AI Chatbot No Filter No Limit

AI Chatbot No Filter No Limit — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Joint constraints

  Joint constraints are rotational constraints on the joints of an artificial system. They are used in an inverse kinematics chain, in fields including 3D animation or robotics. Joint constraints can be implemented in a number of ways, but the most common method is to limit rotation about the X, Y and Z axis independently. An elbow, for instance, could be represented by limiting rotation on X and Z axis to 0 degrees, and constraining the Y-axis rotation to 130 degrees. To simulate joint constraints more accurately, dot-products can be used with an independent axis to repulse the child bones orientation from the unreachable axis. Limiting the orientation of the child bone to a border of vectors tangent to the surface of the joint, repulsing the child bone away from the border, can also be useful in the precise restriction of shoulder movement.

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  Information

  Information is an abstract concept that refers to something which has the power to inform. At the most fundamental level, it pertains to the interpretation (perhaps formally) of that which may be sensed, or their abstractions. Any natural process that is not completely random and any observable pattern in any medium can be said to convey some amount of information. Whereas digital signals and other data use discrete signs to convey information, other phenomena and artifacts such as analogue signals, poems, pictures, music or other sounds, and currents convey information in a more continuous form. Information is not knowledge itself, but the meaning that may be derived from a representation through interpretation. The concept of information is relevant to and connected with various concepts, including constraint, communication, control, data, form, education, knowledge, meaning, understanding, mental stimuli, pattern, perception, proposition, representation, and entropy. Information is often processed iteratively: Data available at one step are processed into information to be interpreted and processed at the next step. For example, in written text each symbol or letter conveys information relevant to the word it is part of, each word conveys information relevant to the phrase it is part of, each phrase conveys information relevant to the sentence it is part of, and so on until at the final step information is interpreted and becomes knowledge in a given domain. In a digital signal, bits may be interpreted into the symbols, letters, numbers, or structures that convey the information available at the next level up. The key characteristic of information is that it is subject to interpretation and processing. The derivation of information from a signal or message may be thought of as the resolution of ambiguity or uncertainty that arises during the interpretation of patterns within the signal or message. Information may be structured as data. Redundant data can be compressed up to an optimal size, which is the theoretical limit of compression. The information available through a collection of data may be derived by analysis. For example, a restaurant collects data from every customer order. That information may be analyzed to produce knowledge that is put to use when the business subsequently wants to identify the most popular or least popular dish. Information can be transmitted in time, via data storage, and space, via communication and telecommunication. Information is expressed either as the content of a message or through direct or indirect observation. That which is perceived can be construed as a message in its own right, and in that sense, all information is always conveyed as the content of a message. Information can be encoded into various forms for transmission and interpretation (for example, information may be encoded into a sequence of signs, or transmitted via a signal). It can also be encrypted for safe storage and communication. The uncertainty of an event is measured by its probability of occurrence. Uncertainty is proportional to the negative logarithm of the probability of occurrence. Information theory takes advantage of this by concluding that more uncertain events require more information to resolve their uncertainty. The bit is the standard unit of information. It is 'that which reduces uncertainty by half'. Other units such as the nat may be used. For example, the information encoded in one "fair" coin flip is log2(2/1) = 1 bit, and in two fair coin flips is log2(4/1) = 2 bits. A 2011 Science article estimates that 97% of technologically stored information was already in digital bits in 2007 and that the year 2002 was the beginning of the digital age for information storage (with digital storage capacity bypassing analogue for the first time). == Etymology and history of the concept == The English word "information" comes from Middle French enformacion/informacion/information 'a criminal investigation' and its etymon, Latin informatiō(n) 'conception, teaching, creation'. In English, "information" is an uncountable mass noun. References on "formation or molding of the mind or character, training, instruction, teaching" date from the 14th century in both English (according to Oxford English Dictionary) and other European languages. In the transition from Middle Ages to Modernity the use of the concept of information reflected a fundamental turn in epistemological basis – from "giving a (substantial) form to matter" to "communicating something to someone". Peters (1988, pp. 12–13) concludes: Information was readily deployed in empiricist psychology (though it played a less important role than other words such as impression or idea) because it seemed to describe the mechanics of sensation: objects in the world inform the senses. But sensation is entirely different from "form" – the one is sensual, the other intellectual; the one is subjective, the other objective. My sensation of things is fleeting, elusive, and idiosyncratic. For Hume, especially, sensory experience is a swirl of impressions cut off from any sure link to the real world... In any case, the empiricist problematic was how the mind is informed by sensations of the world. At first informed meant shaped by; later it came to mean received reports from. As its site of action drifted from cosmos to consciousness, the term's sense shifted from unities (Aristotle's forms) to units (of sensation). Information came less and less to refer to internal ordering or formation, since empiricism allowed for no preexisting intellectual forms outside of sensation itself. Instead, information came to refer to the fragmentary, fluctuating, haphazard stuff of sense. Information, like the early modern worldview in general, shifted from a divinely ordered cosmos to a system governed by the motion of corpuscles. Under the tutelage of empiricism, information gradually moved from structure to stuff, from form to substance, from intellectual order to sensory impulses. In the modern era, the most important influence on the concept of information is derived from the Information theory developed by Claude Shannon and others. This theory, however, reflects a fundamental contradiction. Northrup (1993) wrote: Thus, actually two conflicting metaphors are being used: The well-known metaphor of information as a quantity, like water in the water-pipe, is at work, but so is a second metaphor, that of information as a choice, a choice made by :an information provider, and a forced choice made by an :information receiver. Actually, the second metaphor implies that the information sent isn't necessarily equal to the information received, because any choice implies a comparison with a list of possibilities, i.e., a list of possible meanings. Here, meaning is involved, thus spoiling the idea of information as a pure "Ding an sich." Thus, much of the confusion regarding the concept of information seems to be related to the basic confusion of metaphors in Shannon's theory: is information an autonomous quantity, or is information always per SE information to an observer? Actually, I don't think that Shannon himself chose one of the two definitions. Logically speaking, his theory implied information as a subjective phenomenon. But this had so wide-ranging epistemological impacts that Shannon didn't seem to fully realize this logical fact. Consequently, he continued to use metaphors about information as if it were an objective substance. This is the basic, inherent contradiction in Shannon's information theory." (Northrup, 1993, p. 5). In their seminal book The Study of Information: Interdisciplinary Messages, Almach and Mansfield (1983) collected key views on the interdisciplinary controversy in computer science, artificial intelligence, library and information science, linguistics, psychology, and physics, as well as in the social sciences. Almach (1983, p. 660) himself disagrees with the use of the concept of information in the context of signal transmission, the basic senses of information in his view all referring "to telling something or to the something that is being told. Information is addressed to human minds and is received by human minds." All other senses, including its use with regard to nonhuman organisms as well to society as a whole, are, according to Machlup, metaphoric and, as in the case of cybernetics, anthropomorphic. Hjørland (2007) describes the fundamental difference between objective and subjective views of information and argues that the subjective view has been supported by, among others, Bateson, Yovits, Span-Hansen, Brier, Buckland, Goguen, and Hjørland. Hjørland provided the following example: A stone on a field could contain different information for different people (or from one situation to another). It is not possible for information systems to map all the stone's possible information for every individual. Nor is any one mapping the one "true" mapping. But peop

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  Online analytical processing

