AI Assistant Quotes

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  Schema-agnostic databases

  Schema-agnostic databases or vocabulary-independent databases aim at supporting users to be abstracted from the representation of the data, supporting the automatic semantic matching between queries and databases. Schema-agnosticism is the property of a database of mapping a query issued with the user terminology and structure, automatically mapping it to the dataset vocabulary. The increase in the size and in the semantic heterogeneity of database schemas bring new requirements for users querying and searching structured data. At this scale it can become unfeasible for data consumers to be familiar with the representation of the data in order to query it. At the center of this discussion is the semantic gap between users and databases, which becomes more central as the scale and complexity of the data grows. == Description == The evolution of data environments towards the consumption of data from multiple data sources and the growth in the schema size, complexity, dynamicity and decentralisation (SCoDD) of schemas increases the complexity of contemporary data management. The SCoDD trend emerges as a central data management concern in Big Data scenarios, where users and applications have a demand for more complete data, produced by independent data sources, under different semantic assumptions and contexts of use, which is the typical scenario for Semantic Web Data applications. The evolution of databases in the direction of heterogeneous data environments strongly impacts the usability, semiotics and semantic assumptions behind existing data accessibility methods such as structured queries, keyword-based search and visual query systems. With schema-less databases containing potentially millions of dynamically changing attributes, it becomes unfeasible for some users to become aware of the 'schema' or vocabulary in order to query the database. At this scale, the effort in understanding the schema in order to build a structured query can become prohibitive. == Schema-agnostic queries == Schema-agnostic queries can be defined as query approaches over structured databases which allow users satisfying complex information needs without the understanding of the representation (schema) of the database. Similarly, Tran et al. defines it as "search approaches, which do not require users to know the schema underlying the data". Approaches such as keyword-based search over databases allow users to query databases without employing structured queries. However, as discussed by Tran et al.: "From these points, users however have to do further navigation and exploration to address complex information needs. Unlike keyword search used on the Web, which focuses on simple needs, the keyword search elaborated here is used to obtain more complex results. Instead of a single set of resources, the goal is to compute complex sets of resources and their relations." The development of approaches to support natural language interfaces (NLI) over databases have aimed towards the goal of schema-agnostic queries. Complementarily, some approaches based on keyword search have targeted keyword-based queries which express more complex information needs. Other approaches have explored the construction of structured queries over databases where schema constraints can be relaxed. All these approaches (natural language, keyword-based search and structured queries) have targeted different degrees of sophistication in addressing the problem of supporting a flexible semantic matching between queries and data, which vary from the completely absence of the semantic concern to more principled semantic models. While the demand for schema-agnosticism has been an implicit requirement across semantic search and natural language query systems over structured data, it is not sufficiently individuated as a concept and as a necessary requirement for contemporary database management systems. Recent works have started to define and model the semantic aspects involved on schema-agnostic queries. === Schema-agnostic structured queries === Consist of schema-agnostic queries following the syntax of a structured standard (for example SQL, SPARQL). The syntax and semantics of operators are maintained, while different terminologies are used. ==== Example 1 ==== SELECT ?y { BillClinton hasDaughter ?x . ?x marriedTo ?y . } which maps to the following SPARQL query in the dataset vocabulary: ==== Example 2 ==== which maps to the following SPARQL query in the dataset vocabulary: === Schema-agnostic keyword queries === Consist of schema-agnostic queries using keyword queries. In this case the syntax and semantics of operators are different from the structured query syntax. ==== Example ==== "Bill Clinton daughter married to" "Books by William Goldman with more than 300 pages" == Semantic complexity == As of 2016 the concept of schema-agnostic queries has been developed primarily in academia. Most of schema-agnostic query systems have been investigated in the context of Natural Language Interfaces over databases or over the Semantic Web. These works explore the application of semantic parsing techniques over large, heterogeneous and schema-less databases. More recently, the individuation of the concept of schema-agnostic query systems and databases have appeared more explicitly within the literature. Freitas et al. provide a probabilistic model on the semantic complexity of mapping schema-agnostic queries.

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  Dartmouth workshop

  The Dartmouth Summer Research Project on Artificial Intelligence was a 1956 summer workshop widely considered to be the founding event of artificial intelligence as a field. The workshop has been referred to as "the Constitutional Convention of AI". The project's four organizers, Claude Shannon, John McCarthy, Nathaniel Rochester and Marvin Minsky, are considered some of the "founding fathers" of AI. However it was not the first conference devoted to what would now be described as the question of artificial intelligence: it postdated meetings such as the 1951 Paris cybernetics conference and the Macy meetings. The project lasted approximately six to eight weeks and consisted largely of brainstorming sessions. Eleven mathematicians and scientists originally planned to attend; not all of them attended, but more than ten others came for short times. == Background == In the early 1950s, there were various names for the field of "thinking machines": cybernetics, automata theory, and complex information processing. The variety of names suggests the variety of conceptual orientations. In 1955, John McCarthy, then a young Assistant Professor of Mathematics at Dartmouth College, decided to organize a group to clarify and develop ideas about thinking machines. He picked the name 'Artificial Intelligence' for the new field. He chose the name partly for its neutrality; avoiding a focus on narrow automata theory, and avoiding cybernetics which was heavily focused on analog feedback, as well as him potentially having to accept the assertive Norbert Wiener as guru or having to argue with him. In early 1955, McCarthy approached the Rockefeller Foundation to request funding for a summer seminar at Dartmouth for about 10 participants. In June, he and Claude Shannon, a founder of information theory then at Bell Labs, met with Robert Morison, Director of Biological and Medical Research to discuss the idea and possible funding, though Morison was unsure whether money would be made available for such a visionary project. On September 2, 1955, the project was formally proposed by McCarthy, Marvin Minsky, Nathaniel Rochester and Claude Shannon. The proposal is credited with introducing the term 'artificial intelligence'. The Proposal states: We propose that a 2-month, 10-man study of artificial intelligence be carried out during the summer of 1956 at Dartmouth College in Hanover, New Hampshire. The study is to proceed on the basis of the conjecture that every aspect of learning or any other feature of intelligence can in principle be so precisely described that a machine can be made to simulate it. An attempt will be made to find how to make machines use language, form abstractions and concepts, solve kinds of problems now reserved for humans, and improve themselves. We think that a significant advance can be made in one or more of these problems if a carefully selected group of scientists work on it together for a summer. The proposal goes on to discuss computers, natural language processing, neural networks, theory of computation, abstraction and creativity (these areas within the field of artificial intelligence are considered still relevant to the work of the field). On May 26, 1956, McCarthy notified Robert Morison of the planned 11 attendees: For the full period: 1) Dr. Marvin Minsky 2) Dr. Julian Bigelow 3) Professor D.M. Mackay 4) Mr. Ray Solomonoff 5) Mr. John Holland 6) Dr. John McCarthy For four weeks: 7) Dr. Claude Shannon 8) Mr. Nathaniel Rochester 9) Mr. Oliver Selfridge For the first two weeks: 10) Dr. Allen Newell 11) Professor Herbert Simon He noted, "we will concentrate on a problem of devising a way of programming a calculator to form concepts and to form generalizations. This of course is subject to change when the group gets together." The actual participants came at different times, mostly for much shorter times. Trenchard More replaced Rochester for three weeks and MacKay and Holland did not attend—but the project was set to begin. Around June 18, 1956, the earliest participants (perhaps only Ray Solomonoff, maybe with Tom Etter) arrived at the Dartmouth campus in Hanover, N.H., to join John McCarthy who already had an apartment there. Solomonoff and Minsky stayed at Professors' apartments, but most would stay at the Hanover Inn. == Dates == The Dartmouth Workshop is usually said to have run for six weeks. Ray Solomonoff's notes taken during the workshop, however, indicate that it ran for roughly eight weeks, from about June 18 to August 17. Solomonoff's notes start on June 22; June 28 mentions Minsky, June 30 mentions Hanover, N.H., July 1 mentions Tom Etter. On August 17, Solomonoff gave a final talk. == Participants == Initially, McCarthy lost his list of attendees. Instead, after the workshop, McCarthy sent Solomonoff a preliminary list of participants and visitors plus those interested in the subject. 47 people were listed. Solomonoff, however, made a list of participants in his notes of the summer project: Ray Solomonoff Marvin Minsky John McCarthy Claude Shannon Trenchard More Nat Rochester Oliver Selfridge Julian Bigelow W. Ross Ashby W.S. McCulloch Abraham Robinson Tom Etter John Nash David Sayre Arthur Samuel Kenneth R. Shoulders Shoulders' friend Alex Bernstein Herbert Simon Allen Newell Shannon attended Solomonoff's talk on July 10 and Bigelow gave a talk on August 15. Solomonoff doesn't mention Bernard Widrow, but in 1994 Widrow said that he and an unidentified colleague from the same lab in MIT had attended for one week. In the same interview Widrow recalled that "I think [Wesley] Clark and [Belmont] Farley were there from Lincoln Lab." Trenchard mentions R. Culver and Solomonoff mentions Bill Shutz. Herb Gelernter didn't attend, but was influenced later by what Rochester learned. In an article in IEEE Spectrum, Grace Solomonoff additionally identifies Peter Milner in a photo taken by Nathaniel Rochester in front of Dartmouth Hall. Ray Solomonoff, Marvin Minsky, and John McCarthy were the only three who stayed for the full time. Trenchard took attendance during two weeks of his three-week visit. From three to about eight people would attend the daily sessions. == Event and aftermath == They had the entire top floor of the Dartmouth Math Department to themselves, and most weekdays they would meet at the main math classroom where someone might lead a discussion focusing on his ideas, or more frequently, a general discussion would be held. It was not a directed group research project; discussions covered many topics, but several directions are considered to have been initiated or encouraged by the Workshop: the rise of symbolic methods, systems focused on limited domains (early expert systems), and deductive systems versus inductive systems. One participant, Arthur Samuel, said, "It was very interesting, very stimulating, very exciting". Ray Solomonoff kept notes giving his impression of the talks and the ideas from various discussions. === McCarthy's 1956 AI distribution list === This is the list in the "People Interested in the Artificial Intelligence Problem" document which McCarthy produced in 1956, partly in lieu of a list of attendees at the Dartmouth workshop. According to McCarthy the list was "being sent to the people on the list and a few others", and its purpose was "to let those on it know who is interested in receiving documents on the problem" of artificial intelligence. McCarthy also promised to deliver them a report on the Dartmouth conference, and to send an updated list soon afterwards. It includes people who did not attend the conference and does not include everyone who did attend it.

