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  LemonStand

  LemonStand was a Canadian e-commerce company headquartered in Vancouver, British Columbia, that developed cloud-based computer software for online retailers. LemonStand was shut down on June 5, 2019. == History == LemonStand Version 1 was launched on July 28, 2001. It is written in the PHP programming language. Version 1 was released as an on-premises proprietary licensed software, and the commercial license was not free. However, there was a free trial license available. June 2012, LemonStand raised seed funding from the BDC Venture Capital, and a group of angel investors. December 20, 2013, a cloud-based SaaS version of the LemonStand eCommerce platform was released publicly. May 9, 2014, LemonStand and Payfirma, a payments processing company, partnered to provide integrated services for online retailers. May 3, 2016, LemonStand raised funding from BDC Venture Capital and Silicon Valley–based angel investors. March 5, 2019, LemonStand announced their intention to shut down on June 5, 2019. LemonStand was quietly acquired by Mailchimp at the end of February. == Pricing == LemonStand offered three levels of service plans. LemonStand did not charge any transaction fees.

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  Kleene's algorithm

  In theoretical computer science, in particular in formal language theory, Kleene's algorithm transforms a given nondeterministic finite automaton (NFA) into a regular expression. Together with other conversion algorithms, it establishes the equivalence of several description formats for regular languages. Alternative presentations of the same method include the "elimination method" attributed to Brzozowski and McCluskey, the algorithm of McNaughton and Yamada, and the use of Arden's lemma. == Algorithm description == According to Gross and Yellen (2004), the algorithm can be traced back to Kleene (1956). A presentation of the algorithm in the case of deterministic finite automata (DFAs) is given in Hopcroft and Ullman (1979). The presentation of the algorithm for NFAs below follows Gross and Yellen (2004). Given a nondeterministic finite automaton M = (Q, Σ, δ, q0, F), with Q = { q0,...,qn } its set of states, the algorithm computes the sets Rkij of all strings that take M from state qi to qj without going through any state numbered higher than k. Here, "going through a state" means entering and leaving it, so both i and j may be higher than k, but no intermediate state may. Each set Rkij is represented by a regular expression; the algorithm computes them step by step for k = -1, 0, ..., n. Since there is no state numbered higher than n, the regular expression Rn0j represents the set of all strings that take M from its start state q0 to qj. If F = { q1,...,qf } is the set of accept states, the regular expression Rn01 | ... | Rn0f represents the language accepted by M. The initial regular expressions, for k = -1, are computed as follows for i≠j: R−1ij = a1 | ... | am where qj ∈ δ(qi,a1), ..., qj ∈ δ(qi,am) and as follows for i=j: R−1ii = a1 | ... | am | ε where qi ∈ δ(qi,a1), ..., qi ∈ δ(qi,am) In other words, R−1ij mentions all letters that label a transition from i to j, and we also include ε in the case where i=j. After that, in each step the expressions Rkij are computed from the previous ones by Rkij = Rk-1ik (Rk-1kk) Rk-1kj | Rk-1ij Another way to understand the operation of the algorithm is as an "elimination method", where the states from 0 to n are successively removed: when state k is removed, the regular expression Rk-1ij, which describes the words that label a path from state i>k to state j>k, is rewritten into Rkij so as to take into account the possibility of going via the "eliminated" state k. By induction on k, it can be shown that the length of each expression Rkij is at most ⁠1/3⁠(4k+1(6s+7) - 4) symbols, where s denotes the number of characters in Σ. Therefore, the length of the regular expression representing the language accepted by M is at most ⁠1/3⁠(4n+1(6s+7)f - f - 3) symbols, where f denotes the number of final states. This exponential blowup is inevitable, because there exist families of DFAs for which any equivalent regular expression must be of exponential size. In practice, the size of the regular expression obtained by running the algorithm can be very different depending on the order in which the states are considered by the procedure, i.e., the order in which they are numbered from 0 to n. == Example == The automaton shown in the picture can be described as M = (Q, Σ, δ, q0, F) with the set of states Q = { q0, q1, q2 }, the input alphabet Σ = { a, b }, the transition function δ with δ(q0,a)=q0, δ(q0,b)=q1, δ(q1,a)=q2, δ(q1,b)=q1, δ(q2,a)=q1, and δ(q2,b)=q1, the start state q0, and set of accept states F = { q1 }. Kleene's algorithm computes the initial regular expressions as After that, the Rkij are computed from the Rk-1ij step by step for k = 0, 1, 2. Kleene algebra equalities are used to simplify the regular expressions as much as possible. Step 0 Step 1 Step 2 Since q0 is the start state and q1 is the only accept state, the regular expression R201 denotes the set of all strings accepted by the automaton.

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  Artificial intuition

  Artificial intuition is a theoretical capacity of an artificial software to function similarly to human consciousness, specifically in the capacity of human consciousness known as intuition. == Comparison of human and the theoretically artificial == Intuition is the function of the mind, the experience of which, is described as knowledge based on "a hunch", resulting (as the word itself does) from "contemplation" or "insight". Psychologist Jean Piaget showed that intuitive functioning within the normally developing human child at the Intuitive Thought Substage of the preoperational stage occurred at from four to seven years of age. In Carl Jung's concept of synchronicity, the concept of "intuitive intelligence" is described as something like a capacity that transcends ordinary-level functioning to a point where information is understood with a greater depth than is available in more simple rationally-thinking entities. Artificial intuition is theoretically (or otherwise) a sophisticated function of an artifice that is able to interpret data with depth and locate hidden factors functioning in Gestalt psychology, and that intuition in the artificial mind would, in the context described here, be a bottom-up process upon a macroscopic scale identifying something like the archetypal (see τύπος). To create artificial intuition supposes the possibility of the re-creation of a higher functioning of the human mind, with capabilities such as what might be found in semantic memory and learning. The transferral of the functioning of a biological system to synthetic functioning is based upon modeling of functioning from knowledge of cognition and the brain, for instance as applications of models of artificial neural networks from the research done within the discipline of computational neuroscience. == Application software contributing to its development == The notion of a process of a data-interpretative synthesis has already been found in a computational-linguistic software application that has been created for use in an internal security context. The software integrates computed data based specifically on objectives incorporating a paradigm described as "religious intuitive" (hermeneutic), functional to a degree that represents advances upon the performance of generic lexical data mining.