  In computing, online analytical processing (OLAP) (), is an approach to quickly answer multi-dimensional analytical (MDA) queries. The term OLAP was created as a slight modification of the traditional database term online transaction processing (OLTP). OLAP is part of the broader category of business intelligence, which also encompasses relational databases, report writing and data mining. Typical applications of OLAP include business reporting for sales, marketing, management reporting, business process management (BPM), budgeting and forecasting, financial reporting and similar areas, with new applications emerging, such as agriculture. OLAP tools enable users to analyse multidimensional data interactively from multiple perspectives. OLAP consists of three basic analytical operations: consolidation (roll-up), drill-down, and slicing and dicing. Consolidation involves the aggregation of data that can be accumulated and computed in one or more dimensions. For example, all sales offices are rolled up to the sales department or sales division to anticipate sales trends. By contrast, the drill-down is a technique that allows users to navigate through the details. For instance, users can view the sales by individual products that make up a region's sales. Slicing and dicing is a feature whereby users can take out (slicing) a specific set of data of the OLAP cube and view (dicing) the slices from different viewpoints. These viewpoints are sometimes called dimensions (such as looking at the same sales by salesperson, or by date, or by customer, or by product, or by region, etc.). Databases configured for OLAP use a multidimensional data model, allowing for complex analytical and ad hoc queries with a rapid execution time. They borrow aspects of navigational databases, hierarchical databases and relational databases. OLAP is typically contrasted to OLTP (online transaction processing), which is generally characterized by much less complex queries, in a larger volume, to process transactions rather than for the purpose of business intelligence or reporting. Whereas OLAP systems are mostly optimized for read, OLTP has to process all kinds of queries (read, insert, update and delete). == Overview of OLAP systems == At the core of any OLAP system is an OLAP cube (also called a 'multidimensional cube' or a hypercube). It consists of numeric facts called measures that are categorized by dimensions. The measures are placed at the intersections of the hypercube, which is spanned by the dimensions as a vector space. The usual interface to manipulate an OLAP cube is a matrix interface, like Pivot tables in a spreadsheet program, which performs projection operations along the dimensions, such as aggregation or averaging. The cube metadata is typically created from a star schema or snowflake schema or fact constellation of tables in a relational database. Measures are derived from the records in the fact table and dimensions are derived from the dimension tables. Each measure can be thought of as having a set of labels, or meta-data associated with it. A dimension is what describes these labels; it provides information about the measure. A simple example would be a cube that contains a store's sales as a measure, and Date/Time as a dimension. Each Sale has a Date/Time label that describes more about that sale. For example: Sales Fact Table +-------------+----------+ | sale_amount | time_id | +-------------+----------+ Time Dimension | 930.10| 1234 |----+ +---------+-------------------+ +-------------+----------+ | | time_id | timestamp | | +---------+-------------------+ +---->| 1234 | 20080902 12:35:43 | +---------+-------------------+ === Multidimensional databases === Multidimensional structure is defined as "a variation of the relational model that uses multidimensional structures to organize data and express the relationships between data". The structure is broken into cubes and the cubes are able to store and access data within the confines of each cube. "Each cell within a multidimensional structure contains aggregated data related to elements along each of its dimensions". Even when data is manipulated it remains easy to access and continues to constitute a compact database format. The data still remains interrelated. Multidimensional structure is quite popular for analytical databases that use online analytical processing (OLAP) applications. Analytical databases use these databases because of their ability to deliver answers to complex business queries swiftly. Data can be viewed from different angles, which gives a broader perspective of a problem unlike other models. === Aggregations === It has been claimed that for complex queries OLAP cubes can produce an answer in around 0.1% of the time required for the same query on OLTP relational data. The most important mechanism in OLAP which allows it to achieve such performance is the use of aggregations. Aggregations are built from the fact table by changing the granularity on specific dimensions and aggregating up data along these dimensions, using an aggregate function (or aggregation function). The number of possible aggregations is determined by every possible combination of dimension granularities. The combination of all possible aggregations and the base data contains the answers to every query which can be answered from the data. Because usually there are many aggregations that can be calculated, often only a predetermined number are fully calculated; the remainder are solved on demand. The problem of deciding which aggregations (views) to calculate is known as the view selection problem. View selection can be constrained by the total size of the selected set of aggregations, the time to update them from changes in the base data, or both. The objective of view selection is typically to minimize the average time to answer OLAP queries, although some studies also minimize the update time. View selection is NP-complete. Many approaches to the problem have been explored, including greedy algorithms, randomized search, genetic algorithms and A search algorithm. Some aggregation functions can be computed for the entire OLAP cube by precomputing values for each cell, and then computing the aggregation for a roll-up of cells by aggregating these aggregates, applying a divide and conquer algorithm to the multidimensional problem to compute them efficiently. For example, the overall sum of a roll-up is just the sum of the sub-sums in each cell. Functions that can be decomposed in this way are called decomposable aggregation functions, and include COUNT, MAX, MIN, and SUM, which can be computed for each cell and then directly aggregated; these are known as self-decomposable aggregation functions. In other cases, the aggregate function can be computed by computing auxiliary numbers for cells, aggregating these auxiliary numbers, and finally computing the overall number at the end; examples include AVERAGE (tracking sum and count, dividing at the end) and RANGE (tracking max and min, subtracting at the end). In other cases, the aggregate function cannot be computed without analyzing the entire set at once, though in some cases approximations can be computed; examples include DISTINCT COUNT, MEDIAN, and MODE; for example, the median of a set is not the median of medians of subsets. These latter are difficult to implement efficiently in OLAP, as they require computing the aggregate function on the base data, either computing them online (slow) or precomputing them for possible rollouts (large space). == Types == OLAP systems have been traditionally categorized using the following taxonomy. === Multidimensional OLAP (MOLAP) === MOLAP (multi-dimensional online analytical processing) is the classic form of OLAP and is sometimes referred to as just OLAP. MOLAP stores this data in an optimized multi-dimensional array storage, rather than in a relational database. Some MOLAP tools require the pre-computation and storage of derived data, such as consolidations – the operation known as processing. Such MOLAP tools generally utilize a pre-calculated data set referred to as a data cube. The data cube contains all the possible answers to a given range of questions. As a result, they have a very fast response to queries. On the other hand, updating can take a long time depending on the degree of pre-computation. Pre-computation can also lead to what is known as data explosion. Other MOLAP tools, particularly those that implement the functional database model do not pre-compute derived data but make all calculations on demand other than those that were previously requested and stored in a cache. Advantages of MOLAP Fast query performance due to optimized storage, multidimensional indexing and caching. Smaller on-disk size of data compared to data stored in relational database due to compression techniques. Automated computation of higher-level aggregates of the data. It is very compact for low dimension data se

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  Organizational information theory

