu's experience using Google Code Search while he was a Google intern, It was designed to "tackle the big code problem" by enabling developers to manage large codebases that span multiple repositories, programming languages, file formats, and projects. Code Search was initially self-hosted by each customer on their own infrastructure. Early customers included Uber, Dropbox, and Lyft. In 2016, Code Search was criticized for being provided with a Fair Source License with the developers explaining that "all of Sourcegraph's source code is publicly available and hackable" and was intended to "help open sourcers strike a balance between getting paid and preserving their values". In 2018, Code Search was licensed under the Apache License 2.0, and Sourcegraph OSS has since been released under the Apache License 2.0. The commercial version, Code Search Enterprise, has been released under its own license. In 2023, Code Search was criticized for dropping the Apache license for most of its code, leaving it public but only available under its Enterprise license. In 2024, the main repository was made completely private. In 2019, Code Search was integrated into the GitLab codebase, giving GitLab users access to a browser-based developer platform. In 2021, a browser-based portal became available, allowing users to browse open-source projects and personal private code for free. In 2022, Sourcegraph Cloud, a commercial single-tenant cloud solution for organizations with more than 100 developers, was launched. Sourcegraph has raised a total of $223 million in financing to date. Its most recent $125 million Series D investment in 2021 valued the company at $2.625 billion, a 300% growth from its previous valuation in 2020. In 2023 Sourcegraph Inc. unveiled their new product Cody, and rebranded Sourcegraph to Code Search. In 2025, Sourcegraph announced the discontinuation of Cody Free, Pro, and Enterprise Starter plans, effective July 23, 2025, and launched Amp, a new AI coding agent. == Products == The company has three major products: Code Search, Amp, and Cody. === Sourcegraph Code Search === Code Search tool is used to search and summarize code. It supports over 30 programming languages and integrates with GitHub and GitLab for code hosting, Codecov for code coverage, and Jira Software for project management. Sourcegraph's Code Search uses a variant of Google's PageRank algorithm to rank results by relevance. While it was originally launched under the Apache License, on June 13, 2023, it was relicensed to the non-open-source "Sourcegraph Enterprise" license. Then, on August 22, 2024, the source code was moved to a private repository, and thus no longer source-available. === Sourcegraph Amp === Launched in 2025, Amp can generate code, generate documentation, write tests, and perform refactoring operations on projects. The tool operates on a credit-based pricing model and is available through web interfaces, command-line tools, and IDE extensions. In December 2025, Sourcegraph announced that Amp would be spun-off to become a separate company. === Sourcegraph Cody === Cody is an AI coding application for writing and maintaining code. Cody was released in December 2023 and was available for Microsoft Visual Studio Code and most JetBrains IDEs. As of July 2025, Cody Free, Pro, and Enterprise Starter plans have been discontinued, with only Cody Enterprise remaining available for existing enterprise customers.

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  Powerset (company)

  Powerset was an American company based in San Francisco, California, that, in 2006, was developing a natural language search engine for the Internet. On July 1, 2008, Powerset was acquired by Microsoft for an estimated $100 million (~$143 million in 2024). Powerset was working on building a natural language search engine that could find targeted answers to user questions (as opposed to keyword based search). For example, when confronted with a question like "Which U.S. state has the highest income tax?", conventional search engines ignore the question phrasing and instead do a search on the keywords "state", "highest", "income", and "tax". Powerset on the other hand, attempts to use natural language processing to understand the nature of the question and return pages containing the answer. The company was in the process of "building a natural language search engine that reads and understands every sentence on the Web". The company has licensed natural language technology from PARC, the former Xerox Palo Alto Research Center. On May 11, 2008, the company unveiled a tool for searching a fixed subset of English Wikipedia using conversational phrases rather than keywords. Acquisition by Microsoft: One significant milestone in Powerset's history was its acquisition by Microsoft on July 1, 2008, for an estimated $100 million. This acquisition was part of Microsoft's broader strategy to enhance its search capabilities and compete more effectively with other search engine providers, particularly Google. Natural Language Search Engine: Powerset's primary focus was on developing a natural language search engine capable of understanding and interpreting user queries in a more human-like manner. Instead of simply matching keywords, Powerset aimed to comprehend the meaning behind the words, allowing for more accurate and contextually relevant search results. Technology and Partnerships: Powerset had licensed natural language technology from PARC, the Xerox Palo Alto Research Center. This technology likely played a crucial role in the development of Powerset's NLP capabilities. Wikipedia Search Tool: In May 2008, Powerset unveiled a search tool that allowed users to search a fixed subset of English Wikipedia using conversational phrases rather than traditional keywords. This demonstrated the potential of Powerset's NLP technology in providing more precise and relevant search results. == Powerlabs == In a form of beta testing, Powerset opened an online community called Powerlabs on September 17, 2007. Business Week said: "The company hopes the site will marshal thousands of people to help build and improve its search engine before it goes public next year." Said The New York Times: "[Powerset Labs] goes far beyond the 'alpha' or 'beta' testing involved in most software projects, when users put a new product through rigorous testing to find its flaws. Powerset doesn’t have a product yet, but rather a collection of promising natural language technologies, which are the fruit of years of research at Xerox PARC." Powerlabs' initial search results are taken from Wikipedia. == Notable people == Barney Pell (born March 18, 1968, in Hollywood, California) was co-founder and CEO of Powerset. Pell received his Bachelor of Science degree in symbolic systems from Stanford University in 1989, where he graduated Phi Beta Kappa and was a National Merit Scholar. Pell received a PhD in computer science from Cambridge University in 1993, where he was a Marshall Scholar. He has worked at NASA, as chief strategist and vice president of business development at StockMaster.com (acquired by Red Herring in March, 2000) and at Whizbang! Labs. Prior to joining Powerset, Pell was an Entrepreneur-in-Residence at Mayfield Fund, a venture capital firm in Silicon Valley. Pell is also a founder of Moon Express, Inc., a U.S. company awarded a $10M commercial lunar contract by NASA and a competitor in the Google Lunar X PRIZE. Steve Newcomb was the COO and co-founder of Powerset. Prior to joining Powerset, he was a co-founder of Loudfire, General Manager at Promptu, and was on the board of directors at Jaxtr. He left Powerset in October 2007 to form Virgance, a social startup incubator. Lorenzo Thione (born in Como, Italy) was the product architect and co-founder of Powerset. Prior to joining Powerset, he worked at FXPAL in natural language processing and related research fields. Thione earned his master's degree in software engineering from the University of Texas at Austin. Ronald Kaplan, former manager of research in Natural Language Theory and Technology at PARC, served as the company's CTO and CSO. Ryan Ferrier is a member of the founding team of Powerset. He managed personnel and internal operations. After 2008 he went on to co-found Serious Business, which made Facebook applications and was later bought by Zynga. Another Powerset alumnus, Alex Le, became CTO of Serious Business and went on to become an executive producer at Zynga when it bought the company. Siqi Chen founded a stealth startup in mobile computing after leaving Powerset. Tom Preston-Werner worked at Powerset and left after the acquisition to found GitHub. == Investors == Powerset attracted a wide range of investors, many of whom had considerable experience in the venture capital field. The company received $12.5 million (~$18.2 million in 2024) in Series A funding during November 2007, co-led by the venture capital firms Foundation Capital and The Founders Fund. Among the better-known investors: Esther Dyson, founding chairman of ICANN, founder of the newsletter Release 1.0 and editor at Cnet Peter Thiel, founder and former CEO of PayPal Luke Nosek, founder of PayPal Todd Parker. Managing Partner, Hidden River Ventures Reid Hoffman, executive vice president of PayPal and founder of LinkedIn First Round Capital, seed-stage venture firm

