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  JasPer

  JasPer is a computer software project to create a reference implementation of the codec specified in the JPEG-2000 Part-1 standard (i.e. ISO/IEC 15444-1) - started in 1997 at Image Power Inc. and at the University of British Columbia. It consists of a C library and some sample applications useful for testing the codec. The copyright owner began licensing the code to the public under an MIT License-style license in 2004 in response to requests from the open-source community. As of 2011 JasPer operated as a component of many software projects, both free and proprietary, including (but not limited to) netpbm (as of release 10.12), ImageMagick and KDE (as of version 3.2). As of 22 June 2010 the GEGL graphics library supported JasPer in its latest Git versions. In a series of objective JPEG-2000-compression quality tests conducted in 2004, "JasPer was the best codec, closely followed by IrfanView and Kakadu". However, Jasper remains one of the slowest implementations of the JPEG-2000 codec, as it was designed for reference, not performance. == Etymology == The name "JasPer" has simultaneous connotations with Canada's Jasper National Park, with the semi-precious gemstone, jasper, and with "JP" as an abbreviation of the JPEG-2000 standard.

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  The Sword in the Stoned

  "The Sword in the Stoned" is the fifth episode of the second season of the American fantasy comedy television series Ted. Written by Julius Sharpe, and directed by Seth MacFarlane, it premiered on the American streaming service Peacock, along with the rest of season two, on March 5, 2026. The series acts as a precursor to the Ted film franchise, showcasing the childhood lives of the protagonists. The series, set in 1994, focuses on John Bennett (Max Burkholder), the series' primary protagonist, an awkward high-school aged boy; along with Ted (MacFarlane), the series' titular anthropomorphic teddy bear. The two live with John's family, Susan (Alanna Ubach), his mild mannered mother, and Matty (Scott Grimes), his conservative father. Also residing with the family is Blaire (Giorgia Whigham), his radically liberal cousin whom often clashes with Matty. In the episode, Ted and John join the school play so they can have more extracurricular activities for their college applications, but the latter grows a connection with the school's popular teenager, Erin (Francesca Xuereb). Concurrently, Susan and Matty get a job at Dunkin' Donuts to help with their financial troubles, and Matty is given an opportunity to tell off Bill Clinton. Burkholder wore prop armor during the episode's play scenes. Bill Clinton’s appearance in the episode was portrayed by MacFarlane. After conventional makeup and visual techniques failed to convincingly resemble Clinton, the production used artificial intelligence to digitally replace MacFarlane's face with Clinton's likeness. Upon release, the episode received generally positive reviews from critics, though the use of AI in the Clinton scene was polarizing among audiences and reviewers. == Plot == John tells Ted that he is the last single guy left at their school, to which Ted points out the popular, single cheerleader, Erin, but John dismisses this. At home, Blaire tells John that he needs extracurricular activities to get into college, while Susan and Matty discuss their financial troubles, especially regarding John's college tuition. Looking over their options, they decide to audition for a school production of the play Camelot. Matty takes a job at Dunkin' Donuts, despite being told that nobody will give him a tip, and having to wear an incorrect name tag. Waiting for their auditions, John and Ted watch several poor auditions for the play before seeing Erin's, who delivers a flawless performance; John and Ted do less serious auditions, getting cast as knights, while Erin gets the role of Guinevere. Matty complains about his low salary, and Susan decides to get a job at Dunkin' Donuts beside him to help earn more income. Erin clashes with Lancelot's actor while rehearsing, and John compliments her performance, which she ignores, but, seeing Ted and John give good performances in a repetition exercise, she becomes interested in him, particularly since he treats her better than her stage-partner. Matty and Susan watch an employee training video, explaining how they should treat customers politely, not affecting Matty's nihilistic attitude. The manager announces that Bill Clinton is visiting their Dunkin' Donuts for publicity, and Matty sees this as a chance to tell Bill off. John and Erin practice lines, as she reveals the show is being taped so it can be sent to Emerson College in hopes of her getting in; Erin asks John to go out with her after the show. At dinner, Matty enthusiastically reveals what he plans to tell Bill, as John becomes stressed about the play when Susan tells there will be a large audience. Bill comes to the Dunkin' Donuts, and, seeing Matty is nervously insulting him, stages a private meeting with him, where Bill yells at Matty, calling him a loser before posing for a picture with Matty and subsequently throwing the cold coffee onto him. To ease the pressure, Ted and John take edibles from Blaire, but learn at the show that they contained mushrooms, causing them to stress further. On stage, Ted and John yell nervously that they're on drugs as the latter urinates in his costume, causing Erin to angrily storm off. == Production == "The Sword in the Stoned" was directed by series creator and lead Seth MacFarlane, and written by Julius Sharpe in his third and final writing credit for the series. When Ted and John are doing repetition exercises, they tackle each other to the ground, which required a stuntman named Ashton to play the role of Ted, according to Max Burkholder, who portrays John. Burkholder also recalled that, when Ted was choking John in the scene, he kept making a noise during the choking, which made Bill, the cameraman, laugh, despite being a "stone face" that never laughs, noting that seeing him be amused by the noise he was making assured Burkholder that what he was doing was "hilarious". Burkholder found the filming of the play scenes "weird", as he was put in fake armor with a hose inside his suit—which was filled with water mixed with yellow food coloring—that was made to create the urine stream that comes out of John's armor in the episode; he also noted that it took around 45 minutes to put on and take off the armor. He revealed that he himself had to urinate during the filming, as doing a scene about a character having to do so "really [broke] my brain", with the fact that it took 45 minutes to get the suit off adding to the frustration. Jennifer Ashley Connell, who worked for wardrobe, had to repeatedly go to Burkholder quickly between takes to dry off his pants with two hair dryers to make it look like the fake urine hadn't already streamed down his pants, so they could get as many shots of it as possible. Francesca Xuereb guest stars in the episode as Erin, the cheerleader who stars in the play. Incumbent president Bill Clinton was portrayed by MacFarlane, with artificial intelligence (AI) being used to digitally make MacFarlane's face look like Clinton's during post-production. Before settling on AI, the crew tried to use traditional computer-generated imagery and prosthetics, which made him look "terrifying", resulting in them deciding that AI would give them a more accurate look. One of the original technologies considered was one where, after scanning MacFarlane, a mesh of his head was created, and they had to use computer graphics to replace MacFarlane's face with Clinton's. An issue was faced, however, when they found the archival footage used as reference from the Clinton Library—an official Presidential Library containing information related to Clinton—to be extremely low-quality, making it hard to properly emulate his face, since only still images were of acceptable quality, and there weren't references of his moving face to work off of. A forensic artist was hired to help with this, and they created a 3D model of Clinton's head in ZBrush, based off of his presidential portrait. The model head worked for still frames, but movement was still difficult to do realistically, due to it being made for a "single-point perspective", which made details like the cheekbones or other minor issues more noticeable when using it for the scene. Since this did not work, AI was ultimately chosen through the studio Deep Voodoo, which used large language models to teach the tool how to correctly replicate Clinton's appearance. Defending the episode's use of AI, MacFarlane noted that the crew did not want people to focus on the tool being used, trying to utilize it in a way that wouldn't distract from the humor and narrative. Like the rest of the series, the episode was shot using ViewScreen; MacFarlane was able to act live with the cast as Ted due to ViewScreen, a technology that allows the production crew to visualize what Ted will look like in each scene in real time. == Release and reception == "The Sword in the Stoned" was first released on March 5, 2026, on the American streaming service Peacock, along with the rest of the second season. Nate Richards of Collider highlighted the Dunkin' Donuts subplot as an example of Scott Grimes delivering a "lot of laughs" through his performance as Matty. Dustin Rowles of Pajiba called "The Sword in the Stoned" one of the season's many episodes he'd recommend, particularly for the scenes of Ted and John being high on mushrooms during the play. Oppositely, Nick Valdez of ComicBook.com ranked the episode as the worst of the second season, criticizing it for not having a "huge impact" on the Bennett family dynamic like other episodes of the season do, and Susan and Matty's side story as the main reason he felt it was "[kept] from being great". Valdez noted the episode for likely being an advertisement for Dunkin' Donuts, calling the plot's ending scene involving Clinton the reason "it just all sticks out like a sore thumb". === Response to AI usage === The episode's use of AI for MacFarlane's portrayal of Clinton proved controversial, mainly on social media, where audiences asserted that the crew should have gotten an actor that resembl