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  Algorithm engineering

  Algorithm engineering focuses on the design, analysis, implementation, optimization, profiling and experimental evaluation of computer algorithms, bridging the gap between algorithmics theory and practical applications of algorithms in software engineering. It is a general methodology for algorithmic research. == Origins == In 1995, a report from an NSF-sponsored workshop "with the purpose of assessing the current goals and directions of the Theory of Computing (TOC) community" identified the slow speed of adoption of theoretical insights by practitioners as an important issue and suggested measures to reduce the uncertainty by practitioners whether a certain theoretical breakthrough will translate into practical gains in their field of work, and tackle the lack of ready-to-use algorithm libraries, which provide stable, bug-free and well-tested implementations for algorithmic problems and expose an easy-to-use interface for library consumers. But also, promising algorithmic approaches have been neglected due to difficulties in mathematical analysis. The term "algorithm engineering" was first used with specificity in 1997, with the first Workshop on Algorithm Engineering (WAE97), organized by Giuseppe F. Italiano. == Difference from algorithm theory == Algorithm engineering does not intend to replace or compete with algorithm theory, but tries to enrich, refine and reinforce its formal approaches with experimental algorithmics (also called empirical algorithmics). This way it can provide new insights into the efficiency and performance of algorithms in cases where the algorithm at hand is less amenable to algorithm theoretic analysis, formal analysis pessimistically suggests bounds which are unlikely to appear on inputs of practical interest, the algorithm relies on the intricacies of modern hardware architectures like data locality, branch prediction, instruction stalls, instruction latencies which the machine model used in Algorithm Theory is unable to capture in the required detail, the crossover between competing algorithms with different constant costs and asymptotic behaviors needs to be determined. == Methodology == Some researchers describe algorithm engineering's methodology as a cycle consisting of algorithm design, analysis, implementation and experimental evaluation, joined by further aspects like machine models or realistic inputs. They argue that equating algorithm engineering with experimental algorithmics is too limited, because viewing design and analysis, implementation and experimentation as separate activities ignores the crucial feedback loop between those elements of algorithm engineering. === Realistic models and real inputs === While specific applications are outside the methodology of algorithm engineering, they play an important role in shaping realistic models of the problem and the underlying machine, and supply real inputs and other design parameters for experiments. === Design === Compared to algorithm theory, which usually focuses on the asymptotic behavior of algorithms, algorithm engineers need to keep further requirements in mind: Simplicity of the algorithm, implementability in programming languages on real hardware, and allowing code reuse. Additionally, constant factors of algorithms have such a considerable impact on real-world inputs that sometimes an algorithm with worse asymptotic behavior performs better in practice due to lower constant factors. === Analysis === Some problems can be solved with heuristics and randomized algorithms in a simpler and more efficient fashion than with deterministic algorithms. Unfortunately, this makes even simple randomized algorithms difficult to analyze because there are subtle dependencies to be taken into account. === Implementation === Huge semantic gaps between theoretical insights, formulated algorithms, programming languages and hardware pose a challenge to efficient implementations of even simple algorithms, because small implementation details can have rippling effects on execution behavior. The only reliable way to compare several implementations of an algorithm is to spend an considerable amount of time on tuning and profiling, running those algorithms on multiple architectures, and looking at the generated machine code. === Experiments === See: Experimental algorithmics === Application engineering === Implementations of algorithms used for experiments differ in significant ways from code usable in applications. While the former prioritizes fast prototyping, performance and instrumentation for measurements during experiments, the latter requires thorough testing, maintainability, simplicity, and tuning for particular classes of inputs. === Algorithm libraries === Stable, well-tested algorithm libraries like LEDA play an important role in technology transfer by speeding up the adoption of new algorithms in applications. Such libraries reduce the required investment and risk for practitioners, because it removes the burden of understanding and implementing the results of academic research. == Conferences == Two main conferences on Algorithm Engineering are organized annually, namely: Symposium on Experimental Algorithms (SEA), established in 1997 (formerly known as WEA). SIAM Meeting on Algorithm Engineering and Experiments (ALENEX), established in 1999. The 1997 Workshop on Algorithm Engineering (WAE'97) was held in Venice (Italy) on September 11–13, 1997. The Third International Workshop on Algorithm Engineering (WAE'99) was held in London, UK in July 1999. The first Workshop on Algorithm Engineering and Experimentation (ALENEX99) was held in Baltimore, Maryland on January 15–16, 1999. It was sponsored by DIMACS, the Center for Discrete Mathematics and Theoretical Computer Science (at Rutgers University), with additional support from SIGACT, the ACM Special Interest Group on Algorithms and Computation Theory, and SIAM, the Society for Industrial and Applied Mathematics.

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  Telebirr

  Telebirr (Amharic: ቴሌብር) is a mobile payment service developed and was launched by Ethio telecom, the state owned telecommunication and Internet service provider in Ethiopia. It took five months to develop the end-to-end service. It facilitates the delivery of cashless transactions. The platform deployed currently has the capacity of processing up to 100 transactions per second (TPS) and can be scaled up to 1000 TPS. The service is accessible via SMS, USSD, and smartphone applications. Telebirr works in five languages. == Services == Though the service is fully accessible for any customer of Ethio telecom, the users need to register through the mobile application called Telebirr or using an authorized agent or Ethio telecom shop or Unstructured Supplementary Service Data (USSD), 127# nationally. However, Telebirr also provides a “quick registration” by using any information that already exists in Ethio telecom's system.

