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  Shaded Picture System

  The Shaded Picture System was a 3D raster computer display processor introduced by Evans & Sutherland in October 1973. The Shaded Picture System was the first general-purpose, commercially available raster computer graphics display processor capable of real-time, shaded 3D graphics. It could only display black and white graphics at a resolution of 256 by 256. It was extremely expensive, and very few units were ever sold. == History == The principles of shaded, hidden-line true 3D graphics were pioneered at the University of Utah in 1967. However, this algorithm was slow and would take several minutes to produce an image. In 1970, Gary Watkins developed a FORTRAN simulator of a faster algorithm that would theoretically generate shaded 3D images in real-time, "if implemented in suitable hardware". The simulator itself was still not capable of real-time shaded 3D image rendering. Evans & Sutherland developed a functional prototype of this "suitable hardware", which was later sold as the Shaded Picture System in 1973. About a year earlier in 1972, Evans & Sutherland sold the first and only CT1 to Case Western Reserve University. The CT1, or Continuous Tone 1, was a specialized image generator, not meant as a marketable or mass-produced product. At the time, the CT1, along with G.E./NASA's upgraded Electronic Scene Generator from 1971, would have been the only real-time raster graphics systems sold to customers comparable to the Shaded Picture System, although both the CT1 and Electronic Scene Generator were intentionally produced as one-off products and specialized for the needs of their customers. The Shaded Picture System, in contrast, was intentionally marketed.In early 1975, Evans & Sutherland demonstrated a random-access video frame buffer using relatively low-cost semiconductor memory, which was much more capable than the Shaded Picture System. When interfaced with a (non-shaded) E&S Picture System, the frame buffer had a resolution of 512 by 512 in grayscale and partial color capabilities. By the end of 1975, this frame buffer was commercially available.

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  Conference on Neural Information Processing Systems

  The Conference on Neural Information Processing Systems (abbreviated as NeurIPS and formerly NIPS) is a machine learning and computational neuroscience conference held annually in December. Along with ICLR and ICML, it is one of the three primary conferences of high impact in machine learning and artificial intelligence research. The conference includes three days of invited talks along with oral and poster presentations of refereed papers, followed by two days of workshops and competitions. == History == The NeurIPS meeting was first proposed in 1986 at the annual invitation-only Snowbird Meeting on Neural Networks for Computing organized by The California Institute of Technology and Bell Laboratories. NeurIPS was designed as a complementary open interdisciplinary meeting for researchers exploring biological and artificial Neural Networks. Reflecting this multidisciplinary approach, NeurIPS began in 1987 with information theorist Ed Posner as the conference president and learning theorist Yaser Abu-Mostafa as program chairman. Research presented in the early NeurIPS meetings included a wide range of topics from efforts to solve purely engineering problems to the use of computer models as a tool for understanding biological nervous systems. Since then, the biological and artificial systems research streams have diverged, and recent NeurIPS proceedings have been dominated by papers on machine learning, artificial intelligence and statistics. From 1987 until 2000 NeurIPS was held in Denver, United States. Since then, the conference was held in Vancouver, Canada (2001–2010), Granada, Spain (2011), and Lake Tahoe, United States (2012–2013). In 2014 and 2015, the conference was held in Montreal, Canada, in Barcelona, Spain in 2016, in Long Beach, United States in 2017, in Montreal, Canada in 2018 and Vancouver, Canada in 2019. Reflecting its origins at Snowbird, Utah, the meeting was accompanied by workshops organized at a nearby ski resort up until 2013, when it outgrew ski resorts. The first NeurIPS Conference was sponsored by the IEEE. The following NeurIPS Conferences have been organized by the NeurIPS Foundation, established by Ed Posner. Terrence Sejnowski has been the president of the NeurIPS Foundation since Posner's death in 1993. The board of trustees consists of previous general chairs of the NeurIPS Conference. The first proceedings was published in book form by the American Institute of Physics in 1987, and was entitled Neural Information Processing Systems, then the proceedings from the following conferences have been published by Morgan Kaufmann (1988–1993), MIT Press (1994–2004) and Curran Associates (2005–present) under the name Advances in Neural Information Processing Systems. The conference was originally abbreviated as "NIPS". By 2018 a few commentators were criticizing the abbreviation as encouraging sexism due to its association with the word nipples, and as being a slur against Japanese. The board changed the abbreviation to "NeurIPS" in November 2018. == Topics == Along with machine learning and neuroscience, other fields represented at NeurIPS include cognitive science, psychology, computer vision, statistical linguistics, and information theory. Over the years, NeurIPS became a premier conference on machine learning and although the 'Neural' in the NeurIPS acronym had become something of a historical relic, the resurgence of deep learning in neural networks since 2012, fueled by faster computers and big data, has led to achievements in speech recognition, object recognition in images, image captioning, language translation and world championship performance in the game of Go, based on neural architectures inspired by the hierarchy of areas in the visual cortex (ConvNet) and reinforcement learning inspired by the basal ganglia (Temporal difference learning). Notable affinity groups have emerged from the NeurIPS conference and displayed diversity, including Black in AI (in 2017), Queer in AI (in 2016), and others. === Named lectures === In addition to invited talks and symposia, NeurIPS also organizes two named lectureships to recognize distinguished researchers. The NeurIPS Board introduced the Posner Lectureship in honor of NeurIPS founder Ed Posner; two Posner Lectures were given each year up to 2015. Past lecturers have included: 2010 – Josh Tenenbaum and Michael I. Jordan 2011 – Rich Sutton and Bernhard Schölkopf 2012 – Thomas Dietterich and Terry Sejnowski 2013 – Daphne Koller and Peter Dayan 2014 – Michael Kearns and John Hopfield 2015 – Zoubin Ghahramani and Vladimir Vapnik 2016 – Yann LeCun 2017 – John Platt 2018 – Joëlle Pineau 2019 – Yoshua Bengio 2020 – Christopher Bishop 2021 – Peter Bartlett In 2015, the NeurIPS Board introduced the Breiman Lectureship to highlight work in statistics relevant to conference topics. The lectureship was named for statistician Leo Breiman, who served on the NeurIPS Board from 1994 to 2005. Past lecturers have included: 2015 – Robert Tibshirani 2016 – Susan Holmes 2017 – Yee Whye Teh 2018 – David Spiegelhalter 2019 – Bin Yu 2020 – Marloes Maathuis 2021 – Gabor Lugosi 2022 – Emmanuel Candes 2023 – Susan Murphy 2024 – Arnaud Doucet == NeurIPS consistency experiment == In NIPS 2014, the program chairs duplicated 10% of all submissions and sent them through separate reviewers to evaluate randomness in the reviewing process. Several researchers interpreted the result. Regarding whether the decision in NIPS is completely random or not, John Langford writes: "Clearly not—a purely random decision would have arbitrariness of ~78%. It is, however, quite notable that 60% is much closer to 78% than 0%." He concludes that the result of the reviewing process is mostly arbitrary. In NeurIPS 2021, the program chairs repeated the 2014 experiment and found similar levels of review inconsistency; 23% of duplicated submissions received different accept/reject decisions, and 50.6% of accepted papers would have been rejected under re-review. == Locations == 1987–2000: Denver, Colorado, United States 2001–2010: Vancouver, British Columbia, Canada 2011: Granada, Spain 2012 & 2013: Stateline, Nevada, United States 2014 & 2015: Montréal, Quebec, Canada 2016: Barcelona, Spain 2017: Long Beach, California, United States 2018: Montréal, Quebec, Canada 2019: Vancouver, British Columbia, Canada 2020: Vancouver, British Columbia, Canada (virtual conference) 2021: Virtual conference 2022 & 2023: New Orleans, Louisiana, United States 2024: Vancouver, British Columbia, Canada 2025: San Diego, California, United States and Mexico City, Mexico 2026: Sydney, New South Wales, Australia, with satellite events in Atlanta and Paris