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  Paranoia (role-playing game)

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

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  Nature Manifesto

  Nature Manifesto is an Immersive sound piece and multimedia installation by Icelandic artist Björk and artist and curator Aleph Molinari, created in collaboration with the French Institute for Research and Coordination in Acoustics/Music (IRCAM). The installation was showcased at the Centre Pompidou in Paris, France from November 20, 2024 to December 9, 2024, as part of the museum's "Biodiversity: Which Culture for Which Future?" forum. It combines natural soundscapes, calls of extinct animals reconstructed through artificial intelligence, and Björk's narration to address damages to biodiversity and the collapse of ecosystems. == Background == Björk's work intricately weaves themes of nature and technology, reflecting her deep engagement with both realms. In 2008, she co-founded the Náttúra campaign to protest the construction of foreign-backed aluminum factories in Iceland, aiming to protect the country's natural landscapes. She released the single "Náttúra" featuring Thom Yorke, with all proceeds supporting this environmental initiative. Her 2011 album Biophilia further exemplifies this synthesis, exploring the relationships between music, nature, and technology through a multimedia project that included interactive apps, custom-made instruments, and educational workshops. Björk's Cornucopia tour (2019-2023) seamlessly integrates themes of nature preservation and environmental activism, and featured a recorded message by Swedish climate activist Greta Thunberg. The tour's fusion of music, technology, and natural imagery reflects Björk's vision of a harmonious coexistence between humanity and nature, advocating for sustainable futures. Björk has previously used artificial intelligence in her works. In 2020, she collaborated with Microsoft to create Kórsafn, a sound installation for the Sister City Hotel lobby in New York City which used an AI-powered model that elaborated choral recordings from her discography through a sensor on the rooftop of the building that would generate music according to data like the weather and the seasons. For her charity single "Oral", featuring Spanish singer Rosalía, she released a music video directed by photographer and visual artist Carlota Guerrero, who used AI-generated deepfake versions of the artists. == Concept == Nature Manifesto is a three-minute and forty-second immersive sound piece. The composition merges Björk's voice, as she articulates a manifesto on biodiversity and the climate crisis, with cries of extinct and endangered animals, harmonizing them with natural soundscapes. The installation was curated by Chloé Siganos and Aleph Molinari, with associate curator Delphine Le Gatt. The primary goal of Nature Manifesto is to foster a deeper understanding of humanity's impact on the natural world. Conceived as a "post-optimistic" manifesto, Aleph Molinari stated that the project's purpose was to "offer a voice to nature". He stated that "the modern concept of nature itself is problematic [...] because it’s a concept born in the Romantic period and, with the rise of the industrial era, became an antithesis to human civilisation and everything urban. Nature came to define what was outside, the savage Other... But nature is everything that we’re part of." The soundscape features recreated calls of extinct and endangered species, developed in collaboration with the French sound research institute IRCAM. Artificial intelligence was employed to simulate the vocalizations of animals that no longer exist in the wild. To save energy and lessen the ecological impact of the use of AI, the research institute developed a "frugal AI" model capable of generating audio in real-time on local servers without a graphics processing unit. The sounds were then produced and edited by Björk in collaboration with Robin Meier Wiratunga and Bergur Þórisson. The installation was located within the Centre Pompidou's escalator, known as the "caterpillar". The installation was further supported by videos created by visual artist Sam Balfus (also known as Balfua) by using artificial intelligence, and edited by Santiago Molinari. == Activism == To sustain and broaden the themes presented in Nature Manifesto, Björk publicly urged French President Emmanuel Macron to prohibit bottom trawling within France's marine protected areas (MPA). She criticized the French government's claim of protecting 30% of its marine territories, highlighting that over 90% of these MPAs exist only on paper, allowing destructive practices like bottom trawling to continue unchecked. She collaborated with non-governmental organizations Sustainable Ocean Alliance, Ungir umhverfissinnar and Bloom, to advocate for genuine ocean conservation. Björk promoted the cause through her social media profiles by sharing petitions. In November 2024, Björk lent her Instagram account to French environmental activists to directly address Macron. The activists used the platform to call for stronger protection of the ocean, urging Macron to impose stricter restrictions on harmful fishing practices, particularly bottom trawling. == Reception == Nature Manifesto received mixed to positive reviews from critics. Some critiques focused on the installation's setting, suggesting that the movement inherent to the escalator space diminished the immersive potential of the soundscape. The choice of using artificial intelligence was also questioned. Björk and Molinari defended this, as both see AI as a tool that can be used creatively and sustainably, with Björk focusing on the importance of human input to give AI a "soul", and Molinari stressing the need for sustainable technological practices in the broader context of digital life. After the exhibition ended, Björk further opinionated: "this is how we will work in the future. [...] if there is no soul in tomorrow's music made by AI it is because [no one] put it there and we have to speak out and guard this as listeners", further stating that there is already "soulless muzak" [sic] on Spotify, "mass manufactured without the attention of creativity".

