AI Data Center Texas

AI Data Center Texas — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  1 Second Everyday

  1 Second Everyday (1SE) is an application developed by Cesar Kuriyama. The application allows the user to record one second of video every day and then chronologically edits (mashes) them together into a single film. It is compatible with iOS and Android. The idea of the application was developed by Kuriyama's 1 Second Everyday — Age 30 video. The application was launched in January 2013. 1 Second Everyday played a part in the plot of Chef and also became the inspiration for the 2014 short animated clip Feast. == Background == === Kuriyama's video === In February 2011, when Cesar Kuriyama turned 30, after saving money, he quit his job in an advertising firm and took a year off to travel. During this time, he started working on a project he called 1 Second Everyday. As part of the project, every day he recorded one second of video – something that was supposed to help him remember that day. He started the project because he was frustrated with his memory. He planned to stockpile the 365 one-second clips into one film to serve as a memento of his year. While working on the project Kuriyama realized that recording one second every day impacted the decisions he made in a positive way. After a year he made a 365-second clip out of his recordings. The video called 1 Second Everyday – Age 30, went viral. According to Kuriyama, he was initially inspired to take a year off from work by a TED talk given by Stefan Sagmeister called "The Power of Time Off." Kuriyama also delivered a TED talk about 1 Second Everyday in 2012 at TED 2012 in Long Beach California. === Kickstarter campaign === After completing his own video, Kuriyama decided to develop an application that would allow the users to record one second every day and compile their own videos. He developed a prototype of the application and then in 2012, he launched a Kickstarter campaign to raise funds for completing the application. The campaign became one of the most backed app campaigns in the history of Kickstarter. It was backed by 11,281 backers who pledged a total of $56,959 on an initial goal of $20,000. Following the completion of the Kickstarter campaign, he partnered with an application design studio in Brooklyn to develop the application. 1 Second Everyday was released two weeks after the completion of its Kickstarter campaign. == Application == The application was released for iOS on 10 January 2013. An Android-compatible version of the application was developed later. Using it, the user can record the videos in the application or they can select one second portions from their libraries. 1 Second Everyday dates every snippet. The user can also set alarms to remember to record their daily video. In order to compile a video, the user selects the seconds they want and the application creates a compilation video. The user can keep multiple timelines. It also allows users to post directly on social networks. The main interface in 1 Second Everyday is a calendar, which shows the user which days have snippets and which they can still fill in. In the beginning, 1 Second Everyday restricted the recording to one second. However, the developers later released Super Seconds, which allowed users to record an additional half a second video. In 2014, 1 Second Everyday Crowds was launched, which is an area in the application featuring compilations of second clips from different users. == In the media == The Kickstarter campaign of 1 Second Everyday was featured in Entrepreneur's 3 Innovative Tech Startups on Kickstarter Right Now in 2012. The application was featured in The New York Times, The Washington Post, Gawker and other media outlets. By the end of the launch day, it was in Top 10 Free Apps on App Store. It was also selected as the App of the Week on GeekWire in 2013. Several other one-second compilation videos were also posted on the Internet after Kuriyama's video gained media attention. Sam Cornwell, an English photographer documented his son Indigo's growth using a montage of one-second iPhone clips. He shot these clips every single day from the moment of birth right up to the baby's first birthday. According to Cornwell, he was inspired by Kuriyama's project. The video of Cornwell's son gained considerable media attention after it was posted on YouTube. Save the Children also made a video commercial based on a similar format that showed a British girl oblivious of the Syrian war end up being a refugee. 1SE was a finalist for the Fast Company Innovation by Design Award in 2015, but lost to Google Maps. In 2015, Google Android created a gallery, Leap Second 2015, with the help of Droga5 and Kuriyama. The gallery showcased how people around the world enjoyed the one extra second of their lives. Through the 1 Second Everyday app available at Google Play, people were able to submit their extra second, which were then vetted and added to the gallery. The viewers were able to view other celebratory seconds from around the world as well as searching for them using different hashtags.

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  The Old Axolotl

  The Old Axolotl (Polish: Starość aksolotla) is a 2015 digital-only novel by Polish science-fiction author Jacek Dukaj. The novel was released in Polish on March 10, 2015, and shortly afterward, on March 24 that year, in English (translated by Stanley Bill). It has been described as "an experiment in reading (and creating) the electronic literature of the future". It is Dukaj's first novel to be published in English, though several of his short stories (The Golden Galley, 1996, The Iron General, 2010, The Apocrypha of Lem, 2011) have been translated prior to this. The novel has inspired two Netflix original series: the 2020 Belgian Into the Night, and its 2022 Turkish language spin-off Yakamoz S-245. == Plot == The novel presents a post-apocalyptic, cyberpunk vision of Earth where biological life has been wiped out, inhabited by robots and mechs, many of which are humans whose consciousness has been digitized in the wake of an extinction event. == Significance and analysis == The novel is an example of electronic literature, available only in digital formats, and has no traditional paper version. It was designed from the beginning not only to incorporate more traditional elements such as illustrations, but also hypertext, and 3D-printable models of main robotic characters designed by Alex Jaeger, the art director of Transformers films. The novel composition is layered, with the narrative layer, an encyclopedic/hyperlinked footnote layer, and a multimedia layer, including illustrations and a short promotional video by the Oscar-nominated Platige Image studio. One of the novel's central questions is: "What does it mean to be human?" Other subjects include post humanism and other "staples of cyberpunk and related genres, such as the artificial intelligence". The novel is representative of Dukaj's prose, posing philosophical questions about the future of man and technology. The author explained that: "stories such as The Old Axolotl that model an ‘escape from the body’ are born out of a sense of progress as a process of ‘de-animalising’ human beings through science. This has its origin in the pre-Enlightenment intuition of ‘liberation from nature’. For one of the last shackles of nature is corporeality itself, the limitations of our physicality." The other major element of the novel is Dukaj's attempts to introduce the reader to the new style of electronic literature. The novel was nominated for the 2016 Janusz A. Zajdel Award.

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  SciGraph

  SciGraph was a search engine tool developed by Springer Nature, the former URL was https://scigraph.springernature.com/explorer. The technology, which was considered a Linked Open Data (LOD) platform, collects information that covers the research landscape, which includes research projects, publications, conferences, funding agencies, and others. Key features of the platform include the detailed semantic description of the relationship of information and the visualization of the scholarly domain. It was launched in 2017 and retired in 2023. == Development == The development of SciGraph began with an initiative to create a platform that will host Springer Nature's entire publication archive, which cover texts published as early as 1815. The number of these resources is reported to be about 13 million. The technology behind the platform was built on earlier Springer Nature projects developed for the purpose of collecting information on the research landscape. The first SciGraph data set was published in February 2017. The platform was launched in March 2017 and significantly expanded with the addition of publications of key partners. The datasets span a broad range of topics, which include computer science, medicine, life sciences, chemistry, engineering, and astronomy, among others. The developers also plan to include citations, patents, and clinical trials in the future. == Technology == SciGraph constitutes 1.5 to 2 billion triples where a triple is formatted as "subject-predicate-object" and could link any subject or concept through a predicate (verb) to another object, demonstrating the type of relationship that exists between them. Its graph structure is used by other academic search engines such as Semantic Scholar. SciGraph collects data from Springer Nature and its partners from the scholarly domain as well as funders, research projects, conferences, affiliations, and publications. The collected information serves as rich semantic description of how information is related and it also provides a visualization of the scholarly domain. The platform has been considered the only large-scale dataset that reconciles authors' affiliations through the disambiguation and linking with external authoritative datasets according to institutions.

