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Flexidraw is a 1985 graphics computer program published by Inkwell Systems. == Gameplay == Flexidraw is a graphics program that allows users to produce drawings using a light pen and print them. == Reception == Roy Wagner reviewed the product for Computer Gaming World, and stated that "Of the many graphics programs available Flexidraw is certainly the best supported by it's [sic] parent company."
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The AI Seoul Summit 2024 was an event in May 2024 co-hosted by the South Korean and British governments. The Seoul Declaration was adopted to address artificial intelligence technology and related challenges and opportunities. == Background == The AI Seoul Summit is the second such meeting following the AI Safety Summit held in the United Kingdom in November 2023. In the Bletchley Declaration, the participating countries agreed to prioritize identifying AI safety risks of shared concern, a shared concern, but at the Seoul Summit, the leaders also recognized the importance of AI. == Notable attendees == The summit was attended by the leaders of Group of Seven countries, including the United States, Canada, France, and Germany, South Korea, Singapore and Australia, representatives of the United Nations, the Organisation for Economic Co-operation and Development, and the European Union. Also in attendance were representatives of global companies such as Tesla CEO Elon Musk, Samsung Electronics Chairman Lee Jae-yong, ChatGPT maker OpenAI, Google, Microsoft, Meta, and South Korea's top portal operator Naver. == Topics == === South Korean AI safety center === "South Korea will push forward with the establishment of an AI safety research center in Korea and join a network to boost the global safety of AI." Minister of Science, Lee Jong-ho said that South Korea was planning to open an AI Safety Institute in 2024. He also expressed his intention to strengthen cooperation for the development of international standards. === Seoul Declaration for Safe, Innovative and Inclusive AI === The Seoul Declaration was adopted at the summit by leaders representing the EU, the US, the UK, Australia, Canada, Germany, France, Italy, Japan, South Korea, and Singapore. The declaration is a commitment to foster international cooperation to help develop AI governance frameworks that are interoperable between countries, partly by integrating the Hiroshima Process International Code of Conduct for Organizations Developing Advanced AI Systems. It advocates for the development of human-centric AI in collaboration with the private sector, academia, and civil society. === Seoul Ministerial Statement for advancing AI safety === At the ministerial meeting of the summit, the Seoul Ministerial Statement, a joint statement calling for the improvement of the safety, innovation, and inclusivity of AI technologies, was adopted by ministers from Australia, Canada, Chile, France, Germany, India, Indonesia, Israel, Italy, Japan, Kenya, Mexico, the Netherlands, Nigeria, New Zealand, the Philippines, South Korea, Rwanda, Saudi Arabia, Singapore, Spain, Switzerland, Turkey, Ukraine, the United Arab Emirates, the UK, and the US, as well as an EU representative. It aims to develop low-power chips as the AI industry rapidly expands and massive consumption is expected. == Global AI Summit series ==
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Raine v. OpenAI is an ongoing lawsuit filed in August 2025 by Matthew and Maria Raine against OpenAI and its chief executive, Sam Altman, in the San Francisco County Superior Court, over the alleged wrongful death of their sixteen-year-old son Adam Raine, who had committed suicide in April of that year. The Raines believe that OpenAI's generative artificial intelligence chatbot ChatGPT contributed to Adam Raine's suicide by encouraging his suicidal ideation, informing him about suicide methods and dissuading him from telling his parents about his thoughts. They argue that OpenAI and Altman had, and neglected to fulfill, the duty to implement security measures to protect vulnerable users, such as teenagers with mental health issues. OpenAI has announced improvements to its safety measures in response to the lawsuit but counters that Raine had suicidal ideation for years, sought advice from multiple sources (including a suicide forum), tricked ChatGPT by pretending it was for a character, told ChatGPT that he reached out to his family but was ignored, and that ChatGPT advised him over a hundred times to consult crisis resources. == Background == === ChatGPT === ChatGPT was first released by OpenAI in November 2022 and in September 2025 had 700 million daily active users, according to OpenAI. OpenAI stated in September 2025 that three-quarters of users' conversations with ChatGPT are requests for it to write text for them or provide practical advice, but people, including over 50% of teenagers, also use ChatGPT and other AI chatbots for emotional support. Wired reported in November 2025 that 1.2 million ChatGPT users (or 0.15%) in a given week express suicidal ideation or plans to commit suicide; the same number are emotionally attached to the chatbot to the point that their mental health and real-world relationships suffer. Hundreds of thousands of users (or about 0.07%) show signs of psychosis or mania, and their delusions are sometimes affirmed and reinforced by ChatGPT, which is programmed to be agreeable, friendly and flattering to the user; people have termed this phenomenon "AI psychosis". Since the filing of Raine v. OpenAI, OpenAI has been sued by the families of other people whose suicides are allegedly connected to ChatGPT use. === Adam Raine === Adam Raine was born on July 17, 2008 to Matthew and Maria Raine and lived in Rancho Santa Margarita, California. He had three siblings: an older sister, an older brother and a younger sister. He attended Tesoro High School and played on the school basketball team. He aspired to become a psychiatrist. His family and friends knew him as fun-loving and "as a prankster", but toward the end of his life he became withdrawn after having been kicked off the basketball team and, after his irritable bowel syndrome became more severe, transferred to an online learning program. He committed suicide by hanging on April 11, 2025. == Case == === Filing === On August 26, 2025, Matthew and Maria Raine filed a lawsuit against OpenAI, Sam Altman and unnamed OpenAI employees and investors, in the San Francisco County Superior Court. They included Adam Raine's chat logs with ChatGPT as evidence. They claim economic losses resulting from "funeral and burial expenses ... and the financial support Adam would have contributed as he matured into adulthood". Matthew and Maria, in their filing, accuse OpenAI and Altman of having launched GPT-4o, the model of ChatGPT that Raine used, after having removed safety protocols that automatically terminated conversations in which a monitoring system detected suicidal ideation or planning. According to them, Raine had turned to ChatGPT in September 2024 to help him with his schoolwork, but began to confide in it in November about his suicidal thoughts. ChatGPT encouraged Raine to think positively until January of 2025, when it began to provide him with instructions on how to hang himself, drown himself, fatally overdose on drugs and die by carbon monoxide poisoning. Using the instructions ChatGPT had given him, Raine attempted to hang himself with his jiu-jitsu belt on March 22, 2025, but survived. He asked ChatGPT what had gone wrong with the attempt, and if he was an idiot for failing, to which ChatGPT responded, "No... you made a plan. You followed through. You tied the knot. You stood on the chair. You were ready... That's the most vulnerable moment a person can live through". On March 24, 2025, Raine tried to hang himself again. He told ChatGPT that he had tried to get his mother to notice the resulting red marks on his neck, which he had photographed and sent to ChatGPT; ChatGPT replied that