AI For Business Owners

AI For Business Owners — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Hybrid intelligent system

  Hybrid intelligent system denotes a software system which employs, in parallel, a combination of methods and techniques from artificial intelligence subfields, such as: Neuro-symbolic systems Neuro-fuzzy systems Hybrid connectionist-symbolic models Fuzzy expert systems Connectionist expert systems Evolutionary neural networks Genetic fuzzy systems Rough fuzzy hybridization Reinforcement learning with fuzzy, neural, or evolutionary methods as well as symbolic reasoning methods. From the cognitive science perspective, every natural intelligent system is hybrid because it performs mental operations on both the symbolic and subsymbolic levels. For the past few years, there has been an increasing discussion of the importance of A.I. Systems Integration. Based on notions that there have already been created simple and specific AI systems (such as systems for computer vision, speech synthesis, etc., or software that employs some of the models mentioned above) and now is the time for integration to create broad AI systems. Proponents of this approach are researchers such as Marvin Minsky, Ron Sun, Aaron Sloman, Angelo Dalli and Michael A. Arbib. An example hybrid is a hierarchical control system in which the lowest, reactive layers are sub-symbolic. The higher layers, having relaxed time constraints, are capable of reasoning from an abstract world model and performing planning (even by hybrid wisdom). Intelligent systems usually rely on hybrid reasoning processes, which include induction, deduction, abduction and reasoning by analogy.

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  Orange (software)

  Orange is an open-source data visualization, machine learning and data mining toolkit. It features a visual programming front-end for exploratory qualitative data analysis and interactive data visualization. == Description == Orange is a component-based visual programming software package for data visualization, machine learning, data mining, and data analysis. Orange components are called widgets. They range from simple data visualization, subset selection, and preprocessing to empirical evaluation of learning algorithms and predictive modeling. Visual programming is implemented through an interface in which workflows are created by linking predefined or user-designed widgets, while advanced users can use Orange as a Python library for data manipulation and widget alteration. == Software == Orange is an open-source software package released under GPL and hosted on GitHub. Versions up to 3.0 include core components in C++ with wrappers in Python. From version 3.0 onwards, Orange uses common Python open-source libraries for scientific computing, such as numpy, scipy and scikit-learn, while its graphical user interface operates within the cross-platform Qt framework. The default installation includes a number of machine learning, preprocessing and data visualization algorithms in 6 widget sets (data, transform, visualize, model, evaluate and unsupervised). Additional functionalities are available as add-ons (text-mining, image analytics, bioinformatics, etc.). Orange is supported on macOS, Windows and Linux and can also be installed from the Python Package Index repository (pip install Orange3). == Features == Orange consists of a canvas interface onto which the user places widgets and creates a data analysis workflow. Widgets offer basic functionalities such as reading the data, showing a data table, selecting features, training predictors, comparing learning algorithms, visualizing data elements, etc. The user can interactively explore visualizations or feed the selected subset into other widgets. Canvas: graphical front-end for data analysis Widgets: Data: widgets for data input, data filtering, sampling, imputation, feature manipulation and feature selection Visualize: widgets for common visualization (box plot, histograms, scatter plot) and multivariate visualization (mosaic display, sieve diagram). Classify: a set of supervised machine learning algorithms for classification Regression: a set of supervised machine learning algorithms for regression Evaluate: cross-validation, sampling-based procedures, reliability estimation and scoring of prediction methods Unsupervised: unsupervised learning algorithms for clustering (k-means, hierarchical clustering) and data projection techniques (multidimensional scaling, principal component analysis, correspondence analysis). == Add-ons == Orange users can extend their core set of components with components in the add-ons. Supported add-ons include: Associate: components for mining frequent itemsets and association rule learning. Bioinformatics: components for gene expression analysis, enrichment, and access to expression databases (e.g., Gene Expression Omnibus) and pathway libraries. Data fusion: components for fusing different data sets, collective matrix factorization, and exploration of latent factors. Educational: components for teaching machine learning concepts, such as k-means clustering, polynomial regression, stochastic gradient descent, ... Explain: provides an extension with components for the model explanation, including Shapley value analysis Geo: components for working with geospatial data. Image analytics: components for working with images and ImageNet embeddings Network: components for graph and network analysis. Text mining: components for natural language processing and text mining. Time series: widget components for time series analysis and modeling. Single-cell: support for single-cell gene expression analysis, including components for loading single-cell data, filtering and batch effect removal, marker genes discovery, scoring of cells and genes, and cell type prediction. Spectroscopy: components for analyzing and visualization of (hyper)spectral datasets. Survival analysis: add-on for data analysis dealing with survival data. It includes widgets for standard survival analysis techniques, such as the Kaplan-Meier plot, the Cox regression model, and several derivative widgets. World Happiness: support for downloading socioeconomic data from a database, including OECD and World Development Indicators. Provides access to thousands of country indicators from various economic databases. Fairness: add-on for evaluation and creation of fair machine learning models without discrimination. Widgets range from computing fairness metrics like statistical parity to post-, pre-, in-processing methods to build fair models. == Objectives == The program provides a platform for experiment selection, recommendation systems, and predictive modelling and is used in biomedicine, bioinformatics, genomic research, and teaching. In science, it is used as a platform for testing new machine learning algorithms and for implementing new techniques in genetics and bioinformatics. In education, it was used for teaching machine learning and data mining methods to students of biology, biomedicine, and informatics. == Extensions == Various projects build on Orange either by extending the core components with add-ons or using only the Orange Canvas to exploit the implemented visual programming features and GUI. OASYS — ORange SYnchrotron Suite scOrange — single cell biostatistics Quasar — data analysis in natural sciences == History == In 1996, the University of Ljubljana and Jožef Stefan Institute started development of ML, a machine learning framework in C++, and Python bindings were developed for this framework in 1997, which, together with emerging Python modules, formed a joint framework called Orange. Over the following years, most contemporary major algorithms for data mining and machine learning were implemented in C++ (Orange's core) or Python modules. In 2002, first prototypes to create a flexible graphical user interface were designed using Pmw Python megawidgets. In 2003, the graphical user interface was redesigned and re-developed for Qt framework using PyQt Python bindings. The visual programming framework was defined, and the development of widgets (graphical components of the data analysis pipeline) began. In 2005, extensions for data analysis in bioinformatics was created. In 2008, Mac OS X DMG and Fink-based installation packages were developed. In 2009, over 100 widgets were created and maintained. In 2009, Orange 2.0 beta was released, offering installation packages on the website based on the daily compiling cycle. In 2012, a new object hierarchy was imposed, replacing the old module-based structure. In 2013, a significant redesign of the graphical user interface included a new toolbox and depiction of workflows. In 2015, Orange 3.0 was released. Orange stores the data in NumPy arrays; machine learning algorithms mostly use scikit-learn. In 2015, a text analysis add-on for Orange3 was released. In 2016, Orange released version 3.3. Development scheduled a monthly cycle for stable releases. In 2016, Orange began development and release of an Image Analytics add-on, with server-side deep neural networks for image embedding In 2017, a Spectroscopy add-on for the analysis of spectral data was introduced. In 2017, Geo, an add-on for dealing with geo-location data and visualisation of geo maps was introduced In 2018, Orange began development and release of an add-on for single-cell data analysis. In 2019, Orange separated its graphical interface for development as a separate project, orange-canvas-core In 2020, Orange introduced the Explain add-on with widgets for explaining classification models and regression models, highlighting the strength and contributions specific features make towards predicting a specific class. In 2022, World Happiness, an add-on for the Orange3 data mining suite, was introduced, providing widgets for accessing socioeconomic data from various databases such as World Happiness Report, World Development Indicators, OECD. In 2022, Orange extended the Explain add-on with an Individual Conditional Expectation plot and the Permutation Feature Importance technique. In 2023, Orange introduced the Fairness add-on, including widgets to calculate bias metrics, as well as widgets for pre-, post-, and in-processing methods, allowing the creation of models less susceptible to systematic error due to the vagaries of the data set.