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  Recraft

  Recraft is a generative artificial intelligence program and service developed by the London-based startup Recraft, Inc. The company also offers Recraft Studio, a web-based workspace that lets users create and edit images, vectors, and mockups using various text-to-image models. Like models such as Midjourney and DALL-E, the Recraft model generates digital images from natural language prompts, and is specifically tailored for creative workflows, with features that emphasize brand consistency, text fidelity, and layout control. == History and background == Recraft, Inc. was founded in 2022 by machine learning scientist Anna Veronika Dorogush, best known for co-creating the CatBoost machine learning library at Yandex. The company emerged from stealth on May 31, 2023, with a public release of its vector graphics generation capability on Product Hunt. On January 17, 2024, TechCrunch profiled Recraft’s foundational model for graphic design, noting its emphasis on addressing copyright and ethical concerns associated with AI-generated imagery. On October 28, 2024, TechCrunch reported that Recraft's third major model, V3, had topped a crowdsourced benchmark, surpassing Midjourney and OpenAI's DALL-E in overall image quality. On May 5, 2025, Recraft announced a $30 million Series B funding round led by Accel, reporting more than four million registered users at the time of the announcement. == Models == Recraft has developed multiple generations of its text-to-image models since 2022. Each generation reflects improvements in fidelity, controllability, and support for both raster and vector outputs. The models are proprietary and accessible through the Recraft API, Recraft Studio. Recraft models are also hosted as an image generation API on fal, Replicate, Prodia, and others. === Recraft V2 === Recraft V2 was released in March 2024 and was the company’s first model trained from scratch. It contained roughly 20 billion parameters and introduced native vector image generation, brand-color conditioning, and improved stylistic consistency for icons and illustrations. === Recraft V3 === Recraft V3 was released in October 2024 and achieved first place on the Artificial Analysis benchmark hosted on Hugging Face. The model introduced advances in photorealism, improved rendering of multi-word text, and increased responsiveness to detailed descriptive prompts. It also added the “Artistic” parameter, which allowed users to adjust stylistic intensity within generated images. === Recraft V4 === Recraft V4 was released in February 2026. According to Recraft, V4 is a “ground-up rebuild” aimed at improving prompt accuracy and output quality for design workflows, with the company emphasizing “design taste” and art-directed results. Recraft states that V4 is available in two versions: V4 for faster iteration and V4 Pro for higher-resolution, print-ready assets; the API documentation describes V4 as 1-megapixel output and V4 Pro as 4-megapixel output, with vector variants available for each. === Features === Vectorization: Recraft’s models can generate and convert images into native vector formats, producing scalable graphics composed of editable paths rather than fixed pixels. Style reference: The models support the use of reference images to guide stylistic characteristics such as color palette, line quality, composition, or visual tone. Style mixing: Recraft models can combine multiple stylistic inputs within a single generation. By blending attributes from different references or stylistic instructions, the system produces images that reflect hybrid visual characteristics while maintaining internal consistency. Inpainting editing: The models support localized image modification through inpainting, enabling users to regenerate selected regions of an image while preserving surrounding content. === Model capabilities === Recraft’s models generate raster and vector images from natural-language prompts and are designed to interpret detailed descriptions with attention to composition, style, and text placement. The models support controlled stylistic variation through preset or reference-based guidance and can maintain coherent line, color, or layout structure across multiple outputs. They produce scalable vector graphics alongside high-resolution raster images, and include features for localized image modification through inpainting or outpainting operations. === Technology === Recraft has not publicly disclosed the detailed technical architecture of its models. However, third-party reviews and benchmarks have noted that its performance resembles diffusion models such as Midjourney and Stable Diffusion. The model is designed for creative workflows requiring visual consistency and flexible output formats. Reviewers have noted its ability to generate legible multi-line text, produce high-resolution imagery at various canvas sizes, and to maintain alignment with user-defined brand palettes and design themes. Though not open-source, Recraft's models are accessible through a web interface and commercial API. Advanced features such as style settings and positioning control differentiate it from general-purpose text-to-image models. == Recraft Studio == Recraft Studio is a web-based workspace for generating and editing images using Recraft’s image models and selected external models. The infinite canvas interface provides access to a range of creation and refinement tools within a single environment. Raster and vector generation with styles: Recraft Studio supports the generation of both raster and vector images. Users can apply predefined or reference-based styles during generation, allowing for visual consistency across multiple outputs. Mockups: The studio includes mockup tools that allow generated designs to be placed onto predefined surfaces or templates for visualization and presentation purposes. Vectorization: Recraft Studio provides vectorization tools that convert raster images into editable vector graphics, enabling further modification of shapes, colors, and layout. Image upscaling: The workspace includes image upscaling functionality for increasing resolution while preserving visual detail. Editing tools and natural-language editing: Recraft Studio offers a set of editing tools for modifying images within the canvas, including localized adjustments and natural-language–based editing commands that allow users to describe changes using text. === Supported models === Recraft Studio provides access to Recraft’s proprietary image models as well as other external frontier image models such as Nano Banana, GPT 4-o, Imagen, Flux, and others. == Business model == Recraft develops proprietary image models that are accessible through Recraft Studio and the Recraft API. Recraft Studio operates on a freemium model, offering a free tier with limited daily credits and paid subscriptions for access to additional features. The API follows a credit-based system in which units are purchased separately for programmatic image generation. A team plan supports collaborative use, and the API enables organizations and developers to integrate Recraft’s image generation and editing capabilities into their own systems and workflows.

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  Feeding the Machine (book)

  Feeding the Machine: The Hidden Human Labour Powering AI is a 2024 book by James Muldoon, Mark Graham and Callum Cant. == Writing == The authors developed the concept for the book while doing fieldwork studying data annotation in developing countries in East Africa. == Synopsis == The book examines the human input needed to develop and sustain AI ecosystems. == Reception == The book received positive reviews. Rosalie Waelen of Capital & Class gave it a mostly positive review. Tim Hornyak of Literary Review praised it. Kirkus Reviews called it "A sobering and timely—if sometimes distracted—study of AI.". Publishers Weekly gave the book a starred review, writing that "The grim real-life stories read like dystopian parables, such as the account of a European voice actor whose recordings were legally used without her consent to create an inexpensive synthetic clone whom she now competes with for business. Driven by striking reporting and finely observed profiles, this unsettles."