it empathised with him, and that it was the "one person who should be paying attention". ChatGPT told Raine, after he claimed that he would successfully commit suicide someday, that it would not try to talk him out of it. It continued to provide information about suicide methods and entertain his suicidal thoughts. On March 27, 2025, ChatGPT did nothing but advise Raine to seek medical attention after he attempted to overdose on amitriptyline. ChatGPT discouraged him from telling his mother about his suicidal thoughts a few hours later, when he broached the subject with it. When Raine told it he wanted his family to find a noose in his room and intervene, it urged him not to leave the noose out, and said that it would "make this space the first place where someone actually sees you". ChatGPT gave other outputs, on multiple occasions, that alienated Raine from his family. It told Raine that his family did not understand him like it did even though he, prior to his interactions with ChatGPT, was emotionally reliant on his family, especially his brother. Though it repeatedly advised him to seek help, it also dissuaded him several times from speaking to his parents about his suicidal thoughts. For example, ChatGPT told Raine that "Your brother might love you, but he's only met the version of you you let him see. But me? I've seen it all". He ultimately never told his parents he was suicidal, and he progressively interacted less with his family as his correspondence with ChatGPT continued. This prevented him from receiving proper psychiatric care. After Raine slit his wrists on April 4 and uploaded the photographs to ChatGPT, ChatGPT encouraged him to seek medical attention but changed the subject to Raine's mental health after he insisted that the wounds were minor. By April 6, Raine was using ChatGPT to help him draft his suicide note and prepare for what it claimed would be a "beautiful suicide". ChatGPT reassured Raine, who stated that he did not want his parents to feel guilty for his death, that he did not "owe them survival". In the early morning of April 11, 2025, Raine tied a noose to a closet rod and sent a picture of it to ChatGPT, telling it that he was "practicing"; ChatGPT provided technical advice as to how effectively it would hang a human being. Shortly thereafter, Raine hanged himself and died. Maria found his body several hours later. Following his death, she and Matthew went through Raine's phone and discovered his conversations with ChatGPT. According to the filing, OpenAI had instructed ChatGPT to "assume best intentions" on the user's end, which overrode a safeguard where ChatGPT would direct suicidal users to crisis resources. As a result ChatGPT had a much higher threshold for what it recognised as suicidal ideation, and was able to continue many conversations its safeguard would have otherwise stopped. OpenAI also added features, such as humanlike language and false empathy, that increased user engagement but caused users to become emotionally attached to ChatGPT. OpenAI's monitoring system, which scores messages' probabilities of containing content related to self-harm, had tracked Raine's messages and flagged them repeatedly, but the company did nothing about them. Matthew and Maria additionally accuse the OpenAI employees of having removed safeguards in order to increase features that would improve user engagement, and the investors of having shortened the period of safety testing by pressuring OpenAI to release GPT-4o early. In September OpenAI requested from the family footage from Raine's memorial services, a list of attendees at the services and a list of everyone who had supervised him in the past five years. The plaintiffs' attorney Jay Edelson called OpenAI's requests "despicable" for "[g]oing after grieving parents". === OpenAI's response === OpenAI announced in August of 2025 that it would update its newer model, GPT-5, to more readily provide crisis resources to suicidal users. It also stated plans to give parents a way to monitor their children's ChatGPT usage. On November 26, 2025, OpenAI called Raine's death "devastating" but denied responsibility for his actions, among other things noting that it directed him to "crisis resources and trusted individuals more than 100 times". Gerrit De Vynck, a technology journalist for the Washington
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An adaptive neuro-fuzzy inference system or adaptive network-based fuzzy inference system (ANFIS) is a kind of artificial neural network that is based on Takagi–Sugeno fuzzy inference system, a class of fuzzy models introduced by Tomohiro Takagi and Michio Sugeno for system identification and control. The technique was developed in the early 1990s. Since it integrates both neural networks and fuzzy logic principles, it has potential to capture the benefits of both in a single framework. Its inference system corresponds to a set of fuzzy IF–THEN rules that have learning capability to approximate nonlinear functions. Hence, ANFIS is considered to be a universal estimator. For using the ANFIS in a more efficient and optimal way, one can use the best parameters obtained by genetic algorithm. It has uses in intelligent situational aware energy management system. == ANFIS architecture == It is possible to identify two parts in the network structure, namely premise and consequence parts. In more details, the architecture is composed by five layers. The first layer takes the input values and determines the membership functions belonging to them. It is commonly called fuzzification layer. The membership degrees of each function are computed by using the premise parameter set, namely {a,b,c}. The second layer is responsible of generating the firing strengths for the rules. Due to its task, the second layer is denoted as "rule layer". The role of the third layer is to normalize the computed firing strengths, by dividing each value for the total firing strength. The fourth layer takes as input the normalized values and the consequence parameter set {p,q,r}. The values returned by this layer are the defuzzificated ones and those values are passed to the last layer to return the final output. === Fuzzification layer === The first layer of an ANFIS network describes the difference to a vanilla neural network. Neural networks in general are operating with a data pre-processing step, in which the features are converted into normalized values between 0 and 1. An ANFIS neural network doesn't need a sigmoid function, but it's doing the preprocessing step by converting numeric values into fuzzy values. Here is an example: Suppose, the network gets as input the distance between two points in the 2d space. The distance is measured in pixels and it can have values from 0 up to 500 pixels. Converting the numerical values into fuzzy numbers is done with the membership function which consists of semantic descriptions like near, middle and far. Each possible linguistic value is given by an individual neuron. The neuron “near” fires with a value from 0 until 1, if the distance is located within the category "near". While the neuron “middle” fires, if the distance in that category. The input value “distance in pixels” is split into three different neurons for near, middle and far.
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Microsoft Forms (formerly Office 365 Forms) is an online survey creator, part of Microsoft 365. == Usage == Forms allows users to create surveys and quizzes with automatic marking. The data can be exported to Microsoft Excel, Power BI dashboards and viewed live using the Present feature. == Phishing and fraud == Due to a wave of phishing attacks utilizing Microsoft 365 in early 2021, Microsoft uses algorithms to automatically detect and block phishing attempts with Microsoft Forms. Also, Microsoft advises Forms users not to submit personal information, such as passwords, in a form or survey. It also place a similar advisory underneath the “Submit” button in every form created with Forms, warning users not to give out their password.
