AI Assistant Maker

AI Assistant Maker — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Eat App

  Eat App is a global restaurant technology company that provides a cloud-based management platform for restaurants, hotels, and other venues. The platform enables venues to accept online reservations seamlessly, manage tables, and enhance customer relationship management (CRM). It utilizes AI to improve operational efficiency, provides marketing automation, and helps build a comprehensive guestbook. The company also offers a consumer app and website for discovering and booking restaurant tables online. According to the company, the system has seated over 100 million guests, and the number continues to grow. Eat was founded by Nezar Kadhem and David Feuillard in 2015 and has raised $13M to date from Silicon Valley's 500 startups, Middle East Venture Partners (MEVP), Derayah VC, amongst other business angels. The company is currently operational across the world, with offices in Dubai and the United States. == Product overview == === For restaurants === Eat App’s reservation system allows for a digital record of all reservations, all guests that have previously visited the restaurant, as well as analytics on the performance of the restaurant. The table management feature simplifies traditional restaurant operations by providing a live snapshot of current status, seating optimization, and shift management. The CRM and analytics suite gathers and monitors data to build a segmented guestbook for personalized marketing and provides dashboards for data-driven decision-making. Additionally, the review feature makes it easy for restaurants to automatically collect reviews from their guests. Additionally, Eat App includes a chit printer function that seamlessly prints reservation details at host stands and a review management feature that allows restaurants to manage online reviews directly within the platform. == History == In February 2015, Eat App raised $300k from Bahrain-based business angel group TENMOU. In June 2018, Eat raised $1.2 million from Dubai-based Middle East Venture Partners (MEVP). In February 2020, Eat App raised $5 million in a Series B funding round led by 500 Startups, Derayah Venture Fund, and MEVP, with participation from a few angel investors and family members. In February 2021, Eat App launched its technology with The Emaar Hospitality Group, implementing it across over 50 restaurants in Emaar properties and hotels. The cloud-based system runs natively on iPads in each restaurant, providing Emaar staff access to reservations and guest information, and integrates with the U by Emaar loyalty app to personalize service. On September 28, 2022, Eat App announced the closing of an $11 million Series B funding round. The investment was led by Middle East Venture Partners (MEVP), 500 Startups, Derayah Venture Capital, Dallah Albaraka, Ali Zaid Al Quraishi & Brothers Company, and Rasameel Investment Company, with participation from existing investors.

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  History of artificial life

  Humans have considered and tried to create non-biological life for at least 3,000 years. As seen in tales ranging from Pygmalion to Frankenstein, humanity has long been intrigued by the concept of artificial life. == Pre-computer == The earliest examples of artificial life involve sophisticated automata constructed using pneumatics, mechanics, and/or hydraulics. The first automata were conceived during the third and second centuries BC and these were demonstrated by the theorems of Hero of Alexandria, which included sophisticated mechanical and hydraulic solutions. Many of his notable works were included in the book Pneumatics, which was also used for constructing machines until early modern times. In 1490, Leonardo da Vinci also constructed an armored knight, which is considered the first humanoid robot in Western civilization. Other early famous examples include al-Jazari's humanoid robots. This Arabic inventor once constructed a band of automata, which can be commanded to play different pieces of music. There is also the case of Jacques de Vaucanson's artificial duck exhibited in 1735, which had thousands of moving parts and one of the first to mimic a biological system. The duck could reportedly eat and digest, drink, quack, and splash in a pool. It was exhibited all over Europe until it fell into disrepair. In the late 1600s, following René Descartes' claims that animals could be understood as purely physical machines, there was increasing interest in the question of whether a machine could be designed that, like an animal, could generate offspring (a self-replicating machine). However, it wasn't until the invention of cheap computing power that artificial life as a legitimate science began in earnest, steeped more in the theoretical and computational than the mechanical and mythological. == 1950s–1970s == One of the earliest thinkers of the modern age to postulate the potentials of artificial life, separate from artificial intelligence, was math and computer prodigy John von Neumann. At the Hixon Symposium, hosted by Linus Pauling in Pasadena, California in the late 1940s, von Neumann delivered a lecture titled "The General and Logical Theory of Automata." He defined an "automaton" as any machine whose behavior proceeded logically from step to step by combining information from the environment and its own programming, and said that natural organisms would in the end be found to follow similar simple rules. He also spoke about the idea of self-replicating machines. He postulated a made-up of a control computer, a construction arm, and a long series of instructions, floating in a lake of parts. By following the instructions that were part of its own body, it could create an identical machine. He followed this idea by creating (with Stanislaw Ulam) a purely logic-based automaton, not requiring a physical body but based on the changing states of the cells in an infinite grid – the first cellular automaton. It was extraordinarily complicated compared to later CAs, having hundreds of thousands of cells which could each exist in one of twenty-nine states, but von Neumann felt he needed the complexity in order for it to function not just as a self-replicating "machine", but also as a universal computer as defined by Alan Turing. This "universal constructor" read from a tape of instructions and wrote out a series of cells that could then be made active to leave a fully functional copy of the original machine and its tape. Von Neumann worked on his automata theory intensively right up to his death, and considered it his most important work. Homer Jacobson illustrated basic self-replication in the 1950s with a model train set – a seed "organism" consisting of a "head" and "tail" boxcar could use the simple rules of the system to consistently create new "organisms" identical to itself, so long as there was a random pool of new boxcars to draw from. Edward F. Moore proposed "Artificial Living Plants", which would be floating factories which could create copies of themselves. They could be programmed to perform some function (extracting fresh water, harvesting minerals from seawater) for an investment that would be relatively small compared to the huge returns from the exponentially growing numbers of factories. Freeman Dyson also studied the idea, envisioning self-replicating machines sent to explore and exploit other planets and moons, and a NASA group called the Self-Replicating Systems Concept Team performed a 1980 study on the feasibility of a self-building lunar factory. University of Cambridge professor John Horton Conway invented the most famous cellular automaton in the 1960s. He called it the Game of Life, and publicized it through Martin Gardner's column in Scientific American magazine. Norwegian-Italian mathematician Nils Aall Barricelli, who worked mainly at US institutions, was a pioneer in computer based simulation of biological processes such as symbiogenesis and evolution. == 1970s–1980s == Philosophy scholar Arthur Burks, who had worked with von Neumann (and indeed, organized his papers after Neumann's death), headed the Logic of Computers Group at the University of Michigan. He brought the overlooked views of 19th century American thinker Charles Sanders Peirce into the modern age. Peirce was a strong believer that all of nature's workings were based on logic (though not always deductive logic). The Michigan group was one of the few groups still interested in alife and CAs in the early 1970s; one of its students, Tommaso Toffoli argued in his PhD thesis that the field was important because its results explain the simple rules that underlay complex effects in nature. Toffoli later provided a key proof that CAs were reversible, just as the true universe is considered to be. Christopher Langton was an unconventional researcher, with an undistinguished academic career that led him to a job programming DEC mainframes for a hospital. He became enthralled by Conway's Game of Life, and began pursuing the idea that the computer could emulate living creatures. After years of study, he began attempting to actualize Von Neumann's CA and the work of Edgar F. Codd, who had simplified Von Neumann's original twenty-nine state monster to one with only eight states. He succeeded in creating the first self-replicating computer organism in October 1979, using only an Apple II desktop computer. He entered Burks' graduate program at the Logic of Computers Group in 1982, at the age of 33, and helped to found a new discipline. Langton's official conference announcement of Artificial Life I was the earliest description of a field which had previously barely existed: Artificial life is the study of artificial systems that exhibit behavior characteristic of natural living systems. It is the quest to explain life in any of its possible manifestations, without restriction to the particular examples that have evolved on earth. This includes biological and chemical experiments, computer simulations, and purely theoretical endeavors. Processes occurring on molecular, social, and evolutionary scales are subject to investigation. The ultimate goal is to extract the logical form of living systems. Microelectronic technology and genetic engineering will soon give us the capability to create new life forms in silico as well as in vitro. This capacity will present humanity with the most far-reaching technical, theoretical and ethical challenges it has ever confronted. The time seems appropriate for a gathering of those involved in attempts to simulate or synthesize aspects of living systems. Ed Fredkin founded the Information Mechanics Group at MIT, which united Toffoli, Norman Margolus, and Charles Bennett. This group created a computer especially designed to execute cellular automata, eventually reducing it to the size of a single circuit board. This "cellular automata machine" allowed an explosion of alife research among scientists who could not otherwise afford sophisticated computers. In 1982, computer scientist named Stephen Wolfram turned his attention to cellular automata. He explored and categorized the types of complexity displayed by one-dimensional CAs, and showed how they applied to natural phenomena such as the patterns of seashells and the nature of plant growth. Norman Packard, who worked with Wolfram at the Institute for Advanced Study, used CAs to simulate the growth of snowflakes, following very basic rules. Computer animator Craig Reynolds similarly used three simple rules to create recognizable flocking behaviour in a computer program in 1987 to animate groups of boids. With no top-down programming at all, the boids produced lifelike solutions to evading obstacles placed in their path. Computer animation has continued to be a key commercial driver of alife research as the creators of movies attempt to find more realistic and inexpensive ways to animate natural forms such as plant life, animal movement, hair growth, and complicated org