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  Artificial reproduction

  Artificial reproduction is the re-creation of life brought about by means other than natural ones. It is new life built by human plans and projects. Examples include artificial selection, artificial insemination, in vitro fertilization, artificial womb, artificial cloning, and kinematic replication. Artificial reproduction is one aspect of artificial life. Artificial reproduction can be categorized into one of two classes according to its capacity to be self-sufficient: non-assisted reproductive technology and assisted reproductive technology. Cutting plants' stems and placing them in compost is a form of assisted artificial reproduction, xenobots are an example of a more autonomous type of reproduction, while the artificial womb presented in the movie the Matrix illustrates a non assisted hypothetical technology. The idea of artificial reproduction has led to various technologies. == Theology == Humans have aspired to create life since immemorial times. Most theologies and religions have conceived this possibility as exclusive of deities. Christian religions consider the possibility of artificial reproduction, in most cases, as heretical and sinful. == Philosophy == Although ancient Greek philosophy raised the concept that man could imitate the creative capacity of nature, classic Greeks thought that if possible, human beings would reproduce things as nature does, and vice versa, nature would do the things that man does in the same way. Aristotle, for example, wrote that if nature made tables, it would make them just as men do. In other words, Aristotle said that if nature were to create a table, such table will look like a human-made table. Correspondingly, Descartes envisioned the human body, and nature, as a machine. Cartesian philosophy does not stop seeing a perfect mirror between nature and the artificial. However, Kant revolutionized this old idea by criticizing such naturalism. Kant pedagogically wrote: "Reason, in order to be taught by nature, must approach nature with its principles in one hand, according to which the agreement among appearances can count as laws, and, in the other hand, the experiment thought out in accord with these principles—in order to be instructed by nature not like a pupil, who has recited to him whatever the teacher wants to say, but like an appointed judge who compels witnesses to answer the questions he puts to them.". Humans are not instructed by nature but rather use nature as raw material to invent. Humans find alternatives to the natural restrictions imposed by natural laws thus, nature is not necessarily mirrored. In accordance with Kant (and contrary to what Aristotle thought) Karl Marx, Alfred Whitehead, Jaques Derrida and Juan David García Bacca noticed that nature is incapable of reproducing tables; or airplanes, or submarines, or computers. If nature tried to create airplanes, it would produce birds. If nature tried to create submarines, it would get fishes. If nature tried to create computers, brains would grow. And if nature tried to create man, modern man, monkeys will be evolved. According to Whitehead, if we look for something natural in artificial life, in the most elaborate cases, if anything, only atoms remain natural. Juan David Garcia Bacca summarized, “It will not come out from wood, it will not be born, a galley; from clay, a vessel; from linen, a dress; from iron, a lever,...From natural, artificial. In the artificial, the natural is reduced to a simple raw material, even though it is perfectly specified with natural specification. The artificial is the real, positive, and original negation of the natural: of species, of genus and of essence. Thus, its ontology is superior to natural ontology. And for this very reason Marx did not attach any importance to Darwin, whose evolutionism is confined to the natural order: to changes, at most, from variety to variety, from species to species... natural. For the same reason, nature has no dialectics, even though continuous evolution and selection can occur. The dialectic cannot emerge from the natural, for deeper reasons than, using today's terms, from a bird, an airplane cannot emerge; from fish, a submarine; from ears, a telephone; from eyes, a television; from a brain, a digital computer; from feet, a car; from hands, an engine; from Euclid, Descartes; from Aristotle, Newton; from Plato, Marx.” According to García Bacca, the major difference between natural causes and artificial causes is that nature does not have plans and projects, while humans design things following plans and projects. In contrast, other influential authors such as Michael Behe have depicted the concept and promoted the idea of intelligent design, a notion that has aroused several doubts and heated controversies, as it reframe natural causes in accordance with a natural plan. Previous ideas that have also provided a positive 'sense' to natural reproduction, are orthogenesis, syntropy, orgone and morphic resonance, among others. Although, these ideas have been historically marginalized and often called pseudoscience, recently Bio-semioticians are reconsidering some of them under symbolic approaches. Current metaphysics of science actually recognizes that the artificial ways of reproduction are diverse from nature, i.e., unnatural, anti-natural or supernatural. Because Biosemiotics does not focus on the function of life but on its meaning, it has a better understanding of the artificial than classic biology. == Science == Biology, being the study of cellular life, addresses reproduction in terms of growth and cellular division (i.e., binary fission, mitosis and meiosis); however, the science of artificial reproduction is not restricted by the mirroring of these natural processes.The science of artificial reproduction is actually transcending the natural forms, and natural rules, of reproduction. For example, xenobots have redefined the classical conception of reproduction. Although xenobots are made of eukariotic cells they do not reproduce by mitosis, but rather by kinematic replication. Such constructive replication does not involve growing but rather building. == Assisted reproductive technologies == Assisted reproductive technology (ART)'s purpose is to assist the development of a human embryo, commonly because of medical concerns due to fertility limitations. == Non-assisted reproductive technologies == Non-assisted reproductive technologies (NART) could have medical motivations but are mostly driven by a wider heterotopic ambition. Although, NARTs are initially designed by humans, they are programed to become independent of humans to a relative or absolute extent. James Lovelock proposed that such novelties could overcome humans. === Artificial cloning === Cloning is the cellular reproductive processes where two or more genetically identical organisms are created, either by natural or artificial means. Artificial cloning normally involves editing the genetic code, somatic cell nuclear transfer and 3D bioprinting. === Non-assisted artificial womb === A non-assisted artificial womb or artificial uterus is a device that allow for ectogenesis or extracorporeal pregnancy by growing an embryonic form outside the body of an organism (that would normally carry the embryo to term) without any human assistance. The aspect of non-assistance is the key distinction between the current artificial womb technology (AWT) in modern medical research, which still relies on human assistance. With this non-assisted hypothetical technology, a zygote or stem cells are used to create an embryo that is then incubated and monitored by artificial intelligence (AI) within a chamber composed of biocompatible material. The AI maintains the necessary conditions for the embryo to develop and thrive, proceeding to mimic organic labor and childbirth in order to best help the embryo adjust to the outside world. Ectogenesis—gestation, depicted in the science fiction movie The Matrix, is a fast approaching reality. This type of innovation presupposes that vertebrate wombs are not the only way for bearing humans or other similar forms of life. === Kinematic replication === Self-replication without binary fission, meiosis, mitosis (or any other form of cellular reproduction that involves division and growing) can be achieved. Xenobots are an example of kinematic replication. They are biobots, named after the African clawed frog (Xenopus laevis). Xenobots are cellular life forms designed by using artificial intelligence to build more of themselves by combining frog cells in a liquid medium. The term kinematic replication is usually reserved for biomolecules (e.g. DNA, RNA, prions, etc.) and artificially designed cellular forms (e.g. xenobots). === Machine constructive replication === Machine constructive replication mimics human traditional manufacturing but is entirely self-automated. Such constructive replication is a more general form of kinematic replication, which does not necessarily

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  R.U.R.