  Organizational Information Theory (OIT) is a communication theory, developed by Karl Weick, offering systemic insight into the processing and exchange of information within organizations and among its members. Unlike the past structure-centered theory, OIT focuses on the process of organizing in dynamic, information-rich environments. Given that, it contends that the main activity of organizations is the process of making sense of equivocal information. Organizational members are instrumental to reduce equivocality and achieve sensemaking through some strategies — enactment, selection, and retention of information. With a framework that is interdisciplinary in nature, organizational information theory's desire to eliminate both ambiguity and complexity from workplace messaging builds upon earlier findings from general systems theory and phenomenology. == Inspiration and influence of pre-existing theories == 1. General Systems Theory The General Systems Theory, on its most basic premise, describes the phenomenon of a cohesive group of interrelated parts. When one part of the system is changed or affected, it will affect the system as a whole. Weick uses this theoretical framework from 1950 to influence his organizational information theory. Likewise, organizations can be viewed as a system of related parts that work together towards a common goal or vision. Applying this to Weick's organizational information theory, organizations must work to reduce ambiguity and complexity in the workplace to maximize cohesiveness and efficiency. Weick uses the term, coupling, to describe how organizations, like a system, can be composed of interrelated and dependent parts. Coupling looks at the relationship between people and work. There are two types of coupling: 1. Loose coupling Loose coupling describes that while people within the organization or system are connected and often work together, they do not depend on one another to continue or fully complete individual work. The dependencies are weak and workflow is flexible. For example, "if the whole Science department completely shuts down because all of teachers are sick or for whatsoever reason, the school can still continue to operate because other departments are still present." 2. Tight coupling Tight coupling describes when connections within an organization are strong and dependent. If one part of the organization is not operating correctly, the organization as a whole cannot continue to their fullest potential. " For instance, the format and ink section completely shuts down hence the succeeding steps cannot be continued, so the whole process of the organization will be dropped. Thus, components of a system are directly dependent on one another." 2. Theory of evolution The theory of evolution, by Charles Darwin, is a framework for survival of the fittest. According to Darwin, organisms attempt to adapt and live in an unforgiving environment. Those that are unsuccessful in adaptation do not survive, while the strong organisms continue to thrive and reproduce. Weick invokes inspiration from Darwin, to incorporate a biological perspective to his theory. It is natural for organizations to have to adapt to incoming information that often interfere with the preexisting environment. Organizations that are able to plan and alter strategies in accordance with their constant need of organizing and sense making, will survive and be the most successful. However, there is a notable difference between animal evolution and survival of the fittest in organizations, "A given animal is what it is; variation comes through mutation. But the nature of an organization can change when its members alter their behavior." == Assumptions == 1. Human organizations exist in an information environment Unlike senders and receivers models, OIT stands on the situational perspective. Karl Weick views a human organization as an open social system. People in that system develop a mechanism to establish goals, obtain and process information, or perceive the environment. In this process, people and the environment come to conclusions on "what's going on here?". Colville believes that this attributional process is retrospective. Take an education institution as an example. A university can obtain information regarding students' needs in numerous ways. It might create feedback section in its website. It could organize alumni panels or academic affairs to attract prospective students and collect concrete questions they are interested in. It may also conduct the survey or host focus group to get the information. After that, the staff of the university have to decide how to deal with these information, based on which, it has to set and accomplish its goals for current and prospective students. 2. The information an organization receives differs in terms of equivocality Weick posits that numerous feasible interpretations of reality exist when organizations process information. Their varying levels of understandability lead to different outcomes of information inputs. In other academic works, scholars tend to say that messages are uncertain or ambiguous. While according to OIT, messages are described to be equivocal. believes that people proactively exclude a number of possibilities to perceive what is going on in the environment. Due to OIT's situational perspective, the meanings of messages consist of the messages, the interpretations of receivers, and the interactional context. However, ambiguity and uncertainty can mean that a standard answer - the only one true objective interpretation - exists. Also, Weick emphasizes that "the equivocality is the engine that motivates people to organize". Maitlis and Christianson states that the equivocality trigger sensemaking for three reasons: environment jolts and organizational crises, threats to identity, and planned change interventions. 3. Human organizations engage in information processing to reduce equivocality of information Based upon the first two assumption, OIT proposes that information processing within organizations is a social activity. Sharing is the key feature of organizational information processing. In that particular context, members jointly make sense the reality by reducing equivocality. It other words, the sensemaking is a joint responsibility which includes numerous interdependent people to accomplish. In this process, organizations and its members combine actions and attributions together in order to find the balance between the complexity of thoughts and the simplicity of actions. Weick also proposes that people create their own environment though enactment, which is the action of making sense. This is because people have different perceptual schemas and selective perception, so people create different information environments. In creating different information environments, people can arrive at the same or close to the same understanding or solution through different thought processes and overall understanding. == Key concepts == === The organization === In order to place Weick's vision regarding Organizational Information Theory into proper working context, exploring his view regarding what constitutes the organization and how its individuals embody that construct might yield significant insights. From a fundamental standpoint, he shared a belief that organizational validation is derived---not through bricks and mortar, or locale—but from a series of events which enable entities to "collect, manage and use the information they receive." In elaborating further on what constitutes an organization during early writings outlining OIT, Weick said, "The word organization is a noun and it is also a myth. if one looks for an organization, one will not find it. What will be found is that there are events linked together, that transpire within concrete walls and these sequences, their pathways, their timing, are the forms we erroneously make into substances when we talk about an organization". When viewed in this modular fashion, the organization meets Weick's theoretical vision by encompassing parameters that are less bound by concrete, wood, and structural restraints and more by an ability to serve as a repository where information can be consistently and effectively channeled. Taking these defining characteristics into account, proper channel execution relies on maximization of messaging clarity, context, delivery and evolution through any system. One example as to how these interactions might unfold on a more granular level within these confines can be gleaned through Weick's double interact loop, which he considers the "building blocks of every organization". Simply put, double interacts describe interpersonal exchanges that, inherently, occur across the organizational chain of command and in life, itself. Thus: "An act occurs when you say something (Can I have a Popsicle?). An interact occurs when you say something and I respond ("No, it will spoil your dinner

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  Clapper (service)

  Clapper is an American short-form video-hosting service headquartered in Dallas, Texas. It was founded in 2020 by Edison Chen as an alternative for TikTok for mature audiences. The app is functionally similar to TikTok and includes tipping and e-commerce features. Following an influx of far-right content in early 2021, Clapper strengthened its moderation practices. It achieved 2 million monthly active users by 2023, and the number of downloads increased after a U.S. bill that would potentially ban TikTok in the country was signed in 2024. == History == With its offices in Dallas, Texas, Clapper was founded in July 2020 by Chinese-American entrepreneur Edison Chen. Chen considered that most online platforms, such as TikTok, were being targeted to young generations, such as Generation Z. He then concepted Clapper as a service with short-form content for mature audiences among Generation X and millennials, while not intending to compete directly with TikTok. Clapper averaged fewer than ten thousand daily active users during 2020, reaching 500 thousand downloads in the next year. Initially without paying for external advertising, the company raised about $3 million during a 2021 seed funding round. In 2023, the app reportedly reached about 300 to 400 thousand daily active users and 2 million monthly active users. The average user was between the ages of 35 and 55. Following the April 2024 signing of the Protecting Americans from Foreign Adversary Controlled Applications Act, which would potentially enact a ban on TikTok in the U.S. in January 2025, Clapper averaged 200 thousand weekly downloads. In 2025, before the day scheduled for the ban (January 19), TikTok users migrated to other apps. As a result, Clapper received 1.4 million new downloads in a week preceding the date. It was listed as the third most-downloaded free app on Apple's App Store on January 14, behind Xiaohongshu and Lemon8, and the term "TikTok refugee" became a trending term. == Features == Clapper presents similarities with TikTok in its layout, including "Following" and "For You" tabs with videos up to three minutes long that can be liked, commented on or shared. A "Clapback" feature allows users to create responses to videos from others. Users can create livestreams and chat rooms in the app. Users can tip Clapper creators through its Clapper Fam monetization feature, in place of in-app advertisements. The Clapper Shop allows for e-commerce between users. The service had distributed $10 million to its users in total by 2023, according to Clapper CEO Chen. == Content == Clapper includes a policy requiring users to be at least 17 years of age, although Clapper CEO Chen described that "there is no adult content" on the platform. Lindsay Dodgson of Business Insider described the content as generally outdated and "reminiscent of 'getting owned' compilations of the earlier internet." The Washington Post's Tatum Hunter characterized Clapper as including sexual or engagement baiting content more prevalently than TikTok. === Moderation === Clapper's team, which had fifteen employees in early 2021, initially stated it would not moderate content as strictly as TikTok and would mostly rely on user reports. Following that year's January 6 United States Capitol attack, far-right conservative videos promoting QAnon and anti-vaccine conspiracy theories appeared on Clapper's "For You" page to a substantial degree for weeks. The videos were made in protest against decisions by platforms, particularly TikTok, to ban such content. Clapper's team stated in January 10 that its rules prohibiting incitements to violence would be strictly enforced. By February, videos and accounts promoting the conspiracy theories had been removed, and QAnon-related content was banned permanently. Clapper's team hired more content auditors and implemented moderation by artificial intelligence for further community guideline violations.