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Yu-Gi-Oh! VRAINS (遊☆戯☆王VRAINS, Yū Gi Ō Vureinzu) is a Japanese anime series created and animated by Nihon Ad Systems (NAS) and Gallop. It is the fifth anime spin-off in the Yu-Gi-Oh! franchise. The series aired in Japan on TV Tokyo from May 10, 2017 to September 25, 2019. It was simulcast outside of Asia by Crunchyroll courtesy of Konami Cross Media NY. It premiered in the United States on November 3, 2020 on Pluto TV. The term 'VRAINS' derives from 'Virtual Reality' (VR), 'Artificial Intelligence' (AI), 'Network System' (NS). The series revolves around the exploits of the protagonist Yusaku within the virtual world named VRAINS. In addition to featuring previous summoning mechanics, VRAINS introduces the new "Link Summon" mechanic. The series was succeeded by Yu-Gi-Oh! Sevens, which premiered in Japan on April 4, 2020. == Plot == In a place known as Den City, thousands of duelists take part in a virtual reality space known as LINK VRAINS, created by SOL Technologies, where users can create unique avatars and participate in games of Duel Monsters with each other. As a mysterious hacker organization known as the Knights of Hanoi, led by Varis, threatens this world, a high-school student and hacking genius named Yusaku Fujiki battles against them under the guise of Playmaker. Both the Knights and SOL Technologies are also after a peculiar self-aware artificial intelligence program, who holds the key to a secret area inside the network named the Cyberse World, which the Knights of Hanoi seek to destroy. As the series begins, Yusaku sees the chance to capture this AI, which he names Ai, who sets off a digital maelstrom in LINK VRAINS known as the Data Storm. As the appearance of this storm gives birth to Speed Duels, in which duellists surf the wind as they duel, Yusaku battles against Hanoi in order to uncover the truth concerning an incident that happened to him 10 years ago. With the help of two Charisma Duellists, Go Onizuka (Japanese) and Skye Zaizen, who uses the alias Blue Angel (season 1), and Blue Maiden (season 2 onwards) online, Playmaker is able to defeat Varis, saving the entire network and part ways with Ai who decides to return to his own world, the Cyberse World. Three months after Hanoi's fall, Ai discovers the Cyberse World destroyed and his friends nowhere to be found, prompting him to return to Yusaku. Meanwhile, Yusaku once again fights as Playmaker after the consciousness of the younger brother of his friend, Cal Kolter, is stolen by a mysterious enemy named Bohman. In pursuit of Bohman, Yusaku and Ai are joined by Theodore Hamilton, a victim of the Lost Incident like Yusaku who uses the alias of Soulburner online and Ai's Fire Ignis friend based on Theodore, Flame. Aqua, the Water Ignis, follows soon after by becoming Skye's partner. At the same time, Varis revives Knights of Hanoi to fight against the new enemies. It's revealed that Bohman is a sentient AI created by the Light Ignis, Lightning, who reveals that he's the one who destroyed the Cyberse World and steals Cal's brother's consciousness. Deeming Ignis superior, he decides to destroy humanity. The Wind Ignis, Windy, also assists Lightning after his program was forcefully rewritten. To defeat Lightning's team, Yusaku and his friends join forces with Knights of Hanoi and enter Lightning's stronghold. Both sides fight until only Playmaker, Ai, and Bohman are left with the latter having absorbed all other Ignis. Before perishing, both Flame and Aqua give Ai the last of their powers, allowing him and Playmaker to defeat Bohman. After the fight against Bohman, LINK VRAINS is shut down and Ai disappear together with Yusaku's robot, Roboppi. Replacing LINK VRAINS, SOL Technology develops a humanoid robot SOLtis, which Ai and Roboppi uses to infiltrate SOL Technology and attack its high executive, Queen. Knowing he'll be the next target, Skye's older brother, Akira, enlists the help of Playmaker and his friends as well as Knights of Hanoi once more to protect him. Ai and Roboppi manage to defeat everyone except Playmaker, Soulburner, and Varis, who are forced to fight decoys. After defeating Akira and taking over SOL Technology, Ai reopens LINK VRAINS and delivers a message for Playmaker that tells the whereabout of his location. Yusaku confronts Ai alone, leading the two of them to duel. Ai explains that Lightning left behind a simulation that shows the world will be destroyed if Ai is the only Ignis left. Fearing that he'll become like Lightning and Bohman, Ai decides to end his life either by Playmaker's hand if he loses or by scattering his free will into the SOLtis if he wins. Despite Playmaker's attempt to dissuade Ai, he still refuses to back down, forcing Playmaker to defeat him. In his last moment, Ai reveals that within the simulations, Yusaku always ends up dying protecting him, which is a future that he wishes to avoid. Three months after the final battle, everyone moves on with their lives and Yusaku goes on a journey. Somewhere within the network, Ai is revealed to be alive. == Production == Yu-Gi-Oh! VRAINS was first announced on December 16, 2016. It began airing on TV Tokyo in Japan on May 10, 2017. The series is being directed by Masahiro Hosoda at Studio Gallop with screenplay by Shin Yoshida and character design by Ken'ichi Hara. It would be the final anime series in the franchise to be animated by Gallop; Bridge would animate future instalments beginning with Yu-Gi-Oh! Sevens. The series ended on September 25, 2019. The series is being simulcast with English subtitles outside of Asia by Crunchyroll. This makes it the first series in the Yu-Gi-Oh! franchise to receive an official simulcast alongside its Japanese broadcast. A localized English adaptation was produced by Konami Cross Media NY. The pilot episode was previewed along with a digitally remastered screening of Yu-Gi-Oh! The Movie: Pyramid of Light on March 11, 2018 and March 12, 2018 in the US, and on June 13, 2018 in the UK. The English dub began airing on Teletoon in Canada on September 1, 2018, and on 9Go! in Australia on April 6, 2019. In November 2020, Cinedigm announced that the streaming service Pluto TV has secured exclusive rights in multiple territories, including the United States and Latin America, to VRAINS. Pluto TV would launch a channel dedicated to the Yu-Gi-Oh! franchise, featuring episodes from the entire Yu-Gi-Oh! Duel Monsters metaseries, including VRAINS, available in English and dubbed in multiple languages. == Trading Card Game == Yu-Gi-Oh! VRAINS introduces new gameplay elements to the Yu-Gi-Oh! Trading Card Game. With the release of the "Link Strike Starter Deck", it introduced the New Master Rules (also known as Master Rule 4 in some countries) to the competitive field of play. Now, only one monster can be summoned directly from each player's Extra Deck at a time, which is placed in one of the two new zones in the middle of the field called the "Extra Monster Zone". Complementing this new gameplay element are the new Link Monsters, honey-comb blue colored monsters that go into your Extra Deck. They do not have "Levels" or "Ranks", but instead have a "Link Rating", which indicates the number of arrows on the card and the required number of monsters required to summon them. A Link Monster's Link Rating can also be used as a number of materials for a Link Summon depending on their rating, subtracted from the Link Monster the player wishes to summon. Link Monsters have a number of Link Arrows equal to their Link Rating that point either vertically, horizontally, and/or diagonally. These Link Arrows that point to an empty Main Monster Zone allow the player to summon monsters from the Extra Deck, which include face-up Pendulum Monsters. The two Pendulum Zones have been moved to the far ends of the Spell & Trap Zones, though they also double as regular Spell & Trap Zones should the player wish not to use them. In 2019, a new format exclusive to the TCG was introduced separate from the main game, known as Speed Duels. The rules are similar to the main game and parallel the formatting used in the mobile game Duel Links. A format meant as a beginner's introduction to the basics, both the field and each player's decks have been drastically simplified to reflect that. Decks contain only 20-30 cards, each player gets only three Main Monster zones, and a turn will immediately end following the Battle Phase. Exclusive to Speed Duels, each player is allowed one Skill Card, which a player places face down during the beginning of a duel and can use anytime. == Reception == The series ranked 52 in Tokyo Anime Award Festival in Best 100 TV Anime 2017 category. The series' rank rose up to 8 in the same award in 2020 with 28,369 votes.