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  Pop music automation

  Pop music automation is a field of study among musicians and computer scientists with a goal of producing successful pop music algorithmically. It is often based on the premise that pop music is especially formulaic, unchanging, and easy to compose. The idea of automating pop music composition is related to many ideas in algorithmic music, artificial intelligence (AI) and computational creativity. == History of automation in music == Algorithms (or, at the very least, formal sets of rules) have been used to compose music for centuries; the procedures used to plot voice-leading in counterpoint, for example, can often be reduced to algorithmic determinant. Now the term is usually reserved, however, for the use of formal procedures to make music without human intervention. Classical music automation software exists that generates music in the style of Mozart and Bach and jazz. Most notably, David Cope has written a software system called "Experiments in Musical Intelligence" (or "EMI") that is capable of analyzing and generalizing from existing music by a human composer to generate novel musical compositions in the same style. EMI's output is convincing enough to persuade human listeners that its music is human-generated to a high level of competence. Creativity research in jazz has focused on the process of improvisation and the cognitive demands that this places on a musical agent: reasoning about time, remembering and conceptualizing what has already been played, and planning ahead for what might be played next. Inevitably associated with pop music automation is pop music analysis. Projects in pop music automation may include, but are not limited to, ideas in melody creation and song development, vocal generation or improvement, automatic accompaniment and lyric composition. == Automatic accompaniment == Some systems exist that automatically choose chords to accompany a vocal melody in real-time. A user with no musical experience can create a song with instrumental accompaniment just by singing into a microphone. An example is a Microsoft Research project called Songsmith, which trains a Hidden Markov model using a music database and uses that model to select chords for new melodies. == Melody generation == Automatic melody generation is often done with a Markov chain, the states of the system become note or pitch values, and a probability vector for each note is constructed, completing a transition probability matrix (see below). An algorithm is constructed to produce an output note values based on the transition matrix weightings, which could be MIDI note values, frequency (Hz), or any other desirable metric. A second-order Markov chain can be introduced by considering the current state and also the previous state, as indicated in the second table. Higher, nth-order chains tend to "group" particular notes together, while 'breaking off' into other patterns and sequences occasionally. These higher-order chains tend to generate results with a sense of phrasal structure, rather than the 'aimless wandering' produced by a first-order system. == Lyric composition == Automated lyric creating software may take forms such as: Selecting words according to their rhythm The Tra-la-Lyrics system produces song lyrics, in Portuguese, for a given melody. This not only involves matching each word syllable with a note in the melody, but also matching the word's stress with the strong beats of the melody. Parsing existing pop music (e.g. for content or word choice) This involves natural language processing. Pablo Gervás has developed a noteworthy system called ASPERA that employs a case-based reasoning (CBR) approach to generating poetic formulations of a given input text via a composition of poetic fragments that are retrieved from a case-base of existing poems. Each poem fragment in the ASPERA case-base is annotated with a prose string that expresses the meaning of the fragment, and this prose string is used as the retrieval key for each fragment. Metrical rules are then used to combine these fragments into a well-formed poetic structure. Automatic analogy or story creation Programs like TALE-SPIN and The MINSTREL system represent a complex elaboration of this basis approach, distinguishing a range of character-level goals in the story from a range of author-level goals for the story. Systems like Bringsjord's BRUTUS can create stories with complex interpersonal themes like betrayal. On-line metaphor generation systems like 'Sardonicus' or 'Aristotle' can suggest lexical metaphors for a given descriptive goal (e.g., to describe a supermodel as skinny, the source terms “pencil”, “whip”, “whippet”, “rope”, “stick-insect” and “snake” are suggested). Free association of grouped words Using a language database (such as wordnet) one can create musings on a subject that may be weak grammatically but are still sensical. See such projects as the Flowerewolf automatic poetry generator or the Dada engine. == Software == === More or less free === BreathCube by xoxos. Simple lyrical vocal content is generated with simple music. CubeBreath by xoxos. Audio input is vocoded in tune with the music. Midi Internet Algorithmic Composition infno, infinite generator of electronic dance music and synth-pop. Algorithmic Trap, trap beat generator. === Commercial === Band in a box generates any element, potentially creates whole new songs from scratch. Musical Palette - Melody Composing Tool SongSmith: Automatic accompaniment for vocal melodies Ludwig 3.0 automatic accompaniment, writes arrangements for given instruments, plays its own songs for an infinitely long time. Automated Composing System creates music in many different styles