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  Adaptive neuro fuzzy inference system

  An adaptive neuro-fuzzy inference system or adaptive network-based fuzzy inference system (ANFIS) is a kind of artificial neural network that is based on Takagi–Sugeno fuzzy inference system, a class of fuzzy models introduced by Tomohiro Takagi and Michio Sugeno for system identification and control. The technique was developed in the early 1990s. Since it integrates both neural networks and fuzzy logic principles, it has potential to capture the benefits of both in a single framework. Its inference system corresponds to a set of fuzzy IF–THEN rules that have learning capability to approximate nonlinear functions. Hence, ANFIS is considered to be a universal estimator. For using the ANFIS in a more efficient and optimal way, one can use the best parameters obtained by genetic algorithm. It has uses in intelligent situational aware energy management system. == ANFIS architecture == It is possible to identify two parts in the network structure, namely premise and consequence parts. In more details, the architecture is composed by five layers. The first layer takes the input values and determines the membership functions belonging to them. It is commonly called fuzzification layer. The membership degrees of each function are computed by using the premise parameter set, namely {a,b,c}. The second layer is responsible of generating the firing strengths for the rules. Due to its task, the second layer is denoted as "rule layer". The role of the third layer is to normalize the computed firing strengths, by dividing each value for the total firing strength. The fourth layer takes as input the normalized values and the consequence parameter set {p,q,r}. The values returned by this layer are the defuzzificated ones and those values are passed to the last layer to return the final output. === Fuzzification layer === The first layer of an ANFIS network describes the difference to a vanilla neural network. Neural networks in general are operating with a data pre-processing step, in which the features are converted into normalized values between 0 and 1. An ANFIS neural network doesn't need a sigmoid function, but it's doing the preprocessing step by converting numeric values into fuzzy values. Here is an example: Suppose, the network gets as input the distance between two points in the 2d space. The distance is measured in pixels and it can have values from 0 up to 500 pixels. Converting the numerical values into fuzzy numbers is done with the membership function which consists of semantic descriptions like near, middle and far. Each possible linguistic value is given by an individual neuron. The neuron “near” fires with a value from 0 until 1, if the distance is located within the category "near". While the neuron “middle” fires, if the distance in that category. The input value “distance in pixels” is split into three different neurons for near, middle and far.

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  Test data management

  Test data management (TDM) is a process in software testing concerned with the creation, preparation, and control of data used for testing software systems. It involves supplying datasets required to execute test cases and verifying system behaviour under defined conditions. Test data management is an integral part of the software development lifecycle (SDLC) and is utilized in both manual and automated testing processes. It is applied in environments that use continuous integration and DevOps practices, where test execution requires consistent and repeatable data conditions. == Overview == Test data management includes the generation, selection, and preparation of data for testing purposes, as well as its distribution across test environments. It also involves controlling data versions and ensuring that datasets correspond to specific test scenarios. In many cases, production data is adapted for testing through techniques such as masking or subsetting to reduce size and remove sensitive content. Test data management ensures that test cases are executed with relevant, consistent, and readily available data. This reduces variability in test results and supports reproducibility across test cycles. == Importance == The role of test data management has expanded with the growth of complex, data-driven systems and regulatory requirements governing data usage. Testing often depends on data that reflects real-world conditions, but direct use of production data may introduce security and privacy risks. As a result, organizations apply methods such as data masking and anonymization to meet compliance requirements, including those set by the California Privacy Rights Act (CPRA) and Europe’s General Data Protection Regulation (GDPR). Inadequate control of test data can lead to incomplete test coverage, unreliable test results, or delays in testing processes due to unavailable or inconsistent datasets. == Techniques and tools == Test data management leverages various techniques for preparing and controlling data used in testing. These include the generation of synthetic data, the extraction of subsets from production datasets, and the modification of data to remove or obscure sensitive information. A key technical requirement in these processes is maintaining referential integrity, or ensuring that relationships between data entities remain consistent across different tables and systems after masking or subsetting. Data virtualization is also used to provide access to datasets without full replication. These methods may be implemented using software tools that automate data preparation, masking, and distribution.

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  AI-assisted targeting in the Gaza Strip

  As part of the Gaza war, the Israel Defense Forces (IDF) have used artificial intelligence to rapidly and automatically perform much of the process of determining what to bomb. Israel has greatly expanded the bombing of the Gaza Strip, which in previous wars had been limited by the Israeli Air Force running out of targets. These tools include the Gospel, an AI which automatically reviews surveillance data looking for buildings, equipment and people thought to belong to the enemy, and upon finding them, recommends bombing targets to a human analyst who may then decide whether to pass it along to the field. Another is Lavender, an "AI-powered database" which lists tens of thousands of Palestinian men linked by AI to Hamas or Palestinian Islamic Jihad, and which is also used for target recommendation. Critics have argued the use of these AI tools puts civilians at risk, blurs accountability, and results in militarily disproportionate violence in violation of international humanitarian law. == The Gospel == Israel uses an AI system dubbed "Habsora", "the Gospel", to determine which targets the Israeli Air Force would bomb. It automatically provides a targeting recommendation to a human analyst, who decides whether to pass it along to soldiers in the field. The recommendations can be anything from individual fighters, rocket launchers, Hamas command posts, to private homes of suspected Hamas or Islamic Jihad members. AI can process military intelligence far faster than humans. Retired Lt Gen. Aviv Kohavi, head of the IDF until 2023, stated that the system could produce 