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  List of JavaScript libraries

  This is a list of notable JavaScript libraries. == Constraint programming == Cassowary (software) CHR.js == DOM (manipulation) oriented == Google Polymer Dojo Toolkit jQuery MooTools Prototype JavaScript Framework == Graphical/visualization (canvas, SVG, or WebGL related) == AnyChart Apache ECharts Babylon.js Chart.js Cytoscape D3.js Dojo Toolkit FusionCharts Google Charts JointJS p5.js Plotly.js Processing.js Raphaël RGraph SWFObject Teechart Three.js Velocity.js Verge3D Webix == GUI (Graphical user interface) and widget related == Angular (application platform) by Google AngularJS by Google Bootstrap Dojo Widgets Ext JS by Sencha Foundation by ZURB jQuery UI jQWidgets OpenUI5 by SAP Polymer (library) by Google qooxdoo React.js by Meta/Facebook Vue.js Webix WinJS Svelte === No longer actively developed === Glow Lively Kernel Script.aculo.us YUI Library == Pure JavaScript/Ajax == Google Closure Library JsPHP Microsoft's Ajax library MochiKit PDF.js Socket.IO Spry framework Underscore.js == Template systems == jQuery Mobile Mustache Jinja-JS Twig.js == Unit testing == Jasmine Mocha QUnit == Test automation == Playwright Cypress == Web-application related (MVC, MVVM) == Angular (application platform) by Google AngularJS by Google Backbone.js Echo Ember.js Enyo Express.js Ext JS Google Web Toolkit JsRender/JsViews Knockout Meteor Mojito MooTools Next.js Nuxt.js OpenUI5 by SAP Polymer (library) by Google Prototype JavaScript Framework qooxdoo React.js SproutCore svelte Vue.js == Other == Blockly Cannon.js MathJax Modernizr TensorFlow Brain.js

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  Document AI

  Document AI, also known as Document Intelligence, refers to a field of technology that employs machine learning (ML) techniques, such as natural language processing (NLP). These techniques are used to develop computer models capable of analyzing documents in a manner akin to human review. Through NLP, computer systems are able to understand relationships and contextual nuances in document contents, which facilitates the extraction of information and insights. Additionally, this technology enables the categorization and organization of the documents themselves. The applications of Document AI extend to processing and parsing a variety of semi-structured documents, such as forms, tables, receipts, invoices, tax forms, contracts, loan agreements, and financial reports. == Key features == Machine learning is utilized in Document AI to extract information from both printed and digital documents. This technology recognizes images, text, and characters in various languages, aiding in the extraction of insights from unstructured documents. The use of this technology can improve the speed and quality of decision-making in document analysis. Additionally, the automation of data extraction and validation can contribute to increased efficiency in document analysis processes. Since the early 2020s, the integration of large language models has extended Document AI beyond extraction toward generative tasks, including the automated drafting of forms, contracts, and document summaries. == Example == A business letter contains information in the form of text, as well as other types of information, such as the position of the text. For instance, a typical letter contains two addresses before the body of the text. The address at the very top (sometimes aligned to the right) is the sender address. This is normally followed by the date of the letter, with the place of writing. After this, the receiver address is listed. The distinction between the sender address and the receiver address is conveyed solely by the position of the address on the page, i.e. there is no textual indication like Sender: in front of the addresses. == Data dimensions and ML architecture == Data is typically distinguished into spatial data and time-series data, the former includes things like images, maps and graphs, while the latter includes signals such as stock prices or voice recordings. Document AI combines text data, which has a time dimension, with other types of data, such as the position of an address in a business letter, which is spatial. Historically in machine learning spatial data was analyzed using a convolutional neural network, and temporal data using a recurrent neural network. With the advent of dimension-type agnostic transformer architecture, these two different types of dimension can be more easily combined, Document AI is an example of this. == Benchmarks == Several public datasets are used to evaluate Document AI systems. FUNSD (Form Understanding in Noisy Scanned Documents) contains 199 annotated forms with token- and block-level labels for form understanding tasks. CORD (Consolidated Receipt Dataset) supports key information extraction from receipts. DocVQA contains approximately 50,000 questions over 12,000 document images for layout-aware visual question answering. == Common uses == Document AI systems are used to automate document processing and information extraction in business and financial workflows, including invoice and receipt processing, data entry automation, anomaly detection, mortgage processing, loan portfolio monitoring, credit risk management, and fraud detection such as counterfeit currency and fraudulent checks. They are also applied in regulatory compliance and contract analysis, including assessing changes in legal and regulatory documents. In real estate, Document AI supports document classification and structured information extraction for standardized processing and analytics. With the adoption of generative AI, Document AI systems can also generate and pre-fill structured documents such as contracts or business forms from natural language prompts.