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  The Stories of Ibis

  The Stories of Ibis (アイの物語, Ai no Monogatari) is a Japanese science-fiction light novel by Hiroshi Yamamoto (山本 弘) and translated by Takami Nieda. Yamamoto considered this to be an easier read than his earlier science fiction novel 'God Never Keeps Silent' because of its "light novel touch". The light novel was published in Japanese by Kadokawa Shoten and in English by Viz Media under their 'Haikasoru' imprint. The Stories of Ibis is told through a collection of short stories. All but two had been previously published. The two that Yamamoto wrote for the novel were 'The Day Shion Came' and 'AI's Story'. This is similar to The Illustrated Man by Ray Bradbury. Yamamoto drew from Bradbury's idea of short stories that were loosely connected. He represented this influence in the novel by giving Ibis a facial tattoo. == Plot == The Stories of Ibis begins with a wandering storyteller who encounters Ibis. He has the mindset that all robots are a threat to humanity and must be fought against for survival. He attacks the robot Ibis, not aware of who she is, as a result of his mindset. Ibis tells the storyteller that she is far more proficient in battle. During the battle the storyteller becomes injured and Ibis takes him to an android hospital to care for him. While he is recovering Ibis offers to tell him stories. While originally skeptical he agrees after Ibis makes it clear that the stories are not taboo. The space after each story is referred to as intermission and is a time for Ibis to comment on the story she just told. === The Universe on my Hands === The story is about a group of friends who are writing a science fiction story over the internet. One of the group members kills someone in real life. The rest of the short story is about how the group fights to convince this man to not commit suicide, but to turn himself in. He resolves to turn himself in, being hopeful to the future because he knows he has friends who care about him. The ending words of the story are a commentary. While the story they were writing was not real, the emotions they were feeling were real. === A Romance in Virtual Space === This is another story about human interactions over the internet. The device that allows people to enter virtual reality (VR) is MUGEN Net. Such devices are extremely expensive and most people need to go to a public server to use one. However the girl's parents in this story are wealthy enough to own one. This girl is shopping in VR when a boy meets her and asks her out for ice cream. All goes well and they plan for another. After some time of VR dating and awesome adventures with a female heroine, they agree to meet up in real life. He discovers that in reality, she is blind, yet he thinks she is brave and they continue dating. It's a wonderful short story of a secret utopia inside a dystopian culture of technology. === Mirror Girl === A short story about an artificial intelligence that grows over time with human interaction. The inspiration for this story was Ray Bradbury's I Sing the Body Electric. The mirror girl Shalice starts off with basic knowledge and by interacting with her owner develops. The owner grows up and marries a technician who incubates Shalice by teaching her in the virtual world at many thousand times faster than average life. When he is done, Strong Eye is created. Strong Eye is the fully developed and completely intelligent AI. === Black Hole Diver === A futuristic story about an artificial space station and people who go diving into a black hole. The space station cannot stop people but is sorry that they go to their deaths because none of them get past the event horizon. Then one girl comes who has the space ship, the training, and the research necessary to attempt to dive into the black hole. As she goes into the black hole the space station can no longer observe. She may have made it, she could have been destroyed. === A World Where Justice is Just === An anime flavored story about the intelligence of people being scanned onto a computer network. The AIs in the network fight crime and live repeating lives. At the end of each year they start anew, but different story lines. Thousands of 'extras' populate the network and are the ones subject to harm and deletion. The protagonist has a pen pal in real life who explains to her that the real world is under attack and that there are no respawns and no extras. The AI finds this so cruel that people would willingly kill each other when they can't come back. === The Day Shion Came === The stories leading up to this were all relatively short. This and the next took up over 100 pages each. This is a story about an android named Shion who works in a Japanese nursing facility. Shion comes with only extensive nursing training but lacks the knowledge of how to communicate with the residents. After months of training she informs her adviser that she believes all humans have dementia, which explains their irrational behavior. Near the end of the story one of the residents threatens suicide but Shion convinces him to step down and be rational. === AI's Story === The culminating story of the entire novel. It is about Ibis herself. She starts off as a virtual reality fighting program and over time develops intelligence. Her master gains enough funds to create her a body in the real world or level 0. There is significant hate against TAIs (True Artificial Intelligence) in the real world. Ibis and her friend Raven rebel against their masters to make a point. Human hatred was destroying them. After many years robots took prevalence and most humans realized they were not worthy to be the guardians of Earth and died in peace. The remaining population was stubborn and fought against the robots for centuries. The storyteller is a child of this generation, being raised in hatred and ignorance. The robots sought to take him captive, and teach him the truth so that he could go to the villages where people lived and teach them the truth. The whole point was they cared for the humans and wanted them to live in peace, rather than fighting for their survival. == Reception == It was reviewed by the Denver Post to be an "excellent novel". Being a Japanese novel translated to English, it has a small audience. The novel was given a 3.85 of 5 by the reviewers at Librarything.com. The reviewers of Google Books gave it a 4.33 of 5.

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  Blackboard system

  A blackboard system is an artificial intelligence approach based on the blackboard architectural model, where a common knowledge base, the "blackboard", is iteratively updated by a diverse group of specialist knowledge sources, starting with a problem specification and ending with a solution. Each knowledge source updates the blackboard with a partial solution when its internal constraints match the blackboard state. In this way, the specialists work together to solve the problem. The blackboard model was originally designed as a way to handle complex, ill-defined problems, where the solution is the sum of its parts. == Metaphor == The following scenario provides a simple metaphor that gives some insight into how a blackboard functions: A group of specialists are seated in a room with a large blackboard. They work as a team to brainstorm a solution to a problem, using the blackboard as the workplace for cooperatively developing the solution. The session begins when the problem specifications are written onto the blackboard. The specialists all watch the blackboard, looking for an opportunity to apply their expertise to the developing solution. When someone writes something on the blackboard that allows another specialist to apply their expertise, the second specialist records their contribution on the blackboard, hopefully enabling other specialists to then apply their expertise. This process of adding contributions to the blackboard continues until the problem has been solved. == Components == A blackboard-system application consists of three major components The software specialist modules, which are called knowledge sources (KSs). Like the human experts at a blackboard, each knowledge source provides specific expertise needed by the application. The blackboard, a shared repository of problems, partial solutions, suggestions, and contributed information. The blackboard can be thought of as a dynamic "library" of contributions to the current problem that have been recently "published" by other knowledge sources. The control shell, which controls the flow of problem-solving activity in the system. Just as the eager human specialists need a moderator to prevent them from trampling each other in a mad dash to grab the chalk, KSs need a mechanism to organize their use in the most effective and coherent fashion. In a blackboard system, this is provided by the control shell. === Learnable Task Modeling Language === A blackboard system is the central space in a multi-agent system. It's used for describing the world as a communication platform for agents. To realize a blackboard in a computer program, a machine readable notation is needed in which facts can be stored. One attempt in doing so is a SQL database, another option is the Learnable Task Modeling Language (LTML). The syntax of the LTML planning language is similar to PDDL, but adds extra features like control structures and OWL-S models. LTML was developed in 2007 as part of a much larger project called POIROT (Plan Order Induction by Reasoning from One Trial), which is a Learning from demonstrations framework for process mining. In POIROT, Plan traces and hypotheses are stored in the LTML syntax for creating semantic web services. Here is a small example: A human user is executing a workflow in a computer game. The user presses some buttons and interacts with the game engine. While the user interacts with the game, a plan trace is created. That means the user's actions are stored in a logfile. The logfile gets transformed into a machine readable notation which is enriched by semantic attributes. The result is a textfile in the LTML syntax which is put on the blackboard. Agents (software programs in the blackboard system) are able to parse the LTML syntax. == Implementations == We start by discussing two well known early blackboard systems, BB1 and GBB, below and then discuss more recent implementations and applications. The BB1 blackboard architecture was originally inspired by studies of how humans plan to perform multiple tasks in a trip, used task-planning as a simplified example of tactical planning for the Office of Naval Research. Hayes-Roth & Hayes-Roth found that human planning was more closely modeled as an opportunistic process, in contrast to the primarily top-down planners used at the time: While not incompatible with successive-refinement models, our view of planning is somewhat different. We share the assumption that planning processes operate in a two-dimensional planning space defined on time and abstraction dimensions. However, we assume that people's planning activity is largely opportunistic. That is, at each point in the process, the planner's current decisions and observations suggest various opportunities for plan development. The planner's subsequent decisions follow up on selected opportunities. Sometimes, these decision-sequences follow an orderly path and produce a neat top-down expansion as described above. However, some decisions and observations might also suggest less orderly opportunities for plan development. A key innovation of BB1 was that it applied this opportunistic planning model to its own control, using the same blackboard model of incremental, opportunistic, problem-solving that was applied to solve domain problems. Meta-level reasoning with control knowledge sources could then monitor whether planning and problem-solving were proceeding as expected or stalled. If stalled, BB1 could switch from one strategy to another as conditions – such as the goals being considered or the time remaining – changed. BB1 was applied in multiple domains: construction site planning, inferring 3-D protein structures from X-ray crystallography, intelligent tutoring systems, and real-time patient monitoring. BB1 also allowed domain-general language frameworks to be designed for wide classes of problems. For example, the ACCORD language framework defined a particular approach to solving configuration problems. The problem-solving approach was to incrementally assemble a solution by adding objects and constraints, one at a time. Actions in the ACCORD language framework appear as short English-like commands or sentences for specifying preferred actions, events to trigger KSes, preconditions to run a KS action, and obviation conditions to discard a KS action that is no longer relevant. GBB focused on efficiency, in contrast to BB1, which focused more on sophisticated reasoning and opportunistic planning. GBB improves efficiency by allowing blackboards to be multi-dimensional, where dimensions can be either ordered or not, and then by increasing the efficiency of pattern matching. GBB1, one of GBB's control shells implements BB1's style of control while adding efficiency improvements. Other well-known of early academic blackboard systems are the Hearsay II speech recognition system and Douglas Hofstadter's Copycat and Numbo projects. Some more recent examples of deployed real-world applications include: The PLAN component of the Mission Control System for RADARSAT-1, an Earth observation satellite developed by Canada to monitor environmental changes and Earth's natural resources. The GTXImage CAD software by GTX Corporation was developed in the early 1990s using a set of rulebases and neural networks as specialists operating on a blackboard system. Adobe Acrobat Capture (now discontinued), as it used a blackboard system to decompose and recognize image pages to understand the objects, text, and fonts on the page. This function is currently built into the retail version of Adobe Acrobat as "OCR Text Recognition". Details of a similar OCR blackboard for Farsi text are in the public domain. Blackboard systems are used routinely in many military C4ISTAR systems for detecting and tracking objects. Another example of current use is in Game AI, where they are considered a standard AI tool to help with adding AI to video games. == Recent developments == Blackboard-like systems have been constructed within modern Bayesian machine learning settings, using agents to add and remove Bayesian network nodes. In these 'Bayesian Blackboard' systems, the heuristics can acquire more rigorous probabilistic meanings as proposal and acceptances in Metropolis Hastings sampling though the space of possible structures. Conversely, using these mappings, existing Metropolis-Hastings samplers over structural spaces may now thus be viewed as forms of blackboard systems even when not named as such by the authors. Such samplers are commonly found in musical transcription algorithms for example. Blackboard systems have also been used to build large-scale intelligent systems for the annotation of media content, automating parts of traditional social science research. In this domain, the problem of integrating various AI algorithms into a single intelligent system arises spontaneously, with blackboards providing a way for a collection of distributed, modular natural language processing algorithm