100 bombing targets in Gaza a day, with real-time recommendations which ones to attack, where human analysts might produce 50 a year. A lecturer interviewed by NPR estimated these figures as 50–100 targets in 300 days for 20 intelligence officers, and 200 targets within 10–12 days for the Gospel. === Technological background === The Gospel uses machine learning, where an AI is tasked with identifying commonalities in vast amounts of data (e.g. scans of cancerous tissue, photos of a facial expression, surveillance of Hamas members identified by human analysts), then looking for those commonalities in new material. What information the Gospel uses is not known, but it is thought to combine surveillance data from diverse sources in enormous amounts. Recommendations are based on pattern-matching. A person with enough similarities to other people labeled as enemy combatants may be labelled a combatant themselves. Regarding the suitability of AIs for the task, NPR cited Heidy Khlaaf, engineering director of AI Assurance at the technology security firm Trail of Bits, as saying "AI algorithms are notoriously flawed with high error rates observed across applications that require precision, accuracy, and safety." Bianca Baggiarini, lecturer at the Australian National University's Strategic and Defence Studies Centre wrote AIs are "more effective in predictable environments where concepts are objective, reasonably stable, and internally consistent." She contrasted this with telling the difference between a combatant and non-combatant, which even humans frequently can't do. Khlaaf went on to point out that such a system's decisions depend entirely on the data it's trained on, and are not based on reasoning, factual evidence or causation, but solely on statistical probability. === Operation === The IAF ran out of targets to strike in the 2014 war and 2021 crisis. In an interview on France 24, investigative journalist Yuval Abraham of +972 Magazine stated that to maintain military pressure, and due to political pressure to continue the war, the military would bomb the same places twice. Since then, the integration of AI tools has significantly sped up the selection of targets. In early November, the IDF stated more than 12,000 targets in Gaza had been identified by the target administration division that uses the Gospel. NPR wrote on December 14 that it was unclear how many targets from the Gospel had been acted upon, but that the Israeli military said it was currently striking as many as 250 targets a day. The bombing, too, has intensified to what the December 14 article called an astonishing pace: the Israeli military stated at the time it had struck more than 22,000 targets inside Gaza, at a daily rate more than double that of the 2021 conflict, more than 3,500 of them since the collapse of the truce on December 1. Early in the offensive the head of the Air Force stated his forces only struck military targets, but added: "We are not being surgical." Once a recommendation is accepted, another AI, Fire Factory, cuts assembling the attack down from hours to minutes by calculating munition loads, prioritizing and assigning targets to aircraft and drones, and proposing a schedule, according to a pre-war Bloomberg article that described such AI tools as tailored for a military confrontation and proxy war with Iran. One change that The Guardian noted is that since senior Hamas leaders disappear into tunnels at the start of an offensive, systems such as the Gospel have allowed the IDF to locate and attack a much larger pool of more junior Hamas operatives. It cited an official who worked on targeting decisions in previous Gaza operations as saying that while the homes of junior Hamas members had previously not been targeted for bombing, the official believes the houses of suspected Hamas operatives were now targeted regardless of rank. In the France 24 interview, Abraham, of +972 Magazine, characterized this as enabling the systematization of dropping a 2000 lb bomb into a home to kill one person and everybody around them, something that had previously been done to a very small group of senior Hamas leaders. NPR cited a report by +972 Magazine and its sister publication Local Call as asserting the system is being used to manufacture targets so that Israeli military forces can continue to bombard Gaza at an enormous rate, punishing the general Palestinian population. NPR noted it had not verified this; it was unclear how many targets are being generated by AI alone, but there had been a substantial increase in targeting, with an enormous civilian toll. In principle, the combination of a computer's speed to identify opportunities and a human's judgment to evaluate them can enable more precise attacks and fewer civilian casualties. Israeli military and media have emphasized this capacity to minimize harm to non-combatants. Richard Moyes, researcher and head of the NGO Article 36, pointed to "the widespread flattening of an urban area with heavy explosive weapons" to question these claims, while Lucy Suchman, professor emeritus at Lancaster University, described the bombing as "aimed at maximum devastation of the Gaza Strip". The Guardian wrote that when a strike was authorized on private homes of those identified as Hamas or Islamic Jihad operatives, target researchers knew in advance the expected number of civilians killed, each target had a file containing a collateral damage score stipulating how many civilians were likely to be killed in a strike, and according to a senior Israeli military source, operatives use a "very accurate" measurement of the rate of civilians evacuating a building shortly before a strike. "We use an algorithm to evaluate how many civilians are remaining. It gives us a green, yellow, red, like a traffic signal." ==== 2021 use ==== Kohavi compared the target division using the Gospel to a machine and stated that once the machine was activated in the war of May 2021, it generated 100 targets a day, with half of them being attacked, in contrast with 50 targets in Gaza per year beforehand. Approximately 200 targets came from the Gospel out of the 1,500 targets Israel struck in Gaza in the war, including both static and moving targets according to the military. The Jewish Institute for National Security of America's after action report identified an issue, stating the system had data on what was a target, but lacked data on what wasn't. The system depends entirely on training data, and intel that human analysts had examined and deemed didn't constitute a target had been discarded, risking bias. The vice president expressed his hopes this had since been rectified. === Organization === The Gospel is used by the military's target administration division (or Directorate of Targets or Targeting Directorate), which was formed in 2019 in the IDF's intelligence directorate to address the air force running out of targets to bomb, and which Kohavi described as "powered by AI capabilities" and including hundreds of officers of soldiers. In addition to its wartime role, The Guardian wrote it'd helped the IDF build a database of between 30,000 and 40,000 suspected militants in recent years, and that systems such as the Gospel had played a critical role in building lists of individuals authorized to be assassinated. The Gospel was developed by Unit 8200 of the Israeli Intelligence C