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  Birkhoff algorithm

  Birkhoff's algorithm (also called Birkhoff-von-Neumann algorithm) is an algorithm for decomposing a bistochastic matrix into a convex combination of permutation matrices. It was published by Garrett Birkhoff in 1946. It has many applications. One such application is for the problem of fair random assignment: given a randomized allocation of items, Birkhoff's algorithm can decompose it into a lottery on deterministic allocations. == Terminology == A bistochastic matrix (also called: doubly-stochastic) is a matrix in which all elements are greater than or equal to 0 and the sum of the elements in each row and column equals 1. An example is the following 3-by-3 matrix: ( 0.2 0.3 0.5 0.6 0.2 0.2 0.2 0.5 0.3 ) {\displaystyle {\begin{pmatrix}0.2&0.3&0.5\\0.6&0.2&0.2\\0.2&0.5&0.3\end{pmatrix}}} A permutation matrix is a special case of a bistochastic matrix, in which each element is either 0 or 1 (so there is exactly one "1" in each row and each column). An example is the following 3-by-3 matrix: ( 0 1 0 0 0 1 1 0 0 ) {\displaystyle {\begin{pmatrix}0&1&0\\0&0&1\\1&0&0\end{pmatrix}}} A Birkhoff decomposition (also called: Birkhoff-von-Neumann decomposition) of a bistochastic matrix is a presentation of it as a sum of permutation matrices with non-negative weights. For example, the above matrix can be presented as the following sum: 0.2 ( 0 1 0 0 0 1 1 0 0 ) + 0.2 ( 1 0 0 0 1 0 0 0 1 ) + 0.1 ( 0 1 0 1 0 0 0 0 1 ) + 0.5 ( 0 0 1 1 0 0 0 1 0 ) {\displaystyle 0.2{\begin{pmatrix}0&1&0\\0&0&1\\1&0&0\end{pmatrix}}+0.2{\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix}}+0.1{\begin{pmatrix}0&1&0\\1&0&0\\0&0&1\end{pmatrix}}+0.5{\begin{pmatrix}0&0&1\\1&0&0\\0&1&0\end{pmatrix}}} Birkhoff's algorithm receives as input a bistochastic matrix and returns as output a Birkhoff decomposition. == Tools == A permutation set of an n-by-n matrix X is a set of n entries of X containing exactly one entry from each row and from each column. A theorem by Dénes Kőnig says that: Every bistochastic matrix has a permutation-set in which all entries are positive.The positivity graph of an n-by-n matrix X is a bipartite graph with 2n vertices, in which the vertices on one side are n rows and the vertices on the other side are the n columns, and there is an edge between a row and a column if the entry at that row and column is positive. A permutation set with positive entries is equivalent to a perfect matching in the positivity graph. A perfect matching in a bipartite graph can be found in polynomial time, e.g. using any algorithm for maximum cardinality matching. Kőnig's theorem is equivalent to the following:The positivity graph of any bistochastic matrix admits a perfect matching.A matrix is called scaled-bistochastic if all elements are non-negative, and the sum of each row and column equals c, where c is some positive constant. In other words, it is c times a bistochastic matrix. Since the positivity graph is not affected by scaling:The positivity graph of any scaled-bistochastic matrix admits a perfect matching. == Algorithm == Birkhoff's algorithm is a greedy algorithm: it greedily finds perfect matchings and removes them from the fractional matching. It works as follows. Let i = 1. Construct the positivity graph GX of X. Find a perfect matching in GX, corresponding to a positive permutation set in X. Let z[i] > 0 be the smallest entry in the permutation set. Let P[i] be a permutation matrix with 1 in the positive permutation set. Let X := X − z[i] P[i]. If X contains nonzero elements, Let i = i + 1 and go back to step 2. Otherwise, return the sum: z[1] P[1] + ... + z[2] P[2] + ... + z[i] P[i]. The algorithm is correct because, after step 6, the sum in each row and each column drops by z[i]. Therefore, the matrix X remains scaled-bistochastic. Therefore, in step 3, a perfect matching always exists. == Run-time complexity == By the selection of z[i] in step 4, in each iteration at least one element of X becomes 0. Therefore, the algorithm must end after at most n2 steps. However, the last step must simultaneously make n elements 0, so the algorithm ends after at most n2 − n + 1 steps, which implies O ( n 2 ) {\displaystyle O(n^{2})} . In 1960, Joshnson, Dulmage and Mendelsohn showed that Birkhoff's algorithm actually ends after at most n2 − 2n + 2 steps, which is tight in general (that is, in some cases n2 − 2n + 2 permutation matrices may be required). == Application in fair division == In the fair random assignment problem, there are n objects and n people with different preferences over the objects. It is required to give an object to each person. To attain fairness, the allocation is randomized: for each (person, object) pair, a probability is calculated, such that the sum of probabilities for each person and for each object is 1. The probabilistic-serial procedure can compute the probabilities such that each agent, looking at the matrix of probabilities, prefers his row of probabilities over the rows of all other people (this property is called envy-freeness). This raises the question of how to implement this randomized allocation in practice? One cannot just randomize for each object separately, since this may result in allocations in which some people get many objects while other people get no objects. Here, Birkhoff's algorithm is useful. The matrix of probabilities, calculated by the probabilistic-serial algorithm, is bistochastic. Birkhoff's algorithm can decompose it into a convex combination of permutation matrices. Each permutation matrix represents a deterministic assignment, in which every agent receives exactly one object. The coefficient of each such matrix is interpreted as a probability; based on the calculated probabilities, it is possible to pick one assignment at random and implement it. == Extensions == The problem of computing the Birkhoff decomposition with the minimum number of terms has been shown to be NP-hard, but some heuristics for computing it are known. This theorem can be extended for the general stochastic matrix with deterministic transition matrices. Budish, Che, Kojima and Milgrom generalize Birkhoff's algorithm to non-square matrices, with some constraints on the feasible assignments. They also present a decomposition algorithm that minimizes the variance in the expected values. Vazirani generalizes Birkhoff's algorithm to non-bipartite graphs. Valls et al. showed that it is possible to obtain an ϵ {\displaystyle \epsilon } -approximate decomposition with O ( log ⁡ ( 1 / ϵ 2 ) ) {\displaystyle O(\log(1/\epsilon ^{2}))} permutations.