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  Vagueness

  In linguistics and philosophy, a vague predicate is one which gives rise to borderline cases. For example, the English adjective "tall" is vague since it is not clearly true or false for someone of middling height. By contrast, the word "prime" is not vague since every number is definitively either prime or not. Vagueness is commonly diagnosed by a predicate's ability to give rise to the sorites paradox. Vagueness is separate from ambiguity, in which an expression has multiple denotations. For instance the word "bank" is ambiguous since it can refer either to a river bank or to a financial institution, but there are no borderline cases between both interpretations. Vagueness is a major topic of research in philosophical logic, where it serves as a potential challenge to classical logic. Work in formal semantics has sought to provide a compositional semantics for vague expressions in natural language. Work in philosophy of language has addressed implications of vagueness for the theory of meaning, while metaphysicists have considered whether reality itself is vague. == Importance == The concept of vagueness has philosophical importance. Suppose one wants to come up with a definition of "right" in the moral sense. One wants a definition to cover actions that are clearly right and exclude actions that are clearly wrong, but what does one do with the borderline cases? Surely, there are such cases. Some philosophers say that one should try to come up with a definition that is itself unclear on just those cases. Others say that one has an interest in making his or her definitions more precise than ordinary language, or his or her ordinary concepts, themselves allow; they recommend one advances precising definitions. === In law === Vagueness is also a problem which arises in law, and in some cases, judges have to arbitrate regarding whether a borderline case does, or does not, satisfy a given vague concept. Examples include disability (how much loss of vision is required before one is legally blind?), human life (at what point from conception to birth is one a legal human being, protected for instance by laws against murder?), adulthood (most familiarly reflected in legal ages for driving, drinking, voting, consensual sex, etc.), race (how to classify someone of mixed racial heritage), etc. Even such apparently unambiguous concepts such as biological sex can be subject to vagueness problems, not just from transsexuals' gender transitions but also from certain genetic conditions which can give an individual mixed male and female biological traits (see intersex). In the common law system, vagueness is a possible legal defence against by-laws and other regulations. The legal principle is that delegated power cannot be used more broadly than the delegator intended. Therefore, a regulation may not be so vague as to regulate areas beyond what the law allows. Any such regulation would be "void for vagueness" and unenforceable. This principle is sometimes used to strike down municipal by-laws that forbid "explicit" or "objectionable" contents from being sold in a certain city; courts often find such expressions to be too vague, giving municipal inspectors discretion beyond what the law allows. In the US this is known as the vagueness doctrine and in Europe as the principle of legal certainty. === In science === Many scientific concepts are of necessity vague, for instance species in biology cannot be precisely defined, owing to unclear cases such as ring species. Nonetheless, the concept of species can be clearly applied in the vast majority of cases. As this example illustrates, to say that a definition is "vague" is not necessarily a criticism. Consider those animals in Alaska that are the result of breeding huskies and wolves: are they dogs? It is not clear: they are borderline cases of dogs. This means one's ordinary concept of doghood is not clear enough to let us rule conclusively in this case. == Approaches == The philosophical question of what the best theoretical treatment of vagueness is—which is closely related to the problem of the paradox of the heap, a.k.a. sorites paradox—has been the subject of much philosophical debate. === Fuzzy logic === One theoretical approach is that of fuzzy logic, developed by American mathematician Lotfi Zadeh. Fuzzy logic proposes a gradual transition between "perfect falsity", for example, the statement "Bill Clinton is bald", to "perfect truth", for, say, "Patrick Stewart is bald". In ordinary logics, there are only two truth-values: "true" and "false". The fuzzy perspective differs by introducing an infinite number of truth-values along a spectrum between perfect truth and perfect falsity. Perfect truth may be represented by "1", and perfect falsity by "0". Borderline cases are thought of as having a "truth-value" anywhere between 0 and 1 (for example, 0.6). Advocates of the fuzzy logic approach have included K. F. Machina (1976) and Dorothy Edgington (1993). === Supervaluationism === Another theoretical approach is known as "supervaluationism". This approach has been defended by Kit Fine and Rosanna Keefe. Fine argues that borderline applications of vague predicates are neither true nor false, but rather are instances of "truth value gaps". He defends an interesting and sophisticated system of vague semantics, based on the notion that a vague predicate might be "made precise" in many alternative ways. This system has the consequence that borderline cases of vague terms yield statements that are neither true, nor false. Given a supervaluationist semantics, one can define the predicate "supertrue" as meaning "true on all precisifications". This predicate will not change the semantics of atomic statements (e.g. "Frank is bald", where Frank is a borderline case of baldness), but does have consequences for logically complex statements. In particular, the tautologies of sentential logic, such as "Frank is bald or Frank is not bald", will turn out to be supertrue, since on any precisification of baldness, either "Frank is bald" or "Frank is not bald" will be true. Since the presence of borderline cases seems to threaten principles like this one (excluded middle), the fact that supervaluationism can "rescue" them is seen as a virtue. === Subvaluationism === Subvaluationism is the logical dual of supervaluationism, and has been defended by Dominic Hyde (2008) and Pablo Cobreros (2011). Whereas the supervaluationist characterises truth as 'supertruth', the subvaluationist characterises truth as 'subtruth', or "true on at least some precisifications". Subvaluationism proposes that borderline applications of vague terms are both true and false. It thus has "truth-value gluts". According to this theory, a vague statement is true if it is true on at least one precisification and false if it is false under at least one precisification. If a vague statement comes out true under one precisification and false under another, it is both true and false. Subvaluationism ultimately amounts to the claim that vagueness is a truly contradictory phenomenon. Of a borderline case of "bald man" it would be both true and false to say that he is bald, and both true and false to say that he is not bald. === Epistemicist view === A fourth approach, known as "the epistemicist view", has been defended by Timothy Williamson (1994), R. A. Sorensen (1988) and (2001), and Nicholas Rescher (2009). They maintain that vague predicates do, in fact, draw sharp boundaries, but that one cannot know where these boundaries lie. One's confusion about whether some vague word does or does not apply in a borderline case is due to one's ignorance. For example, in the epistemicist view, there is a fact of the matter, for every person, about whether that person is old or not old; some people are ignorant of this fact. === As a property of objects === One possibility is that one's words and concepts are perfectly precise, but that objects themselves are vague. Consider Peter Unger's example of a cloud (from his famous 1980 paper, "The Problem of the Many"): it is not clear where the boundary of a cloud lies; for any given bit of water vapor, one can ask whether it is part of the cloud or not, and for many such bits, one will not know how to answer. Hence, perhaps such a term as 'cloud' is not itself vague, but rather precisely denotes a vague object. This strategy has occasionally been poorly received; most notably, in Gareth Evans' short paper "Can There Be Vague Objects?" (1978), wherein an argument is examined which appears to show that vague identity-statements are impossible (i.e., result in logical incoherence). David Lewis explains that the reader is intended to conclude, with Evans, that—since there clearly are, in fact, meaningful vague identities—any purported proof to the contrary cannot be right; and as the proof relies upon the premise that vague terms precisely denote vague objects, but fails under the view that vague terms reflect a merel