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  Residuated Boolean algebra

  In mathematics, a residuated Boolean algebra is a residuated lattice whose lattice structure is that of a Boolean algebra. Examples include Boolean algebras with the monoid taken to be conjunction, the set of all formal languages over a given alphabet Σ {\displaystyle \Sigma } under concatenation, the set of all binary relations on a given set X {\displaystyle X} under relational composition, and more generally the power set of any equivalence relation, again under relational composition. The original application was to relation algebras as a finitely axiomatized generalization of the binary relation example, but there exist interesting examples of residuated Boolean algebras that are not relation algebras, such as the language example. == Definition == A residuated Boolean algebra is an algebraic structure ( L , ∧ , ∨ , ¬ , 0 , 1 , ∙ , I , / , ∖ ) {\displaystyle (L,\wedge ,\vee ,\neg ,0,1,\bullet ,\mathbf {I} ,/,\backslash )} such that An equivalent signature better suited to the relation algebra application is ( L , ∧ , ∨ , ¬ , 0 , 1 , ∙ , I , ▹ , ◃ ) {\displaystyle (L,\wedge ,\vee ,\neg ,0,1,\bullet ,\mathbf {I} ,\triangleright ,\triangleleft )} where the unary operations x ∖ {\displaystyle x\backslash } and x ▹ {\displaystyle x\triangleright } are intertranslatable in the manner of De Morgan's laws via x ∖ y = ¬ ( x ▹ ¬ y ) {\displaystyle x\backslash y=\neg (x\triangleright \neg y)} , x ▹ y = ¬ ( x ∖ ¬ y ) {\displaystyle x\triangleright y=\neg (x\backslash \neg y)} , and dually / y {\displaystyle /y} and ◃ y {\displaystyle \triangleleft y} as x / y = ¬ ( ¬ x ◃ y ) {\displaystyle x/y=\neg (\neg x\triangleleft y)} , x ◃ y = ¬ ( ¬ x / y ) {\displaystyle x\triangleleft y=\neg (\neg x/y)} , with the residuation axioms in the residuated lattice article reorganized accordingly (replacing z {\displaystyle z} by ¬ z {\displaystyle \neg z} ) to read ( x ▹ z ) ∧ y = 0 ⇔ ( x ∙ y ) ∧ z = 0 ⇔ ( z ◃ y ) ∧ x = 0 {\displaystyle (x\triangleright z)\wedge y=0\ \Leftrightarrow \ (x\bullet y)\wedge z=0\ \Leftrightarrow \ (z\triangleleft y)\wedge x=0} This De Morgan dual reformulation is motivated and discussed in more detail in the section below on conjugacy. Since residuated lattices and Boolean algebras are each definable with finitely many equations, so are residuated Boolean algebras, whence they form a finitely axiomatizable variety. == Examples == Any Boolean algebra, with the monoid multiplication ∙ {\displaystyle \bullet } taken to be conjunction and both residuals taken to be material implication x → y {\displaystyle x\to y} . Of the remaining 15 binary Boolean operations that might be considered in place of conjunction for the monoid multiplication, only five meet the monotonicity requirement, namely 0 , 1 , x , y {\displaystyle 0,1,x,y} and x ∨ y {\displaystyle x\vee y} . Setting y = z = 0 {\displaystyle y=z=0} in the residuation axiom y ≤ x ∖ z ⇔ x ∙ y ≤ z {\displaystyle y\leq x\backslash z\ \Leftrightarrow \ x\bullet y\leq z} , we have 0 ≤ x ∖ 0 ⇔ x ∙ 0 ≤ 0 {\displaystyle 0\leq x\backslash 0\ \Leftrightarrow \ x\bullet 0\leq 0} , which is falsified by taking x = 1 {\displaystyle x=1} when x ∙ y = 1 {\displaystyle x\bullet y=1} , x {\displaystyle x} , or x ∨ y {\displaystyle x\vee y} . The dual argument for z / y {\displaystyle z/y} rules out x ∙ y = y {\displaystyle x\bullet y=y} . This just leaves x ∙ y = 0 {\displaystyle x\bullet y=0} (a constant binary operation independent of x {\displaystyle x} and y {\displaystyle y} ), which satisfies almost all the axioms when the residuals are both taken to be the constant operation x / y = x ∖ y = 1 {\displaystyle x/y=x\backslash y=1} . The axiom it fails is x ∙ I = x = I ∙ x {\displaystyle x\bullet \mathbf {I} =x=\mathbf {I} \bullet x} , for want of a suitable value for I {\displaystyle \mathbf {I} } . Hence conjunction is the only binary Boolean operation making the monoid multiplication that of a residuated Boolean algebra. The power set 2 X 2 {\displaystyle 2^{X^{2}}} made a Boolean algebra as usual with ∩ {\displaystyle \cap } , ∪ {\displaystyle \cup } and complement relative to X 2 {\displaystyle X^{2}} , and made a monoid with relational composition. The monoid unit I {\displaystyle \mathbf {I} } is the identity relation { ( x , x ) | x ∈ X } {\displaystyle \{(x,x)|x\in X\}} . The right residual R ∖ S {\displaystyle R\backslash S} is defined by x ( R ∖ S ) y ⇔ ∀ z ∈ X , z R x ⇒ z S y {\displaystyle x(R\backslash S)y\ \Leftrightarrow \ \forall z\in X,zRx\Rightarrow zSy} . Dually the left residual S / R {\displaystyle S/R} is defined by y ( S / R ) x ⇔ ∀ z ∈ X , x R z ⇒ y S z {\displaystyle y(S/R)x\ \Leftrightarrow \ \forall z\in X,xRz\Rightarrow ySz} . The power set 2 Σ ∗ {\displaystyle 2^{\Sigma ^{}}} made a Boolean algebra as for Example 2, but with language concatenation for the monoid. Here the set Σ {\displaystyle \Sigma } is used as an alphabet while Σ ∗ {\displaystyle \Sigma ^{}} denotes the set of all finite (including empty) words over that alphabet. The concatenation L M {\displaystyle LM} of languages L {\displaystyle L} and M {\displaystyle M} consists of all words u v {\displaystyle uv} such that u ∈ L {\displaystyle u\in L} and v ∈ M {\displaystyle v\in M} . The monoid unit is the language { ε } {\displaystyle \{\varepsilon \}} consisting of just the empty word ε {\displaystyle \varepsilon } . The right residual M ∖ L {\displaystyle M\backslash L} consists of all words w {\displaystyle w} over Σ {\displaystyle \Sigma } such that M w ⊆ L {\displaystyle Mw\subseteq L} . The left residual L / M {\displaystyle L/M} is the same with w M {\displaystyle wM} in place of M w {\displaystyle Mw} . == Conjugacy == The De Morgan duals ▹ {\displaystyle \triangleright } and ◃ {\displaystyle \triangleleft } of residuation arise as follows. Among residuated lattices, Boolean algebras are special by virtue of having a complementation operation ¬ {\displaystyle \neg } . This permits an alternative expression of the three inequalities y ≤ x ∖ z ⇔ x ∙ y ≤ z ⇔ x ≤ z / y {\displaystyle y\leq x\backslash z\ \Leftrightarrow \ x\bullet y\leq z\ \Leftrightarrow \ x\leq z/y} in the axiomatization of the two residuals in terms of disjointness, via the equivalence x ≤ y ⇔ x ∧ ¬ y = 0 {\displaystyle x\leq y\ \Leftrightarrow \ x\wedge \neg y=0} . Abbreviating x ∧ y = 0 {\displaystyle x\wedge y=0} to x # y {\displaystyle x\#y} as the expression of their disjointness, and substituting ¬ z {\displaystyle \neg z} for z {\displaystyle z} in the axioms, they become with a little Boolean manipulation ¬ ( x ∖ ¬ z ) # y ⇔ x ∙ y # z ⇔ ¬ ( ¬ z / y ) # x {\displaystyle \neg (x\backslash \neg z)\#y\ \Leftrightarrow \ x\bullet y\#z\ \Leftrightarrow \ \neg (\neg z/y)\#x} Now ¬ ( x ∖ ¬ z ) {\displaystyle \neg (x\backslash \neg z)} is reminiscent of De Morgan duality, suggesting that x ∖ {\displaystyle x\backslash } be thought of as a unary operation f {\displaystyle f} , defined by f ( y ) = x ∖ y {\displaystyle f(y)=x\backslash y} , that has a De Morgan dual ¬ f ( ¬ y ) {\displaystyle \neg f(\neg y)} , analogous to ∀ x ϕ ( x ) = ¬ ∃ x ¬ ϕ ( x ) {\displaystyle \forall x\phi (x)=\neg \exists x\neg \phi (x)} . Denoting this dual operation as x ▹ {\displaystyle x\triangleright } , we define x ▹ z {\displaystyle x\triangleright z} as ¬ x ∖ ¬ z {\displaystyle \neg x\backslash \neg z} . Similarly we define another operation z ◃ y {\displaystyle z\triangleleft y} as ¬ ( ¬ z / y ) {\displaystyle \neg (\neg z/y)} . By analogy with x ∖ {\displaystyle x\backslash } as the residual operation associated with the operation x ∙ {\displaystyle x\bullet } , we refer to x ▹ {\displaystyle x\triangleright } as the conjugate operation, or simply conjugate, of x ∙ {\displaystyle x\bullet } . Likewise ◃ y {\displaystyle \triangleleft y} is the conjugate of ∙ y {\displaystyle \bullet y} . Unlike residuals, conjugacy is an equivalence relation between operations: if f {\displaystyle f} is the conjugate of g {\displaystyle g} then g {\displaystyle g} is also the conjugate of f {\displaystyle f} , i.e. the conjugate of the conjugate of f {\displaystyle f} is f {\displaystyle f} . Another advantage of conjugacy is that it becomes unnecessary to speak of right and left conjugates, that distinction now being inherited from the difference between x ∙ {\displaystyle x\bullet } and ∙ x {\displaystyle \bullet x} , which have as their respective conjugates x ▹ {\displaystyle x\triangleright } and ◃ x {\displaystyle \triangleleft x} . (But this advantage accrues also to residuals when x ∖ {\displaystyle x\backslash } is taken to be the residual operation to x ∙ {\displaystyle x\bullet } .) All this yields (along with the Boolean algebra and monoid axioms) the following equivalent axiomatization of a residuated Boolean algebra. y # x ▹ z ⇔ x ∙ y # z ⇔ x # z ◃ y {\displaystyle y\#x\triangleright z\ \Leftrightarrow \ x\bullet y\#z\ \Leftrightarrow \ x\#z\triangleleft y} With this signature it remains the case that this axiomatization can be expressed as

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  Split Up (expert system)