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  DialogOS

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

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  Dreams of Violets

  Dreams of Violets is a film entirely generated by artificial intelligence, produced and directed by brothers Ash and Pooya Koosha. The film will be screened at the Tribeca Film Festival on 10 June 2026. All images and characters in the film were generated using AI-powered video tools and based on journalistic reports, photographs, and eyewitness accounts. == Plot == The film is a fictionalized dramatization of the events surrounding the massacre of Iranian civilians in January 2026. International organizations estimate the death toll at over 7,000, amidst protests and state violence that unfolded during a communications blackout.

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  LTX (text-to-video model)

  LTX is a family of open source artificial intelligence video foundation models developed by Lightricks, and first released in November 2024. The latest models, LTX-2, create videos based on user prompts. They were preceded by LTX Video, which was released in 2024 as the company's first text-to-video model. LTX-2 is part of the LTX family of video generation models, which form the core technology, alongside LTX Studio, of the LTX ecosystem. == History == === Origins: LTX Video (2024–2025) === In November 2024 Lightricks publicly released its first text-to-video model, LTX Video. It was a 2-billion parameter model, available as open source. In May 2025 Lightricks launched LTXV-13b, a version with 13-billion parameters. Two months later, the model broke the 60 second barrier for generated video. === Release of LTX-2 (2025) === In October 2025 Lightricks announced its latest model, and renamed it LTX-2. The model was described as capable of generating synchronized audio and video at native 4K resolution and up to 50 frames per second (fps), using a variety of conditions and prompts, including text-to-video and image-to-video. Google highlighted the fact that LTX-2 was trained on its infrastructure, and saying it was "The first open source AI video generation model, powered by Google Cloud". Upon its release it was ranked in the top-3 models for image-to-video creation by Artificial Analysis, behind Kling 3.5 by Kling AI and Veo 3.1 by Google. Its text-to-image option was ranked 7th. In addition to its open-source release, Lightricks offers API access to LTX-2, allowing developers to generate videos from text and image prompts through a hosted service without running the model locally. === Open Source Release (2026) === In January 2026, Lightricks officially released the full open-source version of LTX-2, making the model’s complete codebase, weights, and associated tooling publicly available. In March 2026 the company released LTX-2.3, which was accompanied by a desktop video editor enabling the entire model to run locally on consumer hardware. == Technical features == === Advancements over LTX Video === LTX-2 builds upon the LTX Video architecture with several major improvements: Unified audio-video generation producing synchronized dialogue, ambience, and motion Native 4K rendering 50-fps output for cinematic motion Three operational modes (Fast, Pro, Ultra) More efficient diffusion pipelines enabling high fidelity on consumer GPUs === Core capabilities === Text-to-video generation Image-to-video generation Multimodal audiovisual synthesis High-resolution spatial and temporal coherence Configurable quality/performance settings Open-source distribution of weights and datasets == Reception == Initial reception to LTX-2 was broadly positive, with several technology and media outlets highlighting its open-source approach and multimodal capabilities. Open Source For You described LTX-2 as “one of the first AI video systems to combine 4K output, synchronized audio, and an open model release,” noting that it positioned Lightricks as a significant competitor to proprietary systems such as OpenAI's Sora and Google's Veo. IEA Green said that the model “could rewrite the AI filmmaking game,” emphasizing that its 50-fps rendering and unified audio-video generation made it suitable for professional studios and independent creators alike. AI News characterized LTX-2 as a “major step forward in the democratization of cinematic-quality video generation,” praising its consumer-grade hardware efficiency and multi-tier generation modes, while also noting ongoing challenges in long-form temporal stability. FinancialContent reported strong interest among creative agencies, attributing the attention to Lightricks’ decision to release model weights and datasets, which reviewers said enabled “a level of transparency not typically seen in commercial AI video models.” === Benchmarks and rankings === Upon release, LTX-2 ranked third for image-to-video creation in the Artificial Analysis benchmark, behind Kling 3.5 and Veo 3.1, while its text-to-video option ranked seventh. As of early 2026, it was the highest-ranked open-source model in the benchmark. === Limitations === Some early reviewers also pointed out quality limitations. The Ray3 technical review noted occasional inconsistencies in lip-sync and motion tracking during long scenes, though it stated these were “in line with the challenges faced by all current AI video diffusion models” and expected to improve with continued iteration. Like other diffusion-based video generators, LTX-2 can produce artifacts in complex multi-person scenes and may struggle with precise text rendering within generated video.

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  The Stories of Ibis

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

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  Estimation of distribution algorithm