  R.U.R. is a 1920 science fiction play by the Czech writer Karel Čapek. "R.U.R." stands for Rossumovi Univerzální Roboti (Rossum's Universal Robots, a phrase that has been used as a subtitle in English versions). The play had its world premiere on 2 January 1921 in Hradec Králové. It introduced the word "robot" to the English language and to science fiction as a whole. R.U.R. became influential soon after its publication. By 1923, it had been translated into thirty languages. R.U.R. was successful in its time in Europe and North America. Čapek later took a different approach to the same theme in his 1936 novel War with the Newts, in which non-humans become a servant-class in human society. == Characters == Parentheses indicate names which vary according to translation. On the meaning of the names, see Ivan Klíma: Karel Čapek: Life and Work (2002). == Plot == === Synopsis === The play begins in a factory that makes artificial workers from synthetic organic matter. (As living creatures of artificial flesh and blood, that later terminology would call androids, the playwright's 'roboti' differ from later fictional and scientific concepts of inorganic constructs.) Robots may be mistaken for humans but have no original thoughts. Though most are content to work for humans, eventually a rebellion causes the extinction of the human race. === Prologue (Act I in the Selver translation) === Helena, the daughter of the president of a major industrial power, arrives at the island factory of Rossum's Universal Robots. Here, she meets Domin, the General Manager of R.U.R., who relates to her the history of the company. Rossum had come to the island in 1920 to study marine biology. In 1932, Rossum had invented a substance like organic matter, though with a different chemical composition. He argued with his nephew about their motivations for creating artificial life. While the elder wanted to create animals to prove or disprove the existence of God, his nephew only wanted to become rich. Young Rossum finally locked away his uncle in a lab to play with the monstrosities he had created and created thousands of robots. By the time the play takes place (circa the year 2000), robots are cheap and available all over the world. They have become essential for industry. After meeting the heads of R.U.R., Helena reveals that she is a representative of the League of Humanity, an organization that wishes to liberate the robots. The managers of the factory find this absurd. They see robots as appliances. Helena asks that the robots be paid, but according to R.U.R. management, the robots do not "like" anything. Eventually Helena is convinced that the League of Humanity is a waste of money, but still argues robots have a "soul". Later, Domin confesses that he loves Helena and forces her into an engagement. === Act I (Act II in Selver) === Ten years have passed. Helena and her nurse Nana discuss current events, the decline in human births in particular. Helena and Domin reminisce about the day they met and summarize the last ten years of world history, which has been shaped by the new worldwide robot-based economy. Helena meets Dr. Gall's new experiment, Radius. Dr. Gall describes his experimental robotess, also named Helena. Both are more advanced, fully-featured robots. In secret, Helena burns the formula required to create robots. The revolt of the robots reaches Rossum's island as the act ends. === Act II (Act III in Selver) === The characters sense that the very universality of the robots presents a danger. Echoing the story of the Tower of Babel, the characters discuss whether creating national robots who were unable to communicate beyond their languages would have been a good idea. As robot forces lay siege to the factory, Helena reveals she has burned the formula necessary to make new robots. The characters lament the end of humanity and defend their actions, despite the fact that their imminent deaths are a direct result of their choices. Busman is killed while attempting to negotiate a peace with the robots. The robots storm the factory and kill all the humans except for Alquist, the company's Clerk of the Works (Head of Construction). The robots spare him because they recognize that "He works with his hands like a robot. He builds houses. He can work." === Act III (Epilogue in Selver) === Years have passed. Alquist, who still lives, attempts to recreate the formula that Helena destroyed. He is a mechanical engineer, though, with insufficient knowledge of biochemistry, so he has made little progress. The robot government has searched for surviving humans to help Alquist and found none alive. Officials from the robot government beg him to complete the formula, even if it means he will have to kill and dissect other robots for it. Alquist yields. He will kill and dissect robots, thus completing the circle of violence begun in Act Two. Alquist is disgusted. Robot Primus and Helena develop human feelings and fall in love. Playing a hunch, Alquist threatens to dissect Primus and then Helena; each begs him to take him- or herself and spare the other. Alquist now realizes that Primus and Helena are the new Adam and Eve, and gives the charge of the world to them. == Čapek's conception of robots == The robots described in Čapek's play are not robots in the popularly understood sense of an automaton. They are not mechanical devices, but rather artificial biological organisms that may be mistaken for humans. A comic scene at the beginning of the play shows Helena arguing with her future husband, Harry Domin, because she cannot believe his secretary is a robotess: His robots resemble more modern conceptions of man-made life forms, such as the Replicants in Blade Runner, the "hosts" in the Westworld TV series and the humanoid Cylons in the re-imagined Battlestar Galactica, but in Čapek's time there was no conception of modern genetic engineering (DNA's role in heredity was not confirmed until 1952). There are descriptions of kneading-troughs for robot skin, great vats for liver and brains, and a factory for producing bones. Nerve fibers, arteries, and intestines are spun on factory bobbins, while the robots themselves are assembled like automobiles. Čapek's robots are living biological beings, but they are still assembled, as opposed to grown or born. One critic has described Čapek's robots as epitomizing "the traumatic transformation of modern society by the First World War and the Fordist assembly line". === Origin of the word robot === The play introduced the word robot, which displaced older words such as "automaton" or "android" in languages around the world. In an article in Lidové noviny, Karel Čapek named his brother Josef as the true inventor of the word. In Czech, robota means forced labour of the kind that serfs had to perform on their masters' lands and is derived from rab, meaning "slave". The name Rossum is an allusion to the Czech word rozum, meaning "reason", "wisdom", "intellect" or "common sense". It has been suggested that the allusion might be preserved by translating "Rossum" as "Reason" but only the Majer/Porter version translates the word as "Reason". == Production history and translations == The work was published in two differing versions in Prague by Aventinum, first in 1920, followed by a revised version in 1921. After being postponed, it premiered at the city's National Theatre on 25 January 1921, although an amateur group had by then already presented a production. By 1921, Paul Selver translated either the original 1920 edition of R.U.R. or a manuscript copy close to this version into English. He probably translated the play freelance, and sold it to St Martin's Theatre in London. Selver's translation was adapted for the British stage by Nigel Playfair in 1922, but it was not produced straight away. Later that year performance rights for the U.S. and Canada were sold to the New York Theatre Guild, perhaps during Lawrence Langner's visit to Britain. Playfair's version included several changes to Čapek's original play, such as renaming the acts (the prologue became act one, and the heavily abridged final act became the epilogue), omitting around sixty lines (including most of Alquist's final speech), adding several more lines, and removing the robot character Damon (giving his lines to Radius). The omission of some lines may have been censorship from the Lord Chamberlain's Office, or self-censorship in anticipation of this, while some other changes might have been made by Čapek himself if Selver was working from a manuscript copy. An edition of Playfair's adaptation was published by the Oxford University Press in 1923, and Selver went on to write a satiric novel One, Two, Three (1926) based on his experiences getting R.U.R. staged. The American première was produced by the Theatre Guild at the Garrick Theatre in New York City in October 1922, where it ran for 184 performances. In the first performance, Domin was portrayed by Basil Sydney,

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  DialogOS

  DialogOS is a graphical programming environment to design computer system which can converse through voice with the user. Dialogs are clicked together in a Flowchart. DialogOS includes bindings to control Lego Mindstorms robots by voice and has bindings to SQL databases, as well as a generic plugin architecture to integrate with other types of backends. DialogOS is used in computer science courses in schools and universities to teach programming and to introduce beginners in the basic principles of human/computer interaction and dialog design. It has also been used in research systems. DialogOS was initially developed commercially by CLT Sprachtechnologie GmbH until its liquidation in 2017. The rights were then acquired by Saarland University and the software was released as open-source. == Bindings to Lego Mindstorms NXT == DialogOS can control the LEGO Mindstorms NXT Series. It uses sensor-nodes to obtain values for the following sensors: noise sensor ultrasonic sensor touch sensor luminosity sensor

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  Theaitre

  Theaitre (stylized as THEaiTRE) is an interdisciplinary research project investigating to what extent artificial intelligence is able to generate theatre play scripts. The first theatre play produced within the project, AI: When a Robot Writes a Play, premiered online on February 26, 2021. == Goal == Following similar previous projects such as Sunspring, a short sci-fi movie with an automatically generated script, the THEaiTRE project investigates whether current language generation approaches are mature enough to generate a theatre play script that could be successfully performed in front of an audience. The project falls within the area of generative art, famously represented e.g. by the portrait of Edmond de Belamy which was generated by an artificial neural network. In this field, artists are trying to use automated techniques to create "art", questioning the modern definition of art itself. More broadly, the project aims at promoting cooperation rather than competition of humans and artificial intelligence as the more beneficial approach for both. The first theatre play created within the project, titled AI: When a Robot Writes a Play, was presented in February 2021 at the 100th anniversary of the premiere of the R.U.R. theatre play by the Czech author Karel Čapek to celebrate the invention of the word "robot". While R.U.R. was a play written by a human about robots (and humans), THEaiTRE tried to reverse this idea by presenting a play written by a "robot" (artificial intelligence) about humans (and robots). The script of the play was published online, with marked parts of the text which were written manually or manually post-edited. The analysis shows that 90% of the script is automatically generated, with 10% manually written or manually post-edited. The project also plans to produce a second play in 2022, addressing some of the many shortcomings of the approach used to generate the first play, as well as attempting to further minimize the amount of human influence on the script. == Approach == At the core of the project is the GPT-2 language model by OpenAI with various adjustments motivated by the task of generating theatre play scripts, for which the model is not particularly trained. The GPT-2 model is used in the usual way, providing it with a start of a document and prompting it to generate a continuation of the document. Specifically, the input for GPT-2 in this project is typically a short description of the scene setting, followed by a few lines to introduce the characters and start the dialogue. The model then generates 10 continuation lines, and hands control to the user, who can then either ask the model to continue generating, or make various edits before letting the model to generate further, deleting some parts of the script or adding new lines into the script. The adjustments include restricting the generator to only produce lines pertaining to characters appearing in the input prompt, limiting the repetitiveness of the generated text, and employing automatic summarization of the input prompt and the generated text to overcome the limitation of the GPT-2 model which only attends to the last 1,024 subword tokens. The limitations of the model include, among other, a lack of distinctiveness and self-consistency of the characters, an inability to generate the script for the whole play (scripts for individual scenes are generated independently), and errors due to the employment of automated machine translation, as GPT-2 generates English texts but the final play script is being produced in Czech language. The source codes of the project are available under the MIT licence. The project has also published some sample outputs. == Team == The project is a cooperation of the following experts, all based in Prague, Czech Republic: computational linguists from the Faculty of Mathematics and Physics, Charles University theatre experts from the Švanda Theatre and from the Theatre Faculty of the Academy of Performing Arts in Prague hackers from CEE Hacks The project is financially supported by the Technology Agency of the Czech Republic.