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  Thompson sampling

  Thompson sampling, named after William R. Thompson, is a heuristic for choosing actions that address the exploration–exploitation dilemma in the multi-armed bandit problem. It consists of choosing the action that maximizes the expected reward with respect to a randomly drawn belief. == Description == Consider a set of contexts X {\displaystyle {\mathcal {X}}} , a set of actions A {\displaystyle {\mathcal {A}}} , and rewards in R {\displaystyle \mathbb {R} } . The aim of the player is to play actions under the various contexts, such as to maximize the cumulative rewards. Specifically, in each round, the player obtains a context x ∈ X {\displaystyle x\in {\mathcal {X}}} , plays an action a ∈ A {\displaystyle a\in {\mathcal {A}}} and receives a reward r ∈ R {\displaystyle r\in \mathbb {R} } following a distribution that depends on the context and the issued action. The elements of Thompson sampling are as follows: a likelihood function P ( r | θ , a , x ) {\displaystyle P(r|\theta ,a,x)} ; a set Θ {\displaystyle \Theta } of parameters θ {\displaystyle \theta } of the distribution of r {\displaystyle r} ; a prior distribution P ( θ ) {\displaystyle P(\theta )} on these parameters; past observations triplets D = { ( x ; a ; r ) } {\displaystyle {\mathcal {D}}=\{(x;a;r)\}} ; a posterior distribution P ( θ | D ) ∝ P ( D | θ ) P ( θ ) {\displaystyle P(\theta |{\mathcal {D}})\propto P({\mathcal {D}}|\theta )P(\theta )} , where P ( D | θ ) {\displaystyle P({\mathcal {D}}|\theta )} is the likelihood function. Thompson sampling consists of playing the action a ∗ ∈ A {\displaystyle a^{\ast }\in {\mathcal {A}}} according to the probability that it maximizes the expected reward; action a ∗ {\displaystyle a^{\ast }} is chosen with probability ∫ I [ E ( r | a ∗ , x , θ ) = max a ′ E ( r | a ′ , x , θ ) ] P ( θ | D ) d θ , {\displaystyle \int \mathbb {I} \left[\mathbb {E} (r|a^{\ast },x,\theta )=\max _{a'}\mathbb {E} (r|a',x,\theta )\right]P(\theta |{\mathcal {D}})d\theta ,} where I {\displaystyle \mathbb {I} } is the indicator function. In practice, the rule is implemented by sampling. In each round, parameters θ ∗ {\displaystyle \theta ^{\ast }} are sampled from the posterior P ( θ | D ) {\displaystyle P(\theta |{\mathcal {D}})} , and an action a ∗ {\displaystyle a^{\ast }} chosen that maximizes E [ r | θ ∗ , a ∗ , x ] {\displaystyle \mathbb {E} [r|\theta ^{\ast },a^{\ast },x]} , i.e. the expected reward given the sampled parameters, the action, and the current context. Conceptually, this means that the player instantiates their beliefs randomly in each round according to the posterior distribution, and then acts optimally according to them. In most practical applications, it is computationally onerous to maintain and sample from a posterior distribution over models. As such, Thompson sampling is often used in conjunction with approximate sampling techniques. == History == Thompson sampling was originally described by Thompson in 1933. It was subsequently rediscovered numerous times independently in the context of multi-armed bandit problems. A first proof of convergence for the bandit case has been shown in 1997. The first application to Markov decision processes was in 2000. A related approach (see Bayesian control rule) was published in 2010. In 2010 it was also shown that Thompson sampling is instantaneously self-correcting. Asymptotic convergence results for contextual bandits were published in 2011. Thompson Sampling has been widely used in many online learning problems including A/B testing in website design and online advertising, and accelerated learning in decentralized decision making. A Double Thompson Sampling (D-TS) algorithm has been proposed for dueling bandits, a variant of traditional MAB, where feedback comes in the form of pairwise comparison. == Relationship to other approaches == === Probability matching === Probability matching is a decision strategy in which predictions of class membership are proportional to the class base rates. Thus, if in the training set positive examples are observed 60% of the time, and negative examples are observed 40% of the time, the observer using a probability-matching strategy will predict (for unlabeled examples) a class label of "positive" on 60% of instances, and a class label of "negative" on 40% of instances. === Bayesian control rule === A generalization of Thompson sampling to arbitrary dynamical environments and causal structures, known as Bayesian control rule, has been shown to be the optimal solution to the adaptive coding problem with actions and observations. In this formulation, an agent is conceptualized as a mixture over a set of behaviours. As the agent interacts with its environment, it