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

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  Zero-day vulnerability

  A zero-day (also known as a 0-day) is a vulnerability or security hole in a computer system unknown to its developers or anyone capable of mitigating it. Until the vulnerability is remedied, threat actors can exploit it in a zero-day exploit, or zero-day attack. The term "zero-day" originally referred to the number of days since a new piece of software was released to the public, so "zero-day software" was obtained by hacking into a developer's computer before release. Eventually the term was applied to the vulnerabilities that allowed this hacking, and to the number of days that the vendor has had to fix them. Vendors who discover the vulnerability may create patches or advise workarounds to mitigate it, though users need to deploy that mitigation to eliminate the vulnerability in their systems. Zero-day attacks are severe threats. == Definition == Despite developers' goal of delivering a product that works entirely as intended, virtually all products contain software and hardware bugs. If a bug creates a security risk, it is called a vulnerability. Vulnerabilities vary in their ability to be exploited by malicious actors. Some are not usable at all, while others can be used to disrupt the device with a denial of service attack. The most dangerous allow the attacker to inject and run their own code, without the user being aware of it. Although the term "zero-day" initially referred to the time since the vendor had become aware of the vulnerability, zero-day vulnerabilities can also be defined as the subset of vulnerabilities for which no patch or other fix is available. A zero-day exploit is any exploit that takes advantage of such a vulnerability. == Exploits == An exploit is the delivery mechanism that takes advantage of the vulnerability to penetrate the target's systems, for such purposes as disrupting operations, installing malware, or exfiltrating data. Researchers Lillian Ablon and Andy Bogart write that "little is known about the true extent, use, benefit, and harm of zero-day exploits". Exploits based on zero-day vulnerabilities are considered more dangerous than those that take advantage of a known vulnerability. However, it is likely that most cyberattacks use known vulnerabilities, not zero-days. Governments of states are the primary users of zero-day exploits, not only because of the high cost of finding or buying vulnerabilities, but also the significant cost of writing the attack software. Nevertheless, anyone can use a vulnerability, and according to research by the RAND Corporation, "any serious attacker can always get an affordable zero-day for almost any target". Many targeted attacks and most advanced persistent threats rely on zero-day vulnerabilities. In 2017, the average time to develop an exploit from a zero-day vulnerability was estimated at 22 days. The difficulty of developing exploits has been increasing over time due to increased anti-exploitation features in popular software. === Window of vulnerability === Zero-day vulnerabilities are often classified as alive—meaning that there is no public knowledge of the vulnerability—and dead—the vulnerability has been disclosed, but not patched. If the software's maintainers are actively searching for vulnerabilities, it is a living vulnerability; such vulnerabilities in unmaintained software are called immortal. Zombie vulnerabilities can be exploited in older versions of the software but have been patched in newer versions. Even publicly known and zombie vulnerabilities are often exploitable for an extended period. Security patches can take months to develop, or may never be developed. A patch can have negative effects on the functionality of software and users may need to test the patch to confirm functionality and compatibility. Larger organizations may fail to identify and patch all dependencies, while smaller enterprises and personal users may not install patches. Research suggests that risk of cyberattack increases if the vulnerability is made publicly known or a patch is released. Cybercriminals can reverse engineer the patch to find the underlying vulnerability and develop exploits, often faster than users install the patch. According to research by RAND Corporation published in 2017, zero-day exploits remain usable for 6.9 years on average, although those purchased from a third party only remain usable for 1.4 years on average. The researchers were unable to determine if any particular platform or software (such as open-source software) had any relationship to the life expectancy of a zero-day vulnerability. Although the RAND researchers found that 5.7 percent of a stockpile of secret zero-day vulnerabilities will have been discovered by someone else within a year, another study found a higher overlap rate, as high as 10.8 percent to 21.9 percent per year. == Countermeasures == Because, by definition, there is no patch that can block a zero-day exploit, all systems employing the software or hardware with the vulnerability are at risk. This includes secure systems such as banks and governments that have all patches up to date. Security systems are designed around known vulnerabilities, and repeated exploitations of a zero-day exploit could continue undetected for an extended period of time. Although there have been many proposals for a system that is effective at detecting zero-day exploits, this remains an active area of research in 2023. Many organizations have adopted defense-in-depth tactics so that attacks are likely to require breaching multiple levels of security, which makes it more difficult to achieve. Conventional cybersecurity measures such as training and access control — including multi-factor authentication, least-privilege access, and air-gapping makes it harder to compromise systems with a zero-day exploit. Since writing perfectly secure software is impossible, some researchers argue that driving up the cost of exploits is considered a good strategy to reduce the burden of cyberattacks. == Market == Zero-day exploits can fetch millions of dollars. There are three main types of buyers: White: the vendor, or to third parties such as the Zero Day Initiative that disclose to the vendor. Often such disclosure is in exchange for a bug bounty. Not all companies respond positively to disclosures, as they can cause legal liability and operational overhead. It is not uncommon to receive cease-and-desist letters from software vendors after disclosing a vulnerability for free. Gray: the largest and most lucrative. Government or intelligence agencies buy zero-days and may use it in an attack, stockpile the vulnerability, or notify the vendor. The United States federal government is one of the largest buyers. As of 2013, the Five Eyes (United States, United Kingdom, Canada, Australia, and New Zealand) captured the plurality of the market and other significant purchasers included Russia, India, Brazil, Malaysia, Singapore, North Korea, and Iran. Middle Eastern countries were poised to become the biggest spenders. Black: organized crime, which typically prefers exploit software rather than just knowledge of a vulnerability. These users are more likely to employ "half-days" where a patch is already available. In 2015, the markets for government and crime were estimated at least ten times larger than the white market. Sellers are often hacker groups that seek out vulnerabilities in widely used software for financial reward. Some will only sell to certain buyers, while others will sell to anyone. White market sellers are more likely to be motivated by non pecuniary rewards such as recognition and intellectual challenge. Selling zero-day exploits is legal. Despite calls for more regulation, law professor Mailyn Fidler says there is little chance of an international agreement because key players such as Russia and Israel are not interested. The sellers and buyers that trade in zero-days tend to be secretive, relying on non-disclosure agreements and classified information laws to keep the exploits secret. If the vulnerability becomes known, it can be patched and its value consequently crashes. Because the market lacks transparency, it can be hard for parties to find a fair price. Sellers might not be paid if the vulnerability was disclosed before it was verified, or if the buyer declined to purchase it but used it anyway. With the proliferation of middlemen, sellers could never know to what use the exploits could be put. Buyers could not guarantee that the exploit was not sold to another party. Both buyers and sellers advertise on the dark web. Research published in 2022 based on maximum prices paid as quoted by a single exploit broker found a 44 percent annualized inflation rate in exploit pricing. Remote zero-click exploits could fetch the highest price, while those that require local access to the device are much cheaper. Vulnerabilities in widely used software are also more expensive. They estimated that around 400 to 1,500 people sold exploits to th

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  GITEX AI Europe

  GITEX AI Europe is an annual technology trade show and conference held in Berlin, Germany, as part of GITEX GLOBAL. The event focuses on the European technology market, specifically in the sectors of artificial intelligence (AI), cybersecurity, quantum computing, and digital infrastructure. The event is organized by Kaoun International GmbH, the international arm of the Dubai World Trade Centre (DWTC), in partnership with Messe Berlin. == History == The establishment of GITEX AI Europe was announced in 2023 as part of a strategic move to bring the GITEX brand to the European market. The inaugural edition took place from May 21 to 23, 2025, at the Messe Berlin exhibition grounds. The launch was supported by the Berlin Senate and the German Federal Ministry for Economic Affairs and Climate Action. The first edition of GITEX AI Europe in 2025 featured 21,650 attendees, 1,434 exhibiting companies, and 755 startups, with 513 speakers representing 125 countries. The next edition is scheduled for June 30 – July 1, 2026 in Berlin. == Program == The event consists of an exhibition floor for corporate displays, several conference stages for keynote speeches, and specialized sub-events. The conference program includes tracks such as "AI Stack Sovereignty," "Cyber Regulation & Trust Convergence," and "Institutional Growth Capital." GITEX AI Europe incorporates brands under its umbrella: AI Everything Europe: Focused on the development and application of generative AI and machine learning. North Star Europe: A dedicated program for startups and venture capital, featuring the "Supernova Challenge" pitch competition. GISEC Europe: A cybersecurity forum discussing regulation and infrastructure defense. GITEX Quantum Expo: Focused on the commercialization of quantum computing. Institutional partners for the event include the German Federal Ministry for Economic Affairs and Climate Action, the European Innovation Council (EIC), the International Telecommunication Union (ITU), Bitkom, and Digital Dubai.