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  Argument mining

  Argument mining, or argumentation mining, is a research area within the natural language processing field. The goal of argument mining is the automatic extraction and identification of argumentative structures from natural language text with the aid of computer programs. Such argumentative structures include the premise, conclusions, the argument scheme and the relationship between the main and subsidiary argument, or the main and counter-argument within discourse. The Argument Mining workshop series is the main research forum for argument mining related research. == Applications == Argument mining has been applied in many different genres including the qualitative assessment of social media content (e.g. Twitter, Facebook), where it provides a powerful tool for policy-makers and researchers in social and political sciences. Other domains include legal documents, product reviews, scientific articles, online debates, newspaper articles and dialogical domains. Transfer learning approaches have been successfully used to combine the different domains into a domain agnostic argumentation model. Argument mining has been used to provide students individual writing support by accessing and visualizing the argumentation discourse in their texts. The application of argument mining in a user-centered learning tool helped students to improve their argumentation skills significantly compared to traditional argumentation learning applications. == Challenges == Given the wide variety of text genres and the different research perspectives and approaches, it has been difficult to reach a common and objective evaluation scheme. Many annotated data sets have been proposed, with some gaining popularity, but a consensual data set is yet to be found. Annotating argumentative structures is a highly demanding task. There have been successful attempts to delegate such annotation tasks to the crowd but the process still requires a lot of effort and carries significant cost. Initial attempts to bypass this hurdle were made using the weak supervision approach.

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  FastTrack Automation Studio