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  Subpixel rendering

  Subpixel rendering is a method used to increase the effective resolution of a color display device. It utilizes the composition of each pixel, which consists of three subpixels of which are red, green, and blue that can each be individually addressable on the display matrix. Subpixel rendering is primarily used for text rendering on standard DPI displays. Despite the inherent color anomalies, it can also be used to render general graphics. == History == The origin of subpixel rendering as used today remains controversial. Apple Inc., IBM, and Microsoft patented various implementations that differed in technical details owing to the different purposes for which their technologies were intended. Microsoft held several patents in the United States for subpixel rendering technology used in text rendering on RGB Stripe layouts. The patents 6,219,025; 6,239,783; 6,307,566; 6,225,973; 6,243,070; 6,393,145; 6,421,054; 6,282,327; and 6,624,828 were filed between October 7, 1998, and October 7, 1999, and expired on July 30, 2019. Analysis of the patent by FreeType indicates that the patent does not cover the idea of subpixel rendering, but rather the actual filter used as a last step to balance the color. Microsoft's patent describes the smallest possible filter that distributes each subpixel value equally among the R, G, and B pixels. Any other filter will either be blurrier or will introduce color artifacts. Apple was able to use it in Mac OS X due to a patent cross-licensing agreement. == Characteristics == A single pixel on a color display is made of several subpixels, typically three arranged left-to-right as red, green, and blue (RGB). The components are readily visible with a small magnifying glass, such as a loupe. These pixel components appear as a single color to the human eye because of blurring by optics and spatial integration by nerve cells in the eye. However, the eye is much more sensitive to the location. Therefore, turning on the G and B of one pixel and the R of the next pixel to the right will produce a white dot, but it will appear to be 1/3 of a pixel to the right of the white dot that would be seen from the RGB of only the first pixel. Subpixel rendering leverages this to provide three times the horizontal resolution of the rendered image. However, it has to blur this image to produce the correct color by ensuring the same amount of red, green, and blue are turned on as when no subpixel rendering is being done. Subpixel rendering does not necessitate the use of antialiasing. It gives a smoother result regardless of whether antialiasing is used or not since it artificially increases the resolution. However, it introduces color aliasing since subpixels are colored. Subsequent filtering applied to remove the color artifacts is a form of antialiasing, although its purpose is not smoothing jagged shapes as in conventional antialiasing. Subpixel rendering requires the software to know the layout of the subpixels. The most common reason it is wrong is monitors that can be rotated 90 (or 180) degrees, though monitors are manufactured with other arrangements of the subpixels, such as BGR or in triangles, or with 4 colors like RGBW squares. On any such display the result of incorrect subpixel rendering will be worse than if no subpixel rendering was done at all (it will not produce color artifacts, but it will produce noisy edges). == Implementations == === Apple II === Steve Gibson has claimed that the Apple II, introduced in 1977, supports an early form of subpixel rendering in its high-resolution (280×192) graphics mode. The Wozniak patent only used 2 "sub-pixels". The bytes that comprise the Apple II high-resolution screen buffer contain seven visible bits (each corresponding directly to a pixel) and a flag bit used to select between purple/green or blue/orange color sets. Each pixel, since it is represented by a single bit, is either on or off; there are no bits within the pixel itself for specifying color or brightness. Color is instead created as an artifact of the NTSC color encoding scheme, determined by horizontal position: pixels with even horizontal coordinates are always purple (or blue, if the flag bit is set), and odd pixels are always green (or orange). Two lit pixels next to each other are always white, regardless of whether the pair is even/odd or odd/even, and irrespective of the value of the flag bit. This is an approximation, but it is what most programmers of the time would have in mind while working with the Apple's high-resolution mode. Gibson's example claims that because two adjacent bits form a white block, there are, in fact, two bits per pixel: one that activates the pixel's purple left half and the other that activates its green right half. If the programmer instead activates the green right half of a pixel and the purple left half of the next pixel, the result is a white block 1/2 pixel to the right, which is indeed an instance of subpixel rendering. However, it is not clear whether any programmers of the Apple II have considered the pairs of bits as pixels—instead calling each bit a pixel. The flag bit in each byte affects color by shifting pixels half a pixel-width to the right. This half-pixel shift was exploited by some graphics software, such as HRCG (High-Resolution Character Generator), an Apple utility that displayed text using the high-resolution graphics mode, to smooth diagonals. === ClearType === Microsoft announced its subpixel rendering technology, called ClearType, at COMDEX in 1998. Microsoft published a paper in May 2000, Displaced Filtering for Patterned Displays, describing the filtering behind ClearType. It was then made available in Windows XP. Still, it was not activated by default until Windows Vista, while Windows XP OEMs could and did change the default setting. === FreeType === FreeType, the library used by most current software on the X Window System, contains two open source implementations. The original implementation uses the ClearType antialiasing filters and carries the following notice: "The colour filtering algorithm of Microsoft's ClearType technology for subpixel rendering is covered by patents; for this reason, the corresponding code in FreeType is disabled by default. Note that subpixel rendering per se is prior art; using a different colour filter thus easily circumvents Microsoft's patent claims." FreeType offers a variety of color filters. Since version 2.6.2, the default filter is light, a filter that is both normalized (value sums up to 1) and color-balanced (eliminate color fringes at the cost of resolution). Since version 2.8.1, a second implementation exists, called Harmony, that "offers high quality LCD-optimized output without resorting to ClearType techniques of resolution tripling and filtering". This is the method enabled by default. When using this method, "each color channel is generated separately after shifting the glyph outline, capitalizing on the fact that the color grids on LCD panels are shifted by a third of a pixel. This output is indistinguishable from ClearType with a light 3-tap filter." Since the Harmony method does not require additional filtering, it is not covered by the ClearType patents. === CoolType === Adobe created their own subpixel renderer called CoolType, allowing them to display documents the same way across various operating systems: Windows, MacOS, Linux etc. When it was launched around the year 2001, CoolType supported a wider range of fonts than Microsoft's ClearType, which at the time was limited to TrueType fonts. In contrast, Adobe's CoolType also supported PostScript fonts (and their OpenType equivalents). === macOS === Mac OS X (later OS X, now macOS) also used subpixel rendering, as part of Quartz 2D. However, it was removed after the introduction of Retina displays. Unlike Microsoft's implementation, which favors a tight fit to the grid (font hinting) to maximize legibility, Apple's implementation prioritizes the shape of the glyphs as set out by their designer.

