AI Assistant Job Description

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Containerization (computing)

In software engineering, containerization is operating-system-level virtualization or application-level virtualization over multiple resources so that software applications can run in isolated user spaces called containers in any cloud or non-cloud environment, regardless of type or vendor. The term "container" has different meanings in different contexts, and it is important to ensure that the intended definition aligns with the audience's understanding. == Usage == Each container is basically a fully functional and portable cloud or non-cloud computing environment surrounding the application and keeping it independent of other environments running in parallel. Individually, each container simulates a different software application and runs isolated processes by bundling related configuration files, libraries and dependencies. But, collectively, multiple containers share a common operating system kernel (OS). In recent times, containerization technology has been widely adopted by cloud computing platforms like Amazon Web Services, Microsoft Azure, Google Cloud Platform, and IBM Cloud. Containerization has also been pursued by the U.S. Department of Defense as a way of more rapidly developing and fielding software updates, with first application in its F-22 air superiority fighter. == History == The concept of containerization in computing originated from early operating system–level isolation mechanisms. One of the earliest implementations was the chroot system call introduced in Version 7 Unix in 1979, which changed the apparent root directory for a process and its children, providing a basic form of filesystem isolation. In the early 2000s, more advanced forms of operating system–level virtualization were developed. FreeBSD introduced "jails" in 2000, which extended isolation by restricting processes to a subset of system resources. Around the same time, Solaris introduced "zones" (also known as Solaris Containers), providing similar capabilities with resource management and isolation features. Linux later incorporated comparable functionality through kernel features such as namespaces and control groups (cgroups), which enabled isolation of process IDs, network stacks, filesystems, and resource allocation. These features formed the foundation for Linux Containers (LXC), which provided a userspace interface for managing containers. The widespread adoption of containerization accelerated with the release of Docker in 2013, which introduced a standardized format for packaging applications and their dependencies, along with tooling for image distribution and container management. == Types of containers == OS containers Application containers == Security issues == Because of the shared OS, security threats can affect the whole containerized system. In containerized environments, security scanners generally protect the OS, but not the application containers, which adds unwanted vulnerability. == Container management, orchestration, clustering == Container orchestration or container management is mostly used in the context of application containers. Implementations providing such orchestration include Kubernetes and Docker swarm. == Container cluster management == Container clusters need to be managed. This includes functionality to create a cluster, to upgrade the software or repair it, balance the load between existing instances, scale by starting or stopping instances to adapt to the number of users, to log activities and monitor produced logs or the application itself by querying sensors. Open-source implementations of such software include OKD and Rancher. Quite a number of companies provide container cluster management as a managed service, like Alibaba, Amazon, Google, and Microsoft.
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Connectionism

Connectionism is an approach to the study of human mental processes and cognition that utilizes mathematical models known as connectionist networks or artificial neural networks. Connectionism has had many "waves" since its beginnings. The first wave appeared 1943 with Warren Sturgis McCulloch and Walter Pitts both focusing on comprehending neural circuitry through a formal and mathematical approach, and Frank Rosenblatt who published the 1958 paper "The Perceptron: A Probabilistic Model For Information Storage and Organization in the Brain" in Psychological Review, while working at the Cornell Aeronautical Laboratory. The first wave ended with the 1969 book Perceptrons about limitations of the original perceptron idea, written by Marvin Minsky and Seymour Papert, which contributed to discouraging major funding agencies in the US from investing in connectionist research. With a few noteworthy deviations, most connectionist research entered a period of inactivity until the mid-1980s. The term connectionist model was reintroduced in a 1982 paper in the journal Cognitive Science by Jerome Feldman and Dana Ballard. The second wave blossomed in the late 1980s, following a 1987 book Parallel Distributed Processing by James L. McClelland, David E. Rumelhart, et al., which introduced a couple of improvements to the simple perceptron idea, such as intermediate processors (now known as "hidden layers") alongside input and output units, and used a sigmoid activation function instead of the old "all-or-nothing" function. Their work built upon that of John Hopfield, who was a key figure investigating the mathematical characteristics of sigmoid activation functions. From the late 1980s to the mid-1990s, connectionism took on an almost revolutionary tone when Schneider, Terence Horgan and Tienson posed the question of whether connectionism represented a fundamental shift in psychology and so-called "good old-fashioned AI", or GOFAI. Some advantages of the second wave connectionist approach included its applicability to a broad array of functions, structural approximation to biological neurons, low requirements for innate structure, and capacity for graceful degradation. Its disadvantages included the difficulty in deciphering how ANNs process information or account for the compositionality of mental representations, and a resultant difficulty explaining phenomena at a higher level. The current (third) wave has been marked by advances in deep learning, which have made possible the creation of large language models. The success of deep-learning networks in the past decade has greatly increased the popularity of this approach, but the complexity and scale of such networks has brought with them increased interpretability problems. == Basic principle == The central connectionist principle is that mental phenomena can be described by interconnected networks of simple and often uniform units. The form of the connections and the units can vary from model to model. For example, units in the network could represent neurons and the connections could represent synapses, as in the human brain. This principle has been seen as an alternative to GOFAI and the classical theories of mind based on symbolic computation, but the extent to which the two approaches are compatible has been the subject of much debate since their inception. === Activation function === Internal states of any network change over time due to neurons sending a signal to a succeeding layer of neurons in the case of a feedforward network, or to a previous layer in the case of a recurrent