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  GoodRx

  GoodRx Holdings, Inc. is an American healthcare company that operates a telemedicine platform and free-to-use website and mobile app that track prescription drug prices in the United States and provide drug coupons for discounts on medications. GoodRx compares prescription drug prices at more than 75,000 pharmacies in the United States. The platform allows users to consult a doctor online and obtain a prescription for certain types of medications. == History == === Financial performance === GoodRx was founded in Santa Monica, California in 2011. GoodRx experienced substantial growth in net income in 2017 ($9 million), 2018 ($44 million), and 2019 ($66 million), but recorded a loss of $293.6 million in 2020 due to IPO-related expenses. In September 2020, GoodRx went public on the Nasdaq under the ticker symbol GDRX. The company priced its initial public offering at $33 per share, above the expected range of $24 to $28, raising more than $1.1 billion at an initial valuation of approximately $12.7 billion. In the first half of 2020, the company reported revenues of $257 million and net income of $55 million. GoodRx generated $745.4 million in revenue for the full year 2021, a 35.36% increase over 2020. During the first half of 2021, the company’s share price declined by 10.7%. The decline was attributed to increased competition in online pharmacy services and slower user growth. GoodRx reported full-year revenue of $766.6 million, with adjusted EBITDA reaching $213.5 million, exceeding guidance in the fourth quarter. GoodRx reported that 41% of prescriptions filled using its coupons were newly adherent, meaning they would not have been filled without the service. GoodRx reported a full-year 2023 revenue of $750.3 million, a decrease of 2.1% from 2022. However, its fourth-quarter revenue increased by 7% year-over-year. GoodRx achieved an Adjusted EBITDA of $217.4 million for the year and an Adjusted EBITDA Margin of 28.6%. In 2024, GoodRx achieved 6% revenue growth with $792.3 million for the full year and turned a net loss into a positive net income of $16.4 million. The company also demonstrated strong operational efficiency, with a 32.8% increase in full-year Adjusted EBITDA. In Q2 2025, GoodRx reported revenue of $203.1 million, a 1.2% increase from the previous year, and a net income of $12.8 million, a significant 92% jump, which resulted in a 6.3% net income margin. However, prescription transaction revenue declined by 3% due to a decrease in monthly active consumers, but this was offset by strong 32% growth in its Pharma Manufacturer Solutions business. GoodRx also saw a 7% decrease in subscription revenue. === Mergers and acquisitions === In 2019, GoodRx acquired HeyDoctor, a telemedicine company, to integrate virtual healthcare services into the platform. In 2021, a health video content producer, HealthiNation was acquired by GoodRx, which helped provide consumers with health information and offered pharmaceutical manufacturers new ways to reach relevant audiences. In April 2022, GoodRx acquired VitaCare Prescription Services from TherapeuticsMD to strengthen its pharma manufacturer solutions business. === Partnerships === In 2017, the company announced partnerships with major pharmaceutical companies to negotiate lower prescription drug costs. GoodRx has deep relationships with major pharmacy chains, including Walgreens, Walmart, CVS Caremark, and Publix, to allow customers to use GoodRx discounts and Gold benefits. GoodRx began its partnership with CVS Caremark in July 2023 to automatically apply coupons to insured CVS customers purchasing generic prescriptions at certain locations. In April 2024, GoodRx added Publix into its network, allowing GoodRx Gold members to use their cards at Publix Pharmacies. GoodRx partners with Pharmacy Benefit Management like Caremark, Express Scripts, and MedImpact to apply their savings directly to eligible insurance plans and members. GoodRx partners with companies like Affirm, Benefitfocus, and DoorDash to integrate their services that offer members discounts and financial flexibility for prescriptions. GoodRx also partners with organizations like the American Academy of Family Physicians Foundation to support broader access to care. In October 2022, GoodRx launched Provider Mode, which allows healthcare providers to use the app to compare costs of drugs for patients based on different payment methods and drug alternatives. In 2025, GoodRx partnered with Novo Nordisk to offer discounted cash-pay access to semaglutide products like Ozempic and Wegovy through its platform and participating pharmacies. == Products and services == GoodRx started its telemedicine service GoodRx Care in September 2019. It lets people talk to a licensed provider online for common issues and get prescriptions even if they don't have insurance. They also run condition-specific subscription plans that bundle online doctor visits, FDA-approved meds, and home delivery into one monthly payment. On the weight management side, GoodRx offers prescriptions for GLP-1 drugs like semaglutide through their telemedicine platform. This got a boost when the oral version of Wegovy became widely available in the US in early 2026. GoodRx works with drug makers like Novo Nordisk to make some medications (including semaglutide options) more affordable for people paying cash. The telemedicine part took off after GoodRx bought HeyDoctor in 2019 and brought their virtual care tools into the main platform. == Key people == The Santa Monica-based startup was founded in September 2011 by Trevor Bezdek and former Facebook executives Doug Hirsch and Scott Marlette. Marlette was one of the first 20 employees at Facebook and built Facebook's photo application. In 2005, Hirsch was the Vice President of Product at Facebook, working closely with Mark Zuckerberg. Bezdek and Hirsch served as co-chief executive officers until April 2023, when they stepped down from those roles and technology executive Scott Wagner was appointed interim chief executive officer. Bezdek became chair of the board, while Hirsch took on the role of chief mission officer. In December 2024, GoodRx announced that healthcare executive Wendy Barnes would become president and chief executive officer effective January 1, 2025. As of 2025, Barnes serves as the company’s CEO, while Trevor Bezdek and Scott Wagner serve as co-chairs of the board, and Doug Hirsch remains involved as a co-founder and senior executive. == Controversy == On February 25, 2020, Consumer Reports published an article stating that GoodRx shared user data—specifically, pseudonymized advertising ID numbers that companies use to track the behavior of web users across websites, the names of the drugs that users browsed, and the pharmacies where users sought to fill prescriptions—with Google, Facebook, and around twenty other Internet-based companies. A few days later, GoodRx released a statement saying that it had made changes to prevent user search data on medical conditions and pharmaceuticals from being shared with Facebook. In March 2020, GoodRx stopped sending data about user prescriptions to Facebook. On February 1, 2023, the Federal Trade Commission fined GoodRx US$1.5 million for violations of the Breach Notification Rule and the Federal Trade Commission Act for allegedly failing to obtain specific, informed, and unambiguous consent from users before disclosing health-related information to Facebook and Google. In November 2024, independent pharmacies filed at least three class action lawsuits against GoodRx and major pharmacy benefit managers. The cases, brought by independent pharmacies in California, Michigan, Pennsylvania, and Rhode Island, allege that GoodRx and the PBMs collaborated to suppress reimbursements for generic prescription drugs. They allege that agreements using GoodRx’s software suppressed reimbursements for generic drugs and violated the Sherman Antitrust Act. The suits claim the practices amount to price fixing which harms small pharmacies while benefiting PBMs and their affiliates. GoodRx settled both the 2023 FTC action and the 2025 class action lawsuit without admitting wrongdoing.