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  Grokipedia

  Grokipedia is an AI-generated online encyclopedia operated by the American company xAI. The site was launched on October 27, 2025. Some entries are generated by Grok, a large language model owned by the same company, while others were forked from Wikipedia, with some altered and some used nearly verbatim. Articles cannot be directly edited, though logged-in visitors to the encyclopedia can suggest new articles or corrections via a pop-up form, which are reviewed by Grok. The xAI founder Elon Musk suggested Grokipedia could be an alternative to Wikipedia that would "purge out the propaganda" he believes is promoted by the latter, describing Wikipedia as "woke" and an "extension of legacy media propaganda". External analysis of Grokipedia's content has focused on its accuracy and biases due to hallucinations and potential algorithmic bias, which reviewers have described as promoting right-wing perspectives and Musk's views. The majority of coverage has described the website as validating, promoting, and legitimizing a variety of debunked conspiracy theories and ideas against scientific consensus on topics such as HIV/AIDS denialism, vaccines and autism, climate change, and race and intelligence. The site has been accused of whitewashing far-right extremism, such as by falsely claiming a white genocide is actively occurring. Several right-wing figures have welcomed the site. Studies have highlighted its use of sources deemed as having very low credibility such as X conversations and neo-Nazi websites, and for writing about far-right figures and topics in a promotional manner. == Background == Wikipedia is an online encyclopedia written and maintained by a community of volunteers. Its possible bias has been studied and debated. In 2018, Haaretz noted "Wikipedia has succeeded in being accused of being both too liberal and too conservative, and has critics from across the spectrum". xAI is an American AI company founded by Elon Musk in 2023. Its flagship product is the family of large language models called Grok. == History == In 2021, Musk expressed affection for Wikipedia on its 20th anniversary. In 2022, however, Musk argued that Wikipedia was "losing its objectivity", and in 2023, said he would donate US$1 billion to the project if it was pejoratively renamed "Dickipedia". In December 2024, Musk called for a boycott of donations to Wikipedia over its perceived left-wing bias, calling it "Wokepedia". In January 2025, Musk made a series of statements on Twitter denouncing Wikipedia for its description of the incident where he made a controversial gesture, which many viewed as resembling a Nazi salute, at president Donald Trump's second inauguration. Musk has since positioned Grokipedia as an alternative to Wikipedia that would "purge out the propaganda" in the latter, with Musk describing Wikipedia as "woke" and an "extension of legacy media propaganda". === Idea and announcement === In September 2025, Musk spoke at the All-In podcast conference with David O. Sacks, the White House advisor on AI and cryptocurrency, about how Grok consumed data from Wikipedia and other sources to gain more complete knowledge of the world. Sacks suggested publishing its knowledge base as an artifact called "Grokipedia", saying "Wikipedia is so biased, it's a constant war". Following the conversation, Musk announced that xAI was building a new AI-generated online encyclopedia called Grokipedia. According to Musk's announcement, it would be an AI-powered knowledge base designed to rival Wikipedia by addressing its perceived biases, errors, and ideological slants. The project positioned itself within a history of ideologically driven alternatives to Wikipedia, such as the conservative Conservapedia (launched in 2006) and the Russian-government-friendly Ruwiki (launched in 2023). However, Grokipedia is distinct in its core reliance on artificial intelligence rather than human community editing. === Launch and traffic === On October 6, 2025, Musk announced that the early version of Grokipedia was scheduled for release in two weeks, but the project was postponed briefly to address content quality issues. It launched on October 27, 2025, labeled "v 0.1", with over 800,000 articles, compared to over seven million English Wikipedia articles as of September 1, 2025. According to an initial analysis of usage figures by Similarweb, which evaluates data from registered users and partners, Grokipedia recorded a peak of over 460,000 website visits in the US on October 28, 2025. After that, traffic dropped significantly and settled at around 35,000 visits per day between November 8 and 11, 2025. As of early 2026, it had over 5.6 million articles. In January 2026, The Guardian reported that GPT-5.2 frequently cited Grokipedia as a source in responses, raising concerns of misinformation on ChatGPT. The same month, The Verge reported that Google's AI Overviews, AI Mode, and Gemini language model, as well as Microsoft Copilot and Perplexity AI, used Grokipedia to answer niche, obscure, or highly specific factual questions or "non-sensitive queries." According to a case study published by SEO Engico, the site received only 19 clicks from Google Search in November 2025 but reached approximately 3.2 million monthly clicks by January 2026, with over 900,000 pages indexed and millions of ranking keywords. Analysts attributed the surge in part to the site's technical structure and large-scale AI-generated content production. In early February 2026, Grokipedia's visibility in Google Search declined sharply. SEO analysts, including Glenn Gabe and Malte Landwehr, reported a significant drop in rankings across Google organic results as well as in Google AI Overviews and AI Mode. The same case study cited independent reviews that identified citation quality concerns, including references to low-credibility sources and instances of self-citation. By mid-February 2026, Grokipedia had reportedly lost much of its previous search visibility, and Wikipedia ranked above it for searches related to its own name. === Updates === ==== Future ==== In November 2025, Musk announced that he eventually plans to change the name of the site to Encyclopedia Galactica when Grokipedia is "good enough", saying that it had a "long way to go". This name is taken from the publication of that title in the works of Isaac Asimov and Douglas Adams. Musk said that he hoped to send copies of the encyclopedia to "the Moon and Mars and out to deep space". == Content == The Grok large language model generates and fact-checks articles on Grokipedia. Users cannot directly edit Grokipedia articles, but logged-in users can suggest edits and report errors, with such submissions being reviewed and implemented by the Grok AI. Some articles are nearly identical to their Wikipedia entries, but the format of Grokipedia citations is different, and some Grokipedia articles were republished almost verbatim, accompanied by a disclaimer noting that the content was "adapted from Wikipedia" under a Creative Commons license. Others were completely rewritten from scratch using Musk's AI chatbot, Grok. Forbes identified the articles AMD, Lamborghini, and PlayStation 5 as examples of copied Wikipedia articles. Articles attributed to Wikipedia carry a Creative Commons Attribution-ShareAlike license, while the license of other articles is licensed under the "X Community License", a license that accepts reuse and remixing for "non-commercial and research purposes" and commercial use that abides to "all of the guardrails provided in xAI's Acceptable Use Policy". On October 31, 2025, Musk clarified that the duplication of Wikipedia articles was intentional, saying that the Grokipedia team instructed Grok to compile Wikipedia's top 1 million articles and make content changes to them. The site's design has been described as minimalist with a simple homepage including little more than a large search bar. In a comparative textual analysis of the most heavily edited matched article pairs from Grokipedia and Wikipedia, Grokipedia entries are substantially longer and less densely referenced, indicating that AI-produced encyclopedias prioritize exposition rather than source-based validation. Starting in version 0.2, Grok reviews and implements approved suggested edits, and a small panel rotates through a display of the names of several recently edited articles. In February 2026, the Columbia Journalism Review reported on an analysis by the Tow Center for Digital Journalism finding that Grok, the AI behind Grokipedia, had increasingly begun suggesting and approving edits to the site itself without human involvement. According to the report, AI-generated edit suggestions overtook human submissions in December 2025 and accounted for more than three-quarters of proposed changes. The analysis raised concerns about transparency, editorial oversight, and fact-checking standards, particularly after instances in which Grok proposed or modified politically s

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  Generative AI pornography

  Generative AI pornography or simply AI pornography is a digitally created pornography produced through generative artificial intelligence (AI) technologies. Unlike traditional pornography, which involves real actors and cameras, this content is synthesized entirely by AI algorithms. These algorithms, including generative adversarial networks (GANs) and text-to-image models, generate lifelike images, videos, or animations from textual descriptions or datasets. == Functions and production strategies == AI pornography platforms, beyond account creation and social media linking, primarily enable users to generate sexual images through feature selection or text prompting. Users can customize bodies, clothing, and sociodemographic traits, and browse categorized galleries of user‑generated content. Several sites also support short pornographic videos or GIFs and modification tools such as nudifiers, deepfakes, and facemorphing. Platforms often allow fine‑tuning of parameters such as settings, style, or theme, and provide prompt enhancers or suggestions to improve outputs. Users may edit generated images, refine prior prompts, modify others’ work, or upload personal material as a basis, with iterative and collaborative content creation. Some websites additionally host interactive “erobots,” customizable in real time for appearance, personality, memories, speech, and profession, enabling tailored sexual and non‑sexual interactions. Less common features include VR integration, AI porn games, audio or doodle prompts, and consensual replication of individuals with verification. == History == The use of generative AI in the adult industry began in the late 2010s, initially focusing on AI-generated art, music, and visual content. This trend accelerated in 2022 with Stability AI's release of Stable Diffusion (SD), an open-source text-to-image model that enables users to generate images, including NSFW content, from text prompts using the LAION-Aesthetics subset of the LAION-5B dataset. Despite Stability AI's warnings against sexual imagery, SD's public release led to dedicated communities exploring both artistic and explicit content, sparking ethical debates over open-access AI and its use in adult media. By 2020, AI tools had advanced to generate highly realistic adult content, amplifying calls for regulation. === AI-generated influencers === One application of generative AI technology is the creation of AI-generated influencers on platforms such as OnlyFans and Instagram. These AI personas interact with users in ways that can mimic real human engagement, offering an entirely synthetic but convincing experience. While popular among niche audiences, these virtual influencers have prompted discussions about authenticity, consent, and the blurring line between human and AI-generated content, especially in adult entertainment. === The growth of AI porn sites === By 2023, websites dedicated to AI-generated adult content had gained traction, catering to audiences seeking customizable experiences. These platforms allow users to create or view AI-generated pornography tailored to their preferences. These platforms enable users to create or view AI-generated adult content appealing to different preferences through prompts and tags, customizing body type, facial features, and art styles. Tags further refine the output, creating niche and diverse content. Many sites feature extensive image libraries and continuous content feeds, combining personalization with discovery and enhancing user engagement. AI porn sites, therefore, attract those seeking unique or niche experiences, sparking debates on creativity and the ethical boundaries of AI in adult media. == Ethical concerns and misuse == The growth of generative AI pornography has also attracted some cause for criticism. AI technology can be exploited to create non-consensual pornographic material, posing risks similar to those seen with deepfake revenge porn and AI-generated NCII (Non-Consensual Intimate Image). A 2023 analysis found that 98% of deepfake videos online are pornographic, with 99% of the victims being women. Some famous celebrities victims of deepfake include Scarlett Johansson, Taylor Swift, and Maisie Williams. OpenAI is exploring whether NSFW content, such as erotica, can be responsibly generated in age-appropriate contexts while maintaining its ban on deepfakes. This proposal has attracted criticism from child safety campaigners who argue it undermines OpenAI's mission to develop "safe and beneficial" AI. Additionally, the Internet Watch Foundation has raised concerns about AI being used to generate sexual abuse content involving children. === AI-generated non-consensual intimate imagery (AI Undress) === Generative AI have extensively been used to produce pornography images and videos of non-consenting individuals. 404 Media reported a particular AI generated porn bot on Telegram has more than 100,000 monthly users. Alibaba, the Chinese tech company, released an AI video generation model in 2025 called Wan 2.1, which was modified to produce non-consensual pornography. Several US states are taking actions against using deepfake apps and sharing them on the internet. In 2024, San Francisco filed a landmark lawsuit to shut down "undress" apps that allow users to generate non-consensual AI nude images, citing violations of state laws. The case aligns with California's recent legislation—SB 926, SB 942, and SB 981—championed by Senators Aisha Wahab and Josh Becker and signed by Governor Gavin Newsom. These bills aim to protect individuals from AI-generated explicit images by criminalizing non-consensual distribution, mandating disclosures, and empowering victims to report and remove harmful content from platforms. === Differences from deepfake pornography === While both generative AI pornography and deepfake pornography rely on synthetic media, they differ in their methods and ethical considerations. Deepfake pornography typically involves altering existing footage of real individuals, often without their consent, using AI to superimpose faces, undress said persons, or modify scenes. In contrast, generative AI pornography is created using algorithms, producing hyper-realistic content without the need to upload real pictures of people. Hany Farid, digital image analysis expert, also described the difference between "AI porn" and "deepfake porn." == Legality == The legality of generative AI pornography varies widely by jurisdiction and remains an evolving issue. In some countries, laws addressing digital impersonation, obscenity, or deepfake technologies may indirectly apply, particularly when AI-generated content involves the likeness of real individuals without consent. The absence of a physical performer further complicates traditional regulatory frameworks, which are often grounded in performer protection and distribution laws. In the United States, legal responses have primarily focused on non-consensual deepfakes and impersonation. Some states, such as Virginia, California, and Texas, have enacted legislation criminalising the creation or distribution of non-consensual explicit deepfake content. However, there is no comprehensive federal law addressing AI-generated pornography, leaving a patchwork of legal interpretations and enforcement standards across different jurisdictions. According to a 2023 report, South Korea accounts for approximately 53% of global deepfake pornography production. In September 2024, South Korea's National Assembly amended the Act on Special Cases Concerning the Punishment of Sexual Crimes, introducing two significant reforms related to deepfake content. The first criminalises the possession, viewing, purchase, and storage of non-consensual deepfake material, with penalties of up to three years in prison or fines of up to 30 million won (approximately USD 20,000). The second reform specifically addresses the exploitation of minors, establishing that individuals who use deepfakes to threaten or blackmail minors face a minimum of three years' imprisonment, and at least five years if they coerce minors into unwanted acts. In England and Wales the Data (Use and Access) Act 2025 has legislated against the creation, or the request for creation, of intimate images by nudifying software or websites of another person who has not consented to this. However as of January 2026 this has not yet been brought into force.