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  CogX Festival

  CogX Festival is a global festival focusing on the impact of artificial intelligence (AI) and emerging technology on industry, government, and society. It takes place annually, usually in September, in London, England. Founded by Charlie Muirhead and Tabitha Goldstaub in 2017, CogX aims to facilitate dialogue and understanding about AI and its implications across various sectors. CogX Festival 2023 was held from September 12 to September 14 across multiple sites in London. == History == The inaugural CogX event took place in 2017, intending to bring together experts from diverse fields to discuss the role and impact of AI and emerging technologies. Since then, it has evolved to include a broader range of topics and attract a diverse audience. In 2018, the first CogX Awards festival was hosted. That year, over 50 awards were shown to 300 guests. In 2021, CogX and Hopin, a video conferencing software, signed an agreement lasting 4 years to make CogX a hybrid conference due to the COVID-19 pandemic. CogX 2021 attracted over 5,000 attendees in-person and over 100,000 virtually. In 2022, they returned to a live event format after two years of hybrid events and controlled physical attendance. They also launched the CogX app, which curated insights from the world's top podcasts. In 2023, after he had delivered the keynote address guest speaker Stephen Fry fell off the stage and subsequently broke his leg, hip, pelvis and a "bunch of ribs". A court filing in 2026 revealed that Fry was seeking £100,000 in damages from CogX Festival Ltd and creative agency Blonstein Events. == Programming == The festival features sessions, discussions, workshops, and exhibitions, encompassing various domains of AI and technology. In recent CogX Festivals, they have featured summits encompassing topics like global leadership and industry transformation.

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  CADE ATP System Competition

  The CADE ATP System Competition (CASC) is an annual competition of fully automated theorem provers for classical logic. == Competition == CASC is associated with the Conference on Automated Deduction and the International Joint Conference on Automated Reasoning organized by the Association for Automated Reasoning. It has inspired similar competition in related fields, in particular the successful SMT-COMP competition for satisfiability modulo theories, the SAT Competition for propositional reasoners, and the modal logic reasoning competition. The first CASC, CASC-13, was held as part of the 13th Conference on Automated Deduction at Rutgers University, New Brunswick, NJ, in 1996. Among the systems competing were Otter and SETHEO.

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  Biohybrid microswimmer

  A biohybrid microswimmer also known as biohybrid nanorobot, can be defined as a microswimmer that consist of both biological and artificial constituents, for instance, one or several living microorganisms attached to one or various synthetic parts. In recent years nanoscopic and mesoscopic objects have been designed to collectively move through direct inspiration from nature or by harnessing its existing tools. Small mesoscopic to nanoscopic systems typically operate at low Reynolds numbers (Re ≪ 1), and understanding their motion becomes challenging. For locomotion to occur, the symmetry of the system must be broken. In addition, collective motion requires a coupling mechanism between the entities that make up the collective. To develop mesoscopic to nanoscopic entities capable of swarming behaviour, it has been hypothesised that the entities are characterised by broken symmetry with a well-defined morphology, and are powered with some material capable of harvesting energy. If the harvested energy results in a field surrounding the object, then this field can couple with the field of a neighbouring object and bring some coordination to the collective behaviour. Such robotic swarms have been categorised by an online expert panel as among the 10 great unresolved group challenges in the area of robotics. Although investigation of their underlying mechanism of action is still in its infancy, various systems have been developed that are capable of undergoing controlled and uncontrolled swarming motion by harvesting energy (e.g., light, thermal, etc.). Over the past decade, biohybrid microrobots, in which living mobile microorganisms are physically integrated with untethered artificial structures, have gained growing interest to enable the active locomotion and cargo delivery to a target destination. In addition to the motility, the intrinsic capabilities of sensing and eliciting an appropriate response to artificial and environmental changes make cell-based biohybrid microrobots appealing for transportation of cargo to the inaccessible cavities of the human body for local active delivery of diagnostic and therapeutic agents. == Background == Biohybrid microswimmers can be defined as microswimmers that consist of both biological and artificial constituents, for instance, one or several living microorganisms attached to one or various synthetic parts. The pioneers of this field, ahead of their time, were Montemagno and Bachand with a 1999 work regarding specific attachment strategies of biological molecules to nanofabricated substrates enabling the preparation of hybrid inorganic/organic nanoelectromechanical systems, so called NEMS. They described the production of large amounts of F1-ATPase from the thermophilic bacteria Bacillus PS3 for the preparation of F1-ATPase biomolecular motors immobilized on a nanoarray pattern of gold, copper or nickel produced by electron beam lithography. These proteins were attached to one micron microspheres tagged with a synthetic peptide. Consequently, they accomplished the preparation of a platform with chemically active sites and the development of biohybrid devices capable of converting energy of biomolecular motors into useful work. One of the most fundamental questions in science is what defines life. Collective motion is one of the hallmarks of life. This is commonly observed in nature at various dimensional levels as energized entities gather, in a concerted effort, into motile aggregated patterns. These motile aggregated events can be noticed, among many others, as dynamic swarms; e.g., unicellular organisms such as bacteria, locust swarms, or the flocking behaviour of birds. Ever since Newton established his equations of motion, the mystery of motion on the microscale has emerged frequently in scientific history, as famously demonstrated by a couple of articles that should be discussed briefly. First, an essential concept, popularized by Osborne Reynolds, is that the relative importance of inertia and viscosity for the motion of a fluid depends on certain details of the system under consideration. The Reynolds number Re, named in his honor, quantifies this comparison as a dimensionless ratio of characteristic inertial and viscous forces: R e = ρ u l μ {\displaystyle \mathrm {Re} ={\frac {\rho ul}{\mu }}} Here, ρ represents the density of the fluid; u is a characteristic velocity of the system (for instance, the velocity of a swimming particle); l is a characteristic length scale (e.g., the swimmer size); and μ is the viscosity of the fluid. Taking the suspending fluid to be water, and using experimentally observed values for u, one can determine that inertia is important for macroscopic swimmers like fish (Re = 100), while viscosity dominates the motion of microscale swimmers like bacteria (Re = 10−4). The overwhelming importance of viscosity for swimming at the micrometer scale has profound implications for swimming strategy. This has been discussed memorably by E. M. Purcell, who invited the reader into the world of microorganisms and theoretically studied the conditions of their motion. In the first place, propulsion strategies of large scale swimmers often involve imparting momentum to the surrounding fluid in periodic discrete events, such as vortex shedding, and coasting between these events through inertia. This cannot be effective for microscale swimmers like bacteria: due to the large viscous damping, the inertial coasting time of a micron-sized object is on the order of 1 μs. The coasting distance of a microorganism moving at a typical speed is about 0.1 angstroms (Å). Purcell concluded that only forces that are exerted in the present moment on a microscale body contribute to its propulsion, so a constant energy conversion method is essential. Microorganisms have optimized their metabolism for continuous energy production, while purely artificial microswimmers (microrobots) must obtain energy from the environment, since their on-board-storage-capacity is very limited. As a further consequence of the continuous dissipation of energy, biological and artificial microswimmers do not obey the laws of equilibrium statistical physics, and need to be described by non-equilibrium dynamics. Mathematically, Purcell explored the implications of low Reynolds number by taking the Navier-Stokes equation and eliminating the inertial terms: μ ∇ 2 u − ∇ p = 0 {\displaystyle {\begin{aligned}\mu \nabla ^{2}\mathbf {u} -{\boldsymbol {\nabla }}p&={\boldsymbol {0}}\\\end{aligned}}} where u {\displaystyle \mathbf {u} } is the velocity of the fluid and ∇ p {\displaystyle {\boldsymbol {\nabla }}p} is the gradient of the pressure. As Purcell noted, the resulting equation — the Stokes equation — contains no explicit time dependence. This has some important consequences for how a suspended body (e.g., a bacterium) can swim through periodic mechanical motions or deformations (e.g., of a flagellum). First, the rate of motion is practically irrelevant for the motion of the microswimmer and of the surrounding fluid: changing the rate of motion will change the scale of the velocities of the fluid and of the microswimmer, but it will not change the pattern of fluid flow. Secondly, reversing the direction of mechanical motion will simply reverse all velocities in the system. These properties of the Stokes equation severely restrict the range of feasible swimming strategies. Recent publications of biohybrid microswimmers include the use of sperm cells, contractive muscle cells, and bacteria as biological components, as they can efficiently convert chemical energy into movement, and additionally are capable of performing complicated motion depending on environmental conditions. In this sense, biohybrid microswimmer systems can be described as the combination of different functional components: cargo and carrier. The cargo is an element of interest to be moved (and possibly released) in a customized way. The carrier is the component responsible for the movement of the biohybrid, transporting the desired cargo, which is linked to its surface. The great majority of these systems rely on biological motile propulsion for the transportation of synthetic cargo for targeted drug delivery/ There are also examples of the opposite case: artificial microswimmers with biological cargo systems. Over the past decade, biohybrid microrobots, in which living mobile microorganisms are physically integrated with untethered artificial structures, have gained growing interest to enable the active locomotion and cargo delivery to a target destination. In addition to the motility, the intrinsic capabilities of sensing and eliciting an appropriate response to artificial and environmental changes make cell-based biohybrid microrobots appealing for transportation of cargo to the inaccessible cavities of the human body for local active delivery of diagnostic and therapeutic agents. Active locomotion, targeting and steering of concentrated therape