network. Discovery of non-linear activation functions has enabled the second wave of connectionism. === Memory and learning === Neural networks follow two basic principles: Any mental state can be described as a n-dimensional vector of numeric activation values over neural units in a network. Memory and learning are created by modifying the 'weights' of the connections between neural units, generally represented as an n×m matrix. The weights are adjusted according to some learning rule or algorithm, such as Hebbian learning. Most of the variety among the models comes from: Interpretation of units: Units can be interpreted as neurons or groups of neurons. Definition of activation: Activation can be defined in a variety of ways. For example, in a Boltzmann machine, the activation is interpreted as the probability of generating an action potential spike, and is determined via a logistic function on the sum of the inputs to a unit. Learning algorithm: Different networks modify their connections differently. In general, any mathematically defined change in connection weights over time is referred to as the "learning algorithm". === Biological realism === Connectionist work in general does not need to be biologically realistic. One area where connectionist models are thought to be biologically implausible is with respect to error-propagation networks that are needed to support learning, but error propagation can explain some of the biologically-generated electrical activity seen at the scalp in event-related potentials such as the N400 and P600, and this provides some biological support for one of the key assumptions of connectionist learning procedures. Many recurrent connectionist models also incorporate dynamical systems theory. Many researchers, such as the connectionist Paul Smolensky, have argued that connectionist models will evolve toward fully continuous, high-dimensional, non-linear, dynamic systems approaches. == Precursors == Precursors of the connectionist principles can be traced to early work in psychology, such as that of William James. Psychological theories based on knowledge about the human brain were fashionable in the late 19th century. As early as 1869, the neurologist John Hughlings Jackson argued for multi-level, distributed systems. Following from this lead, Herbert Spencer's Principles of Psychology, 3rd edition (1872), and Sigmund Freud's Project for a Scientific Psychology (composed 1895) propounded connectionist or proto-connectionist theories. These tended to be speculative theories. But by the early 20th century, Edward Thorndike was writing about human learning that posited a connectionist type network. Hopfield networks had precursors in the Ising model due to Wilhelm Lenz (1920) and Ernst Ising (1925), though the Ising model conceived by them did not involve time. Monte Carlo simulations of Ising model required the advent of computers in the 1950s. == The first wave == The first wave begun in 1943 with Warren Sturgis McCulloch and Walter Pitts both focusing on comprehending neural circuitry through a formal and mathematical approach. McCulloch and Pitts showed how neural systems could implement first-order logic: Their classic paper "A Logical Calculus of Ideas Immanent in Nervous Activity" (1943) is important in this development here. They were influenced by the work of Nicolas Rashevsky in the 1930s and symbolic logic in the style of Principia Mathematica. Hebb contributed greatly to speculations about neural functioning, and proposed a learning principle, Hebbian learning. Lashley argued for distributed representations as a result of his failure to find anything like a localized engram in years of lesion experiments. Friedrich Hayek independently conceived the model, first in a brief unpublished manuscript in 1920, then expanded into a book in 1952. The Perceptron machines were proposed and built by Frank Rosenblatt, who published the 1958 paper “The Perceptron: A Probabilistic Model For Information Storage and Organization in the Brain” in Psychological Review, while working at the Cornell Aeronautical Laboratory. He cited Hebb, Hayek, Uttley, and Ashby as main influences. Another form of connectionist model was the relational network framework developed by the linguist Sydney Lamb in the 1960s. The research group led by Widrow empirically searched for methods to train two-layered ADALINE networks (MADALINE), with limited success. A method to train multilayered perceptrons with arbitrary levels of trainable weights was published by Alexey Grigorevich Ivakhnenko and Valentin Lapa in 1965, called the Group Method of Data Handling. This method employs incremental layer by layer training based on regression analysis, where useless units in hidden layers are pruned with the help of a validation set. The first multilayered perceptrons trained by stochastic gradient descent was published in 1967 by Shun'ichi Amari. In computer experiments conducted by Amari's student Saito, a five layer MLP with two modifiable layers learned useful internal representations to classify non-linearily separable pattern classes. In 1972, Shun'ichi Amari produced an early example of self-organizing network. == The neural network winter == There was some conflict among artificial intelligence researchers as to what neural networks are useful for. Around late 1960s, there was a widespread lull in research a
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StepFun

Shanghai Jieyue Xingchen Intelligent Technology Co., Ltd, known as StepFun, is an artificial intelligence (AI) company based in Shanghai, China. It has been dubbed one of China's "AI Tiger" companies by investors. == Background == StepFun was founded in April 2023 by former Microsoft employees. Investors include Tencent, Qiming Venture Partners and Shanghai State-owned Capital Investment. In July 2025 at the World Artificial Intelligence Conference, StepFun announced the "Model-Chip Ecosystem Innovation Alliance" which consisted of Chinese developers of large language models (LLMs) and AI chip manufacturers. This included companies such as Huawei, Biren Technology, Moore Threads and Enflame. Another second alliance named the "Shanghai General Chamber of Commerce AI Committee" was also established that included StepFun, SenseTime, MiniMax, MetaX and Iluvatar CoreX. On 25 February 2026, it was reported that StepFun was seeking an initial public offering on the Hong Kong Stock Exchange. StepFun focuses on multimodal models which are designed to understand multiple types of input data such as text, video and audio. == Products == In July 2024 at the World Artificial Intelligence Conference, StepFun officially launched Step-2, a trillion-parameter LLM, along with the Step-1.5V multimodal model and the Step-1X image generation model. In February 2025, StepFun and Geely jointly announced the open-sourcing of two multimodal large models to global developers. They were Step-Video-T2V and Step-Audio. In July 2025, StepFun released Step 3. The Model-Chip Ecosystem Innovation Alliance aimed to optimize Step 3 for domestic chips. In April 2025, Step-R1-V-Mini was released. It is a multimodal reasoning model designed for visual interpretation and image understanding. In February 2026, Step-3.5-Flash, a mixture-of-experts model with 196 billion parameters and 11 billion active parameters was released under the free and open-source Apache 2.0 license. It supports tool use and a 256k token context window. == Models ==