  Estimation of distribution algorithms (EDAs), sometimes called probabilistic model-building genetic algorithms (PMBGAs), are stochastic optimization methods that guide the search for the optimum by building and sampling explicit probabilistic models of promising candidate solutions. Optimization is viewed as a series of incremental updates of a probabilistic model, starting with the model encoding an uninformative prior over admissible solutions and ending with the model that generates only the global optima. EDAs belong to the class of evolutionary algorithms. The main difference between EDAs and most conventional evolutionary algorithms is that evolutionary algorithms generate new candidate solutions using an implicit distribution defined by one or more variation operators, whereas EDAs use an explicit probability distribution encoded by a Bayesian network, a multivariate normal distribution, or another model class. Similarly as other evolutionary algorithms, EDAs can be used to solve optimization problems defined over a number of representations from vectors to LISP style S expressions, and the quality of candidate solutions is often evaluated using one or more objective functions. The general procedure of an EDA is outlined in the following: t := 0 initialize model M(0) to represent uniform distribution over admissible solutions while (termination criteria not met) do P := generate N>0 candidate solutions by sampling M(t) F := evaluate all candidate solutions in P M(t + 1) := adjust_model(P, F, M(t)) t := t + 1 Using explicit probabilistic models in optimization allowed EDAs to feasibly solve optimization problems that were notoriously difficult for most conventional evolutionary algorithms and traditional optimization techniques, such as problems with high levels of epistasis. Nonetheless, the advantage of EDAs is also that these algorithms provide an optimization practitioner with a series of probabilistic models that reveal a lot of information about the problem being solved. This information can in turn be used to design problem-specific neighborhood operators for local search, to bias future runs of EDAs on a similar problem, or to create an efficient computational model of the problem. For example, if the population is represented by bit strings of length 4, the EDA can represent the population of promising solution using a single vector of four probabilities (p1, p2, p3, p4) where each component of p defines the probability of that position being a 1. Using this probability vector it is possible to create an arbitrary number of candidate solutions. == Estimation of distribution algorithms (EDAs) == This section describes the models built by some well known EDAs of different levels of complexity. It is always assumed a population P ( t ) {\displaystyle P(t)} at the generation t {\displaystyle t} , a selection operator S {\displaystyle S} , a model-building operator α {\displaystyle \alpha } and a sampling operator β {\displaystyle \beta } . == Univariate factorizations == The most simple EDAs assume that decision variables are independent, i.e. p ( X 1 , X 2 ) = p ( X 1 ) ⋅ p ( X 2 ) {\displaystyle p(X_{1},X_{2})=p(X_{1})\cdot p(X_{2})} . Therefore, univariate EDAs rely only on univariate statistics and multivariate distributions must be factorized as the product of N {\displaystyle N} univariate probability distributions, D Univariate := p ( X 1 , … , X N ) = ∏ i = 1 N p ( X i ) . {\displaystyle D_{\text{Univariate}}:=p(X_{1},\dots ,X_{N})=\prod _{i=1}^{N}p(X_{i}).} Such factorizations are used in many different EDAs, next we describe some of them. === Univariate marginal distribution algorithm (UMDA) === The UMDA is a simple EDA that uses an operator α U M D A {\displaystyle \alpha _{UMDA}} to estimate marginal probabilities from a selected population S ( P ( t ) ) {\displaystyle S(P(t))} . By assuming S ( P ( t ) ) {\displaystyle S(P(t))} contain λ {\displaystyle \lambda } elements, α U M D A {\displaystyle \alpha _{UMDA}} produces probabilities: p t + 1 ( X i ) = 1 λ ∑ x ∈ S ( P ( t ) ) x i , ∀ i ∈ 1 , 2 , … , N . {\displaystyle p_{t+1}(X_{i})={\dfrac {1}{\lambda }}\sum _{x\in S(P(t))}x_{i},~\forall i\in 1,2,\dots ,N.} Every UMDA step can be described as follows D ( t + 1 ) = α UMDA ∘ S ∘ β λ ( D ( t ) ) . {\displaystyle D(t+1)=\alpha _{\text{UMDA}}\circ S\circ \beta _{\lambda }(D(t)).} === Population-based incremental learning (PBIL) === The PBIL, represents the population implicitly by its model, from which it samples new solutions and updates the model. At each generation, μ {\displaystyle \mu } individuals are sampled and λ ≤ μ {\displaystyle \lambda \leq \mu } are selected. Such individuals are then used to update the model as follows p t + 1 ( X i ) = ( 1 − γ ) p t ( X i ) + ( γ / λ ) ∑ x ∈ S ( P ( t ) ) x i , ∀ i ∈ 1 , 2 , … , N , {\displaystyle p_{t+1}(X_{i})=(1-\gamma )p_{t}(X_{i})+(\gamma /\lambda )\sum _{x\in S(P(t))}x_{i},~\forall i\in 1,2,\dots ,N,} where γ ∈ ( 0 , 1 ] {\displaystyle \gamma \in (0,1]} is a parameter defining the learning rate, a small value determines that the previous model p t ( X i ) {\displaystyle p_{t}(X_{i})} should be only slightly modified by the new solutions sampled. PBIL can be described as D ( t + 1 ) = α PIBIL ∘ S ∘ β μ ( D ( t ) ) {\displaystyle D(t+1)=\alpha _{\text{PIBIL}}\circ S\circ \beta _{\mu }(D(t))} === Compact genetic algorithm (cGA) === The CGA, also relies on the implicit populations defined by univariate distributions. At each generation t {\displaystyle t} , two individuals x , y {\displaystyle x,y} are sampled, P ( t ) = β 2 ( D ( t ) ) {\displaystyle P(t)=\beta _{2}(D(t))} . The population P ( t ) {\displaystyle P(t)} is then sorted in decreasing order of fitness, S Sort ( f ) ( P ( t ) ) {\displaystyle S_{{\text{Sort}}(f)}(P(t))} , with u {\displaystyle u} being the best and v {\displaystyle v} being the worst solution. The CGA estimates univariate probabilities as follows p t + 1 ( X i ) = p t ( X i ) + γ ( u i − v i ) , ∀ i ∈ 1 , 2 , … , N , {\displaystyle p_{t+1}(X_{i})=p_{t}(X_{i})+\gamma (u_{i}-v_{i}),\quad \forall i\in 1,2,\dots ,N,} where, γ ∈ ( 0 , 1 ] {\displaystyle \gamma \in (0,1]} is a constant defining the learning rate, usually set to γ = 1 / N {\displaystyle \gamma =1/N} . The CGA can be defined as D ( t + 1 ) = α CGA ∘ S Sort ( f ) ∘ β 2 ( D ( t ) ) {\displaystyle D(t+1)=\alpha _{\text{CGA}}\circ S_{{\text{Sort}}(f)}\circ \beta _{2}(D(t))} == Bivariate factorizations == Although univariate models can be computed efficiently, in many cases they are not representative enough to provide better performance than GAs. In order to overcome such a drawback, the use of bivariate factorizations was proposed in the EDA community, in which dependencies between pairs of variables could be modeled. A bivariate factorization can be defined as follows, where π i {\displaystyle \pi _{i}} contains a possible variable dependent to X i {\displaystyle X_{i}} , i.e. | π i | = 1 {\displaystyle |\pi _{i}|=1} . D Bivariate := p ( X 1 , … , X N ) = ∏ i = 1 N p ( X i | π i ) . {\displaystyle D_{\text{Bivariate}}:=p(X_{1},\dots ,X_{N})=\prod _{i=1}^{N}p(X_{i}|\pi _{i}).} Bivariate and multivariate distributions are usually represented as probabilistic graphical models (graphs), in which edges denote statistical dependencies (or conditional probabilities) and vertices denote variables. To learn the structure of a PGM from data linkage-learning is employed. === Mutual information maximizing input clustering (MIMIC) === The MIMIC factorizes the joint probability distribution in a chain-like model representing successive dependencies between variables. It finds a permutation of the decision variables, r : i ↦ j {\displaystyle r:i\mapsto j} , such that x r ( 1 ) x r ( 2 ) , … , x r ( N ) {\displaystyle x_{r(1)}x_{r(2)},\dots ,x_{r(N)}} minimizes the Kullback–Leibler divergence in relation to the true probability distribution, i.e. π r ( i + 1 ) = { X r ( i ) } {\displaystyle \pi _{r(i+1)}=\{X_{r(i)}\}} . MIMIC models a distribution p t + 1 ( X 1 , … , X N ) = p t ( X r ( N ) ) ∏ i = 1 N − 1 p t ( X r ( i ) | X r ( i + 1 ) ) . {\displaystyle p_{t+1}(X_{1},\dots ,X_{N})=p_{t}(X_{r(N)})\prod _{i=1}^{N-1}p_{t}(X_{r(i)}|X_{r(i+1)}).} New solutions are sampled from the leftmost to the rightmost variable, the first is generated independently and the others according to conditional probabilities. Since the estimated distribution must be recomputed each generation, MIMIC uses concrete populations in the following way P ( t + 1 ) = β μ ∘ α MIMIC ∘ S ( P ( t ) ) . {\displaystyle P(t+1)=\beta _{\mu }\circ \alpha _{\text{MIMIC}}\circ S(P(t)).} === Bivariate marginal distribution algorithm (BMDA) === The BMDA factorizes the joint probability distribution in bivariate distributions. First, a randomly chosen variable is added as a node in a graph, the most dependent variable to one of those in the graph is chosen among those not yet in the graph, this procedure is repeated until no remain

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  DARPA Prize Competitions

  Over the years, the U.S. Defense Advanced Research Projects Agency (DARPA) has conducted numerous prize competitions to spur innovation. A prize competition allows DARPA to establish an ambitious goal, opening the door to novel approaches from the public that might otherwise appear too risky for experts in a particular field to pursue. == Statutory authorities == In 1999, Congress provided prize competition authority to DARPA in the National Defense Authorization Act for Fiscal Year 2000 (P.L. 106–65), 10 U.S.C. § 4025, formerly 10 U.S.C. §2374a. DARPA also conducts prize competitions under the America COMPETES Act, 15 U.S.C. § 3719. == Recent prize competitions == DARPA Grand Challenge (2004 and 2005) was a prize competition to spur the development of autonomous vehicle technologies. The $1 million prize went unclaimed as no vehicles could complete the challenging desert route from Barstow, CA, to Primm, NV, on March 13, 2004. A year later, on October 8, 2005, the Stanford Racing Team won the $2 million prize during the second competition of the Grand Challenge in the desert Southwest near the California/Nevada state line. DARPA Urban Challenge (2007) required the competitors to build an autonomous vehicle capable of driving in traffic and performing complex maneuvers such as merging, passing, parking, and negotiating intersections. On November 3, 2007, the Carnegie Mellon Team won the $2 million prize, and its vehicle became the first autonomous vehicle that interacted with both manned and unmanned vehicle traffic in an urban environment. DARPA Network Challenge (Red Balloon Challenge) (2009) explored the roles that the Internet and social networking play in solving broad-scope, time-critical problems. On December 5, 2009, the Massachusetts Institute of Technology team won $40,000 by locating the ten moored, eight-foot, red weather balloons at ten places in the United States within seven hours. DARPA Digital Manufacturing Analysis, Correlation and Estimation Challenge (DMACE) (2010) was a three-month contest to showcase the potential of digital manufacturing of advanced materials. The University of California at Santa Barbara team won a $50,000 prize for crushing 180 digitally manufactured (DM) titanium mesh spheres with the most accurate predictive model of the components’ properties. DARPA Shredder Challenge (2011) was to identify and assess potential capabilities and vulnerabilities to sensitive information in the national security community. Participating teams must download the images of the documents shredded into more than 10,000 pieces from the Challenge website, reconstruct the documents, and solve the five puzzles. Of almost 9,000 teams, the San Francisco-based All Your Shreds Are Belong to U.S team won the $50,000 prize. DARPA UAVForge Challenge (2011-2012) aimed to build and test a user-intuitive, backpack-portable unmanned aerial vehicle (UAV) that could quietly fly in and out of critical environments to conduct sustained surveillance for up to three hours. The $100,000 prize was not claimed because none of the 140 teams met the technical matrix. DARPA Cash for Locating & Identifying Quick Response Codes (CLIQR) Quest Challenge (2012) explored the role the Internet and social media played in the timely communication, wide-area team-building, and urgent mobilization required to solve broad scope, time-critical problems. The challenge offered $40,000 to the first individual or team that could locate seven posters appearing in U.S. cities bearing the DARPA logo and a quick response code (QR) within 15 days. No team found and submitted all seven codes. DARPA Fast Adaptable Next-Generation Ground Vehicle (FANG) Challenge (2012-2013) was to use three competitions for the design of an infantry fighting vehicle, culminating in prototypes. In April 2013, DARPA awarded US$1 million to a three-man team during the first competition. DARPA decided not to proceed with the second and third competitions as originally planned and transitioned the technologies to the defense and commercial industry through the Digital Manufacturing and Design Innovation Institute (DMDII). DARPA Spectrum Challenge (2013-2014) sought to demonstrate how a software-defined radio can use a given communication channel in the presence of other users and interfering signals. Three teams emerged as the overall winners, winning a total of $150,000 in prizes. DARPA Chikungunya (CHIKV) Challenge (2014-2015) was a health-related effort to develop the most accurate predictions of CHIKV cases for all Western Hemisphere countries and territories between September 2014 and March 2015. On May 12, 2015, DARPA awarded $500,000 in prizes to the 11 winners of the competition during a scientific review DARPA Robotics Challenge (DRC) (2013-2015) aimed to develop semi-autonomous ground robots that could do "complex tasks in dangerous, degraded, human-engineered environments." A South Korean team won the first prize of $2 million, and two U.S. teams won $1 million and $500,000 as second and third winners. DARPA Cyber Grand Challenge (CGC) (2014 - 2016) was to “create automatic defensive systems capable of reasoning about flaws, formulating patches and deploying them on a network in real time.” The top three winners were awarded prizes of $2 million, $1 million, and $750,000, respectively. DARPA Spectrum Collaboration Challenge (SC2) (2016-2019) aimed to encourage the development of AI-enabled wireless networks to “ensure that the exponentially growing number of military and civilian wireless devices would have full access to the increasingly crowded electromagnetic spectrum.” A team from the University of Florida won the overall top prize of US$2 million at the final SC2 competition. DARPA Subterranean (SubT) Challenge (2017-2021) was to develop robotic technologies to map, navigate, search and exploit complex underground environments. The first-place winners of the system final competition and of the virtual final competition were awarded $2 million and $750,000, respectively, with multiple prizes awarded to the second and third-place winners. DARPA Launch Challenge (2018-2020) was a $12 million satellite launch challenge to demonstrate responsive and flexible space launch capabilities from the small launch providers and was to culminate in two separate launch competitions where the competitors must launch a satellite to low Earth orbit (LEO) within days of each other at different locations in the United States. The competition ended without a winner. DARPA Forecasting Floats in Turbulence (FFT) Challenge (2021) was to spur technologies that could predict the location of sea drifters or floats within 10 days. DARPA awarded $25,000 for first place, with prizes of $15,000 and $10,000 for second place and third place. DARPA Artificial Intelligence Cyber Challenge (AIxCC) (2023–2025) was a two-year challenge and asks competitors to design novel AI systems to secure critical software code on which Americans rely. The total prize money is $29.5 million. In March 2024, the Advanced Research Projects Agency for Health (ARPA-H) partnered with DARPA, contributing an additional $20 million to the competition's prize pool to address software vulnerabilities in medical devices, hospital IT, and biotech equipment. AIxCC collaborates with Google, Microsoft, OpenAI, Anthropic, Linux Foundation, Open Source Security Foundation, Black Hat USA, and DEF CON, all of which provide AIxCC with access to large language models. In August 2024, AIxCC held the semifinal at DEF CON in Las Vegas. DARPA and ARPA-H tested all 42 submissions by running them through various open-source coding projects with deliberately injected vulnerabilities and scored the tools based on their effectiveness in identifying and fixing security flaws. Seven teams, each winning $2 million in the semifinals, competed in the final round of the AIxCC at the August 2025 DEF CON conference. Team Atlanta won first place with a $4 million prize for its cyber reasoning systems, which identified and patched vulnerabilities across 54 million lines of code. DARPA Triage Challenge (2023 – 2026) aims to spur the development of novel physiological features for medical triage, with a total prize money of $7 million. In October 2024, Challenge Event 1 was held in Perry, Georgia, featuring to-scale replicas of disaster sites such as an airplane crash and Hurricane Katrina, and teams competed based on how closely their data aligned with the agency’s official data and how quickly and accurately their autonomous systems could identify individuals most urgently in need of medical care. DARPA concluded the second year of competitions and, in November 2025, named the top performers in systems and data categories, which will advance to the final 2026 competition. The DARPA Lift Challenge (2025-2026) is for participants to design unmanned aerial systems capable of carrying up to four times their own weight, with a minimum payload of 110 pounds. Acco