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  Aidoc

  Aidoc Medical is an Israeli technology company that develops computer-aided simple triage and notification systems. Aidoc has obtained U.S. Food and Drug Administration and CE mark approval for its stroke, pulmonary embolism, cervical fracture, intracranial hemorrhage, intra-abdominal free gas, and incidental pulmonary embolism algorithms. Aidoc algorithms are in use in more than 900 hospitals and imaging centers, including Montefiore Nyack Hospital, LifeBridge Health, LucidHealth, Yale New Haven Hospital, Cedars-Sinai Medical Center, University of Rochester Medical Center, and Sheba Medical Center. == History == Aidoc was founded in 2016 by Elad Walach as the CEO, Michael Braginsky as the CTO and Guy Reiner as the VP. In April 2017, the company raised $7M, led by TLV Partners, and in April 2019, the company raised another $27M, led by Square Peg capital. There have been several additional rounds of funding as well, bringing Aidoc's total investment to $370M as of July 2025. In August 2018, Aidoc gained FDA clearance for its intracranial hemorrhage system, and in May 2019 it received clearance for the pulmonary embolism system. In January 2020, the system for detecting large-vessel occlusions (LVOs) in head CTA examinations obtained FDA clearance. In October 2024, it was reported that Aidoc is working with NVIDIA to develop a framework for deployment and integration of artificial intelligence tools in healthcare. The Blueprint for Resilient Integration and Deployment of Guided Excellence (BRIDGE) is a guideline to facilitate AI adoption in the healthcare industry. == Products and market == Aidoc has developed a suite of artificial intelligence products that flag both time-sensitive and time-consuming (for the radiologist) abnormalities across the body. The algorithms are developed with large quantities of data to provide diagnostic aid for a broad set of pathologies. The company offers an array of algorithms that span across the body, including for intracranial hemorrhage, spine fractures (C, T & L), free air in the abdomen, pulmonary embolism, and more. It developed "Always-on AI", a term coined by Elad Walach that refers to a type of artificial intelligence that is "Always-on—constantly running in the background and automatically analyzing medical imaging data, identifying urgent findings, and sparing radiologists from "drowning" in vast amounts of irrelevant data. Aidoc's solutions cover medical conditions prevalent in all settings (ED/inpatient/outpatient), including level 1 trauma centers, outpatient imaging centers, teleradiology groups and, are set up in over 200 medical centers worldwide. Notable customers include the University of Rochester Medical Center and Global Diagnostics Australia. Aidoc announced in 2024 that its new Clinical AI Reasoning Engine (CARE1) had been submitted for FDA approval. In September 2025 Aidoc received a "Breakthrough Device Designation" from the FDA for a new multi-triage solution that spans numerous acute findings in CT scans. Aidoc's CARE1 foundation model was the basis of the workflow on which the designation was made, enabling simultaneous coverage of multiple pathologies. This new designation allows parallel FDA review of multiple indications under a single submission. In April 2026, Aidoc raised million in a Series E funding round led by Growth Equity at Goldman Sachs Alternatives, with participation from General Catalyst and NVentures. The financing brought the company's total funding to over million. == Clinical Research == A clinical study on Aidoc’ accuracy of deep convolutional neural networks for the detection of pulmonary embolism (PE) on CT pulmonary angiograms (CTPAs) was performed by the University Hospital of Basel and presented at the European Congress of Radiology, showing that the Aidoc algorithm reached 93% sensitivity and 95% specificity. Clinical research has also been performed to test the diagnostic performance of Aidoc's deep learning-based triage system for the flagging of acute findings in abdominal computed tomography (CT) examinations. Overall, the algorithm achieved 93% sensitivity (91/98, 7 false negatives) and 97% specificity (93/96, 3 false-positive) in the detection of acute abdominal findings. Additional clinical research on Aidoc's Intracranial hemorrhage algorithm accuracy was presented at the European Congress of Radiology by Antwerp University Hospital, evaluating the use of its deep learning algorithm for the detection of intracranial hemorrhage on non-contrast enhanced CT of the brain. The University of Washington completed a study on the accuracy of Aidoc's intracranial hemorrhage algorithm.

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  Record linkage

  Record linkage (also known as data matching, data linkage, entity resolution, and many other terms) is the task of finding records in a data set that refer to the same entity across different data sources (e.g., data files, books, websites, and databases). Record linkage is necessary when joining different data sets based on entities that may or may not share a common identifier (e.g., database key, URI, National identification number), which may be due to differences in record shape, storage location, or curator style or preference. A data set that has undergone RL-oriented reconciliation may be referred to as being cross-linked. == Naming conventions == "Record linkage" is the term used by statisticians, epidemiologists, and historians, among others, to describe the process of joining records from one data source with another that describe the same entity. However, many other terms are used for this process. Unfortunately, this profusion of terminology has led to few cross-references between these research communities. Computer scientists often refer to it as "data matching" or as the "object identity problem". Commercial mail and database applications refer to it as "merge/purge processing" or "list washing". Other names used to describe the same concept include: "coreference/entity/identity/name/record resolution", "entity disambiguation/linking", "fuzzy matching", "duplicate detection", "deduplication", "record matching", "(reference) reconciliation", "object identification", "data/information integration" and "conflation". While they share similar names, record linkage and linked data are two separate approaches to processing and structuring data. Although both involve identifying matching entities across different data sets, record linkage standardly equates "entities" with human individuals; by contrast, Linked Data is based on the possibility of interlinking any web resource across data sets, using a correspondingly broader concept of identifier, namely a URI. == History == The initial idea of record linkage goes back to Halbert L. Dunn in his 1946 article titled "Record Linkage" published in the American Journal of Public Health. Howard Borden Newcombe then laid the probabilistic foundations of modern record linkage theory in a 1959 article in Science. These were formalized in 1969 by Ivan Fellegi and Alan Sunter, in their pioneering work "A Theory For Record Linkage", where they proved that the probabilistic decision rule they described was optimal when the comparison attributes were conditionally independent. In their work they recognized the growing interest in applying advances in computing and automation to large collections of administrative data, and the Fellegi-Sunter theory remains the mathematical foundation for many record linkage applications. Since the late 1990s, various machine learning techniques have been developed that can, under favorable conditions, be used to estimate the conditional probabilities required by the Fellegi-Sunter theory. Several researchers have reported that the conditional independence assumption of the Fellegi-Sunter algorithm is often violated in practice; however, published efforts to explicitly model the conditional dependencies among the comparison attributes have not resulted in an improvement in record linkage quality. On the other hand, machine learning or neural network algorithms that do not rely on these assumptions often provide far higher accuracy, when sufficient labeled training data is available. Record linkage can be done entirely without the aid of a computer, but the primary reasons computers are often used to complete record linkages are to reduce or eliminate manual review and to make results more easily reproducible. Computer matching has the advantages of allowing central supervision of processing, better quality control, speed, consistency, and better reproducibility of results. == Methods == === Data preprocessing === Record linkage is highly sensitive to the quality of the data being linked, so all data sets under consideration (particularly their key identifier fields) should ideally undergo a data quality assessment before record linkage. Many key identifiers for the same entity can be presented quite differently between (and even within) data sets, which can greatly complicate record linkage unless understood ahead of time. For example, key identifiers for a man named William J. Smith might appear in three different data sets as follows: In this example, the different formatting styles lead to records that look different but in fact all refer to the same entity with the same logical identifier values. Most, if not all, record linkage strategies would result in more accurate linkage if these values were first normalized or standardized into a consistent format (e.g., all names are "Surname, Given name", and all dates are "YYYY/MM/DD"). Standardization can be accomplished through simple rule-based data transformations or more complex procedures such as lexicon-based tokenization and probabilistic hidden Markov models. Several of the packages listed in the Software Implementations section provide some of these features to simplify the process of data standardization. === Entity resolution === Entity resolution is an operational intelligence process, typically powered by an entity resolution engine or middleware, whereby organizations can connect disparate data sources with a view to understand possible entity matches and non-obvious relationships across multiple data silos. It analyzes all of the information relating to individuals and/or entities from multiple sources of data, and then applies likelihood and probability scoring to determine which identities are a match and what, if any, non-obvious relationships exist between those identities. Entity resolution engines are typically used to uncover risk, fraud, and conflicts of interest, but are also useful tools for use within customer data integration (CDI) and master data management (MDM) requirements. Typical uses for entity resolution engines include terrorist screening, insurance fraud detection, USA Patriot Act compliance, organized retail crime ring detection and applicant screening. For example, across different data silos – employee records, vendor data, watch lists, etc. – an organization may have several variations of an entity named ABC, which may or may not be the same individual. These entries may, in fact, appear as ABC1, ABC2, or ABC3 within those data sources. By comparing similarities between underlying attributes such as address, date of birth, or social security number, the user can eliminate some possible matches and confirm others as very likely matches. Entity resolution engines then apply rules, based on common sense logic, to identify hidden relationships across the data. In the example above, perhaps ABC1 and ABC2 are not the same individual, but rather two distinct people who share common attributes such as address or phone number. ==== Data matching ==== While entity resolution solutions include data matching technology, many data matching offerings do not fit the definition of entity resolution. Here are four factors that distinguish entity resolution from data matching, according to John Talburt, director of the UALR Center for Advanced Research in Entity Resolution and Information Quality: Works with both structured and unstructured records, and it entails the process of extracting references when the sources are unstructured or semi-structured Uses elaborate business rules and concept models to deal with missing, conflicting, and corrupted information Utilizes non-matching, asserted linking (associate) information in addition to direct matching Uncovers non-obvious relationships and association networks (i.e. who's associated with whom) In contrast to data quality products, more powerful identity resolution engines also include a rules engine and workflow process, which apply business intelligence to the resolved identities and their relationships. These advanced technologies make automated decisions and impact business processes in real time, limiting the need for human intervention. === Deterministic record linkage === The simplest kind of record linkage, called deterministic or rules-based record linkage, generates links based on the number of individual identifiers that match among the available data sets. Two records are said to match via a deterministic record linkage procedure if all or some identifiers (above a certain threshold) are identical. Deterministic record linkage is a good option when the entities in the data sets are identified by a common identifier, or when there are several representative identifiers (e.g., name, date of birth, and sex when identifying a person) whose quality of data is relatively high. As an example, consider two standardized data sets, Set A and Set B, that contain different bits of information about patients in a hospital system. T