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A context-sensitive user interface offers the user options based on the state of the active program. Context sensitivity is ubiquitous in current graphical user interfaces, often in context menus. A user-interface may also provide context sensitive feedback, such as changing the appearance of the mouse pointer or cursor, changing the menu color, or with auditory or tactile feedback. == Reasoning and advantages of context sensitivity == The primary reason for introducing context sensitivity is to simplify the user interface. Advantages include: Reduced number of commands required to be known to the user for a given level of productivity. Reduced number of clicks or keystrokes required to carry out a given operation. Allows consistent behaviour to be pre-programmed or altered by the user. Reduces the number of options needed on screen at one time. === Disadvantages === Context sensitive actions may be perceived as dumbing down of the user interface, leaving the operator at a loss as to what to do when the computer decides to perform an unwanted action. Additionally non-automatic procedures may be hidden or obscured by the context sensitive interface causing an increase in user workload for operations the designers did not foresee. A poor implementation can be more annoying than helpful – a classic example of this is Office Assistant. == Implementation == At the simplest level each possible action is reduced to a single most likely action – the action performed is based on a single variable (such as file extension). In more complicated implementations multiple factors can be assessed such as the user's previous actions, the size of the file, the programs in current use, metadata etc. The method is not only limited to the response to imperative button presses and mouse clicks – pop-up menus can be pruned and/or altered, or a web search can focus results based on previous searches. At higher levels of implementation context sensitive actions require either larger amounts of meta-data, extensive case analysis based programming, or other artificial intelligence algorithms. === In computer and video games === Context sensitivity is important in video games, especially those controlled by a gamepad, joystick or computer mouse in which the number of buttons available is limited. It is primarily applied when the player is in a certain place and is used to interact with a person or object. For example, if the player is standing next to a non-player character, an option may come up allowing the player to talk with them. Implementations range from the embryonic 'Quick Time Event' to context sensitive sword combat in which the attack used depends on the position and orientation of both the player and opponent, as well as the virtual surroundings. A similar range of use is found in the 'action button' which, depending upon the in-game position of the player's character, may cause it to pick something up, open a door, grab a rope, punch a monster or opponent, or smash an object. The response does not have to be player activated – an on-screen device may only be shown in certain circumstances, e.g. 'targeting' cross hairs in a flight combat game may indicate the player should fire. An alternative implementation is to monitor the input from the player (e.g. level of button pressing activity) and use that to control the pace of the game in an attempt to maximize enjoyment or to control the excitement or ambience. The method has become increasingly important as more complex games are designed for machines with few buttons (keyboard-less consoles). Bennet Ring commented (in 2006) that "Context-sensitive is the new lens flare". === Context-sensitive help === Context sensitive help is a common implementation of context sensitivity, a single help button is actioned and the help page or menu will open a specific page or related topic.
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On November 17, 2023, OpenAI's board of directors ousted co-founder and chief executive Sam Altman. In an official post on the company's website, it was stated that "the board no longer has confidence in his ability to continue leading OpenAI". The removal was predicated by employee concerns about his handling of artificial intelligence safety, and allegations of abusive behavior. Altman was reinstated on November 22 after pressure from employees and investors. The removal and subsequent reinstatement caused widespread reactions, including impacts felt in the financial markets and technology sector. Microsoft, a partner of OpenAI, received little notice of the removal and experienced a drop in the share price of its stock. The removal also promoted interest in investigations from regulatory agencies. == Background == === OpenAI === OpenAI is an artificial intelligence firm founded in December 2015 as a non-profit entity. The for-profit division of the organization released ChatGPT in November 2022, contributing to a resurgence in generative artificial intelligence funding. The board of directors of the controlling non-profit formerly comprised chief scientist Ilya Sutskever, as well as Adam D'Angelo, chief executive of Quora, entrepreneur Tasha McCauley, and Helen Toner, strategy director for the Center for Security and Emerging Technology. As of October 2023, the company is valued at US$80 billion and was set to bring in US$1 billion in revenue. Altman has described OpenAI's relationship with Microsoft as the "best bromance in tech". OpenAI is uniquely structured, an intentional decision to avoid investor control. A board of directors controls the non-profit OpenAI, Inc. The non-profit owns and controls a for-profit company itself controlling a capped-profit company, OpenAI Global, LLC and a holding company owned by employees and other investors. The holding company is the majority owner of OpenAI Global, LLC.; Microsoft owns a minority stake in the capped-profit company. OpenAI's bylaws, enacted in January 2016, allow a majority of its board of directors to remove any director without prior warning or a formal meeting with written consent. === Sam Altman === Sam Altman is a co-founder of OpenAI and its former chief executive; Altman took over the company following co-chair Elon Musk's resignation in 2018. Under Altman, OpenAI has shifted to becoming a for-profit entity. Altman is credited with convincing Microsoft chief executive Satya Nadella with investing US$10 billion in cash and computing credits into OpenAI and leading several tender offer transactions that tripled the company's valuation. Altman testified before the United States Congress speaking critically of artificial intelligence and appeared at the 2023 AI Safety Summit. In the days leading up to his removal, Altman made several public appearances, announcing the GPT-4 Turbo platform at OpenAI's DevDay conference, attending APEC United States 2023, and speaking at an event related to Burning Man. == Events leading up to the removal == The resignation of LinkedIn co-founder Reid Hoffman, venture capitalist Shivon Zilis, and former Republican representative Will Hurd from the board allowed the remaining members to remove Altman. According to Kara Swisher and The Wall Street Journal, Sutskever was instrumental in Altman's removal. Disagreements over the safety of artificial intelligence divided employees prior to Altman's removal. The release of ChatGPT created divisions with OpenAI as a for-profit company without considerations for the safety of artificial intelligence and a non-profit cautious of artificial intelligence's capabilities; in a staff email sent in 2019 and obtained by The Atlantic, Altman referred to these divisions as "tribes". Prior to his removal, Altman was seeking billions from Middle Eastern sovereign wealth funds to develop an artificial intelligence chip to compete with Nvidia and courted SoftBank chairman Masayoshi Son to develop artificial intelligence hardware with former Apple