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  Character computing

  Character computing is a trans-disciplinary field of research at the intersection of computer science and psychology. It is any computing that incorporates the human character within its context. Character is defined as all features or characteristics defining an individual and guiding their behavior in a specific situation. It consists of stable trait markers (e.g., personality, background, history, socio-economic embeddings, culture,...) and variable state markers (emotions, health, cognitive state, ...). Character computing aims at providing a holistic psychologically driven model of human behavior. It models and predicts behavior based on the relationships between a situation and character. Three main research modules fall under the umbrella of character computing: character sensing and profiling, character-aware adaptive systems, and artificial characters. == Overview == Character computing can be viewed as an extension of the well-established field of affective computing. Based on the foundations of the different psychology branches, it advocates defining behavior as a compound attribute that is not driven by either personality, emotions, situation or cognition alone. It rather defines behavior as a function of everything that makes up an individual i.e., their character and the situation they are in. Affective computing aims at allowing machines to understand and translate the non-verbal cues of individuals into affect. Accordingly, character computing aims at understanding the character attributes of an individual and the situation to translate it to predicted behavior, and vice versa. ''In practical terms, depending on the application context, character computing is a branch of research that deals with the design of systems and interfaces that can observe, sense, predict, adapt to, affect, understand, or simulate the following: character based on behavior and situation, behavior based on character and situation, or situation based on character and behavior.'' The Character-Behavior-Situation (CBS) triad is at the core of character computing and defines each of the three edges based on the other two. Character computing relies on simultaneous development from a computational and psychological perspective and is intended to be used by researchers in both fields. Its main concept is aligning the computational model of character computing with empirical results from in-lab and in-the-wild psychology experiments. The model is to be continuously built and validated through the emergence of new data. Similar to affective and personality computing, the model is to be used as a base for different applications towards improving user experience. == History == Character computing as such was first coined in its first workshop in 2017. Since then it has had 3 international workshops and numerous publications. Despite its young age, it has already drawn some interest in the research community, leading to the publication of the first book under the same title in early 2020 published by Springer Nature. Research that can be categorized under the field dates much older than 2017. The notion of combining several factors towards the explanation of behavior or traits and states has long been investigated in both Psychology and Computer Science, for example. == Character == The word character originates from the Greek word meaning “stamping tool”, referring to distinctive features and traits. Over the years it has been given many different connotations, like the moral character in philosophy, the temperament in psychology, a person in literature or an avatar in various virtual worlds, including video games. According to character computing character is a unification of all the previous definitions, by referring back to the original meaning of the word. Character is defined as the holistic concept representing all interacting trait and state markers that distinguish an individual. Traits are characteristics that mainly remain stable over time. Traits include personality, affect, socio-demographics, and general health. States are characteristics that vary in short periods of time. They include emotions, well-being, health, cognitive state. Each characteristic has many representation methods and psychological models. The different models can be combined or one model can be preset for each characteristic. This depends on the use-case and the design choices. == Areas == Research into character computing can be divided into three areas, which complement each other but can each be investigated separately. The first area is sensing and predicting character states and traits or ensuing behavior. The second area is adapting applications to certain character states or traits and the behavior they predict. It also deals with trying to change or monitor such behavior. The final area deals with creating artificial agents e.g., chatbots or virtual reality avatars that exhibit certain characteristics. The three areas are investigated separately and build on existing findings in the literature. The results of each of the three areas can also be used as a stepping stone for the next area. Each of the three areas has already been investigated on its own in different research fields with focus on different subsets of character. For example, affective computing and personality computing both cover different areas with a focus on some character components without the others to account for human behavior. == The Character-Behavior-Situation triad == Character computing is based on a holistic psychologically driven model of human behavior. Human behavior is modeled and predicted based on the relationships between a situation and a human's character. To further define character in a more formal or holistic manner, we represent it in light of the Character–Behavior–Situation triad. This highlights that character not only determines who we are but how we are, i.e., how we behave. The triad investigated in Personality Psychology is extended through character computing to the Character–Behavior–Situation triad. Any member of the CBS triad is a function of the two other members, e.g., given the situation and personality, the behavior can be predicted. Each of the components in the triad can be further decomposed into smaller units and features that may best represent the human's behavior or character in a particular situation. Character is thus behind a person's behavior in any given situation. While this is a causality relation, the correlation between the three components is often more easily used to predict the components that are most difficult to measure from those measured more easily. There are infinitely many components to include in the representation of any of C, B, and S. The challenge is always to choose the smallest subset needed for prediction of a person's behavior in a particular situation.

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  Darwin among the Machines

  "Darwin among the Machines" is a letter to the editor published in The Press newspaper on 13 June 1863 in Christchurch, New Zealand. The title, which was chosen by the author, references the work of Charles Darwin. Written by Samuel Butler but signed Cellarius, the letter raised the possibility that machines were a kind of "mechanical life" undergoing constant evolution, and that eventually machines might supplant humans as the dominant species. == Book of the Machines == Butler developed this and subsequent articles into The Book of the Machines, three chapters of Erewhon, published anonymously in 1872. The Erewhonian society Butler envisioned had long ago undergone a revolution that destroyed most mechanical inventions. The narrator of the story finds a book that details the reasons for this revolution, which he translates for the reader. Despite the initial popularity of Erewhon, Butler commented in the preface to the second edition that reviewers had "in some cases been inclined to treat the chapters on Machines as an attempt to reduce Mr. Darwin's theory to an absurdity." He protested that "few things would be more distasteful to me than any attempt to laugh at Mr. Darwin", but also added "I am surprised, however, that the book at which such an example of the specious misuse of analogy would seem most naturally levelled should have occurred to no reviewer; neither shall I mention the name of the book here, though I should fancy that the hint given will suffice", which may suggest that the chapter on Machines was in fact a satire intended to illustrate the "specious misuse of analogy", even if the target was not Darwin; Butler, fearing that he had offended Darwin, wrote him a letter explaining that the actual target was Joseph Butler's 1736 The Analogy of Religion, Natural and Revealed, to the Constitution and Course of Nature. The Victorian scholar Herbert Sussman has suggested that although Butler's exploration of machine evolution was intended to be whimsical, he may also have been genuinely interested in the notion that living organisms are a type of mechanism and was exploring this notion with his writings on machines, while the philosopher Louis Flaccus called it "a mixture of fun, satire, and thoughtful speculation." == Evolution of Global Intelligence == George Dyson applies Butler's original premise to the artificial life and intelligence of Alan Turing in Darwin Among the Machines: The Evolution of Global Intelligence (1998) ISBN 0-7382-0030-1, to suggest that the internet is a living, sentient being. Dyson's main claim is that the evolution of a conscious mind from today's technology is inevitable. It is not clear whether this will be a single mind or multiple minds, how smart that mind would be, and even if we will be able to communicate with it. He also clearly suggests that there are forms of intelligence on Earth that we are currently unable to understand. From the book: "What mind, if any, will become apprehensive of the great coiling of ideas now under way is not a meaningless question, but it is still too early in the game to expect an answer that is meaningful to us."