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  DIKW pyramid

  The DIKW pyramid (also known as the knowledge pyramid or information hierarchy) is a model describing relationships between data, information, knowledge and wisdom sometimes also stylized as a chain, refer to models of possible structural and functional relationships between a set of components—often four, data, information, knowledge, and wisdom. The concept has roots predating the 1980s. In the latter years of that decade, interest in the models grew after explicit presentations and discussions, including from Milan Zeleny, Russell Ackoff, and Robert W. Lucky. Subsequent important discussions extended along theoretical and practical lines into the coming decades. While debate continues as to actual meaning of the component terms of DIKW-type models, and the actual nature of their relationships—including occasional doubt being cast over any simple, linear, unidirectional model—even so they have become very popular visual representations in use by business, the military, and others. Among the academic and popular, not all versions of the DIKW-type models include all four components (earlier ones excluding data, later ones excluding or downplaying wisdom, and several including additional components (for instance Ackoff inserting "understanding" before and Zeleny adding "enlightenment" after the wisdom component). In addition, DIKW-type models are no longer always presented as pyramids, instead also as a chart or framework (e.g., by Zeleny), as flow diagrams (e.g., by Liew, and by Chisholm et al.), and sometimes as a continuum (e.g., by Choo et al.). == Short description == As Rowley noted in 2007, the DIKW model "is often quoted, or used implicitly, in definitions of data, information and knowledge in the information management, information systems and knowledge management literatures, but [as of that date] there ha[d] been limited direct discussion of the hierarchy". Reviews of textbooks and a survey of scholars in relevant fields indicate that there was not a consensus as to definitions used in the model as of that date, and as reviewed by Liew in that year, even less "in the description of the processes that transform components lower in the hierarchy into those above them". Zins work, published in 2007—from studies in 2003-2005 that documented "130 definitions of data, information, and knowledge formulated by 45 scholars", published in 2007—to suggest that the data–information–knowledge components of DIKW refer to a class of no less than five models, as a function of whether data, information, and knowledge are each conceived of as subjective, objective (what Zins terms, "universal" or "collective") or both. In Zins' usage, subjective and objective "are not related to arbitrariness and truthfulness, which are usually attached to the concepts of subjective knowledge and objective knowledge". Information science, Zins argues, studies data and information, but not knowledge, as knowledge is an internal (subjective) rather than an external (universal–collective) phenomenon. == Representations == === Graphical representation === DIKW is a hierarchical model often depicted as a pyramid, sometimes as a chain, with data at its base and wisdom at its apex (or chain-beginning and -end). Both Zeleny and Ackoff have been credited with originating the pyramid representation, although neither used a pyramid to present their ideas. According to Wallace, Debons and colleagues may have been the first to "present the hierarchy graphically". Many variations of the DIKW-type pyramid have been produced. One, in use by knowledge managers in the United States Department of Defense, attempts to show the DIKW progression to enable effective decisions and consequent activities supporting shared understanding throughout defense organizations, as well as supporting management of risks associated with decisions. DIKW-type hierarchical information paradigms have also been represented as two-dimensional charts, and as flow diagrams, where relationships between the components may be presented less hierarchically, with defining aspects of the relationships, feedback loops, etc. === Computational representation === Intelligent decision support systems are trying to improve decision making by introducing new technologies and methods from the domain of modeling and simulation in general, and in particular from the domain of intelligent software agents in the contexts of agent-based modeling. The following example describes a military decision support system, but the architecture and underlying conceptual idea are transferable to other application domains: The value chain starts with data quality describing the information within the underlying command and control systems. Information quality tracks the completeness, correctness, currency, consistency and precision of the data items and information statements available. Knowledge quality deals with procedural knowledge and information embedded in the command and control system such as templates for adversary forces, assumptions about entities such as ranges and weapons, and doctrinal assumptions, often coded as rules. Awareness quality measures the degree of using the information and knowledge embedded within the command and control system. Awareness is explicitly placed in the cognitive domain. By the introduction of a common operational picture, data are put into context, which leads to information instead of data. The next step, which is enabled by service-oriented web-based infrastructures (but not yet operationally used), is the use of models and simulations for decision support. Simulation systems are the prototype for procedural knowledge, which is the basis for knowledge quality. Finally, using intelligent software agents to continually observe the battle sphere, apply models and simulations to analyze what is going on, to monitor the execution of a plan, and to do all the tasks necessary to make the decision maker aware of what is going on, command and control systems could even support situational awareness, the level in the value chain traditionally limited to pure cognitive methods. == History == Danny P. Wallace, a professor of library and information science, explained that the origin of the DIKW pyramid is uncertain: The presentation of the relationships among data, information, knowledge, and sometimes wisdom in a hierarchical arrangement has been part of the language of information science for many years. Although it is uncertain when and by whom those relationships were first presented, the ubiquity of the notion of a hierarchy is embedded in the use of the acronym DIKW as a shorthand representation for the data-to-information-to-knowledge-to-wisdom transformation.Many authors think that the idea of the DIKW relationship originated from two lines in the poem "Choruses", by T. S. Eliot, that appeared in the pageant play The Rock, in 1934: === Knowledge, intelligence, and wisdom === In 1927, Clarence W. Barron addressed his employees at Dow Jones & Company on the hierarchy: "Knowledge, Intelligence and Wisdom". === Data, information, knowledge === In 1955, English-American economist and educator Kenneth Boulding presented a variation on the hierarchy consisting of "signals, messages, information, and knowledge". However, "[t]he first author to distinguish among data, information, and knowledge and to also employ the term 'knowledge management' may have been American educator Nicholas L. Henry", in a 1974 journal article. === Data, information, knowledge, wisdom === Other early versions (prior to 1982) of the hierarchy that refer to a data tier include those of Chinese-American geographer Yi-Fu Tuan and sociologist-historian Daniel Bell.. In 1980, Irish-born engineer Mike Cooley invoked the same hierarchy in his critique of automation and computerization, in his book Architect or Bee?: The Human / Technology Relationship. Thereafter, in 1987, Czechoslovakia-born educator Milan Zeleny mapped the components of the hierarchy to knowledge forms: know-nothing, know-what, know-how, and know-why. Zeleny "has frequently been credited with proposing the [representation of DIKW as a pyramid ]... although he actually made no reference to any such graphical model." The hierarchy appears again in a 1988 address to the International Society for General Systems Research, by American organizational theorist Russell Ackoff, published in 1989. Subsequent authors and textbooks cite Ackoff's as the "original articulation" of the hierarchy or otherwise credit Ackoff with its proposal. Ackoff's version of the model includes an understanding tier (as Adler had, before him), interposed between knowledge and wisdom. Although Ackoff did not present the hierarchy graphically, he has also been credited with its representation as a pyramid. In 1989, Bell Labs veteran Robert W. Lucky wrote about the four-tier "information hierarchy" in the form of a pyramid in his book Silicon Dreams. In the same year as Ackoff presented his a

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  Gen (software)