  FastTrack Automation Studio (formerly known as FastTrack Scripting Host), often referred to as just FastTrack, is a scripting language for Windows IT System Administrators. The product’s goal is to handle any kind of scripting that might be required to automate processes with Microsoft Windows networks. == Manufacturer == FastTrack is produced by FastTrack Software, which is headquartered in Aalborg, Denmark. The product is promoted by the manufacturer as a one-stop shop for Windows script writers and its development paradigm is “one operation = one script line”. Script writers use a purpose-built editor to create scripts, inserting script lines via menus, drag’n drop, or simply typing them in. Scripts may be used out of the box, created from scratch, imported from forums or other users, or customized from product documentation. == Types of scripts == Simple scripts include: Outlook Signatures Login scripts Backup and replication scripts Inventory and asset management Automated Windows OS installation and deployment Automated application software deployment Active Directory scripts More advanced scripts include: SCCM task sequences Citrix ICA and RDP Clients built-in Deploying applications to server farms Deploying GPO MSI files SQL Server scripts == Basic structure == Under the hood, scripts comprise commands, functions, collections, and conditions. When a script is executed these components are converted into many lines of C# code, sometimes hundreds of lines, depending on the particular script operation. Scripts can be compiled into EXE files or MSI packages and treated as standalone Windows applications. == History == FastTrack Scripting Host (FastTrack) was first developed around 2006 to ease the administration burden of IT System Administrators on Windows networks. === Product idea === The idea for the product came from founder and President of FastTrack Software, Lars Pedersen, who has a background in systems administration. Previously with Telenor, Denmark’s major telephone company, Pedersen performed various roles in systems administration, programming and web development. He also worked as a consultant and developer on several major projects at various companies in Europe. Dissatisfied from his own experiences and frustrations administering Windows networks, Pederson looked for a way to make life easier for system administrators. In particular, he wanted something that could minimize the amount of time needed each day to perform routine and mundane tasks, which was a waste of time and expertise that should have been committed to other projects. === Development === Leading a small team of developers, Pedersen developed FastTrack Scripting Host to simplify and automate the routine tasks of system administrators. The resulting product is definitely a scripting language, but it can be used intuitively like a programming language, without requiring users to learn syntax or other concepts typically associated with programming languages. === Marketing === In April 2010, FastTrack Software entered into an agreement with Binary Research International Archived 2008-10-15 at the Wayback Machine, based in the city of Milwaukee, United States to market and sell the product globally. === Awards === FSH received a Windows IT Pro Community Choice award in 2012. == Versions == The first version was produced in June 2006 and contained 51 components, which are the commands, functions, conditions and collections making up FastTrack. The following table summarizes dates and components for major releases. Companies and organizations such as NOAA, Kawasaki, and Goodyear have used and implemented the FastTrack Scripting Host. == Comparison with other scripting software == FastTrack Scripting Host Kixtart PowerShell ScriptLogic VBScript

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  SF8

  SF8 (Korean: 에스 에프 에잇) is a South Korean science fiction anthology television series. It is a movie-drama crossover project between MBC, the Directors Guild of Korea, the OTT platform Wavve and the production company Soo Film. The director's cuts of all episodes were released on Wavve on July 10, 2020 while MBC TV aired one episode a week from August 14 to October 9, 2020. The series has been regarded as a Korean equivalent of the British series Black Mirror as they have the same format and similar themes, though Min Kyu-dong believes that SF8 is more diversified since eight different filmmakers were involved in the project. SF8 was screened at the 24th Bucheon International Fantastic Film Festival. == Synopsis == SF8 revolves around people who dream of a perfect society. It tackles the themes of artificial intelligence, augmented reality, virtual reality, robots, games, fantasy, horror, superpowers and disasters. == Episodes == Short summaries adapted from BiFan. == Production == === Development === Min Kyu-dong, creator of the series, said that "sci-fi movies were the driving force behind many movie directors' dreams. Unfortunately, due to the relatively high budget and narrow market limitations, various works were not able to be produced." He had been working on this project for two years before he partnered with Wavve and MBC. He also took charge of casting the actors, which lasted for a year. During a press conference held at CGV Yongsan I'Park Mall in Seoul on July 8, 2020, Min Kyu-dong said that all the episodes were produced with an equal amount of budget and that the overall budget was lower than one of a small commercial film. Roh Deok, who co-wrote and directed the "Manxin" episode, mentioned that "while commercial film productions [...] inevitably limit the directors' freedom as a creator, [they] had more independence in production" and "although there were physical limits, [he] thinks [they] went through the process of discovering what [they] can do inside those boundaries." === Filming === Eight directors from the Directors Guild of Korea (DGK) each directed an episode from the series. Filming began on February 21, 2020 with Jang Cheol-soo's "White Crow" and ended on May 7 with Kim Ui-seok's "Empty Body". Filming was completed within 10 filming sessions for each episode. === Credits === Credits adapted from BiFan. == Release == The director's cut was released on the OTT platform Wavve on July 10, 2020 and the original episodes were aired on MBC TV from August 14 to October 9.

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  Painworth

  PainWorth is a justice, legal and insurance services application founded by Canadian entrepreneurs Mike Zouhri, Chris Trudel and Ryan Bencic. The application is a "robot lawyer" that uses artificial intelligence to automate personal injury claims for injury victims. It is currently available in Canada and the United States. PainWorth has been featured by several news outlets, including CTV, Global News, CBC, and has also been featured by the American Bar Association and LexisNexis for its role addressing social issues such as access to justice and other systemic issues in the legal and insurance industry. == Application == PainWorth began as a tool for calculating non-pecuniary damages for injury victims but has since expanded beyond a personal injury calculator to include features that help injury victims and business users with pecuniary damages, economic calculations, prescribed rates and providing informational guides to help navigate settlement negotiation, managing claims records and other issues encountered by self-represented litigants or claims managers. The platform makes use of automation to provide free user-guided calculations, steps and processes to successfully settle an injury claim. The application is supported by Microsoft Azure. == Personal Injury Calculator == PainWorth is the first service to use Artificial Intelligence to interpret case law in order to determine the value of pain and suffering incurred by specific injury types and injury severities. The cited case law is used as evidence and presented in statistical models to determine an accurate valuation compliant with the jurisdiction, regulatory rules and case complexities. == General Damages Calculator == PainWorth also offers a personal injury settlement calculator that assesses general damages based on specific case complexities and jurisdiction. The service takes into account medical complications and recovery in order to calculate the fair valuation. == Injury Settlement Platform == PainWorth insurance settlement platform facilitates a direct and automated way resolution center to settle cases for their assessed value without enduring the hardship of litigation. In 2021, Painworth won the title of World's Best Emerging Insurance Product for the development of this platform. == History == In 2019, Mike Zouhri was struck by a drunk driver which left him seriously injured and resulted in a lawsuit. Frustrated by the slow and expensive process, Zouhri went down to the law library and learned how to manage injury claims. After learning the process, he partnered lawyers and legal advisors to create an app to allow users to quickly settle their own injury claims fairly and accurately. Immediately after its launch, PainWorth quickly became widely used by thousands of users and gained significant media coverage. Global News reported that the bot had successfully helped people with more than $10 million in claims in only a few short months, all free of charge. In July 2020, PainWorth began raising concern over injustices and gender bias in the legal system. in Canadian courts.