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  T-norm fuzzy logics

  T-norm fuzzy logics are a family of non-classical logics, informally delimited by having a semantics that takes the real unit interval [0, 1] for the system of truth values and functions called t-norms for permissible interpretations of conjunction. They are mainly used in applied fuzzy logic and fuzzy set theory as a theoretical basis for approximate reasoning. T-norm fuzzy logics belong in broader classes of fuzzy logics and many-valued logics. In order to generate a well-behaved implication, the t-norms are usually required to be left-continuous; logics of left-continuous t-norms further belong in the class of substructural logics, among which they are marked with the validity of the law of prelinearity, (A → B) ∨ (B → A). Both propositional and first-order (or higher-order) t-norm fuzzy logics, as well as their expansions by modal and other operators, are studied. Logics that restrict the t-norm semantics to a subset of the real unit interval (for example, finitely valued Łukasiewicz logics) are usually included in the class as well. Important examples of t-norm fuzzy logics are monoidal t-norm logic (MTL) of all left-continuous t-norms, basic logic (BL) of all continuous t-norms, product fuzzy logic of the product t-norm, or the nilpotent minimum logic of the nilpotent minimum t-norm. Some independently motivated logics belong among t-norm fuzzy logics, too, for example Łukasiewicz logic (which is the logic of the Łukasiewicz t-norm) or Gödel–Dummett logic (which is the logic of the minimum t-norm). == Motivation == As members of the family of fuzzy logics, t-norm fuzzy logics primarily aim at generalizing classical two-valued logic by admitting intermediary truth values between 1 (truth) and 0 (falsity) representing degrees of truth of propositions. The degrees are assumed to be real numbers from the unit interval [0, 1]. In propositional t-norm fuzzy logics, propositional connectives are stipulated to be truth-functional, that is, the truth value of a complex proposition formed by a propositional connective from some constituent propositions is a function (called the truth function of the connective) of the truth values of the constituent propositions. The truth functions operate on the set of truth degrees (in the standard semantics, on the [0, 1] interval); thus the truth function of an n-ary propositional connective c is a function Fc: [0, 1]n → [0, 1]. Truth functions generalize truth tables of propositional connectives known from classical logic to operate on the larger system of truth values. T-norm fuzzy logics impose certain natural constraints on the truth function of conjunction. The truth function ∗ : [ 0 , 1 ] 2 → [ 0 , 1 ] {\displaystyle \colon [0,1]^{2}\to [0,1]} of conjunction is assumed to satisfy the following conditions: Commutativity, that is, x ∗ y = y ∗ x {\displaystyle xy=yx} for all x and y in [0, 1]. This expresses the assumption that the order of fuzzy propositions is immaterial in conjunction, even if intermediary truth degrees are admitted. Associativity, that is, ( x ∗ y ) ∗ z = x ∗ ( y ∗ z ) {\displaystyle (xy)z=x(yz)} for all x, y, and z in [0, 1]. This expresses the assumption that the order of performing conjunction is immaterial, even if intermediary truth degrees are admitted. Monotony, that is, if x ≤ y {\displaystyle x\leq y} then x ∗ z ≤ y ∗ z {\displaystyle xz\leq yz} for all x, y, and z in [0, 1]. This expresses the assumption that increasing the truth degree of a conjunct should not decrease the truth degree of the conjunction. Neutrality of 1, that is, 1 ∗ x = x {\displaystyle 1x=x} for all x in [0, 1]. This assumption corresponds to regarding the truth degree 1 as full truth, conjunction with which does not decrease the truth value of the other conjunct. Together with the previous conditions this condition ensures that also 0 ∗ x = 0 {\displaystyle 0x=0} for all x in [0, 1], which corresponds to regarding the truth degree 0 as full falsity, conjunction with which is always fully false. Continuity of the function ∗ {\displaystyle } (the previous conditions reduce this requirement to the continuity in either argument). Informally this expresses the assumption that microscopic changes of the truth degrees of conjuncts should not result in a macroscopic change of the truth degree of their conjunction. This condition, among other things, ensures a good behavior of (residual) implication derived from conjunction; to ensure the good behavior, however, left-continuity (in either argument) of the function ∗ {\displaystyle } is sufficient. In general t-norm fuzzy logics, therefore, only left-continuity of ∗ {\displaystyle } is required, which expresses the assumption that a microscopic decrease of the truth degree of a conjunct should not macroscopically decrease the truth degree of conjunction. These assumptions make the truth function of conjunction a left-continuous t-norm, which explains the name of the family of fuzzy logics (t-norm based). Particular logics of the family can make further assumptions about the behavior of conjunction (for example, Gödel–Dummett logic requires its idempotence) or other connectives (for example, the logic IMTL (involutive monoidal t-norm logic) requires the involutiveness of negation). All left-continuous t-norms ∗ {\displaystyle } have a unique residuum, that is, a binary function ⇒ {\displaystyle \Rightarrow } such that for all x, y, and z in [0, 1], x ∗ y ≤ z {\displaystyle xy\leq z} if and only if x ≤ y ⇒ z . {\displaystyle x\leq y\Rightarrow z.} The residuum of a left-continuous t-norm can explicitly be defined as ( x ⇒ y ) = sup { z ∣ z ∗ x ≤ y } . {\displaystyle (x\Rightarrow y)=\sup\{z\mid zx\leq y\}.} This ensures that the residuum is the pointwise largest function such that for all x and y, x ∗ ( x ⇒ y ) ≤ y . {\displaystyle x(x\Rightarrow y)\leq y.} The latter can be interpreted as a fuzzy version of the modus ponens rule of inference. The residuum of a left-continuous t-norm thus can be characterized as the weakest function that makes the fuzzy modus ponens valid, which makes it a suitable truth function for implication in fuzzy logic. Left-continuity of the t-norm is the necessary and sufficient condition for this relationship between a t-norm conjunction and its residual implication to hold. Truth functions of further propositional connectives can be defined by means of the t-norm and its residuum, for instance the residual negation ¬ x = ( x ⇒ 0 ) {\displaystyle \neg x=(x\Rightarrow 0)} or bi-residual equivalence x ⇔ y = ( x ⇒ y ) ∗ ( y ⇒ x ) . {\displaystyle x\Leftrightarrow y=(x\Rightarrow y)(y\Rightarrow x).} Truth functions of propositional connectives may also be introduced by additional definitions: the most usual ones are the minimum (which plays a role of another conjunctive connective), the maximum (which plays a role of a disjunctive connective), or the Baaz Delta operator, defined in [0, 1] as Δ x = 1 {\displaystyle \Delta x=1} if x = 1 {\displaystyle x=1} and Δ x = 0 {\displaystyle \Delta x=0} otherwise. In this way, a left-continuous t-norm, its residuum, and the truth functions of additional propositional connectives determine the truth values of complex propositional formulae in [0, 1]. Formulae that always evaluate to 1 are called tautologies with respect to the given left-continuous t-norm ∗ , {\displaystyle ,} or ∗ - {\displaystyle {\mbox{-}}} tautologies. The set of all ∗ - {\displaystyle {\mbox{-}}} tautologies is called the logic of the t-norm ∗ , {\displaystyle ,} as these formulae represent the laws of fuzzy logic (determined by the t-norm) that hold (to degree 1) regardless of the truth degrees of atomic formulae. Some formulae are tautologies with respect to a larger class of left-continuous t-norms; the set of such formulae is called the logic of the class. Important t-norm logics are the logics of particular t-norms or classes of t-norms, for example: Łukasiewicz logic is the logic of the Łukasiewicz t-norm x ∗ y = max ( x + y − 1 , 0 ) {\displaystyle xy=\max(x+y-1,0)} Gödel–Dummett logic is the logic of the minimum t-norm x ∗ y = min ( x , y ) {\displaystyle xy=\min(x,y)} Product fuzzy logic is the logic of the product t-norm x ∗ y = x ⋅ y {\displaystyle xy=x\cdot y} Monoidal t-norm logic MTL is the logic of (the class of) all left-continuous t-norms Basic fuzzy logic BL is the logic of (the class of) all continuous t-norms It turns out that many logics of particular t-norms and classes of t-norms are axiomatizable. The completeness theorem of the axiomatic system with respect to the corresponding t-norm semantics on [0, 1] is then called the standard completeness of the logic. Besides the standard real-valued semantics on [0, 1], the logics are sound and complete with respect to general algebraic semantics, formed by suitable classes of prelinear commutative bounded integral residuated lattices. == History == Some particular t-norm fuzzy logics have been introduced and investigated long before the family was re

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  List of Tesla Autopilot crashes