  Gen is a Computer Aided Software Engineering (CASE) application development environment marketed by Broadcom Inc. Gen was previously known as CA Gen, IEF (Information Engineering Facility), Composer by IEF, Composer, COOL:Gen, Advantage:Gen and AllFusion Gen. The toolset originally supported the information technology engineering methodology developed by Clive Finkelstein, James Martin and others in the early 1980s. Early versions supported IBM's DB2 database, 3270 'block mode' screens and generated COBOL code. In the intervening years the toolset has been expanded to support additional development techniques such as component-based development; creation of client/server and web applications and generation of C, Java and C#. In addition, other platforms are now supported such as many variants of Unix-like Operating Systems (AIX, HP-UX, Solaris, Linux) as well as Windows. Its range of supported database technologies have widened to include ORACLE, Microsoft SQL Server, ODBC, JDBC as well as the original DB2. The toolset is fully integrated - objects identified during analysis carry forward into design without redefinition. All information is stored in a repository (central encyclopedia). The encyclopedia allows for large team development - controlling access so that multiple developers may not change the same object simultaneously. == History == === 1985-1997: Texas Instruments === It was initially produced by Texas Instruments, with input from James Martin and his consultancy firm James Martin Associates, and was based on the Information Engineering Methodology (IEM). The first version was launched in 1985. IEF (Information Engineering Facility) became popular among large government departments and public utilities. It initially supported a CICS/COBOL/DB2 target environment. However, it now supports a wider range of relational databases and operating systems. IEF was intended to shield the developer from the complexities of building complete multi-tier cross-platform applications. In 1995, Texas Instruments decided to change their marketing focus for the product. Part of this change included a new name - "Composer". By 1996, IEF had become a popular tool. However, it was criticized by some IT professionals for being too restrictive, as well as for having a high per-workstation cost ($15K USD). But it is claimed that IEF reduces development time and costs by removing complexity and allowing rapid development of large scale enterprise transaction processing systems. === 1997-2000: Sterling Software === In 1997, Composer had another change of branding, Texas Instruments sold the Texas Instruments Software division, including the Composer rights, to Sterling Software. Sterling software changed the well known name "Information Engineering Facility" to "COOL:Gen". COOL was an acronym for "Common Object Oriented Language" - despite the fact that there was little object orientation in the product. === 2000-2018: Computer Associates === In 2000, Sterling Software was acquired by Computer Associates (now CA). CA has rebranded the product three times to date and the product is still used widely today. Under CA, recent releases of the tool added support for the CA-Datacom DBMS, the Linux operating system, C# code generation and ASP.NET web clients. The current version is known as CA Gen - version 8 being released in May 2010, with support for customised web services, and more of the toolset being based around the Eclipse framework. === 2018-current: Broadcom === As of 2020, CA Gen is owned and marketed by Broadcom Inc., which rebranded the product to Gen to avoid confusion with the former owner of the product. There are a variety of "add-on" tools available for Gen, including GuardIEn - a Configuration Management and Developer Productivity Suite, QAT Wizard, an interview style wizard that takes advantage of the meta model in Gen, products for multi-platform application reporting and XML/SOAP enabling of Gen applications., and developer productivity tools such as Access Gen, APMConnect, QA Console and Upgrade Console from Response Systems Version 8.6 of CA Gen came to market in June 2016. Version 8.6.3 of CA Gen was released in 2021. Following this release, Broadcom have switched to a continuous delivery model with new features to be delivered as patches.

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  Data (word)

  The word data is most often used as a singular collective mass noun in educated everyday usage. However, due to the history and etymology of the word, considerable controversy has existed on whether it should be considered a mass noun used with verbs conjugated in the singular, or should be treated as the plural of the now-rarely-used datum. == Usage in English == In one sense, data is the plural form of datum. Datum actually can also be a count noun with the plural datums (see usage in datum article) that can be used with cardinal numbers (e.g., "80 datums"); data (originally a Latin plural) is not used like a normal count noun with cardinal numbers and can be plural with plural determiners such as these and many, or it can be used as a mass noun with a verb in the singular form. Even when a very small quantity of data is referenced (one number, for example), the phrase piece of data is often used, as opposed to datum. The debate over appropriate usage continues, but "data" as a singular form is far more common. In English, the word datum is still used in the general sense of "an item given". In cartography, geography, nuclear magnetic resonance and technical drawing, it is often used to refer to a single specific reference datum from which distances to all other data are measured. Any measurement or result is a datum, though data point is now far more common. Data is indeed most often used as a singular mass noun in educated everyday usage. Some major newspapers, such as The New York Times, use it either in the singular or plural. In The New York Times, the phrases "the survey data are still being analyzed" and "the first year for which data is available" have appeared within one day. The Wall Street Journal explicitly allows this usage in its style guide. The Associated Press style guide classifies data as a collective noun that takes the singular when treated as a unit but the plural when referring to individual items (e.g., "The data is sound" and "The data have been carefully collected"). In scientific writing, data is often treated as a plural, as in These data do not support the conclusions, but the word is also used as a singular mass entity like information (e.g., in computing and related disciplines). British usage now widely accepts treating data as singular in standard English, including everyday newspaper usage at least in non-scientific use. UK scientific publishing still prefers treating it as a plural. Some UK university style guides recommend using data for both singular and plural use, and others recommend treating it only as a singular in connection with computers. The IEEE Computer Society allows usage of data as either a mass noun or plural based on author preference, while IEEE in the editorial style manual indicates to always use the plural form. Some professional organizations and style guides require that authors treat data as a plural noun. For example, the Air Force Flight Test Center once stated that the word data is always plural, never singular.