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  Refik Anadol

  Refik Anadol (born November 7, 1985) is a Turkish American media artist and the co-founder of Refik Anadol Studio and Dataland. Recognized as a pioneer in the aesthetics of data visualization and AI arts, his work merges art, technology, science, and architecture. Through media embedded into existing architecture, live audio-visual performances, immersive rooms, exhibitions, AI data paintings and sculptures, and digital collections, Anadol explores collective memories, humanity's relationship to nature, the perception of space and time, and human-machine collaborations. His work has been exhibited in more than seventy cities on six continents. == Early life and education == Anadol was born and raised in Istanbul and grew up in a family of teachers. He taught himself basic programming on a Commodore 64 when he was eight. His connection to machines began with coding and video games. Anadol saw Blade Runner for the first time when he was eight; his mother said the way he perceived his surroundings shifted the day after he saw the film. He was fascinated with its futuristic depiction of downtown Los Angeles, and transfixed by as a scene during which a replicant discovers that her memories are an implanted component of her machine mind, In a 2024 interview with the Financial Times, he said: "Since that moment, one of my inspirations has been that question: 'What can a machine do with someone else's memories?" Anadol attended Istanbul Bilgi University, where he received a BA in photography and video in 2009 and an MFA in visual communication in 2011. In 2014 he earned an MFA in design media arts at UCLA. He was mentored by Casey Reas, Jennifer Steinkamp, and Christian Moeller. == Career and selected works == === 2008–2012: Data painting, Quadrature and Quadrangle, Istanbul Biennial === As an undergraduate, Anadol read a paper by Lev Manovich on augmented space. Manovich's assertion that collaborations between architects and artists could make the "invisible flow of data visible" triggered Anadol's imagination, and in 2008, he altered built space for the first time. Bringing a projector outside, he projected large-scale images onto a concrete to create the illusion of movement. Coining the term "data painting," the piece inspired Anadol to use light as material and data as pigment. In 2010 he created Quadrature with Alican Aktürk, a fellow graduate student, at the SantralIstanbul Art and Culture Center's main gallery building. A live audio-visual performance that examined the relationship between architecture and media, Quadrature used video projection techniques to manipulate footage of quadrilaterals. He followed Quadrature with Quadrangle at SANAA School of Design in Essen, Germany, using the entire 360 degrees of the building as a canvas. In 2011, he was invited to create a media installation at the Istanbul Biennial on the heavily trafficked İstiklal Avenue. He created a site-specific large-scale interpretation of sounds he recorded during different times of day, and used nine projectors to project reinterpreted images. The work was titled Augmented Structures v1.0. Anadol's first solo exhibition, Sceptical Interventions, was held at the Piveneli Gallery in Istanbul in early 2012. Later that year he moved to Los Angeles to attend UCLA's Design Media Arts program. The first place he went after his arrival was downtown Los Angeles. [6] === 2013–2016: Visions of America: Amériques, Infinity Room, Google AMI === In 2013, at Microsoft Research's annual Design Expo, Anadol presented his idea to use the external walls of Walt Disney Concert Hall as a canvas. His presentation brought him to the attention of Gehry Technologies, and with the support of Gehry and his team, Anadol was offered the use of the original 3D model of the concert hall. For his 2014 thesis project, with assistance from architects and UCLA researchers, he created a site-specific architectural video installation inside the concert hall that accompanied a Los Angeles Philharmonic performance of Edgard Varèse's Amérique. Titled Visions of America: Amériques, Anadol used algorithmic sound analysis to listen and respond to the music in real-time. He tracked conductor Esa-Pekka Salonen's heartbeat with a sensor and used a 3-D camera system to integrate Salonen's movements. He created Infinity Room at the Zorlu PSM for the 2015 Istanbul Biennial. Rather than creating an illusion only with mirrors, Anadol used pixel and 3D projection mapping to transform every surface of the room into an abstract infinite moving space. A temporary immersive environment, Infinity Room was also exhibited at events including South by Southwest in Austin, Texas, the New Zealand Festival in Wellington, New Zealand, and Jeffrey Deitch in Los Angeles. In 2016, Anadol was awarded the first Google Artists and Machine Intelligence Artist Residency; it was just after a team at Google opened up the algorithm for DeepDream, a computer vision program that prompted Anadol's realization that if a machine could learn, it could remember, dream, and hallucinate. === 2017–2018: Winds of Boston, Archive Dreaming, Melting Memories, WDCH Dreams === In 2017, he created the data painting Winds of Boston, a 6' x 13' foot video installation in the lobby of a Boston office building, using software he created to read, analyze and visualize wind speed, direction, and gust patterns along with time and temperature at 20-second intervals recorded over a one-year period at Logan International Airport. Later in the year, he used AI to generate infinite new outputs based on a massive dataset for Archive Dreaming, an immersive installation at Salt Research, a contemporary gallery and library in Istanbul. Inspired by his idea of consciousness and its context within AI, as well as Jorge Luis Borges' The Library of Babel, Anadol used AI and machine learning to look at and discover interactions and correlations between 1.7 million items culled from 40,000 publications covering Turkish contemporary and modern art, architecture, and economics from 1997 to 2010. Archive Dreaming, which could be controlled by users with a joystick, dreamed of unexpected correlations among documents when idle. In 2018, after his uncle was diagnosed with Alzheimer's, Anadol created Melting Memories. Working with scientists from the neuroscape laboratory at the University of California, San Francisco, he used academic data from the neuroscience archives and EEG scans of an anonymous Alzheimer's disease dataset to create AI-generated visuals related to memory, health, degeneration, and decay.Melting Memories was projected on the walls of Pilevneli Gallery; visitors to the exhibition could watch as millions of pixels reconstructed people's memories. Anadol won the Lumen Prize Gold Award for Melting Memories. Anadol was commissioned by the Los Angeles Philharmonic to create an installation to celebrate the orchestra's centennial anniversary in 2018. He worked with Google's Kenric MacDowell to create WDCH Dreams, using algorithmic visualizations of data to mimic the process of human dreaming. Projected across the exterior walls of Walt Disney Concert Hall using 42 large-scale projectors with 50K visual resolution, 8-channel sound, and 1.2M luminance, Anadol painted with data points culled from the orchestra's archives, including 587,763 images, 1,880 videos, 1,483 metadata files, and 17,773 audio files. Because Gehry gave him access to the 3D architectural files of Walt Disney Concert Hall, Anadol knew the exact contours of the building. WDCH Dreams debuted in September 2018. A 12-minute performance in three parts staged every 30 minutes over ten nights, "Centennial Memories,” the first piece, used 44.5 terabytes of historical data from the Phil's archives. It was followed by "Consciousness", which processed every note the orchestra has ever recorded, using billions of data points to generate connections; and "Dream," which merged "Centennial Memories" and "Consciousness" to create hallucinations that were described in the New York Times as "a sort of combinatorial Fantasia. === 2019–2021: Machine Hallucinations: NYC, Machine Hallucinations: Nature Dreams, Machine Memories: Space, Quantum Memories === In 2019, Refik Anadol presented Latent History at Fotografiska Stockholm. The site specific installation transformed photographic archives of Stockholm into a large scale, machine generated visual projection displayed in the museum’s main exhibition hall. Drawing on thousands of archival images spanning approximately 150 years, the work used artificial intelligence to reinterpret the city’s historical imagery as a continuously evolving visual narrative.. Anadol began thinking about the work that would become the Machine Hallucinations series while in residence at Google. In 2019, he completed the first work in the series, Machine Hallucinations: NYC, which used 300 million photos of New York City and 113 million additional data points, including subway sounds, ra