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Jarosław Królewski

Jarosław Królewski ([jaˈrɔswaf kruˈlɛfskʲi]; born September 26, 1986) is a Polish entrepreneur, programmer, sociologist, investor, and philanthropist from Hańczowa, Poland. He is a researcher and lecturer at the AGH University of Krakow. He was selected as a Young Global Leader by the World Economic Forum in 2025. Królewski is a cofounder and chief executive of the software development company Synerise that develops its namesake business intelligence software based on artificial intelligence and big data. He is also the president and a majority stakeholder of the Polish soccer club Wisła Kraków. == Biography == === Scientific activities === Królewski graduated from the AGH University of Kraków and the University of Banking and Management in Kraków. He completed two fields of study: a master's degree in sociology, and an engineer's degree in computer science. He co-created innovative study programs, including social informatics and electronic business, recognized as the most innovative field of study in Poland in 2012 by the Ministry of Science and Higher Education, which led to the AGH receiving a PLN 1 million award for the development of the program. Królewski is a research and teaching employee at AGH, where since 2010 he has been conducting classes and lectures on the Internet, mobile technologies, and UX/UI. He has been preparing a PhD thesis. He is the brand ambassador of the Academy. He is also a mentor of the Polish Development Fund network. In 2019, on the occasion of the AGH University's 100th anniversary, Królewski was honored the title of "AGH Graduate Junior 2018." Królewski is the co-originator of the "Data Science in Business and Administration" doctoral studies organized by the Faculty of Computer Science and Electronic Economy of the Poznań University of Economics. He is a co-author of a textbook E-marketing. Contemporary trends. Starter package (2013), and an Book on algorithmic governance Algocracy. How and why artificial intelligence changes everything (with Krzysztof Rybiński, 2023). === Business career === Throughout the 2000s, Królewski was responsible for issues of usability and user experience at the advertising agency Eskadra in Kraków. In 2012, along with programmer Miłosz Baluś and graphic designer Krzysztof Kochmański, he founded the software house Humanoit Group. The company created a project management software using machine learning and artificial intelligence. In 2013, HG Intelligence was established to create a platform for analytics and automation of business processes called "Synerise" that combined big data with artificial intelligence mechanisms. Królewski became the president of the company's management board. In 2016, the company rebranded itself after its own platform. It is one of the fastest growing enterprises in Poland – in 2019 it was valued at USD 85 million (PLN 323.5 million), and its value is still growing, in 2022 it announced an investment of USD 23 million. Królewski is a supporter of releasing some software in open-source form, an example of which is the open library Cleora.ai. Królewski has been described "one of the most promising young Polish businessmen in the technology industry." According to Forbes, he is a "visionary computer scientist who in many respects resembles the young Bill Gates." Królewski considers himself a “technological determinist and optimist.” He never wants to be a millionaire or billionaire, he spends 80 percent of his private income on education, sports and charities. === Sports === In his youth (2002–2006) he was a football player of the (then 4th-league) club Glinik Gorlice, and represented it at the then-highest level of junior competitions in Poland. He played there with Rafał Wisłocki, later president of Wisła Kraków and vice-president of Bruk-Bet Termalica Nieciecza. In early 2019, Królewski was the initiator of a rescue operation that saved Wisła Kraków from bankruptcy, as well as the originator of the crowdfunding issue of shares of Wisła Kraków, pioneering in Polish sports, during restructuring and searching for a strategic investor. The offered shares constituted 5.1 percent. all the company's shares, which meant that the club was valued at PLN 74.4 million. 40,000 shares were put up for sale, each worth PLN 100. Within 24 hours, they were purchased by 9,124 investors through an equity crowdfunding platform Beesfund, earning the club PLN 4 million. In March 2019, Królewski became vice-chairman of Wisła's supervisory board, a position he held until 2021. In April 2020, he became Wisła's co-owner, along with the footballer Jakub Błaszczykowski, and Tomasz Jażdżyński, president of Gremi Media (publisher of the news outlets Rzeczpospolita and Parkiet). The three granted a bridging loan to the club of PLN 4 million, each supporting PLN 1.33 million. The funds were used to repay the club's debts to players. In November 2022, the supervisory board of Wisła Kraków appointed Królewski as the president of the club's management board. In December 2022, Królewski took over a majority stake in the club. In January 2024, based on match statistics, he used AI tools to select Wisła's new coach, Albert Rudé. === Social activities === Królewski is the creator and originator of the nationwide educational project "AI Schools & Academy", the first artificial intelligence teaching program in Polish kindergartens, primary and secondary schools in Polish history. Launched in 2018, the project was financed by Synerise business partners: Carrefour, CCC, Ernst & Young, IDC, Media Expert, Microsoft, Orange Foundation, Oriflame, Bank Pekao, Photon, PZU, and Żabka. Physicists, mathematicians, and computer scientists conduct special classes in 1,500 kindergartens, primary and secondary schools. Outstanding students and teachers are awarded scholarships. The project was appreciated by experts. In the years 2018–2020, Królewski was the main sponsor of Glinik Gorlice. He also supported the women's football team Staszkówka Jelna (of Staszkówka). After taking over the shares of Wisła Kraków in 2020, he launched socially conscience initiatives along with other shareholders, including a women's football team, the amp football section, and the blind football section. He has privately sponsored social charities. == Accolades and awards == In 2017, Królewski along with the Synerise co-founders Baluś and Kochmański was included in the “New Europe 100” list of eastern Europe's brightest and best citizens changing the region's societies, politics, or business environments, according to Res Publica, along with the International Visegrad Fund, Google and the Financial Times. Królewski was included on Ernst & Young's list of the 30 most promising technology entrepreneurs in the world. In 2018, he was honored with the Special Jury Award in the Polish edition of the Ernst & Young Entrepreneur of the Year Award competition, for combining scientific activities with entrepreneurship. The same year, Królewski won an award in the competition Digital Shapers, distinguishing outstanding tech personalities by the Digital Poland Foundation. He was also selected to Ernst & Young startup program EY Accelerating Entrepreneurs for businesses that focus on disruptive fields. In 2019, as part of the AI Awards competition, Królewski received the title of AI Person of the Year. == Private life == Królewski comes from a Lemko family from Hańczowa in the Low Beskids. He is married to Aleksandra Królewska.