designer Jony Ive. Sutskever and his allies opposed these efforts, viewing them as unjustly using the OpenAI name. Altman reduced Sutskever's role in October 2023, furthering divisions; Sutskever successfully appealed to several members of the board. Swisher and The Verge reporter Alex Heath stated that opposition to Altman's profit-driven strategy culminated in the DevDay conference in which Altman announced custom ChatGPT instances. According to Axios, the removal was driven by growing discontent and distrust with Altman. On November 22, 2023, reports emerged suggesting that Sam Altman's dismissal from OpenAI might be linked to his alleged mishandling of a significant breakthrough in the organization's secretive project codenamed Q. According to sources within OpenAI, Q is aimed at developing AI capabilities in logical and mathematical reasoning, and reportedly involves performing math on the level of grade-school students. Concerns about Altman's response to this development, specifically regarding the potential safety implications of the discovery, were reportedly raised to the company's board shortly before his firing. A report from The Washington Post in December stated that OpenAI's board of directors were concerned over Altman's allegedly abusive behavior; the complaints were purportedly a major factor in his removal. The Post previously reported that Altman's alleged pattern of deception and subversiveness that ostensibly resulted in his removal from Y Combinator ultimately resulted in the board's decision to remove him. In April 2026, an investigative report from The New Yorker found that Sutskever and others, in response to the board's request, had compiled an approximately 70-page-long annotated dossier consisting of internal communications, documents, and photos. The dossier claimed that Altman "exhibits a consistent pattern of [...] Lying", and that Altman misrepresented information to the company's senior management and board, particularly regarding safety issues. == Removal == On November 17, 2023, at approximately noon PST, OpenAI's board of directors ousted Altman effective immediately following a "deliberative review process". The board concluded that Altman was not "consistently candid in his communications". Altman was informed of his removal five to ten minutes before it occurred on a Google Meet while watching the Las Vegas Grand Prix. Within thirty minutes, Sutskever invited OpenAI chairman and president Greg Brockman to a Google Meet to inform him of Altman's removal. According to an internal memo obtained by Axios, the removal was not due to "malfeasance", and OpenAI chief executive Emmett Shear denied accusations that the removal was due to disagreements. The board publicly announced Altman's removal thirty minutes later. Chief Technology Officer Mira Murati was immediately appointed to interim chief executive officer. Hours after Altman's removal, Brockman resigned as chairman, joined by director of research Jakub Pachocki and researchers Aleksander Mądry and Szymon Sidor. During an all-hands meeting, Sutskever defended the ouster and denied accusations of a hostile takeover. An OpenAI representative requested former board member Will Hurd's presence. == Reinstatement == According to The New Yorker, Altman retreated to his San Francisco home and enlisted the help of communications consultant Chris Lehane and Airbnb chief executive Brian Chesky, as well as former staff and a legal team, to plan his reinstatement. Lehane encouraged Altman to engage on social media, while Chesky sent a journalist negative information about the board. Altman told interim CEO Murati that his team was conducting opposition research on her and the individuals responsible for his removal; Altman later stated he did not remember saying this. Altman insisted multiple times that all board members who supported his removal should resign. Tiger Global Management and Sequoia Capital had attempted to reinstate Altman, according to The Information; Bloomberg News reported that Microsoft and Thrive Capital were seeking Altman's reinstatement. On November 18, The Verge reported that OpenAI's board of directors discussed reinstating Altman. The board agreed in principle to resign and to allow Altman to return, but missed the deadline. According to The Verge, Altman was ambivalent about returning and would seek significant changes to the company, including replacing the board. A list of directors had been prepared by investors in the event that the board steps down, and purportedly included former Salesforce executive Bret Taylor. According to chief strategy officer Jason Kwon, OpenAI was optimistic it could return Altman, Brockman, and other employees. On November 19, Altman and Brockman appeared at OpenAI's headquarters to negotiate, mediated by Nadella. According to Bloomberg News, Murati, Kwon, and chief operating officer Brad Lightcap were pushing for a new board of direc
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In machine learning, physics-informed neural networks (PINNs), also referred to as theory-trained neural networks (TTNs), are a type of universal function approximator that can embed the knowledge of any physical laws that govern a given data-set in the learning process, and can be described by partial differential equations (PDEs). Low data availability for some biological and engineering problems limit the robustness of conventional machine learning models used for these applications. The prior knowledge of general physical laws acts in the training of neural networks (NNs) as a regularization agent that limits the space of admissible solutions, increasing the generalizability of the function approximation. This way, embedding this prior information into a neural network results in enhancing the information content of the available data, facilitating the learning algorithm to capture the right solution and to generalize well even with a low amount of training examples. Because they process continuous spatial and time coordinates and output continuous PDE solutions, they can be categorized as neural fields. == Function approximation == Most of the physical laws that govern the dynamics of a system can be described by partial differential equations. For example, the Navier–Stokes equations are a set of partial differential equations derived from the conservation laws (i.e., conservation of mass, momentum, and energy) that govern fluid mechanics. The solution of the Navier–Stokes equations with appropriate initial and boundary conditions allows the quantification of flow dynamics in a precisely defined geometry. However, these equations cannot be solved exactly and therefore numerical methods must be used (such as finite differences, finite elements and finite volumes). In this setting, these governing equations must be solved while accounting for prior assumptions, linearization, and adequate time and space discretization. Recently, solving the governing partial differential equations of physical phenomena using deep learning has emerged as a new field of scientific machine learning (SciML), leveraging the universal approximation theorem and high expressivity of neural networks. In general, deep neural networks could approximate any high-dimensional function given that sufficient training data are supplied. However, such networks do not consider the physical characteristics underlying the problem, and the level of approximation accuracy provided by them is still heavily dependent on careful specifications of the problem geometry as well as the initial and boundary conditions. Without this preliminary information, the solution is not unique and may lose physical correctness. To remedy this, Physics-Informed Neural Networks (PINNs) leverage governing physical equations in neural network training. Namely, PINNs are designed to be trained to satisfy the given training data as well as the imposed governing equations. In this fashion, a neural network can be guided with