  Tesla Autopilot, a Level 2 advanced driver assistance system (ADAS), was released in October 2015 and the first fatal crashes involving the system occurred less than one year later. The fatal crashes attracted attention from news publications and United States government agencies, including the National Transportation Safety Board (NTSB) and National Highway Traffic Safety Administration (NHTSA), which has argued the Tesla Autopilot death rate is higher than the reported estimates. In addition to fatal crashes, there have been many nonfatal ones. Causes behind the incidents include the ADAS failing to recognize other vehicles, insufficient Autopilot driver engagement, and violating the operational design domain. As of October 2025, there have been hundreds of nonfatal incidents involving versions of Autopilot and sixty-five reported fatalities, fifty-four of which NHTSA investigations or expert testimony later verified and two that NHTSA's Office of Defect Investigations determined as happening during the engagement of Full Self-Driving (FSD) after 2022. Collectively, these cases culminated in a general recall in December 2023 of all vehicles equipped with Autopilot, which Tesla claims it resolved by an over-the-air software update. Immediately after closing its investigation in April 2024, NHTSA opened a recall query to determine the effectiveness of the recall. == Notable fatal crashes == === Handan, Hebei, China (January 20, 2016) === On January 20, 2016, Gao Yaning, the driver of a Tesla Model S in Handan, Hebei, China, was killed when his car crashed into a stationary truck. The Tesla was following a car in the far left lane of a multi-lane highway; the car in front moved to the right lane to avoid a truck stopped on the left shoulder, and the Tesla, which the driver's father believes was in Autopilot mode, did not slow before colliding with the stopped truck. According to footage captured by a dashboard camera, the stationary street sweeper on the left side of the expressway partially extended into the far left lane, and the driver did not appear to respond to the unexpected obstacle. Initially, Yaning was held responsible for the collision by local traffic police and, in September 2016, his family filed a lawsuit in July against the Tesla dealer who sold the car. The family's lawyer stated the suit was intended "to let the public know that self-driving technology has some defects. We are hoping Tesla when marketing its products, will be more cautious. Do not just use self-driving as a selling point for young people." Tesla released a statement which said they "have no way of knowing whether or not Autopilot was engaged at the time of the crash" since the car telemetry could not be retrieved remotely due to damage caused by the crash. In 2018, the lawsuit was stalled because telemetry was recorded locally to a SD card and was not able to be given to Tesla, who provided a decoding key to a third party for independent review. Tesla stated that "while the third-party appraisal is not yet complete, we have no reason to believe that Autopilot on this vehicle ever functioned other than as designed." Chinese media later reported that the family sent the information from that card to Tesla, which admitted Autopilot was engaged two minutes before the crash. Tesla since then removed the term "Autopilot" from its Chinese website. === Williston, Florida, US (May 7, 2016) === On May 7, 2016, Tesla driver Joshua Brown was killed in a crash with an 18-wheel tractor-trailer in Williston, Florida. By late June 2016, the NHTSA opened a formal investigation into the fatal autonomous accident, working with the Florida Highway Patrol. According to the NHTSA, preliminary reports indicate the crash occurred when the tractor-trailer made a left turn in front of the 2015 Tesla Model S at an intersection on a non-controlled access highway, and the car failed to apply the brakes. The car continued to travel after passing under the truck's trailer. The Tesla was eastbound in the rightmost lane of US 27, and the westbound tractor-trailer was turning left at the intersection with NE 140th Court, approximately 1 mi (1.6 km) west of Williston; the posted speed limit is 65 mph (105 km/h). The diagnostic log of the Tesla indicated it was traveling at a speed of 74 mi/h (119 km/h) when it collided with and traveled under the trailer, which was not equipped with a side underrun protection system. A reconstruction of the accident estimated the driver would have had approximately 10.4 seconds to detect the truck and take evasive action. The underride collision sheared off the Tesla's greenhouse, destroying everything above the beltline, and caused fatal injuries to the driver. In the approximately nine seconds after colliding with the trailer, the Tesla traveled another 886.5 feet (270.2 m) and came to rest after colliding with two chain-link fences and a utility pole. The NHTSA's preliminary evaluation was opened to examine the design and performance of any automated driving systems in use at the time of the crash, which involves a population of an estimated 25,000 Model S cars. On July 8, 2016, the NHTSA requested Tesla Inc. to hand over to the agency detailed information about the design, operation and testing of its Autopilot technology. The agency also requested details of all design changes and updates to Autopilot since its introduction, and Tesla's planned updates scheduled for the next four months. According to Tesla, "neither autopilot nor the driver noticed the white side of the tractor-trailer against a brightly lit sky, so the brake was not applied." The car attempted to drive full speed under the trailer, "with the bottom of the trailer impacting the windshield of the Model S". Tesla also stated that this was Tesla's first known Autopilot-related death in over 130 million miles (208 million km) driven by its customers while Autopilot was activated. According to Tesla there is a fatality every 94 million miles (150 million km) among all type of vehicles in the U.S. It is estimated that billions of miles will need to be traveled before Tesla Autopilot can claim to be safer than humans with statistical significance. Researchers say that Tesla and others need to release more data on the limitations and performance of automated driving systems if self-driving cars are to become safe and understood enough for mass-market use. The truck's driver told the Associated Press that he could hear a Harry Potter movie playing in the crashed car, and said the car was driving so quickly that "he went so fast through my trailer I didn't see him. [The film] was still playing when he died and snapped a telephone pole a quarter-mile down the road." According to the Florida Highway Patrol, they found in the wreckage an aftermarket portable DVD player. (It is not possible to watch videos on the Model S touchscreen display while the car is moving.) A laptop computer was recovered during the post-crash examination of the wreck, along with an adjustable vehicle laptop mount attached to the front passenger's seat frame. The NHTSA concluded the laptop was probably mounted, and the driver may have been distracted at the time of the crash. In January 2017, the NHTSA Office of Defects Investigations (ODI) released a preliminary evaluation, finding that the driver in the crash had seven seconds to see the truck and identifying no defects in the Autopilot system; the ODI also found that the Tesla car crash rate dropped by 40 percent after Autosteer installation, but later also clarified that it did not assess the effectiveness of this technology or whether it was engaged in its crash rate comparison. The NHTSA Special Crash Investigation team published its report in January 2018. According to the report, for the drive leading up to the crash, the driver engaged Autopilot for 37 minutes and 26 seconds, and the system provided 13 "hands not detected" alerts, to which the driver responded after an average delay of 16 seconds. The report concluded "Regardless of the operational status of the Tesla's ADAS technologies, the driver was still responsible for maintaining ultimate control of the vehicle. All evidence and data gathered concluded that the driver neglected to maintain complete control of the Tesla leading up to the crash." In July 2016, the NTSB announced it had opened a formal investigation into the fatal accident while Autopilot was engaged. The NTSB is an investigative body that only has the power to make policy recommendations. An agency spokesman said, "It's worth taking a look and seeing what we can learn from that event, so that as that automation is more widely introduced we can do it in the safest way possible." The NTSB opens annually about 25 to 30 highway investigations. In September 2017, the NTSB released its report, determining that "the probable cause of the Williston, Florida, crash was the truck driver's failure to yield the right of way to the car, combine

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  Zero-shot learning

  Zero-shot learning (ZSL) is a problem setup in deep learning where, at test time, a learner observes samples from classes which were not observed during training, and needs to predict the class that they belong to. The name is a play on words based on the earlier concept of one-shot learning, in which classification can be learned from only one, or a few, examples. Zero-shot methods generally work by associating observed and non-observed classes through some form of auxiliary information, which encodes observable distinguishing properties of objects. For example, given a set of images of animals to be classified, along with auxiliary textual descriptions of what animals look like, an artificial intelligence model which has been trained to recognize horses, but has never been given a zebra, can still recognize a zebra when it also knows that zebras look like striped horses. This problem is widely studied in computer vision, natural language processing, and machine perception. == Background and history == The first paper on zero-shot learning in natural language processing appeared in a 2008 paper by Chang, Ratinov, Roth, and Srikumar, at the AAAI'08, but the name given to the learning paradigm there was dataless classification. The first paper on zero-shot learning in computer vision appeared at the same conference, under the name zero-data learning. The term zero-shot learning itself first appeared in the literature in a 2009 paper from Palatucci, Hinton, Pomerleau, and Mitchell at NIPS'09. This terminology was repeated later in another computer vision paper and the term zero-shot learning caught on, as a take-off on one-shot learning that was introduced in computer vision years earlier. In computer vision, zero-shot learning models learned parameters for seen classes along with their class representations and rely on representational similarity among class labels so that, during inference, instances can be classified into new classes. In natural language processing, the key technical direction developed builds on the ability to "understand the labels"—represent the labels in the same semantic space as that of the documents to be classified. This supports the classification of a single example without observing any annotated data, the purest form of zero-shot classification. The original paper made use of the Explicit Semantic Analysis (ESA) representation but later papers made use of other representations, including dense representations. This approach was also extended to multilingual domains, fine entity typing and other problems. Moreover, beyond relying solely on representations, the computational approach has been extended to depend on transfer from other tasks, such as textual entailment and question answering. The original paper also points out that, beyond the ability to classify a single example, when a collection of examples is given, with the assumption that they come from the same distribution, it is possible to bootstrap the performance in a semi-supervised like manner (or transductive learning). Unlike standard generalization in machine learning, where classifiers are expected to correctly classify new samples to classes they have already observed during training, in ZSL, no samples from the classes have been given during training the classifier. It can therefore be viewed as an extreme case of domain adaptation. == Prerequisite information for zero-shot classes == Naturally, some form of auxiliary information has to be given about these zero-shot classes, and this type of information can be of several types. Learning with attributes: classes are accompanied by pre-defined structured description. For example, for bird descriptions, this could include "red head", "long beak". These attributes are often organized in a structured compositional way, and taking that structure into account improves learning. While this approach was used mostly in computer vision, there are some examples for it also in natural language processing. Learning from textual description. As pointed out above, this has been the key direction pursued in natural language processing. Here class labels are taken to have a meaning and are often augmented with definitions or free-text natural-language description. This could include for example a wikipedia description of the class. Class-class similarity. Here, classes are embedded in a continuous space. A zero-shot classifier can predict that a sample corresponds to some position in that space, and the nearest embedded class is used as a predicted class, even if no such samples were observed during training. == Generalized zero-shot learning == The above ZSL setup assumes that at test time, only zero-shot samples are given, namely, samples from new unseen classes. In generalized zero-shot learning, samples from both new and known classes, may appear at test time. This poses new challenges for classifiers at test time, because it is very challenging to estimate if a given sample is new or known. Some approaches to handle this include: a gating module, which is first trained to decide if a given sample comes from a new class or from an old one, and then, at inference time, outputs either a hard decision, or a soft probabilistic decision a generative module, which is trained to generate feature representation of the unseen classes—a standard classifier can then be trained on samples from all classes, seen and unseen. == Domains of application == Zero shot learning has been applied to the following fields: image classification semantic segmentation image generation object detection natural language processing computational biology abstract reasoning