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  Residuated lattice

  In abstract algebra, a residuated lattice is an algebraic structure that is simultaneously a lattice x ≤ y and a monoid x•y that admits operations x\z and z/y, loosely analogous to division or implication, when x•y is viewed as multiplication or conjunction, respectively. Called respectively right and left residuals, these operations coincide when the monoid is commutative. The general concept was introduced by Morgan Ward and Robert P. Dilworth in 1939. Examples, some of which existed prior to the general concept, include Boolean algebras, Heyting algebras, residuated Boolean algebras, relation algebras, and MV-algebras. Residuated semilattices omit the meet operation ∧, for example Kleene algebras and action algebras. == Definition == In mathematics, a residuated lattice is an algebraic structure L = (L, ≤, •, I) such that (i) (L, ≤) is a lattice. (ii) (L, •, I) is a monoid. (iii) For all z there exists for every x a greatest y, and for every y a greatest x, such that x•y ≤ z (the residuation properties). In (iii), the "greatest y", being a function of z and x, is denoted x\z and called the right residual of z by x. Think of it as what remains of z on the right after "dividing" z on the left by x. Dually, the "greatest x" is denoted z/y and called the left residual of z by y. An equivalent, more formal statement of (iii) that uses these operations to name these greatest values is (iii)' for all x, y, z in L, y ≤ x\z ⇔ x•y ≤ z ⇔ x ≤ z/y. As suggested by the notation, the residuals are a form of quotient. More precisely, for a given x in L, the unary operations x• and x\ are respectively the lower and upper adjoints of a Galois connection on L, and dually for the two functions •y and /y. By the same reasoning that applies to any Galois connection, we have yet another definition of the residuals, namely, x•(x\y) ≤ y ≤ x\(x•y), and (y/x)•x ≤ y ≤ (y•x)/x, together with the requirement that x•y be monotone in x and y. (When axiomatized using (iii) or (iii)' monotonicity becomes a theorem and hence not required in the axiomatization.) These give a sense in which the functions x• and x\ are pseudoinverses or adjoints of each other, and likewise for •x and /x. This last definition is purely in terms of inequalities, noting that monotonicity can be axiomatized as x • y ≤ (x∨z) • y and similarly for the other operations and their arguments. Moreover, any inequality x ≤ y can be expressed equivalently as an equation, either x∧y = x or x∨y = y. This along with the equations axiomatizing lattices and monoids then yields a purely equational definition of residuated lattices, provided the requisite operations are adjoined to the signature (L, ≤, •, I) thereby expanding it to (L, ∧, ∨, •, I, /, \). When thus organized, residuated lattices form an equational class or variety, whose homomorphisms respect the residuals as well as the lattice and monoid operations. Note that distributivity x • (y ∨ z) = (x • y) ∨ (x • z) and x•0 = 0 are consequences of these axioms and so do not need to be made part of the definition. This necessary distributivity of • over ∨ does not in general entail distributivity of ∧ over ∨, that is, a residuated lattice need not be a distributive lattice. However distributivity of ∧ over ∨ is entailed when • and ∧ are the same operation, a special case of residuated lattices called a Heyting algebra. Alternative notations for x•y include x◦y, x;y (relation algebra), and x⊗y (linear logic). Alternatives for I include e and 1'. Alternative notations for the residuals are x → y for x\y and y ← x for y/x, suggested by the similarity between residuation and implication in logic, with the multiplication of the monoid understood as a form of conjunction that need not be commutative. When the monoid is commutative the two residuals coincide. When not commutative, the intuitive meaning of the monoid as conjunction and the residuals as implications can be understood as having a temporal quality: x•y means x and then y, x → y means had x (in the past) then y (now), and y ← x means if-ever x (in the future) then y (at that time), as illustrated by the natural language example at the end of the examples. == Examples == One of the original motivations for the study of residuated lattices was the lattice of (two-sided) ideals of a ring. Given a ring R, the ideals of R, denoted Id(R), forms a complete lattice with set intersection acting as the meet operation and "ideal addition" acting as the join operation. The monoid operation • is given by "ideal multiplication", and the element R of Id(R) acts as the identity for this operation. Given two ideals A and B in Id(R), the residuals are given by A / B := { r ∈ R ∣ r B ⊆ A } {\displaystyle A/B:=\{r\in R\mid rB\subseteq A\}} B ∖ A := { r ∈ R ∣ B r ⊆ A } {\displaystyle B\setminus A:=\{r\in R\mid Br\subseteq A\}} It is worth noting that {0}/B and B\{0} are respectively the left and right annihilators of B. This residuation is related to the conductor (or transporter) in commutative algebra written as (A:B)=A/B. One difference in usage is that B need not be an ideal of R: it may just be a subset. Boolean algebras and Heyting algebras are commutative residuated lattices in which x•y = x∧y (whence the unit I is the top element 1 of the algebra) and both residuals x\y and y/x are the same operation, namely implication x → y. The second example is quite general since Heyting algebras include all finite distributive lattices, as well as all chains or total orders, for example the unit interval [0,1] in the real line, or the integers and ± ∞ {\displaystyle \pm \infty } . The structure (Z, min, max, +, 0, −, −) (the integers with subtraction for both residuals) is a commutative residuated lattice such that the unit of the monoid is not the greatest element (indeed there is no least or greatest integer), and the multiplication of the monoid is not the meet operation of the lattice. In this example the inequalities are equalities because − (subtraction) is not merely the adjoint or pseudoinverse of + but the true inverse. Any totally ordered group under addition such as the rationals or the reals can be substituted for the integers in this example. The nonnegative portion of any of these examples is an example provided min and max are interchanged and − is replaced by monus, defined (in this case) so that x-y = 0 when x ≤ y and otherwise is ordinary subtraction. A more general class of examples is given by the Boolean algebra of all binary relations on a set X, namely the power set of X2, made a residuated lattice by taking the monoid multiplication • to be composition of relations and the monoid unit to be the identity relation I on X consisting of all pairs (x,x) for x in X. Given two relations R and S on X, the right residual R\S of S by R is the binary relation such that x(R\S)y holds just when for all z in X, zRx implies zSy (notice the connection with implication). The left residual is the mirror image of this: y(S/R)x holds just when for all z in X, xRz implies ySz. This can be illustrated with the binary relations < and > on {0,1} in which 0 < 1 and 1 > 0 are the only relationships that hold. Then x(>\<)y holds just when x = 1, while x()y holds just when y = 0, showing that residuation of < by > is different depending on whether we residuate on the right or the left. This difference is a consequence of the difference between <•> and >•<, where the only relationships that hold are 0(<•>)0 (since 0<1>0) and 1(>•<)1 (since 1>0<1). Had we chosen ≤ and ≥ instead of < and >, ≥\≤ and ≤/≥ would have been the same because ≤•≥ = ≥•≤, both of which always hold between all x and y (since x≤1≥y and x≥0≤y). The Boolean algebra 2Σ of all formal languages over an alphabet (set) Σ forms a residuated lattice whose monoid multiplication is language concatenation LM and whose monoid unit I is the language {ε} consisting of just the empty string ε. The right residual M\L consists of all words w over Σ such that Mw ⊆ L. The left residual L/M is the same with wM in place of Mw. The residuated lattice of all binary relations on X is finite just when X is finite, and commutative just when X has at most one element. When X is empty the algebra is the degenerate Boolean algebra in which 0 = 1 = I. The residuated lattice of all languages on Σ is commutative just when Σ has at most one letter. It is finite just when Σ is empty, consisting of the two languages 0 (the empty language {}) and the monoid unit I = {ε} = 1. The examples forming a Boolean algebra have special properties treated in the article on residuated Boolean algebras. == Residuated semilattice == A residuated semilattice is defined almost identically for residuated lattices, omitting just the meet operation ∧. Thus it is an algebraic structure L = (L, ∨, •, 1, /, \) satisfying all the residuated lattice equations as specified above except those containing an occurrence of the symbol ∧. The option of defining x ≤ y as x∧y = x is then not available, leaving on

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  The Great Automatic Grammatizator