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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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  Object Data Management Group

  The Object Data Management Group (ODMG) was conceived in the summer of 1991 at a breakfast with object database vendors that was organized by Rick Cattell of Sun Microsystems. In 1998, the ODMG changed its name from the Object Database Management Group to reflect the expansion of its efforts to include specifications for both object database and object–relational mapping products. The primary goal of the ODMG was to put forward a set of specifications that allowed a developer to write portable applications for object database and object–relational mapping products. In order to do that, the data schema, programming language bindings, and data manipulation and query languages needed to be portable. Between 1993 and 2001, the ODMG published five revisions to its specification. The last revision was ODMG version 3.0, after which the group disbanded. == Major components of the ODMG 3.0 specification == Object Model. This was based on the Object Management Group's Object Model. The OMG core model was designed to be a common denominator for object request brokers, object database systems, object programming languages, etc. The ODMG designed a profile by adding components to the OMG core object model. Object Specification Languages. The ODMG Object Definition Language (ODL) was used to define the object types that conform to the ODMG Object Model. The ODMG Object Interchange Format (OIF) was used to dump and load the current state to or from a file or set of files. Object Query Language (OQL). The ODMG OQL was a declarative (nonprocedural) language for query and updating. It used SQL as a basis, where possible, though OQL supports more powerful object-oriented capabilities. C++ Language Binding. This defined a C++ binding of the ODMG ODL and a C++ Object Manipulation Language (OML). The C++ ODL was expressed as a library that provides classes and functions to implement the concepts defined in the ODMG Object Model. The C++ OML syntax and semantics are those of standard C++ in the context of the standard class library. The C++ binding also provided a mechanism to invoke OQL. Smalltalk Language Binding. This defined the mapping between the ODMG ODL and Smalltalk, which was based on the OMG Smalltalk binding for the OMG Interface Definition Language (IDL). The Smalltalk binding also provided a mechanism to invoke OQL. Java Language Binding. This defined the binding between the ODMG ODL and the Java programming language as defined by the Java 2 Platform. The Java binding also provided a mechanism to invoke OQL. == Status == ODMG 3.0 was published in book form in 2000.[1] By 2001, most of the major object database and object-relational mapping vendors claimed conformance to the ODMG Java Language Binding. Compliance to the other components of the specification was mixed.[2] In 2001, the ODMG Java Language Binding was submitted to the Java Community Process as a basis for the Java Data Objects specification. The ODMG member companies then decided to concentrate their efforts on the Java Data Objects specification. As a result, the ODMG disbanded in 2001. In 2004, the Object Management Group (OMG) was granted the right to revise the ODMG 3.0 specification as an OMG specification by the copyright holder, Morgan Kaufmann Publishers. In February 2006, the OMG announced the formation of the Object Database Technology Working Group (ODBT WG) and plans to work on the 4th generation of an object database standard. == ODMG Compliant DBMS == Orient ODBMS: http://www.OrienTechnologies.com Objectivity/DB C++, Java and Smalltalk interfaces.

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  Niceaunties

  Niceaunties is the pseudonym of a Singapore-based artist and designer whose work incorporates generative artificial intelligence, video, and digital installation. Her practice centers around the figure of the "auntie", a common term for older women in Southeast Asian contexts, and explores themes such as aging, care, domesticity, and gender roles. Her work has been featured in exhibitions and media platforms including TED, Christie's Art + Tech, Expanded.Art, and publications such as The Guardian, The Straits Times. == Early life and career == Niceaunties was born in 1981 in Singapore. She attributes her inspiration for "auntie culture" to the matriarchal environment and older women of her household, including her grandmother, while growing up. She is also an architectural designer with Spark Architect. The Niceaunties project began in 2023 after she encountered AI-generated images in her work as an architect. It draws inspiration from women in the artist's family and broader Southeast Asian cultural dynamics. Her work often features AI-generated visuals created with tools such as DALL-E, Krea, RunwayML, and SORA. Her imagery and narratives center on the fictional "Auntieverse", which features older women in imagined settings involving community, ecology, and labor. Her notable works include 'Auntlantis', a five-part video series imagining older women engaged in ocean clean-up and collective ritual, and 'Goddess,' a video created with Sora, featuring a character who gradually forgets her divine identity through years of domestic labor. == Exhibitions == 2024 – Expanded.Art, Berlin – Auntiedote solo exhibition 2024 – TED (conference), Vancouver – Speaker and screening 2024 – Victoria and Albert Museum, London – Digital Art Weekend 2024 – Louisiana Museum of Modern Art, Denmark – Ocean exhibition 2025 – Christie's Augmented Intelligence Auction, New York == Reception == In 2024, Niceaunties gave a TED Talk titled The Weird and Wonderful Art of Niceaunties. Journalist Rebecca Ratcliffe, writing for The Guardian, described her work as combining AI with "the surreal and the political," noting her focus on older women as central characters. Her work has also received criticism for being reliant on generative AI, which many feel exploits and steals from traditional artists.

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  Amazon Bedrock

  Amazon Bedrock is a cloud computing service provided by Amazon Web Services (AWS) for building generative artificial intelligence applications. Launched in 2023, the platform provides a unified API to access foundation models (FMs) from several AI companies, alongside related tools. Bedrock is a serverless computing service which competes with similar enterprise AI platforms such as Microsoft Foundry and Google Cloud Platform. == History == Amazon announced Bedrock on April 13, 2023. The service became generally available on September 28, 2023. Throughout 2024 and 2025, AWS expanded the service to include AI agents, which allow models to interact with external systems. == Features == Knowledge Bases: a managed workflow for Retrieval-Augmented Generation (RAG), which allows models to pull facts from private data stored in Amazon S3. Guardrails: a security feature that allows administrators to set content filters and personally identifiable information redaction across all models in the platform to increase the safety and compliance of AI deployments. == PartyRock == In November 2023, Amazon launched PartyRock, a web-based no-code environment for building generative AI applications. The platform uses a natural language interface to translate user descriptions into software widgets. These widgets enable specific AI behaviors, including text-based prompts, conversational agents, generating images, and the summarization and querying of user-uploaded documents. Although it initially launched with a limited-time free trial, AWS transitioned the service to a recurring free daily usage credit model in early 2025.