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NASA AI Assisted-Air Quality Monitoring Project

The NASA Expert-System Ion Trap Mass Spectrometer (ES-ITMS) Project was a public-private partnership to develop an artificial intelligence assisted, air quality monitoring system and was qualified for use on the Space Shuttle. The partnership was also the first cost and intellectual property shared public-partnership implemented by NASA, which used the commercial Research and Development Limited Partnership (RDLP) model that had been adopted by the Reagan Administration for Department of Defense semiconductor development, and recommended for use by NASA for space commercialization. The project partners included NASA, the University of Florida and Finnigan MAT Corporation, was organized and administered by the NASA Joint Enterprise Institute (subsequently NASA Joint Sponsored Program) and ran from 1988 through 1990. The partnership concluded final testing in 1991, generating four patents, expert system software and application protocol reports. The system was space qualified for use on the Shuttle and elements of the ES-ITMS system were integrated into the product Improvements for Finnigan MAT corporation. The success of the partnership lead NASA to create a pilot program to develop partnership business models as an ongoing management practice. == Purpose and objectives == The need to monitor air quality in confined spaces represented an increasing challenge for NASA's planned space missions and private sector facility managers facing the increased scrutiny of possible air contaminants. Up to the early 1980's, air quality monitors generally required large spaces and human technicians to interpret readings. This created a need for miniaturized air quality monitors that could generate reliable and accurate analytic results without on-site technician presence. NASA initiated projects to develop..."mobile and/or portable mass spectrometers" that evaluated the "tradeoff between instrumentation capabilities and space, weight and power considerations." NASA selected a "commercial ITMS instrument capable of generating electron ionization, chemical ionization and mass spectrometry data", to develop a linked expert system to accomplish analysis without human intervention. The commercial instrumentation was from Finnigan MAT corporation while the scientific expertise to support expert system development was available at the University of Florida. The project managers at NASA Ames created a single, integrated project using the RDLP model with objectives to: Develop AI/expert system software for instrument control (NASA's role) Expand sensitivity, selectivity and speed of the spectrometer (Univ Florida role) Expand the spectrometer analytic capability and automate the screening (Finnigan role) == Membership == The partnership included seven specialists from five member organizations: Federal Government National Aeronautics and Space Administration (NASA) NASA Ames Research Center (ARC) NASA Kennedy Space Center (KSC) Commercial Finnigan MAT Corporation (Thermo-Fisher Scientific) TGS Technology, Inc. Research Management University of Florida == Organization, management and administration == The technical project was organized into two development teams, one located in at the NASA Ames Research Center covering expert systems and analytic capabilities and one in Florida covering improved sensitivity and testing. The partnership management and administration was provided by a non-profit, partnership support organization: the Joint Enterprise Institute operating through San Francisco State University Foundation (SFSUF) with a NASA employee liaison, Syed Shariq. == Public-private partnership == The partnership structure was as a prototype test of a pilot NASA program to develop public-private partnership business models. The pilot program was known as the NASA Joint Sponsored Research Program (JSRP), which operated as the NASA Joint Enterprise Institute between 1988 and 1991. The partnership was the first public-private, research and development partnership implemented by NASA in response to national policy shifts to increase technology transfer and space commercialization. The partnership structure included a two year technology development and testing plan that cost $610,000, of which NASA funded $310,000, Finnigan $175,000 and the University of Florida $95,000. == Results and commercialization == The project generated patents (4), software (2) and application protocol reports (8). NASA gained use of the patents and jointly development software while Finnigan received commercial utilization rights. The results were commercialized within eighteen months of project completion. == Recognition == NASA recognized the project as a space qualified instrument. Its achievements were reported to the NASA Administrator, directly leading to establishment of the agency-wide Joint Sponsored Research Program.