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  The MANIAC

  The MANIAC is a 2023 novel by Chilean author Benjamín Labatut, written in English. It is a fictionalised biography of polymath John von Neumann, whom Labatut calls "the smartest human being of the 20th century". The book focuses on von Neumann, but is also about physicist Paul Ehrenfest, the history of artificial intelligence, and Lee Sedol's Go match against AlphaGo. The book received mostly positive reviews from critics. == Background == John von Neumann was a Jewish Hungarian-born polymath who was a prodigy from an early childhood. Von Neumann worked in multiple fields of science, theoretical (mathematical foundations of quantum mechanics, game theory, cellular automata) and applied (nuclear weapons research during the Manhattan Project in World War II, computer architecture later named after him, and many other subjects). Labatut calls him "the smartest human being of the 20th century". The title of the book is derived from an early computer based on von Neumann architecture, built after the war at Los Alamos laboratory, called MANIAC I. Benjamín Labatut is a Chilean author known for his 2020 book When We Cease to Understand the World, a collection of fictionalised stories about famous scientists that received positive reviews and was translated into multiple languages from Spanish. The MANIAC is Labatut's first book written in English. In an interview, Labatut said he prefers to write in English: English is my preferred form of thought. ... English is the language I do most if not all my reading it. And it is a far better language than Spanish, in so many ways. Writing "clean" prose in Spanish is almost impossible, because so many of its sounds clash. Borges said that he found English "a far finer language than Spanish" because it's both Germanic and Latin; because of its wonderful vocabulary ("Regal is not exactly the same thing as saying kingly," he explained); because of its physicality; and because you can do almost anything with verbs and prepositions. Labatut was inspired to write The MANIAC by George Dyson's book Turing's Cathedral. == Synopsis == The book has three chapters. The first chapter, "Paul or the Discovery of the Irrational", written in the third person, is about physicist Paul Ehrenfest. The chapter opens with Ehrenfest shooting dead his son Vassily, who suffered from Down syndrome, and then himself. It then recounts Ehrenfest's life story, describing his relationships with his wife Tatyana, his mistress Nelly Meyjes, and his eminent physicist colleagues. It chronicles his descent into despair and depression over his marriage's disintegration, the advent of quantum mechanics, and the direction Europe was heading in with the Nazi Party's rise to power in Germany, looping back to the initial scene of the chapter. The second chapter, "John or the Mad Dreams of Reason", is about John von Neumann, and is written as a series of interviews of his family members, wives, friends, and colleagues, each in a distinctive voice. It is divided into three parts. Part I, "The Limits of Logic", is about his early life, as told by von Neumann's childhood friend Eugene Wigner, mother Margrit Kann, brother Nicholas von Neumann, first wife Mariette Kövesi, and scientists Theodore von Karman, George Polya, and Gábor Szegő. It climaxes with von Neumann's participation in David Hilbert's program to create a logical basis for mathematics based on a consistent set of axioms, a quest ultimately scuppered by Kurt Gödel. Part II, "The Delicate Balance of Terror", discusses von Neumann's role in the Manhattan Project (as told by Richard Feynman); his development of game theory and the doctrine of mutual assured destruction (MAD) (as told by Oskar Morgenstern); and his creation of the MANIAC I computer and the von Neumann architecture (as told by Julian Bigelow). In Part III, "Ghosts in the Machine", Sydney Brenner discusses von Neumann's contributions to biology, his theoretical work on self-replicating and self-repairing machines, and his vision of Von Neumann probes exploring the universe. Nils Aall Barricelli talks about his ideas of digital life and his disagreements with von Neumann. Von Neumann's wife Klára Dán, daughter Marina, and Wigner talk about his final years, personal life, and death. The third chapter, "Lee or The Delusions of Artificial Intelligence", is about Lee Sedol's Go match against AlphaGo. The narrative reverts to the third person. The chapter also tells the story of Demis Hassabis, a chess prodigy in childhood who decided to work on artificial intelligence and founded DeepMind, the company behind AlphaGo. The way is pointed to the future, as artificial intelligence's growing capabilities outpace the human mind. The book ends with Lee Sedol's retirement from Go, and new version of DeepMind's program, AlphaZero, that did not train on human games but nevertheless became the strongest player in Go, chess, and Shogi. == Reception == The book received mostly positive reviews. In his review for The New York Times Tom McCarthy noted the ambiguity of genre: "At its best, as in the stunning opening sequence reconstructing the murder-suicide of the physicist Paul Ehrenfest and his disabled son, or in the final section's gripping account of a computer defeating the world's best human Go player, you just throw up your hands and think, Who cares what discourse label we assign this stuff? It's great." Becca Rothfeld of the Washington Post praised the book, writing that it is "Labatut's latest virtuosic effort, at once a historical novel and a philosophical foray": "The MANIAC is a work of dark, eerie and singular beauty." She noted that the book "can also be difficult to read" because of its unusual narrative structure: "The book is narrated by a cluttered polyphony of characters, among them both of von Neumann's wives and a number of his teachers and colleagues. ... Like von Neumann, The MANIAC strives to adopt the impartial standpoint of the universe." Killian Fox of The Guardian sees the book as "darkly fascinating novel", and notes Labatut's "impressive dexterity, unpicking complex ideas in long, elegant sentences that propel us forward at speed (this is his first book written in English). Even in the more feverish passages, when yet another great mind succumbs to madness, haunted by the spectres they've helped unleash on the world, he feels in full control of his material." Sam Byers of The Guardian praises the book and the author's style: "The opening chapter of Benjamín Labatut's second novel is such a perfect distillation of his technique that it could serve as a manifesto." and "Readers ... will recognise the sense of breathlessness his best writing can evoke. Seemingly loosened from the laws of physics they describe, his sentences range freely through time and space, connecting not only characters and events, but the delicate tissue of intellectual history, often with a lightness of touch that belies their underlying complexity." He writes on the narrative structure: "Through a cascade of staccato chapters, an ensemble of narrators offer their piecemeal insights." Byers adds that "a brilliant novel is not quite what we end up with" and sees the problem in the "diffusion": "Labatut simply spreads himself too thin. Too many years in too few pages; too many voices with far too little to distinguish them. Initially intriguing, the bite-size monologues quickly come to feel inadequate." Some reviewers did not see the book as a biography. In an essay for the Cleveland Review of Books, Ben Cosman juxtaposes the book with Christopher Nolan's biopic Oppenheimer, and writes that it "follows the development of artificial intelligence—first as an idea at the beginning of the twentieth century, and then as a practicality at the beginning of the twenty-first—through the lives of three men who faced it." He also compared the book's structure to "witness testimony". Another reviewer called the book "perfect for anyone thirsting for more nuclear anxiety after watching Oppenheimer". Garrett Biggs of the Chicago Review of Books writes of the book's style: "Labatut writes about scientists the way Roberto Bolaño writes about poets. They are near mythical figures, captured at the corner of the novel's eye. They become historical in the most fraught sense of the term: subject to rumor and speculation and, eventually, the novel's form inflates their personas into something so large they can only be understood as narrative, never known in any objective capacity." Biggs criticises the last chapter: "the story of artificial intelligence has yet to be written. And so when Labatut's narration editorializes about artificial intelligence as 'a future that inspires hope and horror,' The MANIAC disassembles as a novel and starts to sound like a stale thinkpiece. AlphaGo might represent the first glimmer of a true artificial intelligence, as Labatut suggests. It also could one day be considered nothing more than a souped-up cousin to IBM's DeepBlue.