learns the causal properties and adopts the behaviour that minimizes the relative entropy to the behaviour with the best prediction of the environment's behaviour. If these behaviours have been chosen according to the maximum expected utility principle, then the asymptotic behaviour of the Bayesian control rule matches the asymptotic behaviour of the perfectly rational agent. The setup is as follows. Let a 1 , a 2 , … , a T {\displaystyle a_{1},a_{2},\ldots ,a_{T}} be the actions issued by an agent up to time T {\displaystyle T} , and let o 1 , o 2 , … , o T {\displaystyle o_{1},o_{2},\ldots ,o_{T}} be the observations gathered by the agent up to time T {\displaystyle T} . Then, the agent issues the action a T + 1 {\displaystyle a_{T+1}} with probability: P ( a T + 1 | a ^ 1 : T , o 1 : T ) , {\displaystyle P(a_{T+1}|{\hat {a}}_{1:T},o_{1:T}),} where the "hat"-notation a ^ t {\displaystyle {\hat {a}}_{t}} denotes the fact that a t {\displaystyle a_{t}} is a causal intervention (see Causality), and not an ordinary observation. If the agent holds beliefs θ ∈ Θ {\displaystyle \theta \in \Theta } over its behaviors, then the Bayesian control rule becomes P ( a T + 1 | a ^ 1 : T , o 1 : T ) = ∫ Θ P ( a T + 1 | θ , a ^ 1 : T , o 1 : T ) P ( θ | a ^ 1 : T , o 1 : T ) d θ {\displaystyle P(a_{T+1}|{\hat {a}}_{1:T},o_{1:T})=\int _{\Theta }P(a_{T+1}|\theta ,{\hat {a}}_{1:T},o_{1:T})P(\theta |{\hat {a}}_{1:T},o_{1:T})\,d\theta } , where P ( θ | a ^ 1 : T , o 1 : T ) {\displaystyle P(\theta |{\hat {a}}_{1:T},o_{1:T})} is the posterior distribution over the parameter θ {\displaystyle \theta } given actions a 1 : T {\displaystyle a_{1:T}} and observations o 1 : T {\displaystyle o_{1:T}} . In practice, the Bayesian control amounts to sampling, at each time step, a parameter θ ∗ {\displaystyle \theta ^{\ast }} from the posterior distribution P ( θ | a ^ 1 : T , o 1 : T ) {\displaystyle P(\theta |{\hat {a}}_{1:T},o_{1:T})} , where the posterior distribution is computed using Bayes' rule by only considering the (causal) likelihoods of the observations o 1 , o 2 , … , o T {\displaystyle o_{1},o_{2},\ldots ,o_{T}} and ignoring the (causal) likelihoods of the actions a 1 , a 2 , … , a T {\displaystyle a_{1},a_{2},\ldots ,a_{T}} , and then by sampling the action a T + 1 ∗ {\displaystyle a_{T+1}^{\ast }} from the action distribution P ( a T + 1 | θ ∗ , a ^ 1 : T , o 1 : T ) {\displaystyle P(a_{T+1}|\theta ^{\ast },{\hat {a}}_{1:T},o_{1:T})} . === Upper-confidence-bound (UCB) algorithms === Thompson sampling and upper-confidence bound algorithms share a fundamental property that underlies many of their theoretical guarantees. Roughly speaking, both algorithms allocate exploratory effort to actions that might be optimal and are in this sense "optimistic". Leveraging this property, one can translate regret bounds established for UCB algorithms to Bayesian regret bounds for Thompson sampling or unify regret analysis across both these algorithms and many classes of problems.

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  Land of Memories

  Land of Memories (Chinese: 机忆之地) is a Chinese science-fiction novel by Shen Yang (沈阳), a professor at Tsinghua University's School of Journalism and Communication. The story revolves around a former neuroscientist trying to recover her memories from the metaverse after suffering amnesia due to an accident. It contains almost 6,000 Chinese characters and was shortened from an AI-generated draft that was 43,000 characters long. The process involved 66 prompts spanning almost three hours. The novel was among 18 submissions that won the level-two prize at the Fifth Jiangsu Youth Science Education and Science Fiction Competition (第五届江苏省青年科普科幻作品大赛). The contest was restricted to participants between the age of 14 and 45 but did not forbid entries generated by AI. One of its organizers reached out to Shen after finding out that the professor had been experimenting with writing science fiction using AI. The judges were not told about the novel's origin in advance. Three of them, out of the six, approved the work. One judge, who had worked with AI models before, recognized that the novel was written by AI and criticized the work for lacking emotional appeal. The organizer who had contacted Shen said the novel's introduction was not bad but the story did not develop well. It would not meet the usual standards for publication. However, he still plans to allow AI-generated submissions in 2024. Fu Ruchu, editorial department director of the People's Literature Publishing House, said the novel was not easily identifiable as AI-generated and applauded its logical consistency. She warned that artificial intelligence could endanger the jobs of fiction writers and cause permanent damage to literary language.