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  Split Up (expert system)

  Split Up is an intelligent decision support system, which makes predictions about the distribution of marital property following divorce in Australia. It is designed to assist judges, registrars of the Family Court of Australia, mediators and lawyers. Split Up operates as a hybrid system, combining rule – based reasoning with neural network theory. Rule based reasoning operates within strict parameters, in the form: IF < condition(s) > then . Neural networks, by contrast, are considered to be better suited to generate decisions in uncertain domains, since they can be taught to weigh the factors considered by judicial decision makers from case data. Yet, they do not provide an explanation for the conclusions they reach. Split_up, with a view to overcome this flaw, uses argument structures proposed by Toulmin as the basis for representations from which explanations can be generated. == Application == In Australian family law, a judge in determining the distribution of property will: identify the assets of the marriage included in the common pool establish what percentage of the common pool each party will receive determine a final property order in line with the decisions made in 1. and 2. Split_Up implements step 1 and 2 : the common pool determination and the prediction of a percentage split. === The common pool determination === Since the determination of marital property is rule based, it is implemented using directed graphs. However, the percentage split between the parties is discretionary in that a judge has a wide discretion to look at each party's contributions to the marriage under section 79(4) of the Family Law Act 1975. Broadly, the contributions can be taken as financial or non-financial. The party who can demonstrate a larger contribution to the marital relationship will receive a larger proportion of the assets. The court may further look at each party's financial resources and future needs under section 75(2)of the Family Law Act 1975. These needs can include factors such as the inability to gain employment, the continued care of a child under 18 years of age or medical expenses. This means that different judges may and will reach different conclusions based on the same facts, since each judge assigns different relevant weights to each factor. Split_up determines the percentage split by using a combination of rule- based reasoning and neural networks. === The percentage split determination === In order to determine how judges weigh the different factors, 103 written judgements of commonplace cases were used to establish a database comprising 94 relevant factors for percentage split determination. The factors relevant for a percentage split determination are: Past contributions of a husband relative to those of a wife The husband's future needs relative to those of the wife The wealth of the marriage The factors relevant for a determination of past contributions are The relative direct and indirect contributions of both parties The length of the marriage The relative contributions of both parties to the homemaking role The hierarchy provides a structure that is used to decompose the task of predicting an outcome into 35 subtasks. Outputs of tasks further down the hierarchy are used as inputs into sub-tasks higher up the hierarchy. Each sub-task is treated as a separate and smaller data mining exercise. Twenty one solid arcs represent inferences performed with the use of rule sets. For example, the level of wealth of a marriage is determined by a rule, which uses the common pool value. By contrast, the fourteen dashed arcs establish inferences performed with the use of neural networks. These receive their name from the fact that they resemble a nervous system in the brain. They consist of many self – adjusting processing elements cooperating in a densely interconnected network. Each processing element generates a single output that is transmitted to the other processing element. The output signal of a processing element depends on the input to the processing element, i.e. each input is gated by a weighting factor that determines the amount of influence that the input will have on the output. The strength of the weighting factors is adjusted autonomously by the processing element as the data is processed. In Split_Up, the neural network is a statistical technique for learning the weights of each of the relevant attributes used in a percentage split determination of marital property. Hence the inputs to the neural network are contributions, future needs and wealth, and the output the percentage split predicted. On each arc there is a statistical weight. Using back propagation the neural network learns the necessary pattern to recognize the prediction. It is trained by repeatedly exposing it to examples of the problem and learning the significance (weights) of the input nodes. The neural network used by Split_up is said to generalise well if the output of the network is correct (or nearly correct) for examples not seen during training, which classifies it as an intelligent system. === Toulmin Argument Structure === Since the manner in which these weights are learned is primarily statistical, domain knowledge of legal rules and principles is not modelled directly. However, explanations for a legal conclusion in a domain as discretionary as the determining the distribution of property following divorce, are at least as important as the conclusion reached. Hence the creators of Split_Up used Toulmin Argument structures, to provide independent explanations of the conclusions reached. These operate on the basis that every argument makes an assertion based on some data. The assertion of the argument stands as the claim of the argument. Since knowing the data and the claim, does not necessarily mean that the claim follows from the data, a mechanism is required to justify the claim in the light of the data. The justification is known as the warrant. The backing of an argument supports the validity of the warrant. In the legal domain, this is typically a reference to a statute or a precedent. Here, a neural network (or rules), produce a conclusion from the data of an argument and the data, warrant and backing are reproduced to generate an explanation. It is noteworthy, though, that an argument's warrant is reproduced as an explanation regardless of the claim values used. This lack of claim - sensitivity must be overcome by the different users, i.e., the judge, the representatives for the wife and the representatives for the husband, each of whom is encouraged to use the system to prepare their cases, but not to rely exclusively on its outcome.

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  Convolutional neural network