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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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  Ensemble averaging (machine learning)

  In machine learning, ensemble averaging is the process of creating multiple models (typically artificial neural networks) and combining them to produce a desired output, as opposed to creating just one model. Ensembles of models often outperform individual models, as the various errors of the ensemble constituents "average out". == Overview == Ensemble averaging is one of the simplest types of committee machines. Along with boosting, it is one of the two major types of static committee machines. In contrast to standard neural network design, in which many networks are generated but only one is kept, ensemble averaging keeps the less satisfactory networks, but with less weight assigned to their outputs. The theory of ensemble averaging relies on two properties of artificial neural networks: In any network, the bias can be reduced at the cost of increased variance In a group of networks, the variance can be reduced at no cost to the bias. This is known as the bias–variance tradeoff. Ensemble averaging creates a group of networks, each with low bias and high variance, and combines them to form a new network which should theoretically exhibit low bias and low variance. Hence, this can be thought of as a resolution of the bias–variance tradeoff. The idea of combining experts can be traced back to Pierre-Simon Laplace. == Method == The theory mentioned above gives an obvious strategy: create a set of experts with low bias and high variance, and average them. Generally, what this means is to create a set of experts with varying parameters; frequently, these are the initial synaptic weights of a neural network, although other factors (such as learning rate, momentum, etc.) may also be varied. Some authors recommend against varying weight decay and early stopping. The steps are therefore: Generate N experts, each with their own initial parameters (these values are usually sampled randomly from a distribution) Train each expert separately Combine the experts and average their values. Alternatively, domain knowledge may be used to generate several classes of experts. An expert from each class is trained, and then combined. A more complex version of ensemble average views the final result not as a mere average of all the experts, but rather as a weighted sum. If each expert is y i {\displaystyle y_{i}} , then the overall result y ~ {\displaystyle {\tilde {y}}} can be defined as: y ~ ( x ; α ) = ∑ j = 1 p α j y j ( x ) {\displaystyle {\tilde {y}}(\mathbf {x} ;\mathbf {\alpha } )=\sum _{j=1}^{p}\alpha _{j}y_{j}(\mathbf {x} )} where α {\displaystyle \mathbf {\alpha } } is a set of weights. The optimization problem of finding alpha is readily solved through neural networks, hence a "meta-network" where each "neuron" is in fact an entire neural network can be trained, and the synaptic weights of the final network is the weight applied to each expert. This is known as a linear combination of experts. It can be seen that most forms of neural network are some subset of a linear combination: the standard neural net (where only one expert is used) is simply a linear combination with all α j = 0 {\displaystyle \alpha _{j}=0} and one α k = 1 {\displaystyle \alpha _{k}=1} . A raw average is where all α j {\displaystyle \alpha _{j}} are equal to some constant value, namely one over the total number of experts. A more recent ensemble averaging method is negative correlation learning, proposed by Y. Liu and X. Yao. This method has been widely used in evolutionary computing. == Benefits == The resulting committee is almost always less complex than a single network that would achieve the same level of performance The resulting committee can be trained more easily on smaller datasets The resulting committee often has improved performance over any single model The risk of overfitting is lessened, as there are fewer parameters (e.g. neural network weights) which need to be set.