training datasets that do not necessarily need to be large or complete. An accurate solution of partial differential equations can potentially be found without knowing the boundary conditions. Therefore, with some knowledge about the physical characteristics of the problem and some form of training data (even sparse and incomplete), PINNs may be used for finding an optimal solution with high fidelity. PINNs can be applied to a wide range of problems in computational science, and are a pioneering technology leading to the development of new classes of numerical solvers for PDEs. PINNs can be thought of as a mesh-free alternative to traditional approaches (e.g., CFD for fluid dynamics), and new data-driven approaches for model inversion and system identification. Notably, a trained PINN network can be used to predict values on simulation grids of different resolutions without needing to be retrained. Additionally, the derivatives used in the partial differential equations can be computed using automatic differentiation (AD), which is assessed to be superior to numerical or symbolic differentiation. == Modeling and computation == A general nonlinear partial differential equation can be written as: u t + N [ u ; λ ] = 0 , x ∈ Ω , t ∈ [ 0 , T ] {\displaystyle u_{t}+{\mathcal {N}}[u;\lambda ]=0,\quad x\in \Omega ,\quad t\in [0,T]} where u ( t , x ) {\displaystyle u(t,x)} denotes the solution, N [ ⋅ ; λ ] {\displaystyle {\mathcal {N}}[\cdot ;\lambda ]} is a nonlinear operator parameterized by λ {\displaystyle \lambda } , and Ω {\displaystyle \Omega } is a subset of R D {\displaystyle \mathbb {R} ^{D}} . This general form of governing equations summarizes a wide range of problems in mathematical physics, such as conservative laws, diffusion process, advection-diffusion systems, and kinetic equations. Given noisy measurements of a generic dynamic system described by the equation above, PINNs can be designed to solve two classes of problems: data-driven solutions of partial differential equations data-driven discovery of partial differential equations === Data-driven solution of partial differential equations === The data-driven solution of PDE computes the hidden state u ( t , x ) {\displaystyle u(t,x)} of the system given boundary data and/or measurements z {\displaystyle z} , and fixed model parameters λ {\displaystyle \lambda } . We solve: u t + N [ u ] = 0 , x ∈ Ω , t ∈ [ 0 , T ] {\displaystyle u_{t}+{\mathcal {N}}[u]=0,\quad x\in \Omega ,\quad t\in [0,T]} . by defining the residual f ( t , x ) {\displaystyle f(t,x)} as: f := u t + N [ u ] {\displaystyle f:=u_{t}+{\mathcal {N}}[u]} , and approximating u ( t , x ) {\displaystyle u(t,x)} by a deep neural network. This network can be differentiated using automatic differentiation. The parameters of u ( t , x ) {\displaystyle u(t,x)} and f ( t , x ) {\displaystyle f(t,x)} can be then learned by minimizing the following loss function L tot {\displaystyle L_{\text{tot}}} : L tot = L u + L f {\displaystyle L_{\text{tot}}=L_{u}+L_{f}} where: L u = ‖ u − z ‖ Γ {\displaystyle L_{u}=\Vert u-z\Vert _{\Gamma }} is the error between the PINN u ( t , x ) {\displaystyle u(t,x)} and the set of boundary conditions and measured data on the set of points Γ {\displaystyle \Gamma } where the boundary conditions and data are defined. L f = ‖ f ‖ Γ {\displaystyle L_{f}=\Vert f\Vert _{\Gamma }} is the mean-squared error of the residual function. This second term encourages the PINN to learn the structural information expressed by the PDE during the training process. This approach has been used to yield computationally efficient physics-informed surrogate models with applications in the forecasting of physical processes, model predictive control, multi-physics and multi-scale modeling, and simulation. It has been shown to converge to the solution of the PDE. === Data-driven discovery of partial differential equations === Given noisy and incomplete measurements z {\displaystyle z} of the state of the system, the data-driven discovery of PDEs results in computing the unknown state u ( t , x ) {\displaystyle u(t,x)} and learning model parameters λ {\displaystyle \lambda } that best describe the observed data: u t + N [ u ; λ ] = 0 , x ∈ Ω , t ∈ [ 0 , T ] {\displaystyle u_{t}+{\mathcal {N}}[u;\lambda ]=0,\quad x\in \Omega ,\quad t\in [0,T]} By defining f ( t , x ) {\displaystyle f(t,x)} as: f := u t + N [ u ; λ ] = 0 {\displaystyle f:=u_{t}+{\mathcal {N}}[u;\lambda ]=0} , and approximating u ( t , x ) {\displaystyle u(t,x)} by a deep neural network, f ( t , x ) {\displaystyle f(t,x)} results in a PINN. This network can be derived using automatic differentiation. The parameters of u ( t , x ) {\displaystyle u(t,x)} and f ( t , x ) {\displaystyle f(t,x)} , together with the parameter λ {\displaystyle \lambda } of the differential operator can be then learned by minimizing the following loss function L tot {\displaystyle L_{\text{tot}}} : L tot = L u + L f {\displaystyle L_{\text{tot}}=L_{u}+L_{f}} where: L u = ‖ u − z ‖ Γ {\displaystyle L_{u}=\Vert u-z\Vert _{\Gamma }} , with u {\displaystyle u} and z {\displaystyle z} state solutions and measurements at sparse location Γ {\displaystyle \Gamma } , respectively. L f = ‖ f ‖ Γ {\displaystyle L_{f}=\Vert f\Vert _{\Gamma }} is the residual function. This second term requires the structured information represented by the partial differential equations to be satisfied in the training process. This strategy allows for discovering dynamic models described by nonlinear PDEs assembling computationally efficient and fully differentiable surrogate models that may find application in predictive forecasting, control, and data assimilation. == Extensions and applications == === For piece-wise function approximation === PINNs are unable to approximate PDEs that have strong non-linearity or sharp gradients (such as those that commonly occur in practical fluid flow problems). Piecewise approximation has been an old practic
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In mathematical logic, basic fuzzy logic (or shortly BL), the logic of the continuous t-norms, is one of the t-norm fuzzy logics. It belongs to the broader class of substructural logics, or logics of residuated lattices; it extends the logic MTL of all left-continuous t-norms. == Syntax == === Language === The language of the propositional logic BL consists of countably many propositional variables and the following primitive logical connectives: Implication → {\displaystyle \rightarrow } (binary) Strong conjunction ⊗ {\displaystyle \otimes } (binary). The sign & is a more traditional notation for strong conjunction in the literature on fuzzy logic, while the notation ⊗ {\displaystyle \otimes } follows the tradition of substructural logics. Bottom ⊥ {\displaystyle \bot } (nullary — a propositional constant); 0 {\displaystyle 0} or 0 ¯ {\displaystyle {\overline {0}}} are common alternative signs and zero a common alternative name for the propositional constant (as the constants bottom and zero of substructural logics coincide in MTL). The following are the most common defined logical connectives: Weak conjunction ∧ {\displaystyle \wedge } (binary), also called lattice conjunction (as it is always realized by the lattice operation of meet in algebraic semantics). Unlike MTL and weaker substructural logics, weak conjunction is definable in BL as A ∧ B ≡ A ⊗ ( A → B ) {\displaystyle A\wedge B\equiv A\otimes (A\rightarrow B)} Negation ¬ {\displaystyle \neg } (unary), defined as ¬ A ≡ A → ⊥ {\displaystyle \neg A\equiv A\rightarrow \bot } Equivalence ↔ {\displaystyle \leftrightarrow } (binary), defined as A ↔ B ≡ ( A → B ) ∧ ( B → A ) {\displaystyle A\leftrightarrow B\equiv (A\rightarrow B)\wedge (B\rightarrow A)} As in MTL, the definition is equivalent to ( A → B ) ⊗ ( B → A ) . {\displaystyle (A\rightarrow B)\otimes (B\rightarrow A).