  A convolutional neural network (CNN) is a type of feedforward neural network that learns features via filter (or kernel) optimization. This type of deep learning network has been applied to process and make predictions from many different types of data including text, images and audio. CNNs are the de-facto standard in deep learning-based approaches to computer vision and image processing, and have only recently been replaced—in some cases—by newer architectures such as the transformer. Vanishing gradients and exploding gradients, seen during backpropagation in earlier neural networks, are prevented by the regularization that comes from using shared weights over fewer connections. For example, for each neuron in the fully-connected layer, 10,000 weights would be required for processing an image sized 100 × 100 pixels. However, applying cascaded convolution (or cross-correlation) kernels, only 25 weights for each convolutional layer are required to process 5x5-sized tiles. Higher-layer features are extracted from wider context windows, compared to lower-layer features. Some applications of CNNs include: image and video recognition, recommender systems, image classification, image segmentation, medical image analysis, natural language processing, brain–computer interfaces, and financial time series. CNNs are also known as shift invariant or space invariant artificial neural networks, based on the shared-weight architecture of the convolution kernels or filters that slide along input features and provide translation-equivariant responses known as feature maps. Counter-intuitively, most convolutional neural networks are not invariant to translation, due to the downsampling operation they apply to the input. Feedforward neural networks are usually fully connected networks, that is, each neuron in one layer is connected to all neurons in the next layer. The "full connectivity" of these networks makes them prone to overfitting data. Typical ways of regularization, or preventing overfitting, include: penalizing parameters during training (such as weight decay) or trimming connectivity (skipped connections, dropout, etc.) Robust datasets also increase the probability that CNNs will learn the generalized principles that characterize a given dataset rather than the biases of a poorly-populated set. Convolutional networks were inspired by biological processes in that the connectivity pattern between neurons resembles the organization of the animal visual cortex. Individual cortical neurons respond to stimuli only in a restricted region of the visual field known as the receptive field. The receptive fields of different neurons partially overlap such that they cover the entire visual field. CNNs use relatively little pre-processing compared to other image classification algorithms. This means that the network learns to optimize the filters (or kernels) through automated learning, whereas in traditional algorithms these filters are hand-engineered. This simplifies and automates the process, enhancing efficiency and scalability overcoming human-intervention bottlenecks. == Architecture == A convolutional neural network consists of an input layer, hidden layers and an output layer. In a convolutional neural network, the hidden layers include one or more layers that perform convolutions. Typically this includes a layer that performs a dot product of the convolution kernel with the layer's input matrix. This product is usually the Frobenius inner product, and its activation function is commonly ReLU. As the convolution kernel slides along the input matrix for the layer, the convolution operation generates a feature map, which in turn contributes to the input of the next layer. This is followed by other layers such as pooling layers, fully connected layers, and normalization layers. Here it should be noted how close a convolutional neural network is to a matched filter. === Convolutional layers === In a CNN, the input is a tensor with shape: (number of inputs) × (input height) × (input width) × (input channels) After passing through a convolutional layer, the image becomes abstracted to a feature map, also called an activation map, with shape: (number of inputs) × (feature map height) × (feature map width) × (feature map channels). Convolutional layers convolve the input and pass its result to the next layer. This is similar to the response of a neuron in the visual cortex to a specific stimulus. Each convolutional neuron processes data only for its receptive field. Although fully connected feedforward neural networks can be used to learn features and classify data, this architecture is generally impractical for larger inputs (e.g., high-resolution images), which would require massive numbers of neurons because each pixel is a relevant input feature. A fully connected layer for an image of size 100 × 100 has 10,000 weights for each neuron in the second layer. Convolution reduces the number of free parameters, allowing the network to be deeper. For example, using a 5 × 5 tiling region, each with the same shared weights, requires only 25 neurons. Using shared weights means there are many fewer parameters, which helps avoid the vanishing gradients and exploding gradients problems seen during backpropagation in earlier neural networks. To speed processing, standard convolutional layers can be replaced by depthwise separable convolutional layers, which are based on a depthwise convolution followed by a pointwise convolution. The depthwise convolution is a spatial convolution applied independently over each channel of the input tensor, while the pointwise convolution is a standard convolution restricted to the use of 1 × 1 {\displaystyle 1\times 1} kernels. === Pooling layers === Convolutional networks may include local and/or global pooling layers along with traditional convolutional layers. Pooling layers reduce the dimensions of data by combining the outputs of neuron clusters at one layer into a single neuron in the next layer. Local pooling combines small clusters, tiling sizes such as 2 × 2 are commonly used. Global pooling acts on all the neurons of the feature map. There are two common types of pooling in popular use: max and average. Max pooling uses the maximum value of each local cluster of neurons in the feature map, while average pooling takes the average value. === Fully connected layers === Fully connected layers connect every neuron in one layer to every neuron in another layer. It is the same as a traditional multilayer perceptron neural network (MLP). Each neuron in the fully connected layer receives input from all the neurons in the previous layer. These inputs are weighted and summed with the corresponding biases, and then passed through an activation function to perform a nonlinear transformation, generating the output. The flattened matrix goes through a fully connected layer to classify the images. === Receptive field === In neural networks, each neuron receives input from some number of locations in the previous layer. In a convolutional layer, each neuron receives input from only a restricted area of the previous layer called the neuron's receptive field. Typically the area is a square (e.g. 5 by 5 neurons). Whereas, in a fully connected layer, the receptive field is the entire previous layer. Thus, in each convolutional layer, each neuron takes input from a larger area in the input than previous layers. This is due to applying the convolution over and over, which takes the value of a pixel into account, as well as its surrounding pixels. When using dilated layers, the number of pixels in the receptive field remains constant, but the field is more sparsely populated as its dimensions grow when combining the effect of several layers. To manipulate the receptive field size as desired, there are some alternatives to the standard convolutional layer. For example, atrous or dilated convolution expands the receptive field size without increasing the number of parameters by interleaving visible and blind regions. Moreover, a single dilated convolutional layer can comprise filters with multiple dilation ratios, thus having a variable receptive field size. === Weights === Each neuron in a neural network computes an output value by applying a specific function to the input values received from the receptive field in the previous layer. The function that is applied to the input values is determined by a vector of weights and a bias (typically real numbers). Learning consists of iteratively adjusting these biases and weights. The vectors of weights and biases are called filters and represent particular features of the input (e.g., a particular shape). A distinguishing feature of CNNs is that many neurons can share the same filter. This reduces the memory footprint because a single bias and a single vector of weights are used across all receptive fields that share that filter, as opposed to each receptive field having its own bias and vector

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  Generative engine optimization

  Generative engine optimization (GEO) is one of the names given to the practice of structuring digital content and managing online presence to improve visibility in responses generated by generative artificial intelligence (AI) systems. The practice influences the way large language models (LLMs) retrieve, summarize, and present information in response to user queries. Related terms include answer engine optimization (AEO) and artificial intelligence optimization (AIO). The concept of GEO first appeared in response to generative AI technologies being integrated into mainstream search and information retrieval systems. Tools are used to monitor how websites and brands are cited, referenced, or incorporated into responses produced by large language models. == Terminology == Several overlapping terms describe related practices, and usage varies across practitioners, vendors, and publications. No consensus definition distinguishing these terms had been established in the academic literature as of early 2026, and the terms are frequently used interchangeably in trade and practitioner contexts. Other terms for the same concept include answer engine optimization (AEO), large language model optimization (LLMO), artificial intelligence optimization (AIO), and AI SEO. In 2026, Google released documentation entitled "Optimizing your website for generative AI features on Google Search." According to this documentation, "optimizing for generative AI search is optimizing for the search experience, and thus still SEO.” This position had previously been shared at conferences, with 2026 being the first time Google released official documentation stating it. == Factors influencing generative engine optimization == By early 2026, the focus of GEO practitioners shifted from simple keyword placement to "semantic relevance", a metric driven by the integration of advertising into conversational AI. OpenAI and Google began monetizing AI search results, which is not currently considered an aspect of generative engine optimization but is adjacent.

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  Futuresport

  Futuresport is a 1998 American made-for-television sports film directed by Ernest Dickerson, starring Dean Cain, Vanessa Williams, and Wesley Snipes. It originally aired on ABC in October 1998, was released on VHS and DVD in March 1999 and then distributed outside of the U.S. by Minerva Pictures. == Plot == The film is set in 2025, and centers on a sport called "Futuresport" (a combination of basketball, baseball and hockey that uses hoverboards and rollerblades) created as a non-lethal way to reduce gang warfare. Tre Ramzey (Dean Cain) along with his ex-girlfriend Alex Torres (Vanessa Williams) and his old coach Obike Fixx (Wesley Snipes) must prevent an all out war between the North American Alliance and the Pan-Pacific Commonwealth (The Com). At stake is who rules over the Hawaiian Islands—which are being terrorized by Eric Sythe (JR Bourne) and his gang the Hawaiian Liberation Organization (Hilo). It takes a revolutionary sport to stop a revolution. == Cast ==