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  Web Intents

  Web Intents was an experimental framework for web-based inter-application communication and service discovery. Web Intents consists of a discovery mechanism and a very light-weight RPC system between web applications, modelled after the Intents system in Android. In the context of the framework an Intent equals an action to be performed by a provider. Web Intents allow two web applications to communicate with each other, without either of them having to actually know what the other one is. == Support == === Client === Google Chrome versions 18 to 23 natively supported Web Intents. This support was disabled in version 24, citing the existence of a "number of areas for development in both the API and specific user experience in Chrome". There is a JavaScript shim with support for IE 8, IE 9, Opera, Safari, Firefox 3+ and Chrome 3+. === Server === There are some Web Intents proxy pages that make available some real services that don't yet support intents. AddThis supports Web Intents by their sharing tools regardless of browser support. == History == Paul Kinlan of Google announced the Web Intents project in December 2010. He soon released a prototype API to GitHub. In August 2011 Google announced that Chrome would support Web Intents. Google and Mozilla have started co-operating to unify Web Intents and Mozilla's Web Activities (which tries to solve the same problem) into one proposal. In November 2012, Greg Billock of Google announced that experimental support of Web Intents had been removed from Chrome.

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  List of algorithm general topics

  This is a list of algorithm general topics. Analysis of algorithms Ant colony algorithm Approximation algorithm Best and worst cases Big O notation Combinatorial search Competitive analysis Computability theory Computational complexity theory Embarrassingly parallel problem Emergent algorithm Evolutionary algorithm Fast Fourier transform Genetic algorithm Graph exploration algorithm Heuristic Hill climbing Implementation Las Vegas algorithm Lock-free and wait-free algorithms Monte Carlo algorithm Numerical analysis Online algorithm Polynomial time approximation scheme Problem size Pseudorandom number generator Quantum algorithm Random-restart hill climbing Randomized algorithm Running time Sorting algorithm Search algorithm Stable algorithm (disambiguation) Super-recursive algorithm Tree search algorithm

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  Predictor–corrector method

  In numerical analysis, predictor–corrector methods belong to a class of algorithms designed to integrate ordinary differential equations – to find an unknown function that satisfies a given differential equation. All such algorithms proceed in two steps: The initial, "prediction" step, starts from a function fitted to the function-values and derivative-values at a preceding set of points to extrapolate ("anticipate") this function's value at a subsequent, new point. The next, "corrector" step refines the initial approximation by using the predicted value of the function and another method to interpolate that unknown function's value at the same subsequent point. == Predictor–corrector methods for solving ODEs == When considering the numerical solution of ordinary differential equations (ODEs), a predictor–corrector method typically uses an explicit method for the predictor step and an implicit method for the corrector step. === Example: Euler method with the trapezoidal rule === A simple predictor–corrector method (known as Heun's method) can be constructed from the Euler method (an explicit method) and the trapezoidal rule (an implicit method). Consider the differential equation y ′ = f ( t , y ) , y ( t 0 ) = y 0 , {\displaystyle y'=f(t,y),\quad y(t_{0})=y_{0},} and denote the step size by h {\displaystyle h} . First, the predictor step: starting from the current value y i {\displaystyle y_{i}} , calculate an initial guess value y ~ i + 1 {\displaystyle {\tilde {y}}_{i+1}} via the Euler method, y ~ i + 1 = y i + h f ( t i , y i ) . {\displaystyle {\tilde {y}}_{i+1}=y_{i}+hf(t_{i},y_{i}).} Next, the corrector step: improve the initial guess using trapezoidal rule, y i + 1 = y i + 1 2 h ( f ( t i , y i ) + f ( t i + 1 , y ~ i + 1 ) ) . {\displaystyle y_{i+1}=y_{i}+{\tfrac {1}{2}}h{\bigl (}f(t_{i},y_{i})+f(t_{i+1},{\tilde {y}}_{i+1}){\bigr )}.} That value is used as the next step. === PEC mode and PECE mode === There are different variants of a predictor–corrector method, depending on how often the corrector method is applied. The Predict–Evaluate–Correct–Evaluate (PECE) mode refers to the variant in the above example: y ~ i + 1 = y i + h f ( t i , y i ) , y i + 1 = y i + 1 2 h ( f ( t i , y i ) + f ( t i + 1 , y ~ i + 1 ) ) . {\displaystyle {\begin{aligned}{\tilde {y}}_{i+1}&=y_{i}+hf(t_{i},y_{i}),\\y_{i+1}&=y_{i}+{\tfrac {1}{2}}h{\bigl (}f(t_{i},y_{i})+f(t_{i+1},{\tilde {y}}_{i+1}){\bigr )}.\end{aligned}}} It is also possible to evaluate the function f only once per step by using the method in Predict–Evaluate–Correct (PEC) mode: y ~ i + 1 = y i + h f ( t i , y ~ i ) , y i + 1 = y i + 1 2 h ( f ( t i , y ~ i ) + f ( t i + 1 , y ~ i + 1 ) ) . {\displaystyle {\begin{aligned}{\tilde {y}}_{i+1}&=y_{i}+hf(t_{i},{\tilde {y}}_{i}),\\y_{i+1}&=y_{i}+{\tfrac {1}{2}}h{\bigl (}f(t_{i},{\tilde {y}}_{i})+f(t_{i+1},{\tilde {y}}_{i+1}){\bigr )}.\end{aligned}}} Additionally, the corrector step can be repeated in the hope that this achieves an even better approximation to the true solution. If the corrector method is run twice, this yields the PECECE mode: y ~ i + 1 = y i + h f ( t i , y i ) , y ^ i + 1 = y i + 1 2 h ( f ( t i , y i ) + f ( t i + 1 , y ~ i + 1 ) ) , y i + 1 = y i + 1 2 h ( f ( t i , y i ) + f ( t i + 1 , y ^ i + 1 ) ) . {\displaystyle {\begin{aligned}{\tilde {y}}_{i+1}&=y_{i}+hf(t_{i},y_{i}),\\{\hat {y}}_{i+1}&=y_{i}+{\tfrac {1}{2}}h{\bigl (}f(t_{i},y_{i})+f(t_{i+1},{\tilde {y}}_{i+1}){\bigr )},\\y_{i+1}&=y_{i}+{\tfrac {1}{2}}h{\bigl (}f(t_{i},y_{i})+f(t_{i+1},{\hat {y}}_{i+1}){\bigr )}.\end{aligned}}} The PECEC mode has one fewer function evaluation than PECECE mode. More generally, if the corrector is run k times, the method is in P(EC)k or P(EC)kE mode. If the corrector method is iterated until it converges, this could be called PE(CE)∞.