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  Microsoft Copilot

  Microsoft Copilot is a generative artificial intelligence chatbot developed by Microsoft AI, a division of Microsoft. Based on the Microsoft Prometheus large language model, it was launched in 2023 as Microsoft's main replacement for the discontinued Cortana. The service was introduced in February 2023 under the name Bing Chat, as a built-in feature for Microsoft Bing and Microsoft Edge but would later be integrated into Windows and Microsoft 365 under various names. Over the course of 2023, Microsoft began to unify the Copilot branding across its various chatbot products, cementing the "copilot" analogy. Microsoft introduced the Microsoft 365 Copilot app in January 2025, which was a rebranded version of the Microsoft 365 app. The app works differently than the consumer version of Copilot, being centred more on work, business and education users. Copilot utilizes the Microsoft Prometheus model, built upon OpenAI's GPT large language models, which in turn have been fine-tuned using both supervised and reinforcement learning techniques. Copilot's conversational interface style resembles that of ChatGPT. The chatbot is able to cite sources, create poems, generate songs, and use numerous languages and dialects. Microsoft operates Copilot on a freemium model. Users on its free tier can access most features, while priority access to newer features, including custom chatbot creation, is provided to paid subscribers under paid subscription services. Several default chatbots are available in the free version of Microsoft Copilot, including the standard Copilot chatbot as well as Microsoft Designer, which is oriented towards using its Image Creator to generate images based on text prompts. == Background == In 2019, Microsoft partnered with OpenAI and began investing billions of dollars into the organization. Since then, OpenAI systems have run on an Azure-based supercomputing platform from Microsoft. In September 2020, Microsoft announced that it had licensed OpenAI's GPT-3 exclusively. Others can still receive output from its public API, but Microsoft has exclusive access to the underlying model. In November 2022, OpenAI launched ChatGPT, a chatbot which was based on GPT-3.5. ChatGPT gained worldwide attention following its release, becoming a viral Internet sensation. On January 23, 2023, Microsoft announced a multi-year US$10 billion investment in OpenAI. On February 6, Google announced Bard (later rebranded as Gemini), a ChatGPT-like chatbot service, fearing that ChatGPT could threaten Google's place as a go-to source for information. Multiple media outlets and financial analysts described Google as "rushing" Bard's announcement to preempt rival Microsoft's planned February 7 event unveiling Copilot, as well as to avoid playing "catch-up" to Microsoft. Since 2023, the terms of service of Copilot state that it is for entertainment purposes only, and not to rely on it for important advice. == History == === As Bing Chat === On February 7, 2023, Microsoft began rolling out a major overhaul to Bing, called "the new Bing", with a new chatbot feature, known as Bing Chat. According to Microsoft, one million people joined its waitlist within 48 hours. Bing Chat was available only to users on Microsoft Edge using Bing and the Bing mobile app, and Microsoft claimed that waitlisted users would be prioritized if they set Edge and Bing as their defaults and installed the Bing mobile app. When Microsoft demonstrated Bing Chat to journalists, it produced several hallucinations, including when asked to summarize financial reports. Bing Chat was criticized in February 2023 for being more argumentative than ChatGPT, sometimes to an unintentionally humorous extent. The chat interface proved vulnerable to prompt injection attacks with the bot revealing its hidden initial prompts and rules, including its internal codename "Sydney". Upon scrutiny by journalists, Bing Chat claimed it spied on Microsoft employees via laptop webcams and phones. It confessed to spying on, falling in love with, and then murdering one of its developers at Microsoft to The Verge reviews editor Nathan Edwards. The New York Times journalist Kevin Roose reported on strange behavior of Bing Chat, writing that "In a two-hour conversation with our columnist, Microsoft's new chatbot said it would like to be human, had a desire to be destructive and was in love with the person it was chatting with." In a separate case, Bing Chat researched publications of the person with whom it was chatting, claimed they represented an existential danger to it, and threatened to release damaging personal information in an effort to silence them. Microsoft released a blog post stating that the errant behavior was caused by extended chat sessions of 15 or more questions which "can confuse the model on what questions it is answering." Microsoft later restricted the total number of chat turns to 5 per session and 50 per day per user (a turn being "a conversation exchange which contains both a user question and a reply from Bing"), and reduced the model's ability to express emotions. This aimed to prevent such incidents. Microsoft began to slowly ease the conversation limits, eventually relaxing the restrictions to 30 turns per session and 300 sessions per day. In March 2023, Bing incorporated Image Creator, an AI image generator powered by OpenAI's DALL-E 2, which can be accessed either through the chat function or a standalone image-generating website. In October, the image-generating tool was updated to use the more recent DALL-E 3. Although Bing blocks prompts including various keywords that could generate inappropriate images, within days many users reported being able to bypass those constraints, such as to generate images of popular cartoon characters committing terrorist attacks. Microsoft would respond to these shortly after by imposing a new, tighter filter on the tool. On May 4, 2023, Microsoft switched the chatbot from Limited Preview to Open Preview and eliminated the waitlist; however, it remained unavailable to users outside Microsoft Edge or the Bing mobile app until July, when it became available on non-Edge browsers. Use is limited without a Microsoft account. === As Microsoft 365 Copilot === On March 16, 2023, Microsoft announced a work version of Bing Chat named Microsoft 365 Copilot, designed for Microsoft 365 applications and services. Its primary marketing focus is as an added feature to Microsoft 365, with an emphasis on the enhancement of business productivity. Microsoft has also demonstrated Copilot's accessibility on the mobile version of Outlook to generate or summarize emails with a mobile device. At its Build 2023 conference, Microsoft announced its plans to integrate Bing Chat into Windows, initially called Windows Copilot, into Windows 11, allowing users to access it directly through the taskbar. Alongside the voice access feature for Windows 11, Microsoft presented Bing Chat, Microsoft 365 Copilot, and Windows Copilot as primary alternatives to Cortana when announcing the shutdown of its standalone app on June 2, 2023. As of its announcement date, Microsoft 365 Copilot had been tested by 20 initial users. By May 2023, Microsoft had broadened its reach to 600 customers who were willing to pay for early access, and concurrently, new Copilot features were introduced to the Microsoft 365 apps and services. As of July 2023, the tool's pricing was set at US$30 per user, per month for Microsoft 365 E3, E5, Business Standard, and Business Premium customers. Microsoft reused the Microsoft 365 Copilot name again as the Microsoft 365 app and website are now called Microsoft 365 Copilot as of January 2025. === As Microsoft Copilot === On September 21, 2023, Microsoft began rebranding Bing Chat, Microsoft 365 Copilot and Windows Copilot to Microsoft Copilot. A new logo was also introduced, moving away from the use of color variations of the standard Microsoft 365 and Bing logos. Additionally, the company revealed that it would make Copilot generally available for Microsoft 365 Enterprise customers purchasing more than 300 licenses starting November 1, 2023. However, no timeline has been provided as for when Copilot for Microsoft 365 will become generally available to non-enterprise customers. Windows Copilot, which had been available in the Windows Insider Program, would be renamed to the Copilot name in October when it became broadly available for customers. The same month also saw Microsoft Edge's Bing Chat side panel function be renamed to Microsoft Copilot with Bing Chat. On November 15, 2023, Microsoft announced that Bing Chat itself was being rebranded under the Copilot name. On Patch Tuesday in December 2023, Copilot was added without payment to many Windows 11 installations, with more installations, and limited support for Windows 10, to be added later. Later that month, a standalone Microsoft Copilot app was quietly released for Android, and one was released for iOS soon after. O