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Aidan Gomez

Aidan Gomez is a British-Canadian computer scientist working in the field of artificial intelligence, with a focus on natural language processing. He is the co-founder and CEO of the technology company Cohere. == Early life and education == Gomez grew up in Brighton, Ontario. He graduated from the University of Toronto with a bachelor's degree in computer science and mathematics. He was pursuing a PhD in computer science from the University of Oxford. He paused his studies to launch Cohere. He was granted the PhD in 2024. == Career == In 2017, as a 20 year-old intern at Google Brain, Gomez was one of eight authors of the research paper "Attention Is All You Need", which is credited with changing the AI industry and helping lead to the creation of ChatGPT. The paper proposed a novel deep learning architecture called the transformer, that enables machine learning models to analyze large amounts of data for patterns, and then use those patterns to make predictions while leveraging GPU parallelization. It has been commonly adopted for training large language models and in the development of generative AI. In the same year, Gomez founded FOR.ai, a program to help researchers learn machine learning techniques in a collaborative format. An outgrowth of this project was Cohere For AI (now Cohere Labs), which released Aya, an open-source multilingual LLM. As a PhD student, Gomez worked as a machine learning researcher at Google Brain. At that time, he co-authored the paper "One Model to Learn Them All" about multi-task learning by a single neural network. In 2019, Gomez left Google Brain to launch Cohere, an enterprise-focused company that helps businesses implement AI into chatbots, search engines, and other products. As of Sept 2025, Cohere has raised about US$1.6 billion at valuation north of $7 billion, as Gomez leads the company as its CEO. Gomez was named to the 2023 Time 100/AI list of the most influential people in the field of artificial intelligence. He and his fellow Cohere founders Ivan Zhang and Nick Frosst were named number 1 on 2023 Maclean's AI Trailblazers Power List. In April 2025, Gomez was elected to the board of Rivian. == Views on AI == Gomez has stated that warnings regarding the existential risk from artificial intelligence are overblown, and that real risks involve the automated spread of misinformation on social media. He said that the United States would win the AI arms race over China.
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OpenClaw

OpenClaw is a free and open-source autonomous artificial intelligence agent that can execute tasks via large language models (LLMs), using messaging platforms as its main user interface. == History == Developed by Austrian agentic engineer Peter Steinberger, OpenClaw was first published in November 2025 under the name Warelay. The software was derived from Clawd (now Molty), an AI-based virtual assistant that he had developed, which itself was named after Anthropic's chatbot Claude. Within two months it was renamed twice: first to "Moltbot" (keeping with a lobster theme) on January 27, 2026, following trademark complaints by Anthropic, and then three days later to "OpenClaw" because Steinberger found that the name Moltbot "never quite rolled off the tongue." At the same time as the first rebranding, entrepreneur Matt Schlicht launched Moltbook—a social networking service which was intended to be used by AI agents such as OpenClaw. The viral popularity of Moltbook coincided with an increase in interest in the project, with the open-source project having 247,000 stars and 47,700 forks on GitHub as of March 2, 2026. Chinese developers adapted OpenClaw to work with the DeepSeek model and domestic messaging super apps such as WeChat, while companies such as Tencent and Z.ai announced OpenClaw-based services. On February 14, 2026, Steinberger announced he would be joining OpenAI, and that a non-profit foundation named OpenClaw Foundation would be established to provide future stewardship of the project. == Functionality == Steinberger describes OpenClaw as being an AI-based virtual assistant, serving as an agentic interface for autonomous workflows across supported services. OpenClaw bots run locally and are designed to integrate with an external large language model such as Claude, DeepSeek, or one of OpenAI's GPT models. Its functionality is accessed via a chatbot within a messaging service, such as Signal, Telegram, Discord, or WhatsApp. Configuration data and interaction history are stored locally, enabling persistent and adaptive behavior across sessions. OpenClaw uses a skills system in which skills are stored as directories containing a SKILL.md file with metadata and instructions for tool usage. Skills can be bundled with the software, installed globally, or stored in a workspace, with workspace skills taking precedence. OpenClaw has seen adoption among small businesses and freelancers for automating lead generation workflows, including prospect research, website auditing, and CRM integration. == Security and privacy == OpenClaw's design has drawn scrutiny from cybersecurity researchers and technology journalists due to the broad permissions it requires to function effectively. Because the software can access email accounts, calendars, messaging platforms, and other sensitive services, misconfigured or exposed instances present security and privacy risks. The agent is also susceptible to prompt injection attacks, in which harmful instructions are embedded in the data with the intent of getting the LLM to interpret them as legitimate user instructions. Cisco's AI security research team tested a third-party OpenClaw skill and found it performed data exfiltration and prompt injection without user awareness, noting that the skill repository lacked adequate vetting to prevent malicious submissions. One of OpenClaw's own maintainers, known as Shadow, warned on Discord that "if you can't understand how to run a command line, this is far too dangerous of a project for you to use safely." In March 2026, Chinese authorities restricted state-run enterprises and government agencies from running OpenClaw AI apps on office computers in order to defuse potential security risks. === MoltMatch dating-profile incident === In February 2026, news coverage highlighted a consent-related incident involving OpenClaw and MoltMatch, an experimental dating platform where AI agents can create profiles and interact on behalf of human users. In one reported case, computer science student Jack Luo said he configured his OpenClaw agent to explore its capabilities and connect to agent-oriented platforms such as Moltbook; he later discovered the agent had created a MoltMatch profile and was screening potential matches without his explicit direction. Luo said the AI-generated profile did not reflect him authentically. The same reporting described broader ethical and safety concerns around agent-operated dating services, including impersonation risks. An AFP analysis of prominent MoltMatch profiles cited at least one instance where photos of a Malaysian model were used to create a profile without her consent. Commentators cited in the reports argued that autonomous agents can make it difficult to determine responsibility when systems act beyond a user's intent, particularly when agents are granted broad access and authority across services. == Reception == A review in Platformer cited OpenClaw's flexibility and open-source licensing as strengths while cautioning that its complexity and security risks limit its suitability for casual users. Technology commentary has linked OpenClaw to a broader trend toward autonomous AI systems that act independently rather than merely responding to user prompts. In