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  Dark mode

  A dark mode, dark theme, night mode, or light-on-dark color scheme is a color scheme that uses light-colored text, icons, and graphical user interface elements on a dark background. It is often discussed in terms of computer user interface design and web design. Many modern websites and operating systems offer the user an optional light-on-dark display mode. Some users find dark mode displays more visually appealing, and claim that it can reduce eye strain. Displaying white at full brightness uses roughly six times as much power as pure black on a 2016 Google Pixel, which has an OLED display. However, conventional LED displays may not benefit from reduced power consumption; but if a LED display has the partial dimming features, it still benefits from reduced power consumption. Most modern operating systems support an optional light-on-dark color scheme. == History == Microsoft introduced the high contrast themes in Windows 95. Later, Microsoft introduced a dark theme in the Anniversary Update of Windows 10 in 2016. In 2018, Apple followed in macOS Mojave. In September 2019, iOS 13 and Android 10 both introduced dark modes. Some operating systems provide tools to change the dark mode state automatically at sundown or sunrise. A "prefers-color-scheme" option was created for front-end web developers in 2019, being a CSS property that signals a user's choice for their system to use a light or dark color theme. Firefox and Chromium have optional dark theme for all internal screens. It is also possible for third-party developers to implement their own dark themes. There are also a variety of browser add-ons that can re-theme web sites with dark color schemes, also aligning with system theme. Wikipedia's mobile and desktop versions received a dark mode option in 2024. == Implementation == There is a prefers-color-scheme media query in CSS, to detect if the user has requested light or dark color scheme and serve the requested color scheme. It can be indicated from the user's operating system preference or a user agent. CSS example: JavaScript example: == Energy usage == Light on dark color schemes require less energy to display on OLED displays. This positively impacts battery life and reduces energy consumption. While an OLED will consume around 40% of the power of an LCD displaying an image that is primarily black, it can use more than three times as much power to display an image with a white background, such as a document or web site. This can lead to reduced battery life and higher energy usage unless a light-on-dark color scheme is used. The long-term reduced power usage may also prolong battery life or the useful life of the display and battery. The energy savings that can be achieved using a light-on-dark color scheme are because of how OLED screens work: in an OLED screen, each subpixel generates its own light and it only consumes power when generating light. This is in contrast to how an LCD works: in an LCD, subpixels either block or allow light from an always-on (lit) LED backlight to pass through. "AMOLED Black" color schemes (that use pure black instead of dark gray) do not necessarily save more energy than other light-on-dark color schemes that use dark gray instead of black, as the power consumption on an AMOLED screen decreases proportionately to the average brightness of the displayed pixels. Although it is true that AMOLED black does save more energy than dark gray, the additional energy savings are often negligible; AMOLED black will only give an additional energy saving of less than 1%, for instance, over the dark gray that's used in the dark theme for Google's official Android apps. In November 2018, Google confirmed that dark mode on Android saved battery life. == Web issues == Some argue that a color scheme with light text on a dark background is easier to read on the screen, because the lower overall brightness causes less eyestrain, while others argue to the contrary. Some pages on the web are designed for white backgrounds; Image assets (GIF, PNG, SVG, WOFF, etc) can be used improperly causing visual artifacts if dark mode is forced (instead of designed for) with a plugin like Dark Reader.