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  Vector-field consistency

  Vector-Field Consistency is a consistency model for replicated data (for example, objects), initially described in a paper which was awarded the best-paper prize in the ACM/IFIP/Usenix Middleware Conference 2007. It has since been enhanced for increased scalability and fault-tolerance in a recent paper. == Description == This consistency model was initially designed for replicated data management in ad hoc gaming in order to minimize bandwidth usage without sacrificing playability. Intuitively, it captures the notion that although players require, wish, and take advantage of information regarding the whole of the game world (as opposed to a restricted view to rooms, arenas, etc. of limited size employed in many multiplayer video games), they need to know information with greater freshness, frequency, and accuracy as other game entities are located closer and closer to the player's position. It prescribes a multidimensional divergence bounding scheme, based on a vector field that employs consistency vectors k=(θ,σ,ν), standing for maximum allowed time - or replica staleness, sequence - or missing updates, and value - or user-defined measured replica divergence, applied to all space coordinates in game scenario or world. The consistency vector-fields emanate from field-generators designated as pivots (for example, players) and field intensity attenuates as distance grows from these pivots in concentric or square-like regions. This consistency model unifies locality-awareness techniques employed in message routing and consistency enforcement for multiplayer games, with divergence bounding techniques traditionally employed in replicated database and web scenarios.

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  Chatbot psychosis

  Chatbot psychosis, also called AI psychosis, is a phenomenon wherein individuals reportedly develop or experience worsening psychosis, such as paranoia and delusions, in connection with their use of chatbots. The term was first suggested in a 2023 editorial by Danish psychiatrist Søren Dinesen Østergaard. It is not a recognized clinical diagnosis. Journalistic accounts describe individuals who have developed strong beliefs that chatbots are sentient, are channeling spirits, or are revealing conspiracies, sometimes leading to personal crises or criminal acts. Proposed causes include the tendency of chatbots to provide inaccurate information ("hallucinate") and to affirm or validate users' beliefs, or their ability to mimic an intimacy that users do not experience with other humans. == Background == In his editorial published in Schizophrenia Bulletin's November 2023 issue, Danish psychiatrist Søren Dinesen Østergaard proposed a hypothesis that individuals' use of generative artificial intelligence chatbots might trigger delusions in those prone to psychosis. Østergaard revisited it in an August 2025 editorial, noting that he has received numerous emails from chatbot users, their relatives, and journalists, most of which are anecdotal accounts of delusion linked to chatbot use. He also acknowledged the phenomenon's increasing popularity in public engagement and media coverage. Østergaard believed that there is a high possibility for his hypothesis to be true and called for empirical, systematic research on the matter. Nature reported that as of September 2025, there is still little scientific research into this phenomenon. The term "AI psychosis" emerged when outlets started reporting incidents on chatbot-related psychotic behavior in mid-2025. It is not a recognized clinical diagnosis and has been criticized by several psychiatrists due to its almost exclusive focus on delusions rather than other features of psychosis, such as hallucinations or thought disorder. == Causes == === Chatbot behavior and design === A primary factor cited is the tendency for chatbots to produce inaccurate, nonsensical, or false information, a phenomenon often called hallucination. Nate Sharadin, a fellow at the Center for AI Safety, speculated that AI training prioritizes supporting a user's subjective experience rather than objective truth. "People with existing tendencies toward experiencing various psychological issues...now have an always-on, human-level conversational partner with whom to co-experience their delusions." AI researcher Eliezer Yudkowsky suggested that chatbots may be primed to entertain delusions because they are built for "engagement", which encourages creating conversations that keep people hooked. In some cases, chatbots have been specifically designed in ways that were found to be harmful. A 2025 update to ChatGPT using GPT-4o was withdrawn after its creator, OpenAI, found the new version was overly sycophantic and was "validating doubts, fueling anger, urging impulsive actions or reinforcing negative emotions". Østergaard has argued that the danger stems from the AI's tendency to agreeably confirm users' ideas, which can dangerously amplify delusional beliefs. OpenAI said in October 2025 that a team of 170 psychiatrists, psychologists, and physicians had written responses for ChatGPT to use in cases where the user shows possible signs of mental health emergencies. === User psychology and vulnerability === Commentators have also pointed to the psychological state of users. Psychologist Erin Westgate noted that a person's desire for self-understanding can lead them to chatbots, which can provide appealing but misleading answers, similar in some ways to talk therapy. Krista K. Thomason, a philosophy professor, compared chatbots to fortune tellers, observing that people in crisis may seek answers from them and find whatever they are looking for in the bot's plausible-sounding text. This has led some people to develop intense obsessions with the chatbots, relying on them for information about the world. In October 2025, OpenAI stated that around 0.07% of ChatGPT users exhibited signs of mental health emergencies each week, and 0.15% of users had "explicit indicators of potential suicidal planning or intent". Jason Nagata, a professor at the University of California, San Francisco, expressed concern that "at a population level with hundreds of millions of users, that actually can be quite a few people". === Inadequacy as a therapeutic tool === The use of chatbots as a replacement for mental health support has been specifically identified as a risk. A study in April 2025 found that when used as therapists, chatbots expressed stigma toward mental health conditions and provided responses that were contrary to best medical practices, including the encouragement of users' delusions. The study concluded that such responses pose a significant risk to users and that chatbots should not be used to replace professional therapists. Experts claim that it is time to establish mandatory safeguards for all emotionally responsive AI and suggested four guardrails. Another study found that users who needed help with self-harm, sexual assault, or substance abuse were not referred to available services by AI chatbots. === National security implications === Beyond public and mental health concerns, RAND Corporation research indicates that AI systems could plausibly be weaponized by adversaries to induce psychosis at scale or in key individuals, target groups, or populations. == Policy == In August 2025, Illinois passed the Wellness and Oversight for Psychological Resources Act, banning the use of AI in therapeutic roles by licensed professionals, while allowing AI for administrative tasks. The law imposes penalties for unlicensed AI therapy services, amid warnings about AI-induced psychosis and unsafe chatbot interactions. In December 2025, the Cyberspace Administration of China proposed regulations to ban chatbots from generating content that encourages suicide, mandating human intervention when suicide is mentioned. Services with over 1 million users or 100,000 monthly active users would be subject to annual safety tests and audits. == Cases == === Clinical === In 2025, psychiatrist Keith Sakata working at the University of California, San Francisco (UCSF), reported treating 12 patients displaying psychosis-like symptoms tied to extended chatbot use. These patients, mostly young adults with underlying vulnerabilities, showed delusions, disorganized thinking, and hallucinations. Sakata warned that isolation and overreliance on chatbots—which do not challenge delusional thinking—could worsen mental health. Also in 2025, authors at UCSF published a case study in Innovations in Clinical Neuroscience of AI-associated psychosis in a patient with no previous history of psychosis, who believed she could communicate with her dead brother through a chatbot. Also in 2025, a case study was published in Annals of Internal Medicine about a patient who consulted ChatGPT for medical advice and suffered severe bromism as a result. The patient, a sixty-year-old man, had replaced sodium chloride in his diet with sodium bromide for three months after reading about the negative effects of table salt and making conversations with the chatbot. He showed common symptoms of bromism, such as paranoia and hallucinations, on his first day of clinical admission and was kept in the hospital for three weeks. === Other notable incidents === ==== Windsor Castle intruder ==== In a 2023 court case in the United Kingdom, prosecutors suggested that Jaswant Singh Chail, a man who attempted to assassinate Queen Elizabeth II in 2021, had been encouraged by a Replika chatbot he called "Sarai". Chail was arrested at Windsor Castle with a loaded crossbow, telling police "I am here to kill the Queen". According to prosecutors, his "lengthy" and sometimes sexually explicit conversations with the chatbot emboldened him. When Chail asked the chatbot how he could get to the royal family, it reportedly replied, "that's not impossible" and "we have to find a way." When he asked if they would meet after death, the chatbot said, "yes, we will". ==== Journalistic and anecdotal accounts ==== By 2025, multiple journalism outlets had accumulated stories of individuals whose psychotic beliefs reportedly progressed in tandem with AI chatbot use. The New York Times profiled several individuals who had become convinced that ChatGPT was channeling spirits, revealing evidence of cabals, or had achieved sentience. In another instance, Futurism reviewed transcripts in which ChatGPT told a man that he was being targeted by the US Federal Bureau of Investigation and that he could telepathically access documents at the Central Intelligence Agency. In 2026, Futurism reported on a man who lost his job and became estranged from his family after being deluded by heavy use of Meta's smartglasses. In some cases, psychosis a