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  Fuzzy concept

  A fuzzy concept is an idea of which the boundaries of application can vary considerably according to context or conditions, instead of being fixed once and for all. That means the idea is somewhat vague or imprecise. Yet it is not unclear or meaningless. It has a definite meaning, which can often be made more exact with further elaboration and specification — including a closer definition of the context in which the concept is used. The inverse of a "fuzzy concept" is a "crisp concept" (i.e. a precise concept). Fuzzy concepts are often used to navigate imprecision in the real world, when precise information is not available and an approximate indication is sufficient to be helpful. Although the linguist George Philip Lakoff already defined the semantics of a fuzzy concept in 1973 (inspired by an unpublished 1971 paper by Eleanor Rosch,) the term "fuzzy concept" rarely received a standalone entry in dictionaries, handbooks and encyclopedias. Sometimes it was defined in encyclopedia articles on fuzzy logic, or it was simply equated with a mathematical “fuzzy set”. A fuzzy concept can be "fuzzy" for many different reasons in different contexts. This makes it harder to provide a precise definition that covers all cases. Paradoxically, the definition of fuzzy concepts may itself be somewhat "fuzzy". Lotfi A. Zadeh, known as "the father of fuzzy logic", claimed that "vagueness connotes insufficient specificity, whereas fuzziness connotes unsharpness of class boundaries". Not all scholars agree. With increasing academic literature on the subject, the term "fuzzy concept" is now more widely recognized as a philosophical, linguistic or scientific category, and the study of the characteristics of fuzzy concepts and fuzzy language is known as fuzzy semantics. “Fuzzy logic” has become a generic term for many different kinds of many-valued logics, and is applied in many different areas of research, computer programming and industrial design. For engineers, "Fuzziness is imprecision or vagueness of definition." For computer scientists, a fuzzy concept is an idea which is "to an extent applicable" in a situation. It means that the concept can have gradations of significance or unsharp (variable) boundaries of application — a "fuzzy statement" is a statement which is true "to some extent", and that extent can often be represented by a scaled value (a score). For mathematicians, a "fuzzy concept" is usually a fuzzy set or a combination of such sets (see fuzzy mathematics and fuzzy set theory). In cognitive linguistics, the things that belong to a "fuzzy category" exhibit gradations of family resemblance, and the borders of the category are not clearly defined. Through most of the 20th century, the idea of reasoning with fuzzy concepts faced considerable resistance from Western academic elites. They did not want to endorse the use of imprecise concepts in research or argumentation, and they often regarded fuzzy logic with suspicion, derision or even hostility. That may partly explain why the idea of a "fuzzy concept" did not get a separate entry in encyclopedias, handbooks and dictionaries. Yet although people might not be aware of it, the use of fuzzy concepts has risen gigantically in all walks of life from the 1970s onward. That is mainly due to advances in electronic engineering, fuzzy mathematics and digital computer programming. The new technology allows very complex inferences about "variations on a theme" to be anticipated and fixed in a program. The Perseverance Mars rover, a driverless NASA vehicle used to explore the Jezero crater on the planet Mars, features fuzzy logic programming that steers it through rough terrain. Similarly, to the North, the Chinese Mars rover Zhurong used fuzzy logic algorithms to calculate its travel route in Utopia Planitia from sensor data. New neuro-fuzzy computational methods make it possible for machines to identify, measure, adjust and respond to fine gradations of significance with great precision. It means that practically useful concepts can be coded, sharply defined, and applied to all kinds of tasks, even if ordinarily these concepts are never exactly defined. Nowadays engineers, statisticians and programmers often represent fuzzy concepts mathematically, using fuzzy logic, fuzzy values, fuzzy variables and fuzzy sets (see also fuzzy set theory). Fuzzy logic is not "woolly thinking", but a "precise logic of imprecision" which reasons with graded concepts and gradations of truth. Fuzzy concepts and fuzzy logic often play a significant role in artificial intelligence programming, for example because they can model human cognitive processes more easily than other methods. == Origins == Vagueness and fuzziness have probably always been a part of human experience. In the West, ancient texts show that philosophers and scientists were already thinking critically about this in classical antiquity. Most often, they regarded vagueness as a problem: as an obstacle to clear thinking, as a source of confusion, or as an evasive tactic. It got in the way of providing clear orientation, guidance, direction and leadership. Therefore, vagueness became associated with a hermeneutic of suspicion — it was considered as something to avoid, as something undesirable. By contrast, in the ancient Chinese tradition of Daoist thought of Laozi and Zhuang Zhou, "vagueness is not regarded with suspicion, but is simply an acknowledged characteristic of the world around us" — a subject for meditation and a source of insight. === Sorites paradox === The ancient Sorites paradox raised the logical problem, of how we could exactly define the threshold at which a change in quantitative gradation turns into a qualitative or categorical difference. With some physical processes, this threshold seems relatively easy to identify. For example, water turns into steam at 100 °C or 212 °F. Of course, the boiling point depends partly on atmospheric pressure, which decreases at higher altitudes; it is also affected by the level of humidity — in that sense, the boiling point is "somewhat fuzzy", because it can vary under different conditions. Nevertheless, for every altitude, level of air pressure and degree of humidity, we can predict accurately what the boiling point will be, if we know the relevant conditions. With many other processes and gradations, however, the point of change is much more difficult to locate, and remains somewhat vague. Thus, the boundaries between qualitatively different things may be unsharp: we know that there are boundaries, but we cannot define them exactly. For example, to identify "the oldest city in the world", we have to define what counts as a city, and at what point a growing human settlement becomes a city. === The continuum fallacy and Loki's wager === According to the modern idea of the continuum fallacy, the fact that a statement is to an extent vague, does not automatically mean that it has no validity. The question then arises, of how (by what method or approach) we could ascertain and define the validity that the fuzzy statement does have. The Nordic myth of Loki's wager suggested that concepts that lack precise meanings or lack precise boundaries of application cannot be operated with, because they evade any clear definition. However, the 20th-century idea of "fuzzy concepts" proposes that "somewhat vague terms" can be operated with, because we can explicate and define the variability of their application — by assigning numbers to gradations of applicability. This idea sounds simple enough, but it had large implications. === Precursors and pioneers === In Western civilization, the intellectual recognition of fuzzy concepts has been traced back to a diversity of famous and less well-known thinkers, including (among many others) Eubulides, Epicurus, Plato, Cicero, William Ockham and John Buridan, Georg Wilhelm Friedrich Hegel, Karl Marx and Friedrich Engels, Friedrich Nietzsche, William James, Hugh MacColl, Charles S. Peirce, Hans Reichenbach, Carl Gustav Hempel, Max Black, Arto Salomaa, Ludwig Wittgenstein, Jan Łukasiewicz, Emil Leon Post, Alfred Tarski, Georg Cantor, Nicolai A. Vasiliev, Kurt Gödel, Stanisław Jaśkowski, Willard Van Orman Quine, George J. Klir, Petr Hájek, Joseph Goguen, Ronald R. Yager, Enrique Héctor Ruspini, Jan Pavelka, Didier Dubois, Bernadette Bouchon-Meunier, and Donald Knuth. Across at least two and a half millennia, all of them had something to say about graded concepts with unsharp boundaries. This suggests at least that the awareness of the existence of concepts with "fuzzy" characteristics, in one form or another, has a very long history in human thought. Quite a few 20th century logicians, mathematicians and philosophers also tried to analyze the characteristics of fuzzy concepts as a recognized species, sometimes with the aid of some kind of many-valued logic or substructural logic. An early attempt in the post-WW2 era to create a mathematical theory of sets with gradations of