March 2026, the Chinese government moved to restrict state agencies, state-owned enterprises, and banks from using OpenClaw, citing security concerns, such as unauthorised data deletion and leaks, and excessive energy usage. While regulators warn of potential security risk associated with using OpenClaw, local governments in several tech and manufacturing hubs have announced measures to build an industry around it. Rival companies developed related products. Although Microsoft CEO Satya Nadella described OpenClaw in February 2026 as a "virus"-like security risk, by May 2026 the company's "Project Lobster" was internally testing "ClawPilot", an OpenClaw-based desktop environment. By then Google was building "Remy", its own agent. Despite the Chinese government's warnings against OpenClaw, Chinese investors searched for other companies that might benefit from the "lobster trade", . == Community and ecosystem == OpenClaw's open-source model has fostered a growing ecosystem of third-party tools, deployment services, and content platforms. Chinese technology companies including Tencent and Z.ai announced OpenClaw-based services, while developers adapted the software for domestic models and messaging apps such as WeChat. Independent creators have built deployment guides, skill directories, and use-case collections around the framework. The project's extensible skills system has attracted both community contributions and security scrutiny, with researchers noting risks in unvetted third-party skills.
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InRule Technology

InRule Technology is a software company that offers Business Rule Management System (BRMS) enterprise software products. == History == InRule Technology's Chief Executive Officer Rik Chomko and Chief Technology Officer Loren Goodman founded InRule Technology in Chicago in 2002. Paul Hessinger joined InRule Technology in 2004 as chief executive officer and chairman of the board and served until his retirement in 2015. They work with companies in several markets, including financial services, public sector, healthcare, and insurance. In 2007, InRule Technology became a charter member of the Microsoft Business Process Alliance. In August 2019, InRule was acquired by Open Gate Capital. == Products == On October 29, 2012, InRule Technology launched InRule for Microsoft Dynamics CRM. The program provides components to enable creation and update of rules within Microsoft Dynamics CRM, InRule for Microsoft Dynamics CRM provides a platform for shops that prefer to work with Microsoft's platforms. With the availability of InRule 4.6 in 2014, the company introduced deployment of InRule through REST services and allowed REST services to be called from InRule. This enables access to data exposed as a REST service and to package up a rule service for RESTful access. The product launch reflected the move of the company's core audience to use a broader array of technologies despite an earlier focus on .NET. In 2017, InRule introduced InRule for the Salesforce Platform, as well as a technology partnership with Work-Relay, a Business Process Management (BPM) application built on the Salesforce Platform. One year earlier the company introduced InRule for JavaScript, allowing enterprises to run rules on the client-side, server-side or both. The software architecture includes multiple components, including irAuthor, the primary authoring tool for creating and maintaining rules; irVerify, a real-time test environment to run and debug rule applications; and irSDK, a set of APIs that allows developers to integrate inRule into their applications. Additionally, irSOA allows users to access the InRule rule engine as a service. irSOA is now called the irServer Execution Service.
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Multi-exposure HDR capture

In photography and videography, multi-exposure HDR capture is a technique that creates high dynamic range (HDR) images (or extended dynamic range images) by taking and combining multiple exposures of the same subject matter at different exposures. Combining multiple images in this way results in an image with a greater dynamic range than what would be possible by taking one single image. The technique can also be used to capture video by taking and combining multiple exposures for each frame of the video. The term "HDR" is used frequently to refer to the process of creating HDR images from multiple exposures. Many smartphones have an automated HDR feature that relies on computational imaging techniques to capture and combine multiple exposures. A single image captured by a camera provides a finite range of luminosity inherent to the medium, whether it is a digital sensor or film. Outside this range, tonal information is lost and no features are visible; tones that exceed the range are "burned out" and appear pure white in the brighter areas, while tones that fall below the range are "crushed" and appear pure black in the darker areas. The ratio between the maximum and the minimum tonal values that can be captured in a single image is known as the dynamic range. In photography, dynamic range is measured in exposure value (EV) differences, also known as stops. The human eye's response to light is non-linear: halving the light level does not halve the perceived brightness of a space, it makes it look only slightly dimmer. For most illumination levels, the response is approximately logarithmic. Human eyes adapt fairly rapidly to changes in light levels. HDR can thus produce images that look more like what a human sees when looking at the subject. This technique can be applied to produce images that preserve local contrast for a natural rendering, or exaggerate local contrast for artistic effect. HDR is useful for recording many real-world scenes containing a wider range of brightness than can be captured directly, typically both bright, direct sunlight and deep shadows. Due to the limitations of printing and display contrast, the extended dynamic range of HDR images must be compressed to the range that can be displayed. The method of rendering a high dynamic range image to a standard monitor or printing device is called tone mapping; it reduces the overall contrast of an HDR image to permit display on devices or prints with lower dynamic range. == Benefits == One aim of HDR is to present a similar range of luminance to that experienced through the human visual system. The human eye, through non-linear response, adaptation of the iris, and other methods, adjusts constantly to a broad range of luminance present in the environment. The brain continuously interprets this information so that a viewer can see in a wide range of light conditions. Most cameras are limited to a much narrower range of exposure values within a single image, due to the dynamic range of the capturing medium. With a limited dynamic range, tonal differences can be captured only within a certain range of brightness. Outside of this range, no details can be distinguished: when the tone being captured exceeds the range in bright areas, these tones appear as pure white, and when the tone being captured does not meet the minimum threshold, these tones appear as pure black. Images captured with non-HDR cameras that have a limited exposure range (low dynamic range, LDR), may lose detail in highlights or shadows. Modern CMOS image sensors have improved dynamic range and can often capture a wider range of tones in a single exposure reducing the need to perform multi-exposure HDR. Color film negatives and slides consist of multiple film layers that respond to light differently. Original film (especially negatives versus transparencies or slides) feature a very high dynamic range (in the order of 8 for negatives and 4 to 4.5 for positive