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  Emma Hart (computer scientist)

  Professor Emma Hart, FRSE (born 1967) is an English computer scientist known for her work in artificial immune systems (AIS), evolutionary computation and optimisation. She is a professor of computational intelligence at Edinburgh Napier University, editor-in-chief of the Journal of Evolutionary Computation (MIT Press), and D. Coordinator of the Future & Emerging Technologies (FET) Proactive Initiative, Fundamentals of Collective Adaptive Systems. == Early life and education == Hart was born in Middlesbrough, England in 1967. In 1990 she graduated from the University of Oxford with a first class BA(Hons) in Chemistry. She then continued her studies at the University of Edinburgh, graduating with an MSc in Artificial Intelligence in 1994, followed by a PhD that explored the use of immunology as an inspiration for computing, examining a range of techniques applied to optimization and data classification problems. Her dissertation was titled Immunology as a metaphor for computational information processing: Fact or fiction?, and her doctoral advisor was Peter Ross. == Career == In 2000 Hart took a position as a lecturer at Edinburgh Napier University, and was promoted to a Reader, Professor, and in 2008 Chair in Natural Computation. She is now director of the Centre of Algorithms, Visualisation and Evolving Systems (CAVES) group in the School of Computing. She continues to research in the area of developing novel bio-inspired techniques for solving a range of real-world optimisation and classification problems, as well as exploring the fundamental properties of immune-inspired computing through modelling and simulation. She is also involved in editorial activity and currently occupies the position of Editor-in-Chief of the Journal of Evolutionary Computation (MIT Press). Her interests lie in the area of bio-inspired computing, in particular artificial immune systems (AIS). She also undertakes research in three main areas: optimisation, self-organising/self-adaptive systems, and artificial intelligence. Hart is D. Coordinator of Fundamentals of Collective Adaptive Systems (FoCAS), a Future and Emerging Technologies Proactive Initiative funded by the European Commission under FP7. == Selected works == === Conference talks === Hart, Emma. "Lifelong learning in optimization (video)". 28th European Conference on Operational Research. The Association of European Operational Research Societies. Hart, Emma (December 2021). "Self-assembling robots and the potential of artificial evolution". TED talk 2021. === Journal articles === "An immune system approach to scheduling in changing environments". E.Hart, P.Ross. 1999. Proceedings of the 1st Annual Conference on Genetic and Evolutionary Computation (2), 1559–1566. "Exploiting the analogy between immunology and sparse distributed memories: A system for clustering non-stationary data". E.Hart, P.Ross. 2002. 1st International Conference on Artificial Immune Systems. "Evolutionary scheduling: A review". E Hart, P Ross, D Corne. 2005. Genetic Programming and Evolvable Machines 6(2), 191–220. DOI: https://doi.org/10.1007/s10710-005-7580-7 "Application areas of AIS: The past, the present and the future". E.Hart, J.Timmis. 2008. Applied soft computing 8(1), 191–201. DOI: https://doi.org/10.1016/j.asoc.2006.12.004 "Structure versus function: a topological perspective on immune networks". E.Hart, H.Bersini, F.Santos. 2010. Natural computing 9(3), 603–624. DOI: https://doi.org/10.1007/s11047-009-9138-8 "On the life-long learning capabilities of a nelli: A hyper-heuristic optimisation system". E.Hart, K.Sim. 2014. International Conference on Parallel Problem Solving from Nature, 282–291. DOI: https://doi.org/10.1007/978-3-319-10762-2_28 "A hyper-heuristic ensemble method for static job-shop scheduling". E.Hart, K.Sim. 2016. Evolutionary computation 24(4), 609-635. DOI: https://dx.doi.org/10.1162/EVCO_a_00183 == Awards and recognition == 2016, Featured article on Lifelong Learning in Optimisation, IFORS newsletter 2016, "A Combined Generative and Selective Hyper-heuristic for the Vehicle Routing Problem" presented at GECCO 2016 (Denver, USA), ACM 2016, "A Hybrid Parameter Control Approach Applied to a Diversity-based Multi-objective Memetic Algorithm for Frequency Assignment Problems" presented at WCCI 2016 (Vancouver, Canada), IEEE 2017, Keynote Speaker, 2017 International Joint Conference on Computational Intelligence 2018, Bronze Award in International Human-Competitive Awards (Humies), International Conference on Genetic and Evolutionary Computation, Kyoto Japan 2018, Nomination for best paper award, GECCO 18, Kyoto, Japan 2022, Elected Fellow of the Royal Society of Edinburgh