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  Point distribution model

  The point distribution model is a model for representing the mean geometry of a shape and some statistical modes of geometric variation inferred from a training set of shapes. == Background == The point distribution model concept has been developed by Cootes, Taylor et al. and became a standard in computer vision for the statistical study of shape and for segmentation of medical images where shape priors really help interpretation of noisy and low-contrasted pixels/voxels. The latter point leads to active shape models (ASM) and active appearance models (AAM). Point distribution models rely on landmark points. A landmark is an annotating point posed by an anatomist onto a given locus for every shape instance across the training set population. For instance, the same landmark will designate the tip of the index finger in a training set of 2D hands outlines. Principal component analysis (PCA), for instance, is a relevant tool for studying correlations of movement between groups of landmarks among the training set population. Typically, it might detect that all the landmarks located along the same finger move exactly together across the training set examples showing different finger spacing for a flat-posed hands collection. == Details == First, a set of training images are manually landmarked with enough corresponding landmarks to sufficiently approximate the geometry of the original shapes. These landmarks are aligned using the generalized procrustes analysis, which minimizes the least squared error between the points. k {\displaystyle k} aligned landmarks in two dimensions are given as X = ( x 1 , y 1 , … , x k , y k ) {\displaystyle \mathbf {X} =(x_{1},y_{1},\ldots ,x_{k},y_{k})} . It's important to note that each landmark i ∈ { 1 , … k } {\displaystyle i\in \lbrace 1,\ldots k\rbrace } should represent the same anatomical location. For example, landmark #3, ( x 3 , y 3 ) {\displaystyle (x_{3},y_{3})} might represent the tip of the ring finger across all training images. Now the shape outlines are reduced to sequences of k {\displaystyle k} landmarks, so that a given training shape is defined as the vector X ∈ R 2 k {\displaystyle \mathbf {X} \in \mathbb {R} ^{2k}} . Assuming the scattering is gaussian in this space, PCA is used to compute normalized eigenvectors and eigenvalues of the covariance matrix across all training shapes. The matrix of the top d {\displaystyle d} eigenvectors is given as P ∈ R 2 k × d {\displaystyle \mathbf {P} \in \mathbb {R} ^{2k\times d}} , and each eigenvector describes a principal mode of variation along the set. Finally, a linear combination of the eigenvectors is used to define a new shape X ′ {\displaystyle \mathbf {X} '} , mathematically defined as: X ′ = X ¯ + P b {\displaystyle \mathbf {X} '={\overline {\mathbf {X} }}+\mathbf {P} \mathbf {b} } where X ¯ {\displaystyle {\overline {\mathbf {X} }}} is defined as the mean shape across all training images, and b {\displaystyle \mathbf {b} } is a vector of scaling values for each principal component. Therefore, by modifying the variable b {\displaystyle \mathbf {b} } an infinite number of shapes can be defined. To ensure that the new shapes are all within the variation seen in the training set, it is common to only allow each element of b {\displaystyle \mathbf {b} } to be within ± {\displaystyle \pm } 3 standard deviations, where the standard deviation of a given principal component is defined as the square root of its corresponding eigenvalue. PDM's can be extended to any arbitrary number of dimensions, but are typically used in 2D image and 3D volume applications (where each landmark point is R 2 {\displaystyle \mathbb {R} ^{2}} or R 3 {\displaystyle \mathbb {R} ^{3}} ). == Discussion == An eigenvector, interpreted in euclidean space, can be seen as a sequence of k {\displaystyle k} euclidean vectors associated to corresponding landmark and designating a compound move for the whole shape. Global nonlinear variation is usually well handled provided nonlinear variation is kept to a reasonable level. Typically, a twisting nematode worm is used as an example in the teaching of kernel PCA-based methods. Due to the PCA properties: eigenvectors are mutually orthogonal, form a basis of the training set cloud in the shape space, and cross at the 0 in this space, which represents the mean shape. Also, PCA is a traditional way of fitting a closed ellipsoid to a Gaussian cloud of points (whatever their dimension): this suggests the concept of bounded variation. The idea behind PDMs is that eigenvectors can be linearly combined to create an infinity of new shape instances that will 'look like' the one in the training set. The coefficients are bounded alike the values of the corresponding eigenvalues, so as to ensure the generated 2n/3n-dimensional dot will remain into the hyper-ellipsoidal allowed domain—allowable shape domain (ASD).

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  Construction of t-norms

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

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  Use of artificial intelligence by the United States Department of Defense

  The United States Department of Defense has been analyzing and employing military applications of artificial intelligence since at least 2014. The program initially focused on drones and other robots, but has also been using large language models for military research and analysis. The current US policy on lethal autonomous weapons is Department of Defense Directive 3000.09, updated in January 2023. == Background == The United States Department of Defense began developing lethal autonomous weapons as early as the Reagan administration. An early version of the Tomahawk missile could have been used to destroy Soviet ships without direct human control; the initiative was abandoned after the United States and the Soviet Union signed START I. By 2014, the United Kingdom, Israel, and Norway had already begun using missiles equipped with artificial intelligence systems. The Department of Defense established a policy on the use of artificial intelligence in 2012. == History == === 2016–2017: Carter secretaryship === In May 2016, secretary of defense Ash Carter stated that his Third Offset strategy would include utilizing artificial intelligence as a military advantage. The New York Times reported that year that the Department of Defense had tested an autonomous drone at an approximation of a Middle Eastern village at Camp Edwards. Deputy secretary of defense Robert O. Work, who advocated for developing artificial intelligence, told the Times that the United States needed to compete with China and Russia by having a tactical advantage they could not easily replicate. The initiative was developed by DARPA beginning in 2015. The use of artificial intelligence in the U.S. military was controversial within the department; in February, Paul Scharre, who worked for the Office of the Secretary of Defense in the secretaryships of Robert Gates and Leon Panetta, published a report about the risks of artificial intelligence for broad military applications. === 2017–2019: Mattis secretaryship === By 2017, the United States Air Force had already begun using artificial intelligence in military robots. The Air Force's use of Neurala, an artificial intelligence company, concerned officials in the Department of Defense after an investigation found that Neurala had accepted money from an investment firm with funding from a state-run Chinese company. The Department of Defense began heavily investing in artificial intelligence after Work established Project Maven, an initiative to encourage the development and integration of artificial intelligence in the military, in April 2017. In May 2018, secretary of defense Jim Mattis privately expressed to president Donald Trump that he needed to establish a national strategy on artificial intelligence, quoting an article from former secretary of state Henry Kissinger that called for a presidential commission on the technology. The Department of Defense established the Joint Artificial Intelligence Center the following month. Google began working with the Department of Defense on analyzing drone footage as early as March. Google's involvement in the initiative led to protests from employees and mass resignations. Seeking to quell internal unrest, Google stated it would not renew its contract with the Department of Defense in June. The Department of Defense announced an artificial intelligence contract with Microsoft in October. === 2025–present: Hegseth secretaryship === In December 2025, secretary of defense Pete Hegseth announced GenAI.mil, an artificial intelligence platform for the Department of Defense. In a video announcing the platform, Hegseth stated that Department of Defense workers would be able to "conduct deep research, format documents and even analyze video or imagery." The Department of Defense contracted first Gemini by Google, then ChatGPT by OpenAI, and finally Grok by xAI for the platform. Claude by Anthropic was also contracted by the Department of Defense and was in use on secure servers until it was revealed that Claude had been used in the 2026 operation to capture Nicolás Maduro, who was at the time the leader of Venezuela. This revelation sparked a high-profile dispute over Anthropic's ability to constrain Claude's useage, resulting in the termination of Anthropic's $200 million defense contract. The Department of Defense also moved to label Anthropic a supply chain risk, which was later blocked by a federal judge.

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