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  Flux (text-to-image model)

  Flux (also known as FLUX.1 and FLUX.2) is a text-to-image model developed by Black Forest Labs (BFL), based in Freiburg im Breisgau, Germany. Black Forest Labs was founded by former employees of Stability AI. As with other text-to-image models, Flux generates images from natural language descriptions, called prompts. == History == Black Forest Labs (BFL) was founded in 2024 by Robin Rombach, Andreas Blattmann, and Patrick Esser, former employees of Stability AI. All three founders had previously researched the artificial intelligence image generation at LMU Munich as research assistants under Björn Ommer. They published their research results on image generation in 2022, which resulted in creation of Stable Diffusion. Investors in BFL included venture capital firm Andreessen Horowitz, Brendan Iribe, Michael Ovitz, Garry Tan, and Vladlen Koltun. The company received an initial investment of US$31 million. In August 2024, Flux was integrated into the Grok chatbot developed by xAI and made available as part of premium feature on X (formerly Twitter). Grok later switched to its own text-to-image model Aurora in December 2024. On 18 November 2024, Mistral AI announced that its Le Chat chatbot had integrated Flux Pro as its image generation model. On 21 November 2024, BFL announced the release of Flux.1 Tools, a suite of editing tools designed to be used on top of existing Flux models. The tools consisting of Flux.1 Fill for inpainting and outpainting, Flux.1 Depth for control based on extracted depth map of input images and prompts, Flux.1 Canny for control based on extracted canny edges of input images and prompts, and Flux.1 Redux for mixing existing input images and prompts. Each tools are available in both Pro and Dev models. In January 2025, BFL announced a partnership with Nvidia for inclusion of Flux models as foundation models for Nvidia's Blackwell microarchitecture. The company also announced the release of Flux Pro Finetuning API, designed for customisation and fine-tuning of Flux-generated images and a partnership with German media company Hubert Burda Media for usage of Flux Pro as part of content creation. On 29 May 2025, BFL announced Flux.1 Kontext, a suite of models that enable in-context image generation and editing, allowing users to prompt with both text and images. Alongside this, BFL Playground, an interface for testing Flux models was released. On 31 July 2025, BFL announced Flux.1 Krea Dev, a model developed in collaboration with Krea AI that trained to achieve better performance, more varied aesthetics, and better realism compared to existing text-to-image models. In September 2025, Adobe Inc. announced that Photoshop (beta) users can use Flux.1 Kontext Pro as a model for its generative fill tool. BFL collaborated with Meta on Vibes, a video-generation app. On 25 November 2025, BFL announced the release of Flux.2 model series, consisting of Pro, Flex, Dev, and Apache 2.0-licensed Klein (meaning Little or Small in German language) models along with Flux.2 variational autoencoder which also released as open-source software under Apache 2.0 licence. This series claimed improvements for image reference, photorealism, typography, and prompt understanding. == Models == Flux is a series of text-to-image models. The models are based on rectified flow transformer blocks scaled to 12 billion parameters. Flux.1 models were released under different licences with Schnell (meaning Fast or Quick in German language) released as open-source software under Apache License, Dev released as source-available software under a non-commercial licence (users can obtain a self-serving commercial licence for Dev from BFL), and Pro released as proprietary software and only available as API that can be licensed by third-party users. Users retained the ownership of resulting output regardless of models used. An improved flagship model, Flux 1.1 Pro was released on 2 October 2024. Two additional modes were added on 6 November, Ultra which can generate image at four times higher resolution and up to 4 megapixel without affecting generation speed and Raw which can generate hyper-realistic image in the style of candid photography. Flux.1 Kontext is a series with in-context image generation and editing capabilities. It is available in Max, Pro, and Dev models. Max is the highest quality model and can be used to iteratively modify an existing image by using prompt while Pro is optimized to balance quality and speed of generation. Dev is an open-weight model released under non-commercial license, same as Flux.1 Dev. Flux.2 models are based on latent flow matching architecture with Mistral AI's Mistral-3 model (24 billion parameters) for its vision-language model. As with Flux.1, Flux.2 models were also released under different licences with Klein released as open-source software under Apache License, Dev released as source-available software under a non-commercial licence (users can obtain a self-serving commercial licence from BFL), and both Flex and Pro released as proprietary software and only available as API. The models can be used either online or locally by using generative AI user interfaces such as ComfyUI, Recraft Studio and Stable Diffusion WebUI Forge (a fork of Automatic1111 WebUI). Related to Flux is a text-to-video model by Black Forest Labs, under development as of February 2026. == Reception == According to a test performed by Ars Technica, the outputs generated by Flux.1 Dev and Flux.1 Pro are comparable with DALL-E 3 in terms of prompt fidelity, with the photorealism closely matched Midjourney 6 and generated human hands with more consistency over previous models such as Stable Diffusion XL. Flux has been criticised for its very realistic generated images. According to media reports, depictions ranged from an image of Donald Trump posing with guns to disturbing scenes, which triggered discussions about ethical implications of Flux models. After the release of the model, social media platform X was flooded with Flux-generated images. Black Forest Labs has not provided exact details of the data used to train the model. Ars Technica suspected that Flux is based on a large, unauthorised collection of images scraped from the internet, a controversial practice with potential legal consequences. According to a test performed by Japanese technology news website Gigazine for Flux.1 Kontext, the model series has a good understanding of the English language and can easily transfer style of the image from photorealistic into anime-style according to prompts given by the user; however, its ability to understand Japanese is quite poor. == Availability == In addition to the official BFL Playground on its website, the Flux models are also widely available through various third-party platforms for creative and professional use. These include repositories on platforms like Hugging Face and Replicate. == Further readings == FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space (29 May 2025) FLUX.2: Analyzing and Enhancing the Latent Space of FLUX – Representation Comparison (25 November 2025)