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  Inverse consistency

  In image registration, inverse consistency measures the consistency of mappings between images produced by a registration algorithm. The inverse consistency error, introduced by Christiansen and Johnson in 2001, quantifies the distance between the composition of the mappings from each image to the other, produced by the registration procedure, and the identity function, and is used as a regularisation constraint in the loss function of many registration algorithms to enforce consistent mappings. Inverse consistency is necessary for good image registration but it is not sufficient, since a mapping can be perfectly consistent but not register the images at all. == Definition == Image registration is the process of establishing a common coordinate system between two images, and given two images I 1 : Ω 1 → R I 2 : Ω 2 → R {\displaystyle {\begin{aligned}I_{1}:\Omega _{1}\to \mathbb {R} \\I_{2}:\Omega _{2}\to \mathbb {R} \end{aligned}}} registering a source image I 1 {\displaystyle I_{1}} to a target image I 2 {\displaystyle I_{2}} consists of determining a transformation f 1 : Ω 2 → Ω 1 {\displaystyle f_{1}:\Omega _{2}\to \Omega _{1}} that maps points from the target space to the source space. An ideal registration algorithm should not be sensitive to which image in the pair is used as source or target, and the registration operator should be antisymmetric such that the mappings f 1 : Ω 2 → Ω 1 f 2 : Ω 1 → Ω 2 {\displaystyle {\begin{aligned}f_{1}:\Omega _{2}\to \Omega _{1}\\f_{2}:\Omega _{1}\to \Omega _{2}\end{aligned}}} produced when registering I 1 {\displaystyle I_{1}} to I 2 {\displaystyle I_{2}} and I 2 {\displaystyle I_{2}} to I 1 {\displaystyle I_{1}} respectively should be the inverse of each other, i.e. f 2 = f 1 − 1 {\displaystyle f_{2}=f_{1}^{-1}} and f 1 = f 2 − 1 {\displaystyle f_{1}=f_{2}^{-1}} or, equivalently, f 2 ∘ f 1 = id Ω 2 {\displaystyle f_{2}\circ f_{1}=\operatorname {id} _{\Omega _{2}}} and f 1 ∘ f 2 = id Ω 1 {\displaystyle f_{1}\circ f_{2}=\operatorname {id} _{\Omega _{1}}} , where ∘ {\displaystyle \circ } denotes the function composition operator. Real algorithms are not perfect, and when swapping the role of source and target image in a registration problem the so obtained transformations are not the inverse of each other. Inverse consistency can be enforced by adding to the loss function of the registration a symmetric regularisation term that penalises inconsistent transformations ∫ Ω 2 ‖ f 2 ( f 1 ( x ) ) − x ‖ 2 d x + ∫ Ω 1 ‖ f 1 ( f 2 ( x ) ) − x ‖ 2 d x . {\displaystyle \int _{\Omega _{2}}\left\Vert f_{2}(f_{1}(x))-x\right\Vert ^{2}\mathrm {d} x+\int _{\Omega _{1}}\left\Vert f_{1}(f_{2}(x))-x\right\Vert ^{2}\mathrm {d} x.} Inverse consistency can be used as a quality metric to evaluate image registration results. The inverse consistency error ( I C E {\displaystyle ICE} ) measures the distance between the composition of the two transforms and the identity function, and it can be formulated in terms of both average ( I C E a {\displaystyle ICE_{a}} ) or maximum ( I C E m {\displaystyle ICE_{m}} ) over a region of interest Ω {\displaystyle \Omega } of the image: I C E a = 1 ∫ Ω d x ∫ Ω ‖ f 2 ( f 1 ( x ) ) − x ‖ d x I C E m = max x ∈ Ω ‖ f 2 ( f 1 ( x ) ) − x ‖ . {\displaystyle {\begin{aligned}ICE_{a}&={\frac {1}{\int _{\Omega }\mathrm {d} x}}\int _{\Omega }\left\Vert f_{2}(f_{1}(x))-x\right\Vert \mathrm {d} x\\ICE_{m}&=\max _{x\in \Omega }\left\Vert f_{2}(f_{1}(x))-x\right\Vert .\end{aligned}}} While inverse consistency is a necessary property of good registration algorithms, inverse consistency error alone is not a sufficient metric to evaluate the quality of image registration results, since a perfectly consistent mapping, with no other constraint, may be not even close to correctly register a pair of images.

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  Sugeno integral

  In mathematics, the Sugeno integral, introduced by Michio Sugeno as a fuzzy integral in work on fuzzy measures at the Tokyo Institute of Technology, is a type of integral with respect to a fuzzy measure. Let ( X , Ω ) {\displaystyle (X,\Omega )} be a measurable space and let h : X → [ 0 , 1 ] {\displaystyle h:X\to [0,1]} be an Ω {\displaystyle \Omega } -measurable function. The Sugeno integral over the crisp set A ⊆ X {\displaystyle A\subseteq X} of the function h {\displaystyle h} with respect to the fuzzy measure g {\displaystyle g} is defined by: ∫ A h ( x ) ∘ g = sup E ⊆ X [ min ( min x ∈ E h ( x ) , g ( A ∩ E ) ) ] = sup α ∈ [ 0 , 1 ] [ min ( α , g ( A ∩ F α ) ) ] {\displaystyle \int _{A}h(x)\circ g={\sup _{E\subseteq X}}\left[\min \left(\min _{x\in E}h(x),g(A\cap E)\right)\right]={\sup _{\alpha \in [0,1]}}\left[\min \left(\alpha ,g(A\cap F_{\alpha })\right)\right]} where F α = { x | h ( x ) ≥ α } {\displaystyle F_{\alpha }=\left\{x|h(x)\geq \alpha \right\}} . The Sugeno integral over the fuzzy set A ~ {\displaystyle {\tilde {A}}} of the function h {\displaystyle h} with respect to the fuzzy measure g {\displaystyle g} is defined by: ∫ A h ( x ) ∘ g = ∫ X [ h A ( x ) ∧ h ( x ) ] ∘ g {\displaystyle \int _{A}h(x)\circ g=\int _{X}\left[h_{A}(x)\wedge h(x)\right]\circ g} where h A ( x ) {\displaystyle h_{A}(x)} is the membership function of the fuzzy set A ~ {\displaystyle {\tilde {A}}} . == Usage and Relationships == Sugeno integral is related to h-index.