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  Type-1 OWA operators

  Type-1 OWA operators are a set of aggregation operators that generalise the Yager's OWA (ordered weighted averaging) operators in the interest of aggregating fuzzy sets rather than crisp values in soft decision making and data mining. These operators provide a mathematical technique for directly aggregating uncertain information with uncertain weights via OWA mechanism in soft decision making and data mining, where these uncertain objects are modelled by fuzzy sets. The two definitions for type-1 OWA operators are based on Zadeh's Extension Principle and α {\displaystyle \alpha } -cuts of fuzzy sets. The two definitions lead to equivalent results. == Definitions == === Definition 1 === Let F ( X ) {\displaystyle F(X)} be the set of fuzzy sets with domain of discourse X {\displaystyle X} , a type-1 OWA operator is defined as follows: Given n linguistic weights { W i } i = 1 n {\displaystyle \left\{{W^{i}}\right\}_{i=1}^{n}} in the form of fuzzy sets defined on the domain of discourse U = [ 0 , 1 ] {\displaystyle U=[0,1]} , a type-1 OWA operator is a mapping, Φ {\displaystyle \Phi } , Φ : F ( X ) × ⋯ × F ( X ) ⟶ F ( X ) {\displaystyle \Phi \colon F(X)\times \cdots \times F(X)\longrightarrow F(X)} ( A 1 , ⋯ , A n ) ↦ Y {\displaystyle (A^{1},\cdots ,A^{n})\mapsto Y} such that μ Y ( y ) = sup ∑ k = 1 n w ¯ i a σ ( i ) = y ( μ W 1 ( w 1 ) ∧ ⋯ ∧ μ W n ( w n ) ∧ μ A 1 ( a 1 ) ∧ ⋯ ∧ μ A n ( a n ) ) {\displaystyle \mu _{Y}(y)=\displaystyle \sup _{\displaystyle \sum _{k=1}^{n}{\bar {w}}_{i}a_{\sigma (i)}=y}\left({\begin{array}{{1}l}\mu _{W^{1}}(w_{1})\wedge \cdots \wedge \mu _{W^{n}}(w_{n})\wedge \mu _{A^{1}}(a_{1})\wedge \cdots \wedge \mu _{A^{n}}(a_{n})\end{array}}\right)} where w ¯ i = w i ∑ i = 1 n w i {\displaystyle {\bar {w}}_{i}={\frac {w_{i}}{\sum _{i=1}^{n}{w_{i}}}}} , and σ : { 1 , ⋯ , n } ⟶ { 1 , ⋯ , n } {\displaystyle \sigma \colon \{1,\cdots ,n\}\longrightarrow \{1,\cdots ,n\}} is a permutation function such that a σ ( i ) ≥ a σ ( i + 1 ) , ∀ i = 1 , ⋯ , n − 1 {\displaystyle a_{\sigma (i)}\geq a_{\sigma (i+1)},\ \forall i=1,\cdots ,n-1} , i.e., a σ ( i ) {\displaystyle a_{\sigma (i)}} is the i {\displaystyle i} th highest element in the set { a 1 , ⋯ , a n } {\displaystyle \left\{{a_{1},\cdots ,a_{n}}\right\}} . === Definition 2 === Using the alpha-cuts of fuzzy sets: Given the n linguistic weights { W i } i = 1 n {\displaystyle \left\{{W^{i}}\right\}_{i=1}^{n}} in the form of fuzzy sets defined on the domain of discourse U = [ 0 , 1 ] {\displaystyle U=[0,\;\;1]} , then for each α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,\;1]} , an α {\displaystyle \alpha } -level type-1 OWA operator with α {\displaystyle \alpha } -level sets { W α i } i = 1 n {\displaystyle \left\{{W_{\alpha }^{i}}\right\}_{i=1}^{n}} to aggregate the α {\displaystyle \alpha } -cuts of fuzzy sets { A i } i = 1 n {\displaystyle \left\{{A^{i}}\right\}_{i=1}^{n}} is: Φ α ( A α 1 , … , A α n ) = { ∑ i = 1 n w i a σ ( i ) ∑ i = 1 n w i | w i ∈ W α i , a i ∈ A α i , i = 1 , … , n } {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\ldots ,A_{\alpha }^{n}}\right)=\left\{{{\frac {\sum \limits _{i=1}^{n}{w_{i}a_{\sigma (i)}}}{\sum \limits _{i=1}^{n}{w_{i}}}}\left|{w_{i}\in W_{\alpha }^{i},\;a_{i}}\right.\in A_{\alpha }^{i},\;i=1,\ldots ,n}\right\}} where W α i = { w | μ W i ( w ) ≥ α } , A α i = { x | μ A i ( x ) ≥ α } {\displaystyle W_{\alpha }^{i}=\{w|\mu _{W_{i}}(w)\geq \alpha \},A_{\alpha }^{i}=\{x|\mu _{A_{i}}(x)\geq \alpha \}} , and σ : { 1 , ⋯ , n } → { 1 , ⋯ , n } {\displaystyle \sigma :\{\;1,\cdots ,n\;\}\to \{\;1,\cdots ,n\;\}} is a permutation function such that a σ ( i ) ≥ a σ ( i + 1 ) , ∀ i = 1 , ⋯ , n − 1 {\displaystyle a_{\sigma (i)}\geq a_{\sigma (i+1)},\;\forall \;i=1,\cdots ,n-1} , i.e., a σ ( i ) {\displaystyle a_{\sigma (i)}} is the i {\displaystyle i} th largest element in the set { a 1 , ⋯ , a n } {\displaystyle \left\{{a_{1},\cdots ,a_{n}}\right\}} . == Representation theorem of Type-1 OWA operators == Given the n linguistic weights { W i } i = 1 n {\displaystyle \left\{{W^{i}}\right\}_{i=1}^{n}} in the form of fuzzy sets defined on the domain of discourse U = [ 0 , 1 ] {\displaystyle U=[0,\;\;1]} , and the fuzzy sets A 1 , ⋯ , A n {\displaystyle A^{1},\cdots ,A^{n}} , then we have that Y = G {\displaystyle Y=G} where Y {\displaystyle Y} is the aggregation result obtained by Definition 1, and G {\displaystyle G} is the result obtained by in Definition 2. == Programming problems for Type-1 OWA operators == According to the Representation Theorem of Type-1 OWA Operators, a general type-1 OWA operator can be decomposed into a series of α {\displaystyle \alpha } -level type-1 OWA operators. In practice, this series of α {\displaystyle \alpha } -level type-1 OWA operators is used to construct the resulting aggregation fuzzy set. So we only need to compute the left end-points and right end-points of the intervals Φ α ( A α 1 , ⋯ , A α n ) {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)} . Then, the resulting aggregation fuzzy set is constructed with the membership function as follows: μ G ( x ) = ⋁ α : x ∈ Φ α ( A α 1 , ⋯ , A α n ) α ⁡ α {\displaystyle \mu _{G}(x)=\operatorname {\bigvee } \limits _{\alpha :x\in \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)_{\alpha }}\alpha } For the left end-points, we need to solve the following programming problem: Φ α ( A α 1 , ⋯ , A α n ) − = min W α − i ≤ w i ≤ W α + i A α − i ≤ a i ≤ A α + i ⁡ ∑ i = 1 n w i a σ ( i ) / ∑ i = 1 n w i {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)_{-}=\operatorname {\min } \limits _{\begin{array}{l}W_{\alpha -}^{i}\leq w_{i}\leq W_{\alpha +}^{i}A_{\alpha -}^{i}\leq a_{i}\leq A_{\alpha +}^{i}\end{array}}\sum \limits _{i=1}^{n}{w_{i}a_{\sigma (i)}/\sum \limits _{i=1}^{n}{w_{i}}}} while for the right end-points, we need to solve the following programming problem: Φ α ( A α 1 , ⋯ , A α n ) + = max W α − i ≤ w i ≤ W α + i A α − i ≤ a i ≤ A α + i ⁡ ∑ i = 1 n w i a σ ( i ) / ∑ i = 1 n w i {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)_{+}=\operatorname {\max } \limits _{\begin{array}{l}W_{\alpha -}^{i}\leq w_{i}\leq W_{\alpha +}^{i}A_{\alpha -}^{i}\leq a_{i}\leq A_{\alpha +}^{i}\end{array}}\sum \limits _{i=1}^{n}{w_{i}a_{\sigma (i)}/\sum \limits _{i=1}^{n}{w_{i}}}} A fast method has been presented to solve two programming problem so that the type-1 OWA aggregation operation can be performed efficiently, for details, please see the paper. == Alpha-level approach to Type-1 OWA operation == Three-step process: Step 1—To set up the α {\displaystyle \alpha } - level resolution in [0, 1]. Step 2—For each α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,1]} , Step 2.1—To calculate ρ α + i 0 ∗ {\displaystyle \rho _{\alpha +}^{i_{0}^{\ast }}} Let i 0 = 1 {\displaystyle i_{0}=1} ; If ρ α + i 0 ≥ A α + σ ( i 0 ) {\displaystyle \rho _{\alpha +}^{i_{0}}\geq A_{\alpha +}^{\sigma (i_{0})}} , stop, ρ α + i 0 {\displaystyle \rho _{\alpha +}^{i_{0}}} is the solution; otherwise go to Step 2.1-3. i 0 ← i 0 + 1 {\displaystyle i_{0}\leftarrow i_{0}+1} , go to Step 2.1-2. Step 2.2 To calculate ρ α − i 0 ∗ {\displaystyle \rho _{\alpha -}^{i_{0}^{\ast }}} Let i 0 = 1 {\displaystyle i_{0}=1} ; If ρ α − i 0 ≥ A α − σ ( i 0 ) {\displaystyle \rho _{\alpha -}^{i_{0}}\geq A_{\alpha -}^{\sigma (i_{0})}} , stop, ρ α − i 0 {\displaystyle \rho _{\alpha -}^{i_{0}}} is the solution; otherwise go to Step 2.2-3. i 0 ← i 0 + 1 {\displaystyle i_{0}\leftarrow i_{0}+1} , go to step Step 2.2-2. Step 3—To construct the aggregation resulting fuzzy set G {\displaystyle G} based on all the available intervals [ ρ α − i 0 ∗ , ρ α + i 0 ∗ ] {\displaystyle \left[{\rho _{\alpha -}^{i_{0}^{\ast }},\;\rho _{\alpha +}^{i_{0}^{\ast }}}\right]} : μ G ( x ) = ⋁ α : x ∈ [ ρ α − i 0 ∗ , ρ α + i 0 ∗ ] ⁡ α {\displaystyle \mu _{G}(x)=\operatorname {\bigvee } \limits _{\alpha :x\in \left[{\rho _{\alpha -}^{i_{0}^{\ast }},\;\rho _{\alpha +}^{i_{0}^{\ast }}}\right]}\alpha } == Some Examples == The type-1 OWA operator with the weights shown in the top figure is used to aggregate the fuzzy sets (solide lines) in the bottom figure, and the dashed line is the aggregation result. == Special cases == Any OWA operators, like maximum, minimum, mean operators; Join operators of (type-1) fuzzy sets, i.e., fuzzy maximum operators; Meet operators of (type-1) fuzzy sets, i.e., fuzzy minimum operators; Join-like operators of (type-1) fuzzy sets; Meet-like operators of (type-1) fuzzy sets. == Generalizations == Type-2 OWA operators have been suggested to aggregate the type-2 fuzzy sets for soft decision making. == Applications == Type-1 OWA operators have been applied to different domains for soft decision making. Improved efficiency of computing approach ; Type reduction of type-2 fuzzy sets ; Group decision making ; Credit risk evaluation ; Information fusion ; Linguistic expressions and symbolic translation ; Sentiment analysis ; Ro