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  Gödel machine

  A Gödel machine is a hypothetical self-improving computer program that solves problems in an optimal way. It uses a recursive self-improvement protocol in which it rewrites its own code when it can prove the new code provides a better strategy. The machine was invented by Jürgen Schmidhuber (first proposed in 2003), but is named after Kurt Gödel who inspired the mathematical theories. The Gödel machine is often discussed when dealing with issues of meta-learning, also known as "learning to learn." Applications include automating human design decisions and transfer of knowledge between multiple related tasks, and may lead to design of more robust and general learning architectures. Though theoretically possible, no full implementation has been created. The Gödel machine is often compared with Marcus Hutter's AIXI, another formal specification for an artificial general intelligence. Schmidhuber points out that the Gödel machine could start out by implementing AIXItl as its initial sub-program, and self-modify after it finds proof that another algorithm for its search code will be better. == Limitations == Traditional problems solved by a computer only require one input and provide some output. Computers of this sort had their initial algorithm hardwired. This does not take into account the dynamic natural environment, and thus was a goal for the Gödel machine to overcome. The Gödel machine has limitations of its own, however. According to Gödel's First Incompleteness Theorem, any formal system that encompasses arithmetic is either flawed or allows for statements that cannot be proved in the system. Hence even a Gödel machine with unlimited computational resources must ignore those self-improvements whose effectiveness it cannot prove. == Variables of interest == There are three variables that are particularly useful in the run time of the Gödel machine. At some time t {\displaystyle t} , the variable time {\displaystyle {\text{time}}} will have the binary equivalent of t {\displaystyle t} . This is incremented steadily throughout the run time of the machine. Any input meant for the Gödel machine from the natural environment is stored in variable x {\displaystyle x} . It is likely the case that x {\displaystyle x} will hold different values for different values of variable time {\displaystyle {\text{time}}} . The outputs of the Gödel machine are stored in variable y {\displaystyle y} , where y ( t ) {\displaystyle y(t)} would be the output bit-string at some time t {\displaystyle t} . At any given time t {\displaystyle t} , where ( 1 ≤ t ≤ T ) {\displaystyle (1\leq t\leq T)} , the goal is to maximize future success or utility. A typical utility function follows the pattern u ( s , E n v ) : S × E → R {\displaystyle u(s,\mathrm {Env} ):S\times E\rightarrow \mathbb {R} } : u ( s , E n v ) = E μ [ ∑ τ = time T r ( τ ) ∣ s , E n v ] {\displaystyle u(s,\mathrm {Env} )=E_{\mu }{\Bigg [}\sum _{\tau ={\text{time}}}^{T}r(\tau )\mid s,\mathrm {Env} {\Bigg ]}} where r ( t ) {\displaystyle r(t)} is a real-valued reward input (encoded within s ( t ) {\displaystyle s(t)} ) at time t {\displaystyle t} , E μ [ ⋅ ∣ ⋅ ] {\displaystyle E_{\mu }[\cdot \mid \cdot ]} denotes the conditional expectation operator with respect to some possibly unknown distribution μ {\displaystyle \mu } from a set M {\displaystyle M} of possible distributions ( M {\displaystyle M} reflects whatever is known about the possibly probabilistic reactions of the environment), and the above-mentioned time = time ⁡ ( s ) {\displaystyle {\text{time}}=\operatorname {time} (s)} is a function of state s {\displaystyle s} which uniquely identifies the current cycle. Note that we take into account the possibility of extending the expected lifespan through appropriate actions. == Instructions used by proof techniques == The nature of the six proof-modifying instructions below makes it impossible to insert an incorrect theorem into proof, thus trivializing proof verification. === get-axiom(n) === Appends the n-th axiom as a theorem to the current theorem sequence. Below is the initial axiom scheme: Hardware Axioms formally specify how components of the machine could change from one cycle to the next. Reward Axioms define the computational cost of hardware instruction and the physical cost of output actions. Related Axioms also define the lifetime of the Gödel machine as scalar quantities representing all rewards/costs. Environment Axioms restrict the way new inputs x are produced from the environment, based on previous sequences of inputs y. Uncertainty Axioms/String Manipulation Axioms are standard axioms for arithmetic, calculus, probability theory, and string manipulation that allow for the construction of proofs related to future variable values within the Gödel machine. Initial State Axioms contain information about how to reconstruct parts or all of the initial state. Utility Axioms describe the overall goal in the form of utility function u. === apply-rule(k, m, n) === Takes in the index k of an inference rule (such as Modus tollens, Modus ponens), and attempts to apply it to the two previously proved theorems m and n. The resulting theorem is then added to the proof. === delete-theorem(m) === Deletes the theorem stored at index m in the current proof. This helps to mitigate storage constraints caused by redundant and unnecessary theorems. Deleted theorems can no longer be referenced by the above apply-rule function. === set-switchprog(m, n) === Replaces switchprog S pm:n, provided it is a non-empty substring of S p. === check() === Verifies whether the goal of the proof search has been reached. A target theorem states that given the current axiomatized utility function u (Item 1f), the utility of a switch from p to the current switchprog would be higher than the utility of continuing the execution of p (which would keep searching for alternative switchprogs). === state2theorem(m, n) === Takes in two arguments, m and n, and attempts to convert the contents of Sm:n into a theorem. == Example applications == === Time-limited NP-hard optimization === The initial input to the Gödel machine is the representation of a connected graph with a large number of nodes linked by edges of various lengths. Within given time T it should find a cyclic path connecting all nodes. The only real-valued reward will occur at time T. It equals 1 divided by the length of the best path found so far (0 if none was found). There are no other inputs. The by-product of maximizing expected reward is to find the shortest path findable within the limited time, given the initial bias. === Fast theorem proving === Prove or disprove as quickly as possible that all even integers > 2 are the sum of two primes (Goldbach’s conjecture). The reward is 1/t, where t is the time required to produce and verify the first such proof. === Maximizing expected reward with bounded resources === A cognitive robot that needs at least 1 liter of gasoline per hour interacts with a partially unknown environment, trying to find hidden, limited gasoline depots to occasionally refuel its tank. It is rewarded in proportion to its lifetime, and dies after at most 100 years or as soon as its tank is empty or it falls off a cliff, and so on. The probabilistic environmental reactions are initially unknown but assumed to be sampled from the axiomatized Speed Prior, according to which hard-to-compute environmental reactions are unlikely. This permits a computable strategy for making near-optimal predictions. One by-product of maximizing expected reward is to maximize expected lifetime.