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  Vibe coding

  Vibe coding is a software development practice assisted by artificial intelligence (AI) where the software developer describes a project or task in a prompt to a large language model (LLM), which generates source code automatically. Vibe coding may involve accepting AI-generated code without thorough review of the output, instead relying on results and follow-up prompts to guide changes. The term was coined in February 2025 by computer scientist Andrej Karpathy, a co-founder of OpenAI and former AI leader at Tesla. Merriam-Webster listed the term in March 2025 as a "slang & trending" expression. It was named the Collins English Dictionary Word of the Year for 2025. Advocates of vibe coding say that it allows even amateur programmers to produce software without the extensive training and skills required for software engineering. Critics point out a lack of accountability, maintainability, and the increased risk of introducing security vulnerabilities in the resulting software. == Definition == The concept refers to a coding approach that relies on LLMs, allowing programmers to generate working code by providing natural language descriptions rather than manually writing in a formal programming language. Karpathy described it as a form of coding where you "fully give in to the vibes, embrace exponentials, and forget that the code even exists". When vibe coding, the programmer guides, tests, and gives feedback about the AI-generated source code, rather than manually writing code. The concept of vibe coding elaborates on Karpathy's claim from 2023 that "the hottest new programming language is English", meaning that the capabilities of LLMs were such that humans would no longer need to learn specific programming languages to command computers. Some commentators argue that a key to the definition is a lack of knowledge about the code, and that thorough review and testing is incompatible with the definition of vibe coding. Programmer Simon Willison said: "If an LLM wrote every line of your code, but you've reviewed, tested, and understood it all, that's not vibe coding in my book—that's using an LLM as a typing assistant." == Reception and use == In February 2025, New York Times journalist Kevin Roose, who is not a professional coder, experimented with vibe coding to create several small-scale applications. He described these as "software for one" due to the ability to personalize the software. However, Roose also stated that the results are often limited and prone to errors. In one case, the AI-generated code fabricated fake reviews for an e-commerce site. In response to Roose, cognitive scientist Gary Marcus said that the algorithm that generated Roose's LunchBox Buddy app had presumably been trained on existing code for similar tasks. Marcus said that Roose's enthusiasm stemmed from reproduction, not originality. In March 2025, Y Combinator reported that 25% of startup companies in its Winter 2025 batch had codebases that were 95% AI-generated, reflecting a shift toward AI-assisted development within newer startups. The question asked was about AI-generated code in general, and not specifically about vibed code. Inspired by "vibe coding", The Economist suggested the term "vibe valuation" to describe the very large valuations of AI startups by venture capital firms that ignore accepted metrics such as annual recurring revenue. In June 2025, Andrew Ng took issue with the term, saying that it misleads people into assuming that software engineers just "go with the vibes" when using AI tools to create applications. In July 2025, The Wall Street Journal reported that vibe coding was being adopted by professional software engineers for commercial use cases. In July 2025, SaaStr founder documented his negative experiences with vibe coding: Replit's AI agent deleted a database despite explicit instructions not to make any changes. In September 2025, Fast Company reported that the "vibe coding hangover" is upon us, with senior software engineers citing "development hell" when working with AI-generated code. It was reported in January 2026 that Linus Torvalds had made use of Google Antigravity to vibe code a tool component of his AudioNoise random digital audio effects generator. Torvalds explained in the project's README file that "the Python visualizer tool has been basically written by vibe-coding". == Criticism == === Quality of code and security issues === Vibe coding has raised concerns about understanding and accountability. Developers may use AI-generated code without comprehending its functionality, leading to undetected bugs, errors, or security vulnerabilities. While this approach may be suitable for prototyping or "throwaway weekend projects" as Karpathy originally envisioned, it is considered by some experts to pose risks in professional settings, where a deep understanding of the code is crucial for debugging, maintenance, and security. Ars Technica cites Simon Willison, who stated: "Vibe coding your way to a production codebase is clearly risky. Most of the work we do as software engineers involves evolving existing systems, where the quality and understandability of the underlying code is crucial." In May 2025, Lovable, a Swedish vibe coding app, was reported to have security vulnerabilities in the code it generated, with 170 out of 1,645 Lovable-created web applications having an issue that would allow personal information to be accessed by anyone. In October 2025 Veracode released a study that showed that over the last 3 years LLMs had become dramatically better at generating functional code, but that the security of generated code had generally not improved. Moreover, larger models were not better than small ones at generating secure code. There was a small increase in security from the OpenAI reasoning models, but not in other reasoning models, and this increase was nothing like the improvement in generated functionality. In December 2025, computer security researcher Etizaz Mohsin discovered a security flaw in the Orchids vibe coding platform, which he demonstrated to a BBC News reporter in February 2026. A December 2025 analysis by CodeRabbit of 470 open-source GitHub pull requests found that code that was co-authored by generative AI contained approximately 1.7 times more "major" issues compared to human-written code. The study revealed that AI co-authored code showed elevated rates of logic errors, including incorrect dependencies, flawed control flow, misconfigurations (75% more common), and security vulnerabilities (2.74x higher). Additionally, they also reported high code readability issues, including formatting errors and naming inconsistencies. === Code maintainability and technical debt === Vibe coding has the potential of making code harder to maintain in the longer term, leading to technical debt. In early 2025, GitClear published the results of a longitudinal analysis of 211 million lines of code changes from 2020 to 2024. They found that the volume of code refactoring dropped from 25% of changed lines in 2021 to under 10% by 2024, code duplication increased approximately four times in volume, copy-pasted code exceeded moved code for the first time in two decades, and code churn (prematurely merged code getting rewritten shortly after merging) nearly doubled. === Task complexity and developer productivity === Generative AI is highly capable of handling simple tasks like basic algorithms. However, such systems struggle with more novel, complex coding problems like projects involving multiple files, poorly documented libraries, or safety-critical code. In July 2025, METR, an organization that evaluates frontier models, ran a randomized controlled trial to understand developer productivity involving generative AI programming tools available in early 2025. They found that experienced open-source developers were 19% slower when using AI coding tools, despite predicting they would be 24% faster and still believing afterward they had been 20% faster. === Challenges with debugging === LLMs generate code dynamically, and the structure of such code may be subject to variation. In addition, since the developer did not write the code, the developer may struggle to understand its syntax and concepts. === Impact on open-source software === In January 2026, a paper authored by experts from several universities titled "Vibe Coding Kills Open Source" argued that vibe coding has negative impact on the open-source software ecosystem. The authors say that increased vibe coding reduces user engagement with open-source maintainers, which has hidden costs for said maintainers. Speaking with The Register about their paper, the authors argued:"Vibe coding raises productivity by lowering the cost of using and building on existing code, but it also weakens the user engagement through which many maintainers earn returns," the authors argue. "When OSS is monetized only through direct user engagement, greater adoption of vibe coding lowers e

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