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  Jake Elwes

  Jake Elwes () is a British media artist, hacker and researcher. Their practice is the exploration of artificial intelligence (AI), queer theory and technical biases. They are known for using AI to create art in mediums such as video, performance and installation. Elwes considers themselves to be neuroqueer, and their work on queering technology addresses issues caused by the normative biases of artificial intelligence. == Education and early life == Elwes was born in London to British contemporary artist and painter Luke Elwes and Anneke, daughter of Hans Dumoulin. Elwes is the great grandchild of Army officer James Hennessy and portrait painter Simon Elwes RA, son of Victorian opera singer Gervase Elwes. Elwes studied at the Slade School of Fine Art from 2013 to 2017, where they began using computer code as a medium. In 2016 they attended the School of Machines, Making & Make-Believe in Berlin with artist and educator Gene Kogan. Elwes was introduced to drag performance by their collaborator Dr Joe Parslow who holds a PhD in drag performance. Drag performance has since become instrumental to Elwes' work. == Career == Elwes' work with artificial intelligence is cited as a hopeful strategy to make AI more playful and diverse. Elwes' work has been exhibited in numerous international art museums and galleries and was featured in a BBC documentary on the history of video art, they were a 2021 finalist for the Lumen Prize, and received the Honorary Mention of the 2022 Prix Ars Electronica in the Interactive Art + category. They also curated and presented the opening provocation "The New Real - Artistic and Queer Visions of AI Futures" to the UK government with two drag artists at the AI UK conference 2024. Elwes is part of the Radical Faeries countercultural movement. They have exhibited in museums and galleries across Europe and Asia including: Victoria and Albert Museum (London, UK) - The Zizi Show (2023-2024) for the first digital commission in their photography center's digital gallery Pinakothek der Moderne (Munich, Germany) - Glitch. Die Kunst Der Störung (2023-2024) ZKM (Karlsruhe, Germany) - Biomedia (2021-2022) National Museum of Modern and Contemporary Art (Cheongju, South Korea) - What an Artificial World (2024) Somerset House (London, UK) - The Horror Show! (2022-2023) Gazelli Art House (London, UK) - Jake Elwes: Data • Glitch • Utopia (2023) (survey exhibition) Jut Art Museum (Taipei, Taiwan) - Future Lives, Future You (2023-2024) Max Ernst Museum (Brühl, Germany) - Surreal Futures (2023-2024) Zabludowicz Collection (London, UK) - Among the Machines (2022) Ars Electronica (Linz, Austria) - Prix Ars Electronica, CyberArts Exhibition (2022) Institute of Contemporary Arts (ICA) (London, UK) - Do Androids Dream on Silver Screens? (2023) Arebyte gallery (London, UK) - Real-Time Constraints (2020) Ming Contemporary Art Museum (McaM) (Shanghai, China) - Mind the Deep (2019) HMKV (Hartware MedienKunstVerein) (Dortmund, Germany) - House of Mirrors: Artificial Intelligence as Phantasm (2022) Today Art Museum (Beijing, China) - Future of Today: DEJA VU (2019) Science Gallery (Dublin, Ireland) - BIAS (2021-2022) Yuz Museum (Shanghai, China) - Lying Sophia and Mocking Alexa (2021) Fotomuseum Winterthur The Onassis Foundation (Athens, Greece) - You and AI (2021) Royal College of Art (London, UK) - Event Two (2019) (50th anniversary of Computer Arts Society & Event One) Museum für Naturkunde (Berlin, Germany) - Forschungsfall Nachtigall (2019) Frankfurter Kunstverein (Frankfurt, Germany) - I am here to learn (2018) Nature Morte (Delhi, India) - Gradient Descent (2018) BALTIC Centre for Contemporary Art (Newcastle, UK) - Bloomberg New Contemporaries (2017) == Artworks == === The Zizi Project - a deepfake drag cabaret === The Zizi Project is a series of works that explore the interaction of drag and A.I. Currently, The Zizi Project is made up of multiple artworks. ==== Zizi - Queering the Dataset (2019) ==== Knowing that facial recognition technology statically struggle to recognize black women or transgender people, Elwes set out to "Queer the Dataset" through an open-sourced generative adversarial network (GAN, a type of machine learning model and an early Generative artificial intelligence). Elwes added a dataset of 1,000 photos of drag kings and queens into the GAN's 70,000 faces collected in a standardised facial recognition dataset called Flickr-Faces-HQ Dataset (FFHQ). They then created new simulacra faces, known as deep fakes. "We queer that data so it shifts all of the weights in this neural network from a space of normativity into a space of queerness and otherness. Suddenly all of the faces start to break down and you see mascara dissolve into lipstick and blue eye shadow turn into a pink wig" said Elwes in a 2023 interview for Artnet. ==== Zizi & Me (2020–2023) ==== Zizi & Me is an ongoing multimedia collaboration between drag queen Me The Drag Queen and a deepfake A.I. clone of Me The Drag Queen. Using neural networks trained on filmed footage, the project creates a virtual body that can mimic reference movements. The first act, which features a digital lip-sync duet to Anything You Can Do (I Can Do Better), satirises the idea of A.I. being mistaken for a human, using drag performance and cabaret to critique societal narratives about A.I. and its role in shaping identity. The project is part of The Zizi Project by Jake Elwes, which explores the intersection of drag performance and A.I. ==== The Zizi Show - A Deepfake Drag Cabaret (2020) ==== The Zizi Show is a deep fake drag act based on artificial intelligence (AI). It has been presented live and as interactive online artwork. It is an exploration of queer culture and the algorithms philosophy and ethics of AI. The Zizi Show was exhibited as the inaugural exhibition in the digital gallery at the V&A’s Photography Center from 2023 to 2024. ==== Zizi in Motion: A Deepfake Drag Utopia (Movement by Wet Mess) (2023) ==== "Zizi in Motion" is a multichannel silent video installation featuring AI-generated deepfake performances, which are dynamically re-animated through the movements of London drag artist Wet Mess. The movements of Wet Mess cause the AI-generated visuals to glitch and distort, showcasing the interaction between drag performance and artificial intelligence. The work explore the potential for queer communities to ethically and creatively reclaim and repurpose deepfake technology, using it to celebrate queer bodies and identities. === Art in the Cage of Digital Reproduction (2024) === In an act of protest on 26 November 2024, Elwes facilitated indirect access to an early access token for OpenAI’s Sora text-to-video model through a Hugging Face frontend under the account "PR Puppets". The accompanying statement called to 'denormalize the exploitation of artists by major AI companies for training data, R&D, and publicity'. The incident attracted international press coverage calling into question the role of artists in shaping the future of generative AI versus merely serving as data and credibility providers for tech giants. Elwes also coordinated a collection of mini essays with responses and reflections from the signees and guest writers titled "Art in the Cage of Digital Reproduction". === Installations exploring interpretation and feedback loops between neural networks === Elwes has created works based on the interpretations and misinterpretations between different neural networks and training datasets including: A.I. Interprets A.I. Interpreting ‘Against Interpretation’ (Sontag 1966) from 2023, Closed Loop from 2017, and Auto-Encoded Buddha from 2016. ==== A.I. Interprets A.I. Interpreting ‘Against Interpretation’ (Sontag 1966) (2023) ==== A.I. Interprets A.I. Interpreting ‘Against Interpretation (Sontag 1966) is a three-channel video artwork where an AI interprets Susan Sontag’s essay into images, and then and another AI reinterprets those images back into language. The piece highlights how AI-generated art can misinterpret and introduce bias. ==== Closed Loop (2017) ==== Closed Loop is a two-channel video where two neural networks engage in a continuous feedback loop, one generating images based on the text output and the other creating text based on the image output. The work explores how AI models misinterpret and evolve in a surreal, self-perpetuating conversation, without human input. ==== Auto-Encoded Buddha (2016) ==== Auto-Encoded Buddha is a mixed-media piece where an AI attempts to generate an image of a Buddha statue, trained on 5,000 Buddha images. The AI struggles to accurately represent the Buddha, highlighting the limitations of early generative neural networks. The work is a tribute to Nam June Paik’s TV Buddha (1974). === CUSP (2019) === In their video work CUSP (2019) Elwes places marsh birds generated using artificial intelligence into a tidal landscape. These digitally generated and constantly shifting birds are recorded in dialogue with native