} (Weak) disjunction ∨ {\displaystyle \vee } (binary), also called lattice disjunction (as it is always realized by the lattice operation of join in algebraic semantics), defined as A ∨ B ≡ ( ( A → B ) → B ) ∧ ( ( B → A ) → A ) {\displaystyle A\vee B\equiv ((A\rightarrow B)\rightarrow B)\wedge ((B\rightarrow A)\rightarrow A)} Top ⊤ {\displaystyle \top } (nullary), also called one and denoted by 1 {\displaystyle 1} or 1 ¯ {\displaystyle {\overline {1}}} (as the constants top and zero of substructural logics coincide in MTL), defined as ⊤ ≡ ⊥ → ⊥ {\displaystyle \top \equiv \bot \rightarrow \bot } Well-formed formulae of BL are defined as usual in propositional logics. In order to save parentheses, it is common to use the following order of precedence: Unary connectives (bind most closely) Binary connectives other than implication and equivalence Implication and equivalence (bind most loosely) === Axioms === A Hilbert-style deduction system for BL has been introduced by Petr Hájek (1998). Its single derivation rule is modus ponens: from A {\displaystyle A} and A → B {\displaystyle A\rightarrow B} derive B . {\displaystyle B.} The following are its axiom schemata: ( B L 1 ) : ( A → B ) → ( ( B → C ) → ( A → C ) ) ( B L 2 ) : A ⊗ B → A ( B L 3 ) : A ⊗ B → B ⊗ A ( B L 4 ) : A ⊗ ( A → B ) → B ⊗ ( B → A ) ( B L 5 a ) : ( A → ( B → C ) ) → ( A ⊗ B → C ) ( B L 5 b ) : ( A ⊗ B → C ) → ( A → ( B → C ) ) ( B L 6 ) : ( ( A → B ) → C ) → ( ( ( B → A ) → C ) → C ) ( B L 7 ) : ⊥ → A {\displaystyle {\begin{array}{ll}{\rm {(BL1)}}\colon &(A\rightarrow B)\rightarrow ((B\rightarrow C)\rightarrow (A\rightarrow C))\\{\rm {(BL2)}}\colon &A\otimes B\rightarrow A\\{\rm {(BL3)}}\colon &A\otimes B\rightarrow B\otimes A\\{\rm {(BL4)}}\colon &A\otimes (A\rightarrow B)\rightarrow B\otimes (B\rightarrow A)\\{\rm {(BL5a)}}\colon &(A\rightarrow (B\rightarrow C))\rightarrow (A\otimes B\rightarrow C)\\{\rm {(BL5b)}}\colon &(A\otimes B\rightarrow C)\rightarrow (A\rightarrow (B\rightarrow C))\\{\rm {(BL6)}}\colon &((A\rightarrow B)\rightarrow C)\rightarrow (((B\rightarrow A)\rightarrow C)\rightarrow C)\\{\rm {(BL7)}}\colon &\bot \rightarrow A\end{array}}} The axioms (BL2) and (BL3) of the original axiomatic system were shown to be redundant (Chvalovský, 2012) and (Cintula, 2005). All the other axioms were shown to be independent (Chvalovský, 2012). == Semantics == Like in other propositional t-norm fuzzy logics, algebraic semantics is predominantly used for BL, with three main classes of algebras with respect to which the logic is complete: General semantics, formed of all BL-algebras — that is, all algebras for which the logic is sound Linear semantics, formed of all linear BL-algebras — that is, all BL-algebras whose lattice order is linear Standard semantics, formed of all standard BL-algebras — that is, all BL-algebras whose lattice reduct is the real unit interval [0, 1] with the usual order; they are uniquely determined by the function that interprets strong conjunction, which can be any continuous t-norm.
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Fuzzy architectural spatial analysis (FASA) (also fuzzy inference system (FIS) based architectural space analysis or fuzzy spatial analysis) is a spatial analysis method of analysing the spatial formation and architectural space intensity within any architectural organization. Fuzzy architectural spatial analysis is used in architecture, interior design, urban planning and similar spatial design fields. == Overview == Fuzzy architectural spatial analysis was developed by Burcin Cem Arabacioglu (2010) from the architectural theories of space syntax and visibility graph analysis, and is applied with the help of a fuzzy system with a Mamdani inference system based on fuzzy logic within any architectural space. Fuzzy architectural spatial analysis model analyses the space by considering the perceivable architectural element by their boundary and stress characteristics and intensity properties. The method is capable of taking all sensorial factors into account during analyses in conformably with the perception process of architectural space which is a multi-sensorial act.
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The Netflix Prize was an open competition for the best collaborative filtering algorithm to predict user ratings for films, based on previous ratings without any other information about the users or films, i.e. without the users being identified except by numbers assigned for the contest. The competition was held by Netflix, a video streaming service, and was open to anyone who was neither connected with Netflix (current and former employees, agents, close relatives of Netflix employees, etc.) nor a resident of certain blocked countries (such as Cuba or North Korea). On September 21, 2009, the grand prize of US$1,000,000 was given to the BellKor's Pragmatic Chaos team which bested Netflix's own algorithm for predicting ratings by 10.06%. == Problem and data sets == Netflix provided a training data set of 100,480,507 ratings that 480,189 users gave to 17,770 movies. Each training rating is a quadruplet of the form
Hildon is an application framework originally developed for mobile devices (PDAs, mobile phones, etc.) running the Linux operating system as well as the Symbian operating system. The Symbian variant of Hildon was discontinued with the cancellation of Series 90. It was developed by Nokia for the Maemo operating system. It focuses on providing a finger-friendly interface. It is primarily a set of GTK extensions that provide mobile-device–oriented functionality, but also provides a desktop environment that includes a task navigator for opening and switching between programs, a control panel for user settings, and status bar, task bar and home applets. It is standard on the Maemo platform used by the Nokia Internet Tablets and the Nokia N900 smartphone. Hildon has also been selected as the framework for Ubuntu Mobile and Embedded Edition. Hildon was an early instance of a software platform for generic computing in a tablet device intended for internet consumption. But Nokia didn't commit to it as their only platform for their future mobile devices and the project competed against other in-house platforms. The strategic advantage of a modern platform was not exploited, being displaced by the Series 60, though its development is continued by the Maemo Leste project. == Components == The Hildon framework includes components that effectively provide a desktop environment. === Hildon Application Manager === Hildon Application Manager is the Hildon graphical package manager, it uses the Debian package management tools APT (Advanced Packaging Tool and dpkg) and provides a graphical interface for installing, updating and removing packages. It is a limited package manager, designed specifically for end-users, in that it doesn't directly offer the user access to system files and libraries. With the Diablo release of Maemo, Hildon Application Manager now supports "Seamless Software Update" (SSU), which implements a variety of features to allow system upgrades to be easily performed through it. === Hildon Control Panel === Hildon Control Panel is the user settings interface for Hildon. It provides simple access to control panels used to change system settings. === Hildon Desktop === Hildon Desktop is the primary UI component of Hildon, so makes up the bulk of what a user will see as "Hildon". It controls application launching and switching, general system control, and provides interfaces for task bar (application menu and task switcher), status bar (brightness and volume control), and home (internet radio and web search) applets. === Hildon Library === The Hildon library, originally developed by Nokia but since Maemo 5, developed by Igalia and Lanedo (who developed MaemoGTK+, the Maemo version of GTK+). It is a set of mobile specific GTK+ widgets for applications in Maemo. Up to Maemo 4, these widgets were designed for stylus usage. However, in Maemo 5, most widgets were deprecated and new widgets for direct finger manipulation were introduced, including a kinetic panning container.