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  Megami Tensei

  Megami Tensei, marketed internationally as Shin Megami Tensei (formerly Revelations), is a Japanese media franchise created by Aya Nishitani, Kouji "Cozy" Okada, Ginichiro Suzuki, and Kazunari Suzuki. Primarily developed and published by Atlus, the franchise consists of multiple subseries and covers multiple role-playing video game genres including tactical role-playing, action role-playing, and massively multiplayer online role-playing. The first two titles in the series were published by Namco (now Bandai Namco Entertainment), but have been almost always published by Atlus in Japan and North America since the release of Shin Megami Tensei. For Europe, Atlus publishes the games through third-party companies. The series was originally based on Digital Devil Story, a science fiction novel series by Aya Nishitani. The series takes its name from the first book's subtitle. Most Megami Tensei titles are stand-alone entries with their own stories and characters. Recurring elements include plot themes, a story shaped by the player's choices, and the ability to fight using and often recruit creatures (demons, Personas) to aid the player in battle. Elements of philosophy, religion, occultism, and science fiction have all been incorporated into the series at different times. While not maintaining as high a profile as series such as Final Fantasy and Dragon Quest, it is highly popular in Japan and maintains a strong cult following in the West, finding critical and commercial success. The series has become well known for its artistic direction, challenging gameplay, and music, but raised controversy over its mature content, dark themes, and use of Christian religious imagery. Additional media include manga adaptations, anime films, and television series. In Japan, some games in the series do not use the "Megami Tensei" title, such as the Persona sub-series. Many of the early games in the series were not localized due to potentially controversial content including religious references, and later due to their age. English localizations have used the "Shin Megami Tensei" moniker since the release of Shin Megami Tensei: Nocturne in 2004. == Titles == === Games === The first installment in the franchise, Digital Devil Story: Megami Tensei, was released on September 11, 1987. The following entries have nearly always been unrelated to each other except in carrying over thematic and gameplay elements. The Megami Tensei games, and the later Shin Megami Tensei titles form the core of the series, while other subseries such as Persona, Devil Children, and Devil Summoner are spin-offs marketed as part of the franchise. There are also stand-alone spin-off titles. ==== Main series ==== Two entries were released for the Famicom: Digital Devil Story: Megami Tensei in 1987, and Digital Devil Story: Megami Tensei II in 1990. The two titles are unrelated to each other in terms of story, and each introduced the basic gameplay and story mechanics that would come to define the series. Three entries were released for the Super Famicom: Shin Megami Tensei in 1992, followed byShin Megami Tensei II in 1994, and Shin Megami Tensei If..., released later in the same year. Shin Megami Tensei III: Nocturne was released in 2003 for the PlayStation 2. Its Maniax Edition director's cut was released in Japan and North America in 2004, and in Europe in 2005. The numeral was dropped for its North American release, and its title changed to Shin Megami Tensei: Lucifer's Call in Europe. Shin Megami Tensei IV for the Nintendo 3DS was released in 2013 in Japan and North America, and a year later in Europe as a digital-only release. Another game set in the same universe, Shin Megami Tensei IV: Apocalypse, was released for the 3DS in February 2016 in Japan. Shin Megami Tensei V was released on the Nintendo Switch in 2021. An enhanced version of the game titled Shin Megami Tensei V: Vengeance was released in June 2024 for Microsoft Windows, Nintendo Switch, PlayStation 4, PlayStation 5, Xbox One and Xbox Series X/S. In addition to the main series, there are also numerous spin-offs. Shin Megami Tensei: Nine, was released for the Xbox in 2002. Originally designed as a massively multiplayer online role-playing game (MMORPG), it was later split into a dual single-player and multiplayer package, and the single-player version released first. The online version was delayed and eventually cancelled as the developers could not manage the required online capacities using Xbox Live. Shin Megami Tensei: Imagine, a true MMOROG released for Microsoft Windows, was released in 2007 in Japan, 2008 in North America, and 2009 in Europe. Western service was terminated in 2014 when Marvelous USA, the game's then-handlers, shut down their PC Online game department. Shin Megami Tensei: Strange Journey was released for the Nintendo DS in 2009 in Japan and 2010 in North America. Its Japanese service ended in May 2016. A smartphone game, Shin Megami Tensei: Liberation Dx2, was released in 2018. ==== Persona ==== The Persona series is the largest and most popular spin-off from the Megami Tensei series. The first entry in the series, Megami Ibunroku Persona (originally released overseas as Revelations: Persona), was released in 1996 in Japan and North America. The first Persona 2 title, Innocent Sin, was released in 1999 in Japan. The second game, Eternal Punishment, was released in 2000 in Japan and North America. Persona 3 was released in 2006 in Japan, 2007 in North America, and 2008 in Europe. Its sequel, Persona 4, was released in 2008 in Japan and North America, and in 2009 in Europe. A sixth entry in the series, Persona 5, was released in Japan on September 15, 2016, and was released in North America and Europe on April 4, 2017, to critical acclaim. The series also features spin-offs, including Persona Q: Shadow of the Labyrinth and Persona Q2: New Cinema Labyrinth, two fighting games Persona 4 Arena and its sequel Arena Ultimax as well as the crossover fighting game BlazBlue: Cross Tag Battle, tactical role-playing game Persona 5 Tactica, action role-playing game Persona 5 Strikers and rhythm games Persona 4: Dancing All Night, Persona 3: Dancing in Moonlight, and Persona 5: Dancing in Starlight. While Persona 3 and 4 used the Shin Megami Tensei moniker in the West, it was dropped for the Persona 4 Arena duology and Persona 4 Golden as it would have made the titles too long to be practical. ==== Devil Summoner ==== The Devil Summoner subseries began in 1995 with the release of Shin Megami Tensei: Devil Summoner. It was followed by Devil Summoner: Soul Hackers in 1997, then followed by Soul Hackers 2, released in 2022. Two action role-playing prequels set in 1920s Tokyo were also developed, which revolve around demon summoner Raidou Kuzunoha: Raidou Kuzunoha vs. the Soulless Army was released in 2006, and Raidou Kuzunoha vs. King Abaddon was released in 2008. ==== Other spin-offs ==== Aside from Persona and Devil Summoner, there are other spin-off series covering multiple genres. After the release of Shin Megami Tensei II, Atlus began focusing work on building spin-offs and subseries that would form part of the Megami Tensei franchise. Shortly after Nocturne's release, a duology titled Digital Devil Saga (Digital Devil Saga: Avatar Tuner in Japan) was created based around similar systems to Nocturne, and was also intended as a more accessible gaming experience. Two tactical role-playing games have been developed by Atlus for the DS under the Devil Survivor moniker: the original Devil Survivor and Devil Survivor 2. Both have received expanded ports for the 3DS. Other subseries include Last Bible, a series aimed at a younger audience and using a pure fantasy setting; Devil Children, which was inspired by the popular Pokémon series; and Majin Tensei, a series of strategy games. Two notable stand-alone spin-offs are action spin-off Jack Bros. and Tokyo Mirage Sessions ♯FE, a crossover with Intelligent Systems' Fire Emblem series. === Related media === Several titles in the franchise have received anime and manga adaptations. Persona 3 received both a four-part theatrical adaptation (#1 Spring of Birth, #2 Midsummer Knight's Dream, #3 Falling Down, #4 Winter of Rebirth), and a spin-off series titled Persona: Trinity Soul. Persona 4 received two adaptations: Persona 4: The Animation, based on the original game, and Persona 4: The Golden Animation, based on its expanded PlayStation Vita port. A live-action television series based on the original Devil Summoner was broadcast between 1997 and 1998. Devil Survivor 2 also received an anime adaptation of the same name, and the Devil Children series received two anime adaptations. Multiple Shin Megami Tensei and Persona titles have received manga and CD drama adaptations. Action figures and merchandise related to Persona have also been produced. == Common elements == Despite most games in the series taking place in different continuities, they do share certain elements

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