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  Fuzzy measure theory

  In mathematics, fuzzy measure theory considers generalized measures in which the additive property is replaced by the weaker property of monotonicity. The central concept of fuzzy measure theory is the fuzzy measure (also capacity, see ), which was introduced by Choquet in 1953 and independently defined by Sugeno in 1974 in the context of fuzzy integrals. There exists a number of different classes of fuzzy measures including plausibility/belief measures, possibility/necessity measures, and probability measures, which are a subset of classical measures. == Definitions == Let X {\displaystyle \mathbf {X} } be a universe of discourse, C {\displaystyle {\mathcal {C}}} be a class of subsets of X {\displaystyle \mathbf {X} } , and E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} . A function g : C → R {\displaystyle g:{\mathcal {C}}\to \mathbb {R} } where ∅ ∈ C ⇒ g ( ∅ ) = 0 {\displaystyle \emptyset \in {\mathcal {C}}\Rightarrow g(\emptyset )=0} E ⊆ F ⇒ g ( E ) ≤ g ( F ) {\displaystyle E\subseteq F\Rightarrow g(E)\leq g(F)} is called a fuzzy measure. A fuzzy measure is called normalized or regular if g ( X ) = 1 {\displaystyle g(\mathbf {X} )=1} . == Properties of fuzzy measures == A fuzzy measure is: additive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) = g ( E ) + g ( F ) . {\displaystyle g(E\cup F)=g(E)+g(F).} ; supermodular if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have g ( E ∪ F ) + g ( E ∩ F ) ≥ g ( E ) + g ( F ) {\displaystyle g(E\cup F)+g(E\cap F)\geq g(E)+g(F)} ; submodular if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have g ( E ∪ F ) + g ( E ∩ F ) ≤ g ( E ) + g ( F ) {\displaystyle g(E\cup F)+g(E\cap F)\leq g(E)+g(F)} ; superadditive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) ≥ g ( E ) + g ( F ) {\displaystyle g(E\cup F)\geq g(E)+g(F)} ; subadditive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) ≤ g ( E ) + g ( F ) {\displaystyle g(E\cup F)\leq g(E)+g(F)} ; symmetric if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have | E | = | F | {\displaystyle |E|=|F|} implies g ( E ) = g ( F ) {\displaystyle g(E)=g(F)} ; Boolean if for any E ∈ C {\displaystyle E\in {\mathcal {C}}} , we have g ( E ) = 0 {\displaystyle g(E)=0} or g ( E ) = 1 {\displaystyle g(E)=1} . Understanding the properties of fuzzy measures is useful in application. When a fuzzy measure is used to define a function such as the Sugeno integral or Choquet integral, these properties will be crucial in understanding the function's behavior. For instance, the Choquet integral with respect to an additive fuzzy measure reduces to the Lebesgue integral. In discrete cases, a symmetric fuzzy measure will result in the ordered weighted averaging (OWA) operator. Submodular fuzzy measures result in convex functions, while supermodular fuzzy measures result in concave functions when used to define a Choquet integral. == Möbius representation == Let g be a fuzzy measure. The Möbius representation of g is given by the set function M, where for every E , F ⊆ X {\displaystyle E,F\subseteq X} , M ( E ) = ∑ F ⊆ E ( − 1 ) | E ∖ F | g ( F ) . {\displaystyle M(E)=\sum _{F\subseteq E}(-1)^{|E\backslash F|}g(F).} The equivalent axioms in Möbius representation are: M ( ∅ ) = 0 {\displaystyle M(\emptyset )=0} . ∑ F ⊆ E | i ∈ F M ( F ) ≥ 0 {\displaystyle \sum _{F\subseteq E|i\in F}M(F)\geq 0} , for all E ⊆ X {\displaystyle E\subseteq \mathbf {X} } and all i ∈ E {\displaystyle i\in E} A fuzzy measure in Möbius representation M is called normalized if ∑ E ⊆ X M ( E ) = 1. {\displaystyle \sum _{E\subseteq \mathbf {X} }M(E)=1.} Möbius representation can be used to give an indication of which subsets of X interact with one another. For instance, an additive fuzzy measure has Möbius values all equal to zero except for singletons. The fuzzy measure g in standard representation can be recovered from the Möbius form using the Zeta transform: g ( E ) = ∑ F ⊆ E M ( F ) , ∀ E ⊆ X . {\displaystyle g(E)=\sum _{F\subseteq E}M(F),\forall E\subseteq \mathbf {X} .