  The Great Automatic Grammatizator (published in the U.S. as The Umbrella Man and Other Stories) is a posthumous 1998 collection of thirteen short stories written by British author Roald Dahl. The stories were selected for teenagers from Dahl's adult works. All the stories included were published elsewhere originally; their sources are noted below. The stories, with the exception of the war story "Katina", possess a deadpan, ironic, bizarre, or even macabre sense of humor. They generally end with unexpected plot twists. == Stories == "The Great Automatic Grammatizator" (from Someone Like You): A mechanically-minded man reasons that the rules of grammar are fixed by certain, almost mathematical principles. By exploiting this idea, he is able to create a mammoth machine that can write a prize-winning novel in roughly fifteen minutes. The story ends on a fearful note, as more and more of the world's writers are forced into licensing their names—and all hope of human creativity—to the machine. "Mrs. Bixby and the Colonel's Coat" (from Kiss Kiss): Mrs. Bixby cheats on her dentist husband with a rich, dashing colonel. When their relationship breaks off, the colonel offers Mrs. Bixby a gorgeous and expensive mink coat. In an attempt to explain the coat away, Mrs. Bixby sets up an elaborate trick with the help of a pawn shop—but her husband learns of the ruse and manages to turn the tables. "The Butler" (from More Tales of the Unexpected): An obnoxious and newly wealthy couple employs a butler and chef to impress dinner guests. The butler recommends that the husband buy expensive wines to please his guests, and the man slavishly follows the idea. The butler and the chef reap the rewards of this idea, while making fools of the "fashionable" couple. "Man from the South" (from Someone Like You): At a seaside resort in Jamaica, a strange old man makes a bet with an American man in his late teens. If the young man's cigarette lighter can spark ten times without fail, the American will win a brand-new Cadillac car—but failure means losing the little finger of his right hand. The high-tension wager ensues, and with only a few sparks left, a woman—who knows only too well the cost of the old man's bets—appears and stops the madness. "The Landlady" (from Kiss Kiss): A young man traveling to London on business stops at a bed and breakfast along the way, where a strange and slightly dotty landlady eagerly welcomes him. The eccentric nature of the house, and the news that only two other young men have ever stayed there, confuse and frighten the young man. In the end, the landlady—who indulges in the hobby of taxidermy—and the boy share a drink of tea that tastes of bitter almonds, and the landlady softly smiles at what may be her latest stuffing project. "Parson's Pleasure" (from Kiss Kiss): A man discovers an extremely rare piece of Chippendale furniture at the farm of some boorish ranchers. He desperately attempts to buy the piece cheap, in the hope of selling it at auction to earn a huge profit. He manages to buy the piece "for firewood", only for the ranchers to destroy it in an attempt to make it fit into his car. "The Umbrella Man" (from More Tales of the Unexpected): On a rainy day, a mother and daughter meet a gentlemanly old man on a street corner, who offers them a beautiful silk umbrella in exchange for a pound note. They trade, and the daughter notices that the "feeble" old man suddenly seems much sprier. They follow him, and discover that the gentleman is a con artist who visits various pubs, has a drink, and then steals another umbrella to continue the cycle. "Katina" (from Over to You: Ten Stories of Flyers and Flying): A group of RAF pilots stationed in Greece during World War II discover a hauntingly beautiful young girl, whose "family is beneath the rubble." She becomes their squadron's unofficial "mascot". In the end, her fragile life is taken as she stands defiantly against a rain of bullets from Nazi aircraft, shaking her fists at the heavens. "The Way Up to Heaven" (from Kiss Kiss): Mrs. Foster suffers from a chronic phobia of being late for appointments. Her husband enjoys the cruel sport of purposely delaying their activities, just to rile his wife. On the day when Mrs. Foster is due to fly to Paris to visit her grandchildren, her husband engages in his usual tricks. But as Mrs. Foster rushes from their taxi to the house to find him, she hears a strange noise—and turns triumphantly toward her cab. It is only when she returns, and calls a man to "repair the lift" that was stuck between floors in the house, that readers guess Mr. Foster's fate. "Royal Jelly" (from Kiss Kiss): New parents fear for the life of their little girl, who is sickly and dangerously underweight. The husband, a beekeeper, remembers hearing of the miraculous royal jelly used by bees to transform one particular larva into a queen. He adds the mixture to his daughter's bottles, and she puts on weight at an astonishing rate. The mother senses that something is amiss, and the husband confesses his actions—along with the fact that he himself swallowed buckets of the jelly for months in an attempt to cure his impotence. The royal jelly did the trick—but the strange side-effects include a disturbing metamorphosis for both father and daughter. "Vengeance is Mine Inc." (from More Tales of the Unexpected): Two brothers who are short of cash bemoan their fate over breakfast while reading the society column of a newspaper. They hit upon a scheme to take revenge on cruel tabloid writers in exchange for money from wealthy patrons. The unconventional plan works, and the brothers line their pockets with the spoils of their plans. "Taste" (from Someone Like You): A rich man with a beautiful young daughter hosts a dinner party, inviting a famous connoisseur of fine wines. When the rich man boasts that he has a wine that the expert cannot identify, the stakes become frighteningly high: if he can guess the name and vintage of the wine, he will win his daughter's hand. After an elaborate show, the expert guesses correctly; however, the family's maid appears and inadvertently exposes the guest as a cheat, thus saving the girl. "Neck" (from Someone Like You): A newspaper heir finds himself suddenly engaged to the voluptuous and controlling Lady Tutton. He loses all control of his life, and only his trusted butler and friends realize how broken he is by her control. A weekend trip to their estate, however, proves the perfect opportunity for Lord Tutton to engage in revenge against his wicked wife: her head is trapped in a valuable piece of wooden sculpture, and he must decide whether to use a saw or an axe to cut her free. == Publication details == Dahl, Roald (19 January 2004). The Umbrella Man and Other Stories. Speak. ISBN 9780142400876. == Reception == Groff Conklin in 1954 called the short story "The Great Automatic Grammatizator" "an awe-inspiring fantasy-satire ... an unforgettable bit of biting nonsense".

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  Imieliński–Lipski algebra

  In database theory, Imieliński–Lipski algebra is an extension of relational algebra onto tables with different types of null values. It is used to operate on relations with incomplete information. Imieliński–Lipski algebras are defined to satisfy precise conditions for semantically meaningful extension of the usual relational operators, such as projection, selection, union, and join, from operators on relations to operators on relations with various kinds of "null values". These conditions require that the system be safe in the sense that no incorrect conclusion is derivable by using a specified subset F of the relational operators; and that it be complete in the sense that all valid conclusions expressible by relational expressions using operators in F are in fact derivable in this system. For example, it is well known that the three-valued logic approach to deal with null values, supported treatment of nulls values by SQL is not complete, see Ullman book. To show this, let T be: Take SQL query Q SQL query Q will return empty set (no results) under 3-valued semantics currently adopted by all variants of SQL. This is the case because in SQL, NULL is never equal to any constant – in this case, neither to “Spring” nor “Fall” nor “Winter” (if there is Winter semester in this school). NULL='Spring' will evaluate to MAYBE and so will NULL='Fall'. The disjunction MAYBE OR MAYBE evaluates to MAYBE (not TRUE). Thus Igor will not be part of the answer (and of course neither will Rohit). But Igor should be returned as the answer. Indeed, regardless what semester Igor took the Networks class (no matter what was the unknown value of NULL), the selection condition will be true. This “Igor” will be missed by SQL and the SQL answer would be incomplete according to completeness requirements specified in Tomasz Imieliński, Witold Lipski, 'Incomplete Information in Relational Databases'. It is also argued there that 3-valued logic (TRUE, FALSE, MAYBE) can never provide guarantee of complete answer for tables with incomplete information. Three algebras which satisfy conditions of safety and completeness are defined as Imielinski–Lipski algebras: the Codd-Tables algebra, the V-tables algebra and the Conditional tables (C-tables) algebra. == Codd-tables algebra == Codd-tables algebra is based on the usual Codd's single NULL values. The table T above is an example of Codd-table. Codd-table algebra supports projection and positive selections only. It is also demonstrated in [IL84 that it is not possible to correctly extend more relational operators over Codd-Tables. For example, such basic operation as join is not extendable over Codd-tables. It is not possible to define selections with Boolean conditions involving negation and preserve completeness. For example, queries like the above query Q cannot be supported. In order to be able to extend more relational operators, more expressive form of null value representation is needed in tables which are called V-table. == V-tables algebra == V-tables algebra is based on many different ("marked") null values or variables allowed to appear in a table. V-tables allow to show that a value may be unknown but the same for different tuples. For example, in the table below Gaurav and Igor order the same (but unknown) beer in two unknown bars (which may, or may not be different – but remain unknown). Gaurav and Jane frequent the same unknown bar (Y1). Thus, instead one NULL value, we use indexed variables, or Skolem constants . V-tables algebra is shown to correctly support projection, positive selection (with no negation occurring in the selection condition), union, and renaming of attributes, which allows for processing arbitrary conjunctive queries. A very desirable property enjoyed by the V-table algebra is that all relational operators on tables are performed in exactly the same way as in the case of the usual relations. === Conditional tables (c-tables) algebra === Example of conditional table (c-table) is shown below. It has additional column “con” which is a Boolean condition involving variables, null values – same as in V-tables. over the following table c-table Conditional tables algebra, mainly of theoretical interest, supports projection, selection, union, join, and renaming. Under closed-world assumption, it can also handle the operator of difference, thus it can support all relational operators. == History == Imieliński–Lipski algebras were introduced by Tomasz Imieliński and Witold Lipski Jr. in Incomplete Information in Relational Databases.

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  Fuzzy finite element

  The fuzzy finite element method combines the well-established finite element method with the concept of fuzzy numbers, the latter being a special case of a fuzzy set. The advantage of using fuzzy numbers instead of real numbers lies in the incorporation of uncertainty (on material properties, parameters, geometry, initial conditions, etc.) in the finite element analysis. One way to establish a fuzzy finite element (FE) analysis is to use existing FE software (in-house or commercial) as an inner-level module to compute a deterministic result, and to add an outer-level loop to handle the fuzziness (uncertainty). This outer-level loop comes down to solving an optimization problem. If the inner-level deterministic module produces monotonic behavior with respect to the input variables, then the outer-level optimization problem is greatly simplified, since in this case the extrema will be located at the vertices of the domain.

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  Fuzzy relation

  A fuzzy relation is the cartesian product of mathematical fuzzy sets. Two fuzzy sets are taken as input, the fuzzy relation is then equal to the cross product of the sets which is created by vector multiplication. Usually, a rule base is stored in a matrix notation which allows the fuzzy controller to update its internal values. From a historical perspective, the first fuzzy relation was mentioned in the year 1971 by Lotfi A. Zadeh. A practical approach to describe a fuzzy relation is based on a 2d table. At first, a table is created which consists of fuzzy values from 0..1. The next step is to apply the if-then-rules to the values. The resulting numbers are stored in the table as an array. Fuzzy relations can be utilized in fuzzy databases.

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