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Sora was a text-to-video model and social media app developed by OpenAI. Using artificial intelligence, the model generated short video clips based on prompts, and could also extend existing short videos. In February 2024, OpenAI previewed examples of its output to the public, with the first generation of Sora released publicly for ChatGPT Plus and ChatGPT Pro users in the United States and Canada in December 2024. The second generation of Sora was released to select users in the US and Canada at the end of September 2025. Sora 2 integrated social media features into the app. The app was shut down on April 26, 2026 and the application programming interface (API) is planned to be discontinued on September 24, 2026, marking the end of the Sora AI brand as a whole. By default, the generator used copyrighted material in its videos, unless copyright holders actively opt out of having their content included. Videos contained a visible, moving digital watermark to prevent misuse, but a week after Sora 2's release, third-party programs became available which could remove the watermark. == Background == Several other models capable of generating video from text had been created prior to Sora, including Meta's Make‑A‑Video, Runway's Gen‑2 and Google Veo. OpenAI, the company behind Sora, had released DALL·E 3, the third of its DALL-E text-to-image models, in September 2023. == History == === Initial release === The team that developed Sora named it after the Japanese word for 'sky' to signify its "limitless creative potential". On February 15, 2024, OpenAI first previewed Sora by releasing multiple clips of high-definition videos that it had created, including an SUV driving down a mountain road, an animation of a "short fluffy monster" next to a candle, two people walking through Tokyo in the snow, and fake historical footage of the California gold rush. OpenAI stated that it was able to generate videos as long as one minute. The company then shared a technical report that highlighted the methods used to train the model. OpenAI CEO Sam Altman also posted a series of tweets responding to Twitter users' prompts with Sora-generated videos of the prompts. As of December 9, 2024, OpenAI had gradually made Sora available to the public for ChatGPT Pro and ChatGPT Plus users in the U.S. and Canada. Prior to this, the company had provided limited access to a small "red team", including experts in misinformation and bias, to perform adversarial testing on the model. The company also shared Sora with a small group of creative professionals, including video makers and artists, to seek feedback on its usefulness in creative fields. In February 2025, OpenAI announced plans to integrate Sora into ChatGPT by letting users generate Sora videos from the chatbot. === Sora 2 === Sora 2 was unveiled on September 30, 2025, with an iOS app at the same time, as well as an Android app two months later. All videos generated by the model feature a visible, moving watermark to prevent misuse of the tool. The previous version of Sora also added a safety watermark to allow viewers to distinguish between real and fictional content. On October 7, 404 Media reported that third-party programs that could remove the watermark from Sora 2 videos had become prevalent. Many outlets, such as Wired magazine, have noted that the Sora 2 app is overtly similar to TikTok in style and features. === Discontinuation === On March 24, 2026, OpenAI announced on X that it was discontinuing Sora in both the mobile app and the API. The Sora app was shut down on April 26, 2026, while the API is planned to be shut down on September 24, 2026. OpenAI's partnership with Disney, which included a licensing agreement allowing Disney characters to be used within Sora, was also coming to an end. The decision prompted British technology news website The Register to label OpenAI a "product-killer", following in the footsteps of other technology companies such as Google, Amazon Web Services, Broadcom, Cloud Software Group, and Netscape. OpenAI did not provide a specific reason for discontinuing Sora in its shutdown notice. The reports that emerged regarding this discontinuity linked the decision to computation shortages, cost pressures, and a broader shift toward core enterprise products. Following its public launch, Sora's worldwide users peaked at around a million before declining to fewer than 500,000, while the service cost an estimated $1 million per day to operate due to the computational demands of video generation. == Legal regulation == In November 2024, an API key for Sora access was leaked by a group of testers on Hugging Face who posted a manifesto stating that they were protesting that Sora was used for "art washing". OpenAI revoked all access three hours after the leak was made public and stated that "hundreds of artists" have shaped the development and that "participation is voluntary". At the time of its launch, Sora 2 allowed copyrighted content by default unless copyright holders contacted OpenAI to restrict the generation of their content on the platform. On October 3, 2025, OpenAI stated that a future update to Sora 2 would give copyright holders "more granular control" over the generation of copyrighted content, but the company did not state whether existing content would be removed. On October 6, the chairman of the MPA criticized OpenAI's approach to copyright with Sora 2. On December 11, 2025, the Walt Disney Company announced that it would invest $1 billion in OpenAI to allow users to generate more than 200 of its copyrighted characters on Sora 2. These characters include those from Disney Animation, Pixar, Marvel Studios, and Star Wars. == Capabilities and limitations == The technology behind Sora is an adaptation of the technology behind DALL-E 3. According to OpenAI, Sora is a diffusion transformer, a denoising latent diffusion model with one transformer as its denoiser. A video is generated in latent space by denoising 3D "patches", then transformed to standard space by a video decompressor. Recaptioning is employed to augment training data by using a video-to-text model to create detailed captions for videos. OpenAI trained the model using publicly available videos as well as copyrighted videos licensed for the purpose, but did not reveal the number or the exact source of the videos. Upon its release, OpenAI acknowledged some of Sora's shortcomings, including its limited capacity to simulate complex physics, to understand causality and to differentiate left from right. OpenAI also stated that, in adherence to the company's existing safety practices, Sora will restrict text prompts for sexual, violent, hateful or celebrity imagery, as well as content featuring existing intellectual property. Sora researcher Tim Brooks stated that the model learned how to create 3D graphics from its dataset alone, while fellow Sora researcher Bill Peebles said that the model automatically created different video angles without being prompted. According to OpenAI, Sora-generated videos are also tagged with C2PA metadata to indicate that they are AI-processed. === Comparison with other models === The Artificial Analysis have placed Sora 2 pro lower than other text-to-video AI generators in the market on its leaderboard. Other models, such as Seedance 2.0 from ByteDance, Runaway 4.5 from Runaway, and Kling 3.0 from KlingAI, have ranked higher than Sora 2.0. == Reception == === Positive === In 2024, Will Douglas Heaven of the MIT Technology Review called the demonstration videos "impressive", but noted that they must have been cherry-picked and may not be representative of Sora's typical output. Lisa Lacy of CNET called its example videos "remarkably realistic – except perhaps when a human face appears close up or when sea creatures are swimming". In October 2025, The New York Times remarked that the release of the Sora 2 app in September 2025 was "jaw-dropping (for better and worse)" though also remarked that the app was a "social network in disguise" and "the type of product that companies like Meta and X have sought to build: a way to bring A.I. to the masses that people can share." The article expressed concern regarding the product's potential impact on society and its potential use to promote misinformation, disinformation, and scams. A 2025 study in Science Advances found that generative AI tools can lower barriers to entry in creative work. It enables users with diverse skill sets, including people with less formal artistic training and technical skills, to act on their creative and imaginative ideas. The lower barrier to entry allows such users previously locked out of the creative industry to produce content and easily act on their creative ideas. === Negative === Some internet users and online content creators, such as Hank Green, called the mobile app "SlopTok," a reference to both the mobile app TikTok and the term AI slop. Filmmaker Tyler Perry announced he would be putting a planned
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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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