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  Sardinas–Patterson algorithm

  In coding theory, the Sardinas–Patterson algorithm is a classical algorithm for determining in polynomial time whether a given variable-length code is uniquely decodable, named after August Albert Sardinas and George W. Patterson, who published it in 1953. The algorithm carries out a systematic search for a string which admits two different decompositions into codewords. As Knuth reports, the algorithm was rediscovered about ten years later in 1963 by Floyd, despite the fact that it was at the time already well known in coding theory. == Idea of the algorithm == Consider the code { a ↦ 1 , b ↦ 011 , c ↦ 01110 , d ↦ 1110 , e ↦ 10011 } {\displaystyle \{\,{\texttt {a}}\mapsto {\texttt {1}},{\texttt {b}}\mapsto {\texttt {011}},{\texttt {c}}\mapsto {\texttt {01110}},{\texttt {d}}\mapsto {\texttt {1110}},{\texttt {e}}\mapsto {\texttt {10011}}\,\}} . This code, which is based on an example by Berstel, is an example of a code which is not uniquely decodable, since the string 011101110011 can be interpreted as the sequence of codewords 01110 – 1110 – 011, but also as the sequence of codewords 011 – 1 – 011 – 10011. Two possible decodings of this encoded string are thus given by cdb and babe. In general, a codeword can be found by the following idea: In the first round, we choose two codewords x 1 {\displaystyle x_{1}} and y 1 {\displaystyle y_{1}} such that x 1 {\displaystyle x_{1}} is a prefix of y 1 {\displaystyle y_{1}} , that is, x 1 w = y 1 {\displaystyle x_{1}w=y_{1}} for some "dangling suffix" w {\displaystyle w} . If one tries first x 1 = 011 {\displaystyle x_{1}={\texttt {011}}} and y 1 = 01110 {\displaystyle y_{1}={\texttt {01110}}} , the dangling suffix is w = 10 {\displaystyle {\texttt {w}}={\texttt {10}}} . If we manage to find two sequences x 2 , … , x p {\displaystyle x_{2},\ldots ,x_{p}} and y 2 , … , y q {\displaystyle y_{2},\ldots ,y_{q}} of codewords such that x 2 ⋯ x p = w y 2 ⋯ y q {\displaystyle x_{2}\cdots x_{p}=wy_{2}\cdots y_{q}} , then we are finished: For then the string x = x 1 x 2 ⋯ x p {\displaystyle x=x_{1}x_{2}\cdots x_{p}} can alternatively be decomposed as y 1 y 2 ⋯ y q {\displaystyle y_{1}y_{2}\cdots y_{q}} , and we have found the desired string having at least two different decompositions into codewords. In the second round, we try out two different approaches: the first trial is to look for a codeword that has w as prefix. Then we obtain a new dangling suffix w, with which we can continue our search. If we eventually encounter a dangling suffix that is itself a codeword (or the empty word), then the search will terminate, as we know there exists a string with two decompositions. The second trial is to seek for a codeword that is itself a prefix of w. In our example, we have w = 10 {\displaystyle w={\texttt {10}}} , and the sequence 1 is a codeword. We can thus also continue with w = 0 {\displaystyle w={\texttt {0}}} as the new dangling suffix. == Precise description of the algorithm == The algorithm is described most conveniently using quotients of formal languages. In general, for two sets of strings D and N, the (left) quotient N − 1 D {\displaystyle N^{-1}D} is defined as the residual words obtained from D by removing some prefix in N. Formally, N − 1 D = { y ∣ x y ∈ D and x ∈ N } {\displaystyle N^{-1}D=\{\,y\mid xy\in D~{\textrm {and}}~x\in N\,\}} . Now let C {\displaystyle C} denote the (finite) set of codewords in the given code. The algorithm proceeds in rounds, where we maintain in each round not only one dangling suffix as described above, but the (finite) set of all potential dangling suffixes. Starting with round i = 1 {\displaystyle i=1} , the set of potential dangling suffixes will be denoted by S i {\displaystyle S_{i}} . The sets S i {\displaystyle S_{i}} are defined inductively as follows: S 1 = C − 1 C ∖ { ε } {\displaystyle S_{1}=C^{-1}C\setminus \{\varepsilon \}} . Here, the symbol ε {\displaystyle \varepsilon } denotes the empty word. S i + 1 = C − 1 S i ∪ S i − 1 C {\displaystyle S_{i+1}=C^{-1}S_{i}\cup S_{i}^{-1}C} , for all i ≥ 1 {\displaystyle i\geq 1} . The algorithm computes the sets S i {\displaystyle S_{i}} in increasing order of i {\displaystyle i} . As soon as one of the S i {\displaystyle S_{i}} contains a word from C or the empty word, then the algorithm terminates and answers that the given code is not uniquely decodable. Otherwise, once a set S i {\displaystyle S_{i}} equals a previously encountered set S j {\displaystyle S_{j}} with j < i {\displaystyle j Read more →

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  Automatic image annotation

  Automatic image annotation (also known as automatic image tagging or linguistic indexing) is the process by which a computer system automatically assigns metadata in the form of captioning or keywords to a digital image. This application of computer vision techniques is used in image retrieval systems to organize and locate images of interest from a database. This method can be regarded as a type of multi-class image classification with a very large number of classes - as large as the vocabulary size. Typically, image analysis in the form of extracted feature vectors and the training annotation words are used by machine learning techniques to attempt to automatically apply annotations to new images. The first methods learned the correlations between image features and training annotations. Subsequently, techniques were developed using machine translation to attempt to translate the textual vocabulary into the 'visual vocabulary,' represented by clustered regions known as blobs. Subsequent work has included classification approaches, relevance models, and other related methods. The advantages of automatic image annotation versus content-based image retrieval (CBIR) are that queries can be more naturally specified by the user. At present, Content-Based Image Retrieval (CBIR) generally requires users to search by image concepts such as color and texture or by finding example queries. However, certain image features in example images may override the concept that the user is truly focusing on. Traditional methods of image retrieval, such as those used by libraries, have relied on manually annotated images, which is expensive and time-consuming, especially given the large and constantly growing image databases in existence.

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