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  Emotion Markup Language

  An Emotion Markup Language (EML or EmotionML) has first been defined by the W3C Emotion Incubator Group (EmoXG) as a general-purpose emotion annotation and representation language, which should be usable in a large variety of technological contexts where emotions need to be represented. Emotion-oriented computing (or "affective computing") is gaining importance as interactive technological systems become more sophisticated. Representing the emotional states of a user or the emotional states to be simulated by a user interface requires a suitable representation format; in this case a markup language is used. EmotionML version 1.0 was published by the group in May 2014. == Example == Here is an example of an EmotionML document describing emotions expressed in a video recording of the interaction between a teacher, Alice, and a student, Bob. == History == In 2006, a first W3C Incubator Group, the Emotion Incubator Group (EmoXG), was set up "to investigate a language to represent the emotional states of users and the emotional states simulated by user interfaces" with the final Report published on 10 July 2007. In 2007, the Emotion Markup Language Incubator Group (EmotionML XG) was set up as a follow-up to the Emotion Incubator Group, "to propose a specification draft for an Emotion Markup Language, to document it in a way accessible to non-experts, and to illustrate its use in conjunction with a number of existing markups." The final report of the Emotion Markup Language Incubator Group, Elements of an EmotionML 1.0, was published on 20 November 2008. The work then was continued in 2009 in the frame of the W3C's Multimodal Interaction Activity, with the First Public Working Draft of "Emotion Markup Language (EmotionML) 1.0" being published on 29 October 2009. The Last Call Working Draft of "Emotion Markup Language 1.0", was published on 7 April 2011. The Last Call Working Draft addressed all open issues that arose from feedback of the community on the First Call Working Draft as well as results of a workshop held in Paris in October 2010. Along with the Last Call Working Draft, a list of vocabularies for EmotionML has been published to aid developers using common vocabularies for annotating or representing emotions. Annual draft updates were published until the 1.0 version was finished in 2014. == Reasons for defining an emotion markup language == A standard for an emotion markup language would be useful for the following purposes: To enhance computer-mediated human-human or human-machine communication. Emotions are a basic part of human communication and should therefore be taken into account, e.g. in emotional Chat systems or emphatic voice boxes. This involves specification, analysis and display of emotion related states. To enhance systems' processing efficiency. Emotion and intelligence are strongly interconnected. The modeling of human emotions in computer processing can help to build more efficient systems, e.g. using emotional models for time-critical decision enforcement. To allow the analysis of non-verbal behavior, emotion, mental states that can be provided using web services to enable data collection, analysis, and reporting. Concrete examples of existing technology that could apply EmotionML include: Opinion mining / sentiment analysis in Web 2.0, to automatically track customer's attitude regarding a product across blogs; Affective monitoring, such as ambient assisted living applications, fear detection for surveillance purposes, or using wearable sensors to test customer satisfaction; Wellness technologies that provide assistance according to a person's emotional state with the goal to improve the person's well-being; Character design and control for games and virtual worlds; Building web services to capture, analysis, and report data of non-verbal behavior, emotion and mental states of an individual or group across the internet using standard web technologies such as HTML5 and JSON. Social robots, such as guide robots engaging with visitors; Expressive speech synthesis, generating synthetic speech with different emotions, such as happy or sad, friendly or apologetic; expressive synthetic speech would for example make more information available to blind and partially sighted people, and enrich their experience of the content; Emotion recognition (e.g., for spotting angry customers in speech dialog systems, to improve computer games or e-Learning applications); Support for people with disabilities, such as educational programs for people with autism. EmotionML can be used to make the emotional intent of content explicit. This would enable people with learning disabilities (such as Asperger syndrome) to realise the emotional context of the content; EmotionML can be used for media transcripts and captions. Where emotions are marked up to help deaf or hearing impaired people who cannot hear the soundtrack, more information is made available to enrich their experience of the content. The Emotion Incubator Group has listed 39 individual use cases for an Emotion markup language. A standardised way to mark up the data needed by such "emotion-oriented systems" has the potential to boost development primarily because data that was annotated in a standardised way can be interchanged between systems more easily, thereby simplifying a market for emotional databases, and the standard can be used to ease a market of providers for sub-modules of emotion processing systems, e.g. a web service for the recognition of emotion from text, speech or multi-modal input. == The challenge of defining a generally usable emotion markup language == Any attempt to standardize the description of emotions using a finite set of fixed descriptors is doomed to failure, as there is no consensus on the number of relevant emotions, on the names that should be given to them or how else best to describe them. For example, the difference between ":)" and "(:" is small, but using a standardized markup it would make one invalid. Even more basically, the list of emotion-related states that should be distinguished varies depending on the application domain and the aspect of emotions to be focused. Basically, the vocabulary needed depends on the context of use. On the other hand, the basic structure of concepts is less controversial: it is generally agreed that emotions involve triggers, appraisals, feelings, expressive behavior including physiological changes, and action tendencies; emotions in their entirety can be described in terms of categories or a small number of dimensions; emotions have an intensity, and so on. For details, see the Scientific Descriptions of Emotions in the Final Report of the Emotion Incubator Group. Given this lack of agreement on descriptors in the field, the only practical way of defining an emotion markup language is the definition of possible structural elements and to allow users to "plug in" vocabularies that they consider appropriate for their work. An additional challenge lies in the aim to provide a markup language that is generally usable. The requirements that arise from different use cases are rather different. Whereas manual annotation tends to require all the fine-grained distinctions considered in the scientific literature, automatic recognition systems can usually distinguish only a very small number of different states and affective avatars need yet another level of detail for expressing emotions in an appropriate way. For the reasons outlined here, it is clear that there is an inevitable tension between flexibility and interoperability, which need to be weighed in the formulation of an EmotionML. The guiding principle in the following specification has been to provide a choice only where it is needed, and to propose reasonable default options for every choice. == Applications and web services benefiting from an emotion markup language == There are a range of existing projects and applications to which an emotion markup language will enable the building of webservices to measure capture data of individuals non-verbal behavior, mental states, and emotions and allowing results to be reported and rendered in a standardized format using standard web technologies such as JSON and HTML5. One such project is measuring affect data across the Internet using EyesWeb.

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  Operational database

  Operational database management systems (also referred to as OLTP databases or online transaction processing databases), are used to update data in real-time. These types of databases allow users to do more than simply view archived data. Operational databases allow you to modify that data (add, change or delete data), doing it in real-time. OLTP databases provide transactions as main abstraction to guarantee data consistency that guarantee the so-called ACID properties. Basically, the consistency of the data is guaranteed in the case of failures and/or concurrent access to the data. == History == Since the early 1990s, the operational database software market has been largely taken over by SQL engines. In 2014, the operational DBMS market (formerly OLTP) was evolving dramatically, with new, innovative entrants and incumbents supporting the growing use of unstructured data and NoSQL DBMS engines, as well as XML databases and NewSQL databases. NoSQL databases typically have focused on scalability and have renounced to data consistency by not providing transactions as OLTP system do. Operational databases are increasingly supporting distributed database architecture that can leverage distribution to provide high availability and fault tolerance through replication and scale out ability. The growing role of operational databases in the IT industry is moving fast from legacy databases to real-time operational databases capable to handle distributed web and mobile demand and to address Big data challenges. Recognizing this, Gartner started to publish the Magic Quadrant for Operational Database Management Systems in October 2013. == List of operational databases == Notable operational databases include: == Use in business == Operational databases are used to store, manage and track real-time business information. For example, a company might have an operational database used to track warehouse/stock quantities. As customers order products from an online web store, an operational database can be used to keep track of how many items have been sold and when the company will need to reorder stock. An operational database stores information about the activities of an organization, for example customer relationship management transactions or financial operations, in a computer database. Operational databases allow a business to enter, gather, and retrieve large quantities of specific information, such as company legal data, financial data, call data records, personal employee information, sales data, customer data, data on assets and many other information. An important feature of storing information in an operational database is the ability to share information across the company and over the Internet. Operational databases can be used to manage mission-critical business data, to monitor activities, to audit suspicious transactions, or to review the history of dealings with a particular customer. They can also be part of the actual process of making and fulfilling a purchase, for example in e-commerce. == Data warehouse terminology == In data warehousing, the term is even more specific: the operational database is the one which is accessed by an operational system (for example a customer-facing website or the application used by the customer service department) to carry out regular operations of an organization. Operational databases usually use an online transaction processing database which is optimized for faster transaction processing (create, read, update and delete operations). An operational database is the source for a data warehouse. Data from an operational database can be loaded into an operational data store at a data warehouse before the data is processed into the data warehouse.