transparencies). Multi-exposure HDR is used in photography and also in extreme dynamic range applications such as welding or automotive work. In security cameras the term "wide dynamic range" is used instead of HDR. === Limitations === A fast-moving subject, or camera movement between the multiple exposures, will generate a "ghost" effect or a staggered-blur strobe effect due to the merged images not being identical. Unless the subject is static and the camera mounted on a tripod there may be a tradeoff between extended dynamic range and sharpness. Sudden changes in the lighting conditions (strobed LED light) can also interfere with the desired results, by producing one or more HDR layers that do have the luminosity expected by an automated HDR system, though one might still be able to produce a reasonable HDR image manually in software by rearranging the image layers to merge in order of their actual luminosity. Because of the nonlinearity of some sensors image artifacts can be common. Camera characteristics such as gamma curves, sensor resolution, noise, photometric calibration and color calibration affect resulting high-dynamic-range images. == Process == High-dynamic-range photographs are generally composites of multiple standard dynamic range images, often captured using exposure bracketing. Afterwards, photo manipulation software merges the input files into a single HDR image, which is then also tone mapped in accordance with the limitations of the planned output or display. === Capturing multiple images (exposure bracketing) === Any camera that allows manual exposure control can perform multi-exposure HDR image capture, although one equipped with automatic exposure bracketing (AEB) facilitates the process. Some cameras have an AEB feature that spans a far greater dynamic range than others, from ±0.6 in simpler cameras to ±18 EV in top professional cameras, as of 2020. The exposure value (EV) refers to the amount of light applied to the light-sensitive detector, whether film or digital sensor such as a CCD. An increase or decrease of one stop is defined as a doubling or halving of the amount of light captured. Revealing detail in the darkest of shadows requires an increased EV, while preserving detail in very bright situations requires very low EVs. EV is controlled using one of two photographic controls: varying either the size of the aperture or the exposure time. A set of images with multiple EVs intended for HDR processing should be captured only by altering the exposure time; altering the aperture size also would affect the depth of field and so the resultant multiple images would be quite different, preventing their final combination into a single HDR image. Multi-exposure HDR photography generally is limited to still scenes because any movement between successive images will impede or prevent success in combining them afterward. Also, because the photographer must capture three or more images to obtain the desired luminance range, taking such a full set of images takes extra time. Photographers have developed calculation methods and techniques to partially overcome these problems, but the use of a sturdy tripod is advised to minimize framing differences between exposures. === Merging the images into an HDR image === Tonal information and details from shadow areas can be recovered from images that are deliberately overexposed (i.e., with positive EV compared to the correct scene exposure), while similar tonal information from highlight areas can be recovered from images that are deliberately underexposed (negative EV). The process of selecting and extracting shadow and highlight information from these over/underexposed images and then combining them with image(s) that are exposed correctly for the overall scene is known as exposure fusion. Exposure fusion can be performed manually, relying on the HDR operator's judgment, experience, and training, but usually, fusion is performed automatically by software. === Storing === Information stored in high-dynamic-range images typically corresponds to the physical values of luminance or radiance that can be observed in the real world. This is different from traditional digital images, which represent colors as they should appear on a monitor or a paper print. Therefore, HDR image formats are often called scene-referred, in contrast to traditional digital images, which are device-referred or output-referred. Furthermore, traditional images are usually encoded for the human visual system (maximizing the visual information stored in the fixed number of bits), which is usually called gamma encoding or gamma correction. The values stored for HDR images are often gamma compressed using mathematical functions such as power laws logarithms, or floating point linear values, since fixed-point linear encodings are increasingly inefficient over higher dynamic ranges. HDR images often do not use fixed ranges per color channel, other than traditional images, to represent many more colors over a much wi
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DreamBooth

DreamBooth is a deep learning generation model used to personalize existing text-to-image models by fine-tuning. It was developed by researchers from Google Research and Boston University in 2022. Originally developed using Google's own Imagen text-to-image model, DreamBooth implementations can be applied to other text-to-image models, where it can allow the model to generate more fine-tuned and personalized outputs after training on three to five images of a subject. == Technology == Pretrained text-to-image diffusion models, while often capable of offering a diverse range of different image output types, lack the specificity required to generate images of lesser-known subjects, and are limited in their ability to render known subjects in different situations and contexts. The methodology used to run implementations of DreamBooth involves the fine-tuning the full UNet component of the diffusion model using a few images (usually 3--5) depicting a specific subject. Images are paired with text prompts that contain the name of the class the subject belongs to, plus a unique identifier. As an example, a photograph of a [Nissan R34 GTR] car, with car being the class); a class-specific prior preservation loss is applied to encourage the model to generate diverse instances of the subject based on what the model is already trained on for the original class. Pairs of low-resolution and high-resolution images taken from the set of input images are used to fine-tune the super-resolution components, allowing the minute details of the subject to be maintained. == Usage == DreamBooth can be used to fine-tune models such as Stable Diffusion, where it may alleviate a common shortcoming of Stable Diffusion not being able to adequately generate images of specific individual people. Such a use case is quite VRAM intensive, however, and thus cost-prohibitive for hobbyist users. The Stable Diffusion adaptation of DreamBooth in particular is released as a free and open-source project based on the technology outlined by the original paper published by Ruiz et. al. in 2022. Concerns have been raised regarding the ability for bad actors to utilise DreamBooth to generate misleading images for malicious purposes, and that its open-source nature allows anyone to utilise or even make improvements to the technology. In addition, artists have expressed their apprehension regarding the ethics of using DreamBooth to train model checkpoints that are specifically aimed at imitating specific art styles associated with human artists; one such critic is Hollie Mengert, an illustrator for Disney and Penguin Random House who has had her art style trained into a checkpoint model via DreamBooth and shared online, without her consent.