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  Void Trilogy

  The Void Trilogy is a space opera series by British author Peter F. Hamilton. The series is set in the same universe as The Commonwealth Saga, 1,200 years after the end of Judas Unchained. Peter F. Hamilton sold the American rights to the series to Random House. The series includes the following books: The Dreaming Void (2007) The Temporal Void (2008) The Evolutionary Void (2010) == Synopsis == === The Dreaming Void === What was formerly believed to be a supermassive black hole at the centre of the Milky Way is revealed to be an artificial construct, known as the Void. Inside, there is a strange universe where the laws of physics are very different from standard physics. It is slowly consuming the other stars of the galactic core—one day it will have devoured the entire galaxy. In AD 3320, a human member of the Commonwealth, Inigo, begins to have dreams of the wonderful existence inside the Void. His dreams inspire the disaffected, who desire to travel into the Void, where their every wish will be fulfilled. By AD 3456, the pseudo-religious Living Dream movement exceeds 5 billion members, organizing the followers into a powerful political force. Other star-faring species fear their migration will cause the Void to expand again thus devouring the galaxy. They are prepared to stop the pilgrimage fleet no matter what the cost. The Dreaming Void is broken into two distinct sections. The first follows Edeard, a young boy who lives inside the Void on a planet called Querencia, the subject of Inigo's dreams. Edeard, an orphan and apprentice, lives in Ashwell, a town in Rulan province. A gifted psychic, he is trained by Master Akeem in crafting and modding. Initially a loner, he comes to prominence in his village after designing an alternative pump mechanism for the local well. Unfortunately his luck changes for the worse after Ashwell is raided by bandits. Forced to flee, he joins the local caravan and travels to Makkathran, the capital of Querencia. In Makkathran, Edeard joins the constables and after a brutal couple of months in training, he graduates and is promoted to the commander of his Squad. He makes little progress battling the rigid and backward judicial system of Makkathran; his first real break is when his squad overcomes a trap set by the local gang, and Edeard walks on water chasing the leader of the gang. A testament to his growing psychic abilities, Edeard's stunt earns him the title of Waterwalker, and he becomes an instant star in Makkathran. The second section of The Dreaming Void is set back in the Commonwealth. Inigo, the first dreamer, and founder of Living Dream, has disappeared, leaving the 5 billion strong Living Dream movement in a state of flux. When Ethan, succeeding Inigo as the head of the movement, proclaims that the Living Dream will embark on a pilgrimage into the Void, the Commonwealth is thrown into a state of political chaos. Fearing that the human migration might cause the Void to expand (and in the process destroy whole systems or even the whole Galaxy) other spacefaring races such as the Raiel and Ocisen Empire are deeply concerned, with the latter threatening military action. This has left the Commonwealth government deeply divided, with the two largest factions in disagreement, the Accelerators faction/party supporting the pilgrimage and the Conservative faction opposing. As both parties are unable to solve the situation politically they have resolved to take matters into their own hands, with each party sending agents to further its interests. Aaron, a sleeper cell agent, is tasked with finding Inigo. He kidnaps and manipulates Corrie-Lyn, a former lover of Inigo and interrogates her for information. He also travels to Kuhmo (Inigo's homeworld) to get further information and robs Inigo's secure storage (a bank for memory). He eventually tracks Inigo to Hanko, a desolate and barren world. However, before Aaron can extract Inigo, Accelerator agents destroy Aaron's starship leaving him marooned on Hanko. Meanwhile, Accelerator agents make a deal with Ethan, agreeing to give the Living Dream movement Ultra Drives to power their ships. Accelerator plans are halted when the Delivery Man, a Conservative party agent, destroys valuable FTL Drive tech. Troblum, an Accelerator physicist, also defects, further slowing the Accelerators plans. === The Temporal Void === The Temporal Void picks up after The Dreaming Void. The Intersolar Commonwealth faces mounting turmoil as the deadline for Living Dream's Pilgrimage into the Void approaches. An Ocisen Empire fleet advances on a mission of genocide, while an internecine war erupts among post-human factions over humanity's future. Amidst the chaos, investigator Paula Myo struggles to counter the increasingly desperate actions of various agents and factions. Relentless in her pursuit, she contends with adversaries from her distant past and colleagues of uncertain loyalty, all while racing against time. At the center of the unfolding crisis is Edeard the Waterwalker, a figure from the distant past who lived deep within the Void. As the messiah of Living Dream, his life—broadcast through visions—captivates and inspires billions. His story fuels the Pilgrimage's momentum, a force seemingly impossible to stop. As Edeard approaches his ultimate victory, the true nature of the Void is finally revealed. === The Evolutionary Void === The Evolutionary Void picks up after The Temporal Void. Exposed as the Second Dreamer, Araminta has become the target of a galaxy-wide search by government agent Paula Myo and the psychopath known as the Cat, along with others equally determined to prevent, or facilitate, the pilgrimage of the Living Dream cult into the heart of the Void. An indestructible microuniverse, the Void may contain paradise, as the cultists believe, but it is also a deadly threat. For the miraculous reality that exists inside its boundaries demands energy, energy drawn from everything outside those boundaries: from planets, stars, galaxies, and everything that lives, for the Pilgrimage will trigger a super-massive expansion of the Void. Meanwhile, the parallel story of Edeard, the Waterwalker, as told through a series of dreams communicated to the gaiafield via Inigo, the First Dreamer, continues to unfold. But the inspirational tale of this idealistic young man takes a darker and more troubling turn as he finds himself faced with powerful new enemies, and temptations more powerful still, to reach fulfilment in the end. Named a Silfen Friend like her ancestress Mellanie, Araminta chooses to face her unwanted responsibilities, with no guarantee of success or survival. She takes on the role of Second Dreamer to lead the first wave of Living Dream, 24 million people, into the Void, leaving everyone confused and lost by her actions. However, in actuality, she is playing a double game. Using her original body to lead the Living Dream as a diversion, she borrows one of her fiancé's (Mr. Bovey) bodies to set out to destroy the Void. She is able to connect with a Skylord and travel the Silfen Paths. With time running out, a repentant Inigo decides to release Edeard's final dream whose message is scarcely less dangerous than the pilgrimage promises to be, where perfection is achieved, so that nothing else is left to strive for and the human race in the Void has started to devolve. He goes to the Spike to meet Ozzie and stays there to meet with Araminta, who is using one of her fiancé's bodies, and Oscar. Third Dreamer Gore Burnelli has a plan to reason with the Heart, the core of the Void. He secures the help of the Delivery Man and travels to the Anomine homeworld to retrieve the mechanism that allowed them to go post-physical. He is able to connect with Justine, his daughter, who is currently in the Void, by way of Dreams. The monomaniacal Ilanthe, leader of the breakaway Accelerator Faction, seeks dominion in the Void. It is not Fusion with the Void to attain post-physical status that she wants, but to have control over everything. Using Dark Fortress technology, she sets up a barrier around the Sol system which leaves ANA and the deterrence fleet trapped inside. It is this technology which she has equipped the ships travelling to the Void with, the ability to create a forcefield which the Warrior Raiel cannot penetrate. == Technology == The Commonwealth uses a number of advanced technologies. In the early days of the Commonwealth, humans used static and permanently opened wormholes to travel from planet to planet. However, after the events of the Starflyer War (detailed in the Commonwealth Saga), the CST corporation's monopoly on space travel was ended. With the advent of wormholes that could wrap around ships, the Commonwealth saw a shift from wormholes to spaceships. Another development in the Commonwealth is the gaiafield. Developed by Ozzie Issac in AD 3000, the gaiafield is based on Silfen technology; when Ozzie was named a friend of the Silfen during the Starflye

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  Object Data Management Group

  The Object Data Management Group (ODMG) was conceived in the summer of 1991 at a breakfast with object database vendors that was organized by Rick Cattell of Sun Microsystems. In 1998, the ODMG changed its name from the Object Database Management Group to reflect the expansion of its efforts to include specifications for both object database and object–relational mapping products. The primary goal of the ODMG was to put forward a set of specifications that allowed a developer to write portable applications for object database and object–relational mapping products. In order to do that, the data schema, programming language bindings, and data manipulation and query languages needed to be portable. Between 1993 and 2001, the ODMG published five revisions to its specification. The last revision was ODMG version 3.0, after which the group disbanded. == Major components of the ODMG 3.0 specification == Object Model. This was based on the Object Management Group's Object Model. The OMG core model was designed to be a common denominator for object request brokers, object database systems, object programming languages, etc. The ODMG designed a profile by adding components to the OMG core object model. Object Specification Languages. The ODMG Object Definition Language (ODL) was used to define the object types that conform to the ODMG Object Model. The ODMG Object Interchange Format (OIF) was used to dump and load the current state to or from a file or set of files. Object Query Language (OQL). The ODMG OQL was a declarative (nonprocedural) language for query and updating. It used SQL as a basis, where possible, though OQL supports more powerful object-oriented capabilities. C++ Language Binding. This defined a C++ binding of the ODMG ODL and a C++ Object Manipulation Language (OML). The C++ ODL was expressed as a library that provides classes and functions to implement the concepts defined in the ODMG Object Model. The C++ OML syntax and semantics are those of standard C++ in the context of the standard class library. The C++ binding also provided a mechanism to invoke OQL. Smalltalk Language Binding. This defined the mapping between the ODMG ODL and Smalltalk, which was based on the OMG Smalltalk binding for the OMG Interface Definition Language (IDL). The Smalltalk binding also provided a mechanism to invoke OQL. Java Language Binding. This defined the binding between the ODMG ODL and the Java programming language as defined by the Java 2 Platform. The Java binding also provided a mechanism to invoke OQL. == Status == ODMG 3.0 was published in book form in 2000.[1] By 2001, most of the major object database and object-relational mapping vendors claimed conformance to the ODMG Java Language Binding. Compliance to the other components of the specification was mixed.[2] In 2001, the ODMG Java Language Binding was submitted to the Java Community Process as a basis for the Java Data Objects specification. The ODMG member companies then decided to concentrate their efforts on the Java Data Objects specification. As a result, the ODMG disbanded in 2001. In 2004, the Object Management Group (OMG) was granted the right to revise the ODMG 3.0 specification as an OMG specification by the copyright holder, Morgan Kaufmann Publishers. In February 2006, the OMG announced the formation of the Object Database Technology Working Group (ODBT WG) and plans to work on the 4th generation of an object database standard. == ODMG Compliant DBMS == Orient ODBMS: http://www.OrienTechnologies.com Objectivity/DB C++, Java and Smalltalk interfaces.

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  SF8

  SF8 (Korean: 에스 에프 에잇) is a South Korean science fiction anthology television series. It is a movie-drama crossover project between MBC, the Directors Guild of Korea, the OTT platform Wavve and the production company Soo Film. The director's cuts of all episodes were released on Wavve on July 10, 2020 while MBC TV aired one episode a week from August 14 to October 9, 2020. The series has been regarded as a Korean equivalent of the British series Black Mirror as they have the same format and similar themes, though Min Kyu-dong believes that SF8 is more diversified since eight different filmmakers were involved in the project. SF8 was screened at the 24th Bucheon International Fantastic Film Festival. == Synopsis == SF8 revolves around people who dream of a perfect society. It tackles the themes of artificial intelligence, augmented reality, virtual reality, robots, games, fantasy, horror, superpowers and disasters. == Episodes == Short summaries adapted from BiFan. == Production == === Development === Min Kyu-dong, creator of the series, said that "sci-fi movies were the driving force behind many movie directors' dreams. Unfortunately, due to the relatively high budget and narrow market limitations, various works were not able to be produced." He had been working on this project for two years before he partnered with Wavve and MBC. He also took charge of casting the actors, which lasted for a year. During a press conference held at CGV Yongsan I'Park Mall in Seoul on July 8, 2020, Min Kyu-dong said that all the episodes were produced with an equal amount of budget and that the overall budget was lower than one of a small commercial film. Roh Deok, who co-wrote and directed the "Manxin" episode, mentioned that "while commercial film productions [...] inevitably limit the directors' freedom as a creator, [they] had more independence in production" and "although there were physical limits, [he] thinks [they] went through the process of discovering what [they] can do inside those boundaries." === Filming === Eight directors from the Directors Guild of Korea (DGK) each directed an episode from the series. Filming began on February 21, 2020 with Jang Cheol-soo's "White Crow" and ended on May 7 with Kim Ui-seok's "Empty Body". Filming was completed within 10 filming sessions for each episode. === Credits === Credits adapted from BiFan. == Release == The director's cut was released on the OTT platform Wavve on July 10, 2020 and the original episodes were aired on MBC TV from August 14 to October 9.