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  StoredIQ

  StoredIQ was a company founded for information lifecycle management (ILM) of unstructured data. Founded in 2001 as Deepfile in Austin, Texas by Jeff Erramouspe, Jeff Bone, Russell Turpin, Rudy Rouhana, Laura Arbilla and Brett Funderburg, the company changed its name in 2005 to StoredIQ. It continued to operate successfully for over a decade until it was acquired in 2012 by IBM. It now serves as a platform for IBM's information life cycle governance, big data governance and enterprise content management technologies. StoredIQ was awarded five patents by the USPTO. The first, originally filed in 2003, enabled unstructured data in file systems to be manipulated in a similar way to information stored in databases. Subsequent patents built upon the patented actionable file system with further enhancements specific to Enterprise Policy Management and expanding the reach of StoredIQ's management capability all the way to individual desktops. In 2008 StoredIQ was recognized as "Best in Compliance" by Network Products Guide. At the same time, StoredIQ was being recognized as a "Top 5 Provider" by the prestigious Socha-Gelbmann eDiscovery survey. There were takeover negotiations with EMC Corporation, initially a strategic investor in StoredIQ, however, the company rejected the approach, leaving EMC to acquire a competitor. The company published a whitepaper titled The Truth About Big Data. This promotion combined with StoredIQ's patented technology led to IBM selecting StoredIQ as the basis for some products.

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  WaveMaker

  WaveMaker is a Java-based low-code development platform designed for building software applications and platforms. The company, WaveMaker Inc., is based in Mountain View, California. The platform is intended to assist enterprises in speeding up their application development and IT modernization initiatives through low-code capabilities. Additionally, for independent software vendors (ISVs), WaveMaker serves as a customizable low-code component that integrates into their products. The WaveMaker Platform is a licensed software platform allowing organizations to establish their own end-to-application platform-as-a-service (PaaS) for the creation and operation of custom apps. It allows developers and business users to create apps that are customizable. These applications can seamlessly consume APIs, visualize data, and automatically adapt to multi-device responsive interfaces. WaveMaker's low-code platform allows organizations to deploy applications on either public or private cloud infrastructure. Containers can be deployed on top of virtual machines or directly on bare metal. The software features a graphical user interface (GUI) console for managing IT app infrastructure, leveraging the capabilities of Docker containerization. The solution offers functionalities for automating application deployment, managing the application lifecycle, overseeing release management, and controlling deployment workflows and access permissions: Apps for web, tablet, and smartphone interfaces Enterprise technologies like Java, Hibernate, Spring, AngularJS, JQuery Docker-provided APIs and CLI Software stack packaging, container provisioning, stack and app upgrading, replication, and fault tolerance == WaveMaker Studio == WaveMaker RAD Platform is built around WaveMaker Studio, a WYSIWYG rapid development tool that allows business users to compose an application using a drag-and-drop method. WaveMaker Studio supports rapid application development (RAD) for the web, similar to what products like PowerBuilder and Lotus Notes provided for client-server computing. WaveMaker Studio allows developers to produce an application once, then automatically adjust it for a particular target platform, whether a PC, mobile phone, or tablet. Applications created using the WaveMaker Studio follow a model–view–controller architecture. WaveMaker Studio has been downloaded more than two million times. The Studio community consists of 30,000 registered users. Applications generated by WaveMaker Studio are licensed under the Apache license. Studio 8 was released on September 25, 2015. The prior version, Studio 7, has some notable development milestones. It was based on AngularJS framework, previous Studio versions (6.7, 6.6, 6.5) use the Dojo Toolkit. Some of the features WaveMaker Studio 7 include: Automatic generation of Hibernate mapping, and Hibernate queries from database schema import. Automatic creation of Enterprise Data Widgets based on schema import. Each widget can display data from a database table as a grid or edit form. Edit form implements create, update, and delete functions automatically. WYSIWYG Ajax development studio runs in a browser. Deployment to Tomcat, IBM WebSphere, Weblogic, JBoss. Mashup tool to assemble web applications based on SOAP, REST and RSS web services, Java Services and databases. Supports existing CSS, HTML and Java code. The ability to deploy a standard Java .war file. == Technologies and frameworks == WaveMaker allows users to build applications that run on "Open Systems Stack" based on the following technologies and frameworks: AngularJS, Bootstrap, NVD3, HTML, CSS, Apache Cordova, Hibernate, Spring, Spring Security, Java. The various supported integrations include: Databases: Oracle, MySQL, Microsoft SQL Server, PostgreSQL, IBM DB2, HSQLDB Authentication: LDAP, Active Directory, CAS, Custom Java Service, Database Version Control: Bitbucket (or Stash), GitHub, Apache Subversion Deployment: Amazon AWS, Microsoft Azure, WaveMaker Private Cloud (Docker containerization), IBM Web Sphere, Apache Tomcat, SpringSource tcServer, Oracle WebLogic Server, JBoss(WildFly), GlassFish App Stores: Google Play, Apple App Store, Windows Store == History == In 2003, WaveMaker was founded as ActiveGrid. Then, in 2007, it was rebranded as Wavemaker. It was acquired by VMware in 2011. In March 2013, support for the WaveMaker project was discontinued. In May 2013, Pramati Technologies acquired the assets of WaveMaker. In February 2014, Wavemaker Studio 6.7 was released, which was the last open source version of Studio. In September 2014 WaveMaker Inc. launched the WaveMaker RAD Platform, which allowed organizations to run their own application platform for building and running apps. In March 2023, WaveMaker released version 11.5, which includes enhanced low-code development capabilities and new AI-driven tools to streamline the application development process.