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  Fuzzy logic

  Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by mathematician Lotfi Zadeh. Basic fuzzy logic had, however, been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski. The works of Zadeh and Joseph Goguen in the 1960s and 1970s went further by considering issues such as linguistic variables and lattices. Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or fuzzy sets are mathematical means of representing vagueness and imprecise information (hence the term fuzzy). These models have the capability of recognising, representing, manipulating, interpreting, and using data and information that are vague and lack certainty. Fuzzy logic has been applied to many fields, from control theory to artificial intelligence. == Overview == Classical logic only permits conclusions that are either true or false. However, there are also propositions with variable answers, which one might find when asking a group of people to identify a color. In such instances, the truth appears as the result of reasoning from inexact or partial knowledge in which the sampled answers are mapped on a spectrum. Both degrees of truth and probabilities range between 0 and 1 and hence may seem identical at first, but fuzzy logic uses degrees of truth as a mathematical model of vagueness, while probability is a mathematical model of ignorance. === Applying truth values === A basic application might characterize various sub-ranges of a continuous variable. For instance, a temperature measurement for anti-lock brakes might have several separate membership functions defining particular temperature ranges needed to control the brakes properly. Each function maps the same temperature value to a truth value in the 0 to 1 range. These truth values can then be used to determine how the brakes should be controlled. Fuzzy set theory provides a means for representing uncertainty. === Linguistic variables === In fuzzy logic applications, non-numeric values are often used to facilitate the expression of rules and facts. A linguistic variable such as age may accept values such as young and its antonym old. Because natural languages do not always contain enough value terms to express a fuzzy value scale, it is common practice to modify linguistic values with adjectives or adverbs. For example, we can use the hedges rather and somewhat to construct the additional values rather old or somewhat young. == Fuzzy systems == === Mamdani === The most well-known system is the Mamdani rule-based one. It uses the following rules: Fuzzify all input values into fuzzy membership functions. Execute all applicable rules in the rulebase to compute the fuzzy output functions. De-fuzzify the fuzzy output functions to get "crisp" output values. ==== Fuzzification ==== Fuzzification is the process of assigning the numerical input of a system to fuzzy sets with some degree of membership. This degree of membership may be anywhere within the interval [0,1]. If it is 0 then the value does not belong to the given fuzzy set, and if it is 1 then the value completely belongs within the fuzzy set. Any value between 0 and 1 represents the degree of uncertainty that the value belongs in the set. These fuzzy sets are typically described by words, and so by assigning the system input to fuzzy sets, we can reason with it in a linguistically natural manner. For example, in the image below, the meanings of the expressions cold, warm, and hot are represented by functions mapping a temperature scale. A point on that scale has three "truth values"—one for each of the three functions. The vertical line in the image represents a particular temperature that the three arrows (truth values) gauge. Since the red arrow points to zero, this temperature may be interpreted as "not hot"; i.e. this temperature has zero membership in the fuzzy set "hot". The orange arrow (pointing at 0.2) may describe it as "slightly warm" and the blue arrow (pointing at 0.8) "fairly cold". Therefore, this temperature has 0.2 membership in the fuzzy set "warm" and 0.8 membership in the fuzzy set "cold". The degree of membership assigned for each fuzzy set is the result of fuzzification. Fuzzy sets are often defined as triangle or trapezoid-shaped curves, as each value will have a slope where the value is increasing, a peak where the value is equal to 1 (which can have a length of 0 or greater) and a slope where the value is decreasing. They can also be defined using a sigmoid function. One common case is the standard logistic function defined as S ( x ) = 1 1 + e − x {\displaystyle S(x)={\frac {1}{1+e^{-x}}}} which has the following symmetry property S ( x ) + S ( − x ) = 1. {\displaystyle S(x)+S(-x)=1.} From this it follows that ( S ( x ) + S ( − x ) ) ⋅ ( S ( y ) + S ( − y ) ) ⋅ ( S ( z ) + S ( − z ) ) = 1 {\displaystyle (S(x)+S(-x))\cdot (S(y)+S(-y))\cdot (S(z)+S(-z))=1} ==== Fuzzy logic operators ==== Fuzzy logic works with membership values in a way that mimics Boolean logic. To this end, replacements for basic operators ("gates") AND, OR, NOT must be available. There are several ways to accomplish this. A common replacement is called the Zadeh operators: For TRUE/1 and FALSE/0, the fuzzy expressions produce the same result as the Boolean expressions. There are also other operators, more linguistic in nature, called hedges that can be applied. These are generally adverbs such as very, or somewhat, which modify the meaning of a set using a mathematical formula. However, an arbitrary choice table does not always define a fuzzy logic function. In the paper (Zaitsev, et al), a criterion has been formulated to recognize whether a given choice table defines a fuzzy logic function and a simple algorithm of fuzzy logic function synthesis has been proposed based on introduced concepts of constituents of minimum and maximum. A fuzzy logic function represents a disjunction of constituents of minimum, where a constituent of minimum is a conjunction of variables of the current area greater than or equal to the function value in this area (to the right of the function value in the inequality, including the function value). Another set of AND/OR operators is based on multiplication, where Given any two of AND/OR/NOT, it is possible to derive the third. The generalization of AND is an instance of a t-norm. ==== IF-THEN rules ==== IF-THEN rules map input or computed truth values to desired output truth values. Example: Given a certain temperature, the fuzzy variable hot has a certain truth value, which is copied to the high variable. Should an output variable occur in several THEN parts, the values from the respective IF parts are combined using the OR operator. ==== Defuzzification ==== The goal is to get a continuous variable from fuzzy truth values. This would be easy if the output truth values were exactly those obtained from fuzzification of a given number. Since, however, all output truth values are computed independently, in most cases they do not represent such a set of numbers. One has then to decide for a number that matches best the "intention" encoded in the truth value. For example, for several truth values of fan_speed, an actual speed must be found that best fits the computed truth values of the variables 'slow', 'moderate' and so on. There is no single algorithm for this purpose. A common algorithm is For each truth value, cut the membership function at this value Combine the resulting curves using the OR operator Find the center-of-weight of the area under the curve The x position of this center is then the final output. === Takagi–Sugeno–Kang (TSK) === The Takagi–Sugeno or Takagi–Sugeno–Kang (TSK) system was introduced by Tomohiro Takagi and Michio Sugeno for fuzzy identification of systems and applications to modeling and control. Sugeno and Kang later developed methods for structure identification of such fuzzy models from input-output data. The TSK system is similar to Mamdani, but the defuzzification process is included in the execution of the fuzzy rules. These are also adapted, so that instead the consequent of the rule is represented through a polynomial function, usually constant in a zero-order model or linear in a first-order model. An example of a rule with a constant output would be: In this case, the output will be equal to the constant of the consequent (e.g. 2). In most scenarios we would have an entire rule base, with 2 or more rules. If this is the case, the output of the entire rule base will be the average of the consequent of each rule i (Y

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  Oriented energy filters

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