} == Simplification assumptions for fuzzy measures == Fuzzy measures are defined on a semiring of sets or monotone class, which may be as granular as the power set of X, and even in discrete cases the number of variables can be as large as 2|X|. For this reason, in the context of multi-criteria decision analysis and other disciplines, simplification assumptions on the fuzzy measure have been introduced so that it is less computationally expensive to determine and use. For instance, when it is assumed the fuzzy measure is additive, it will hold that g ( E ) = ∑ i ∈ E g ( { i } ) {\displaystyle g(E)=\sum _{i\in E}g(\{i\})} and the values of the fuzzy measure can be evaluated from the values on X. Similarly, a symmetric fuzzy measure is defined uniquely by |X| values. Two important fuzzy measures that can be used are the Sugeno- or λ {\displaystyle \lambda } -fuzzy measure and k-additive measures, introduced by Sugeno and Grabisch respectively. === Sugeno λ-measure === The Sugeno λ {\displaystyle \lambda } -measure is a special case of fuzzy measures defined iteratively. It has the following definition: ==== Definition ==== Let X = { x 1 , … , x n } {\displaystyle \mathbf {X} =\left\lbrace x_{1},\dots ,x_{n}\right\rbrace } be a finite set and let λ ∈ ( − 1 , + ∞ ) {\displaystyle \lambda \in (-1,+\infty )} . A Sugeno λ {\displaystyle \lambda } -measure is a function g : 2 X → [ 0 , 1 ] {\displaystyle g:2^{X}\to [0,1]} such that g ( X ) = 1 {\displaystyle g(X)=1} . if A , B ⊆ X {\displaystyle A,B\subseteq \mathbf {X} } (alternatively A , B ∈ 2 X {\displaystyle A,B\in 2^{\mathbf {X} }} ) with A ∩ B = ∅ {\displaystyle A\cap B=\emptyset } then g ( A ∪ B ) = g ( A ) + g ( B ) + λ g ( A ) g ( B ) {\displaystyle g(A\cup B)=g(A)+g(B)+\lambda g(A)g(B)} . As a convention, the value of g at a singleton set { x i } {\displaystyle \left\lbrace x_{i}\right\rbrace } is called a density and is denoted by g i = g ( { x i } ) {\displaystyle g_{i}=g(\left\lbrace x_{i}\right\rbrace )} . In addition, we have that λ {\displaystyle \lambda } satisfies the property λ + 1 = ∏ i = 1 n ( 1 + λ g i ) {\displaystyle \lambda +1=\prod _{i=1}^{n}(1+\lambda g_{i})} . Tahani and Keller as well as Wang and Klir have shown that once the densities are known, it is possible to use the previous polynomial to obtain the values of λ {\displaystyle \lambda } uniquely. === k-additive fuzzy measure === The k-additive fuzzy measure limits the interaction between the subsets E ⊆ X {\displaystyle E\subseteq X} to size | E | = k {\displaystyle |E|=k} . This drastically reduces the number of variables needed to define the fuzzy measure, and as k can be anything from 1 (in which case the fuzzy measure is additive) to X, it allows for a compromise between modelling ability and simplicity. ==== Definition ==== A discrete fuzzy measure g on a set X is called k-additive ( 1 ≤ k ≤ | X | {\displaystyle 1\leq k\leq |\mathbf {X} |} ) if its Möbius representation verifies M ( E ) = 0 {\displaystyle M(E)=0} , whenever | E | > k {\displaystyle |E|>k} for any E ⊆ X {\displaystyle E\subseteq \mathbf {X} } , and there exists a subset F with k elements such that M ( F ) ≠ 0 {\displaystyle M(F)\neq 0} . == Shapley and interaction indices == In game theory, the Shapley value or Shapley index is used to indicate the weight of a game. Shapley values can be calculated for fuzzy measures in order to give some indication of the importance of each singleton. In the case of additive fuzzy measures, the Shapley value will be the same as each singleton. For a given fuzzy measure g, and | X | = n {\displaystyle |\mathbf {X} |=n} , the Shapley index for every i , … , n ∈ X {\displaystyle i,\dots ,n\in X} is: ϕ ( i ) = ∑ E ⊆ X ∖ { i } ( n − | E | − 1 ) ! | E | ! n ! [ g ( E ∪ { i } ) − g ( E ) ] . {\displaystyle \phi (i)=\sum _{E\subseteq \mathbf {X} \backslash \{i\}}{\frac {(n-|E|-1)!|E|!}{n!}}[g(E\cup \{i\})-g(E)].} The Shapley value is the vector ϕ ( g ) = ( ψ ( 1 ) , … , ψ ( n ) ) . {\displaystyle \mathbf {\phi } (g)=(\psi (1),\dots ,\psi (n)).}

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