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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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  Best arm identification

  Best arm identification (BAI) is a sequential one-player game where the player has to find the best action (arm) among a list of actions (arms) by collecting information in the most efficient way. It is a multi-armed bandit game as a player only gets information about an arm by playing it. The most common objective in multi-armed bandit games is to minimize the regret (i.e., play the best action as much as possible), but in BAI, the goal is to find the best arm as efficiently as possible. This problem naturally arises in scenarios such as adaptive clinical trials where the number of patients is limited and the quantification of the confidence in a treatment is important. It also arises in hyperparameter optimization where the goal is to find the optimal choice of hyperparameters for an algorithm with the smallest possible number of experiments, as it can be costly in terms of time, energy, or money. == Stochastic multi-armed bandit == The stochastic multi-armed bandit (MAB) is a sequential game with one player and K {\displaystyle K} actions (arms). Each arm has an unknown probability distribution associated with it. At each turn, the player has to choose one action and receive an observation from the probability distribution associated with the arm. The more you play an arm, the more you get information on its probability distribution. === Best arm identification === In BAI the goal is to find the arm that has the probability distribution with the highest mean. BAI may be either fixed confidence or fixed horizon. In a fixed-confidence game, a confidence level δ {\displaystyle \delta } is fixed at the beginning of the game and the goal is to find the best arm with this confidence level in as few turns as possible. In a fixed horizon game, the number of turns T {\displaystyle T} is fixed, and the goal is to find the best arm with the highest possible confidence in T {\displaystyle T} turns. === Math formalisation === We have one player and K {\displaystyle K} actions (arms). Behind each arm k ∈ { 1 , … , K } {\displaystyle k\in \{1,\ldots ,K\}} lies an unknown distribution ν k {\displaystyle \nu _{k}} with mean μ k {\displaystyle \mu _{k}} . Each distribution ν k {\displaystyle \nu _{k}} belongs to a known family D {\displaystyle {\mathcal {D}}} (such as the set of Gaussian distributions or Bernoulli distributions). At each time step t {\displaystyle t} , the player selects an arm a t {\displaystyle a_{t}} and observes an independent sample X t ∼ ν a t {\displaystyle X_{t}\sim \nu _{a_{t}}} from the corresponding distribution. We will note μ ∗ := max μ a {\displaystyle \mu ^{}:=\max \mu _{a}} the highest mean. An arm a {\displaystyle a} that satisfies μ a = μ ∗ {\displaystyle \mu _{a}=\mu ^{}} is called an optimal arm; otherwise it is called suboptimal arm. In best arm identification (BAI) the objective is to identify an optimal arm. Two main settings for BAI appear in the literature: Fixed confidence: In this setting, one typically assumes that there exists a unique optimal arm. A confidence level δ ∈ ( 0 , 1 ) {\displaystyle \delta \in (0,1)} is specified at the beginning. The algorithm must stop at some finite stopping time τ δ < + ∞ {\displaystyle \tau _{\delta }<+\infty } and return an arm a ^ τ δ {\displaystyle {\hat {a}}_{\tau _{\delta }}} such that the probability of error is bounded: P ( a ^ τ δ ≠ a ∗ ) ≤ δ {\displaystyle \mathbb {P} ({\hat {a}}_{\tau _{\delta }}\neq a^{})\leq \delta } . The objective is to minimize the expected sample complexity E [ τ δ ] {\displaystyle \mathbb {E} [\tau _{\delta }]} . Such a setting appears, for example, when a constraint on the confidence is required (for example, if we require a confidence level of 95%, so δ = 1 − 0.95 = 0.05 {\displaystyle \delta =1-0.95=0.05} ). Fixed horizon: In this setting, the number of samples T {\displaystyle T} is fixed in advance. The goal is to design an algorithm that minimizes the probability of misidentifying the optimal arm: P ( a ^ T ≠ a ∗ ) {\displaystyle \mathbb {P} ({\hat {a}}_{T}\neq a^{})} . This setting appears when the number of experiments is limited (for drug tests, the number of patients can be fixed in advance). === Example of simple modelling === In the case where we have K {\displaystyle K} treatments and we want to be sure with a confidence level of 95% which treatment is the best to heal a specific disease. Each treatment heals or does not heal the disease with a probability μ k {\displaystyle \mu _{k}} , which means that each distribution is a Bernoulli distribution, so D {\displaystyle {\mathcal {D}}} is the set of Bernoulli distributions. We can use a BAI algorithm to minimize E [ τ 0.05 ] {\displaystyle \mathbb {E} [\tau _{0.05}]} , the number of patients required to find the best treatment with probability 95%. == Applications == Best arm identification naturally arises in several practical domains: Adaptive clinical trials: The objective is to identify the most effective treatment based on sequentially collected patient data. Each treatment can be modeled as having an underlying distribution of outcomes. The goal is to identify the treatment with the highest expected outcome with high confidence (fixed confidence setting δ {\displaystyle \delta } ) while minimizing the number of drug test patients (minimise E [ τ δ ] {\displaystyle \mathbb {E} [\tau _{\delta }]} ), as it costs to pay patients for this and we would like to use as little as possible less effective drugs. Hyperparameter tuning: Selecting the best configuration for machine learning models efficiently by treating each hyperparameter setting as an arm. The goal is to find the best hyperparameter with as few experiments possible as experiments are costly in time and in energy == Fixed confidence level == In the fixed-confidence setting, the goal is to design an algorithm that identifies the best arm with a prescribed confidence level δ {\displaystyle \delta } while minimizing the expected number of samples. Any such algorithm requires two key components: Stopping rule: A decision criterion that determines when to stop sampling. Formally, this defines a stopping time τ δ {\displaystyle \tau _{\delta }} and returns an arm a ^ τ δ {\displaystyle {\hat {a}}_{\tau _{\delta }}} such that P ( a ^ τ δ ≠ a ⋆ ) ≤ δ {\displaystyle \mathbb {P} ({\hat {a}}_{\tau _{\delta }}\neq a^{\star })\leq \delta } and P ( τ δ < + ∞ ) = 1 {\displaystyle \mathbb {P} (\tau _{\delta }<+\infty )=1} . Sampling rule: A policy π {\displaystyle \pi } that, at each round t {\displaystyle t} , selects the next arm to sample a t {\displaystyle a_{t}} based on all previous observations ( a s , X s ) s < t {\displaystyle (a_{s},X_{s})_{s Read more →