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  Construction of t-norms

  In mathematics, t-norms are a special kind of binary operations on the real unit interval [0, 1]. Various constructions of t-norms, either by explicit definition or by transformation from previously known functions, provide a plenitude of examples and classes of t-norms. This is important, e.g., for finding counter-examples or supplying t-norms with particular properties for use in engineering applications of fuzzy logic. The main ways of construction of t-norms include using generators, defining parametric classes of t-norms, rotations, or ordinal sums of t-norms. Relevant background can be found in the article on t-norms. == Generators of t-norms == The method of constructing t-norms by generators consists in using a unary function (generator) to transform some known binary function (most often, addition or multiplication) into a t-norm. In order to allow using non-bijective generators, which do not have the inverse function, the following notion of pseudo-inverse function is employed: Let f: [a, b] → [c, d] be a monotone function between two closed subintervals of extended real line. The pseudo-inverse function to f is the function f (−1): [c, d] → [a, b] defined as f ( − 1 ) ( y ) = { sup { x ∈ [ a , b ] ∣ f ( x ) < y } for f non-decreasing sup { x ∈ [ a , b ] ∣ f ( x ) > y } for f non-increasing. {\displaystyle f^{(-1)}(y)={\begin{cases}\sup\{x\in [a,b]\mid f(x)y\}&{\text{for }}f{\text{ non-increasing.}}\end{cases}}} === Additive generators === The construction of t-norms by additive generators is based on the following theorem: Let f: [0, 1] → [0, +∞] be a strictly decreasing function such that f(1) = 0 and f(x) + f(y) is in the range of f or in [f(0+), +∞] for all x, y in [0, 1]. Then the function T: [0, 1]2 → [0, 1] defined as T(x, y) = f (-1)(f(x) + f(y)) is a t-norm. Alternatively, one may avoid using the notion of pseudo-inverse function by having T ( x , y ) = f − 1 ( min ( f ( 0 + ) , f ( x ) + f ( y ) ) ) {\displaystyle T(x,y)=f^{-1}\left(\min \left(f(0^{+}),f(x)+f(y)\right)\right)} . The corresponding residuum can then be expressed as ( x ⇒ y ) = f − 1 ( max ( 0 , f ( y ) − f ( x ) ) ) {\displaystyle (x\Rightarrow y)=f^{-1}\left(\max \left(0,f(y)-f(x)\right)\right)} . And the biresiduum as ( x ⇔ y ) = f − 1 ( | f ( x ) − f ( y ) | ) {\displaystyle (x\Leftrightarrow y)=f^{-1}\left(\left|f(x)-f(y)\right|\right)} . If a t-norm T results from the latter construction by a function f which is right-continuous in 0, then f is called an additive generator of T. Examples: The function f(x) = 1 – x for x in [0, 1] is an additive generator of the Łukasiewicz t-norm. The function f defined as f(x) = –log(x) if 0 < x ≤ 1 and f(0) = +∞ is an additive generator of the product t-norm. The function f defined as f(x) = 2 – x if 0 ≤ x < 1 and f(1) = 0 is an additive generator of the drastic t-norm. Basic properties of additive generators are summarized by the following theorem: Let f: [0, 1] → [0, +∞] be an additive generator of a t-norm T. Then: T is an Archimedean t-norm. T is continuous if and only if f is continuous. T is strictly monotone if and only if f(0) = +∞. Each element of (0, 1) is a nilpotent element of T if and only if f(0) < +∞. The multiple of f by a positive constant is also an additive generator of T. T has no non-trivial idempotents. (Consequently, e.g., the minimum t-norm has no additive generator.) === Multiplicative generators === The isomorphism between addition on [0, +∞] and multiplication on [0, 1] by the logarithm and the exponential function allow two-way transformations between additive and multiplicative generators of a t-norm. If f is an additive generator of a t-norm T, then the function h: [0, 1] → [0, 1] defined as h(x) = e−f (x) is a multiplicative generator of T, that is, a function h such that h is strictly increasing h(1) = 1 h(x) · h(y) is in the range of h or equal to 0 or h(0+) for all x, y in [0, 1] h is right-continuous in 0 T(x, y) = h (−1)(h(x) · h(y)). Vice versa, if h is a multiplicative generator of T, then f: [0, 1] → [0, +∞] defined by f(x) = −log(h(x)) is an additive generator of T. == Parametric classes of t-norms == Many families of related t-norms can be defined by an explicit formula depending on a parameter p. This section lists the best known parameterized families of t-norms. The following definitions will be used in the list: A family of t-norms Tp parameterized by p is increasing if Tp(x, y) ≤ Tq(x, y) for all x, y in [0, 1] whenever p ≤ q (similarly for decreasing and strictly increasing or decreasing). A family of t-norms Tp is continuous with respect to the parameter p if lim p → p 0 T p = T p 0 {\displaystyle \lim _{p\to p_{0}}T_{p}=T_{p_{0}}} for all values p0 of the parameter. === Schweizer–Sklar t-norms === The family of Schweizer–Sklar t-norms, introduced by Berthold Schweizer and Abe Sklar in the early 1960s, is given by the parametric definition T p S S ( x , y ) = { T min ( x , y ) if p = − ∞ ( x p + y p − 1 ) 1 / p if − ∞ < p < 0 T p r o d ( x , y ) if p = 0 ( max ( 0 , x p + y p − 1 ) ) 1 / p if 0 < p < + ∞ T D ( x , y ) if p = + ∞ . {\displaystyle T_{p}^{\mathrm {SS} }(x,y)={\begin{cases}T_{\min }(x,y)&{\text{if }}p=-\infty \\(x^{p}+y^{p}-1)^{1/p}&{\text{if }}-\infty −∞ Continuous if and only if p < +∞ Strict if and only if −∞ < p ≤ 0 (for p = −1 it is the Hamacher product) Nilpotent if and only if 0 < p < +∞ (for p = 1 it is the Łukasiewicz t-norm). The family is strictly decreasing for p ≥ 0 and continuous with respect to p in [−∞, +∞]. An additive generator for T p S S {\displaystyle T_{p}^{\mathrm {SS} }} for −∞ < p < +∞ is f p S S ( x ) = { − log ⁡ x if p = 0 1 − x p p otherwise. {\displaystyle f_{p}^{\mathrm {SS} }(x)={\begin{cases}-\log x&{\text{if }}p=0\\{\frac {1-x^{p}}{p}}&{\text{otherwise.}}\end{cases}}} === Hamacher t-norms === The family of Hamacher t-norms, introduced by Horst Hamacher in the late 1970s, is given by the following parametric definition for 0 ≤ p ≤ +∞: T p H ( x , y ) = { T D ( x , y ) if p = + ∞ 0 if p = x = y = 0 x y p + ( 1 − p ) ( x + y − x y ) otherwise. {\displaystyle T_{p}^{\mathrm {H} }(x,y)={\begin{cases}T_{\mathrm {D} }(x,y)&{\text{if }}p=+\infty \\0&{\text{if }}p=x=y=0\\{\frac {xy}{p+(1-p)(x+y-xy)}}&{\text{otherwise.}}\end{cases}}} The t-norm T 0 H {\displaystyle T_{0}^{\mathrm {H} }} is called the Hamacher product. Hamacher t-norms are the only t-norms which are rational functions. The Hamacher t-norm T p H {\displaystyle T_{p}^{\mathrm {H} }} is strict if and only if p < +∞ (for p = 1 it is the product t-norm). The family is strictly decreasing and continuous with respect to p. An additive generator of T p H {\displaystyle T_{p}^{\mathrm {H} }} for p < +∞ is f p H ( x ) = { 1 − x x if p = 0 log ⁡ p + ( 1 − p ) x x otherwise. {\displaystyle f_{p}^{\mathrm {H} }(x)={\begin{cases}{\frac {1-x}{x}}&{\text{if }}p=0\\\log {\frac {p+(1-p)x}{x}}&{\text{otherwise.}}\end{cases}}} === Frank t-norms === The family of Frank t-norms, introduced by M.J. Frank in the late 1970s, is given by the parametric definition for 0 ≤ p ≤ +∞ as follows: T p F ( x , y ) = { T m i n ( x , y ) if p = 0 T p r o d ( x , y ) if p = 1 T L u k ( x , y ) if p = + ∞ log p ⁡ ( 1 + ( p x − 1 ) ( p y − 1 ) p − 1 ) otherwise. {\displaystyle T_{p}^{\mathrm {F} }(x,y)={\begin{cases}T_{\mathrm {min} }(x,y)&{\text{if }}p=0\\T_{\mathrm {prod} }(x,y)&{\text{if }}p=1\\T_{\mathrm {Luk} }(x,y)&{\text{if }}p=+\infty \\\log _{p}\left(1+{\frac {(p^{x}-1)(p^{y}-1)}{p-1}}\right)&{\text{otherwise.}}\end{cases}}} The Frank t-norm T p F {\displaystyle T_{p}^{\mathrm {F} }} is strict if p < +∞. The family is strictly decreasing and continuous with respect to p. An additive generator for T p F {\displaystyle T_{p}^{\mathrm {F} }} is f p F ( x ) = { − log ⁡ x if p = 1 1 − x if p = + ∞ log ⁡ p − 1 p x − 1 otherwise. {\displaystyle f_{p}^{\mathrm {F} }(x)={\begin{cases}-\log x&{\text{if }}p=1\\1-x&{\text{if }}p=+\infty \\\log {\frac {p-1}{p^{x}-1}}&{\text{otherwise.}}\end{cases}}} === Yager t-norms === The family of Yager t-norms, introduced in the early 1980s by Ronald R. Yager, is given for 0 ≤ p ≤ +∞ by T p Y ( x , y ) = { T D ( x , y ) if p = 0 max ( 0 , 1 − ( ( 1 − x ) p + ( 1 − y ) p ) 1 / p ) if 0 < p < + ∞ T m i n ( x , y ) if p = + ∞ {\displaystyle T_{p}^{\mathrm {Y} }(x,y)={\begin{cases}T_{\mathrm {D} }(x,y)&{\text{if }}p=0\\\max \left(0,1-((1-x)^{p}+(1-y)^{p})^{1/p}\right)&{\text{if }}0 Read more →