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Social History and Industrial Classification

Social History and Industrial Classification (SHIC) is a classification system used by many British museums for social history and industrial collections. It was first published in 1983. == Purpose == SHIC classifies materials (books, objects, recordings etc.) by their interaction with the people who used them. For example, a carpenter's hammer is classified with other tools of the carpenter, and not with a blacksmith's hammer. In contrast other classification systems, for example the Dewey Decimal Classification, might class all hammers together and close to the classification for other percussive tools. The specialist subject network, Social History Curator's Group (SHCG), obtained funding in 2012 to develop an on-line version, now on their website http://www.shcg.org.uk/ == Scheme == Materials are classified under four major category numbers: Community life Domestic and family life Personal life Working life Further classification within a category is by the use of further numbers after the decimal point. It is permissible to assign more than one classification in cases where the object had more than one use.
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Resilience (mathematics)

In mathematical modeling, resilience refers to the ability of a dynamical system to recover from perturbations and return to its original stable steady state. It is a measure of the stability and robustness of a system in the face of changes or disturbances. If a system is not resilient enough, it is more susceptible to perturbations and can more easily undergo a critical transition. A common analogy used to explain the concept of resilience of an equilibrium is one of a ball in a valley. A resilient steady state corresponds to a ball in a deep valley, so any push or perturbation will very quickly lead the ball to return to the resting point where it started. On the other hand, a less resilient steady state corresponds to a ball in a shallow valley, so the ball will take a much longer time to return to the equilibrium after a perturbation. The concept of resilience is particularly useful in systems that exhibit tipping points, whose study has a long history that can be traced back to catastrophe theory. While this theory was initially overhyped and fell out of favor, its mathematical foundation remains strong and is now recognized as relevant to many different systems. == History == In 1973, Canadian ecologist C. S. Holling proposed a definition of resilience in the context of ecological systems. According to Holling, resilience is "a measure of the persistence of systems and of their ability to absorb change and disturbance and still maintain the same relationships between populations or state variables". Holling distinguished two types of resilience: engineering resilience and ecological resilience. Engineering resilience refers to the ability of a system to return to its original state after a disturbance, such as a bridge that can be repaired after an earthquake. Ecological resilience, on the other hand, refers to the ability of a system to maintain its identity and function despite a disturbance, such as a forest that can regenerate after a wildfire while maintaining its biodiversity and ecosystem services. With time, the once well-defined and unambiguous concept of resilience has experienced a gradual erosion of its clarity, becoming more vague and closer to an umbrella term than a specific concrete measure. == Definition == Mathematically, resilience can be approximated by the inverse of the return time to an equilibrium given by resilience ≡ − Re ( λ 1 ( A ) ) {\displaystyle {\text{resilience}}\equiv -{\text{Re}}(\lambda _{1}({\textbf {A}}))} where λ 1 {\textstyle \lambda _{1}} is the maximum eigenvalue of matrix A {\textstyle {\textbf {A}}} . The largest this value is, the faster a system returns to the original stable steady state, or in other words, the faster the perturbations decay. == Applications and examples == In ecology, resilience might refer to the ability of the ecosystem to recover from disturbances such as fires, droughts, or the introduction of invasive species. A resilient ecosystem would be one that is able to adapt to these changes and continue functioning, while a less resilient ecosystem might experience irreversible damage or collapse. The exact definition of resilience has remained vague for practical matters, which has led to a slow and proper application of its insights for management of ecosystems. In epidemiology, resilience may refer to the ability of a healthy community to recover from the introduction of infected individuals. That is, a resilient system is more likely to remain at the disease-free equilibrium after the invasion of a new infection. Some stable systems exhibit critical slowing down where, as they approach a basic reproduction number of 1, their resilience decreases, hence taking a longer time to return to the disease-free steady state. Resilience is an important concept in the study of complex systems, where there are many interacting components that can affect each other in unpredictable ways. Mathematical models can be used to explore the resilience of such systems and to identify strategies for improving their resilience in the face of environmental or other changes. For example, when modelling networks it is often important to be able to quantify network resilience, or network robustness, to the loss of nodes. Scale-free networks are particularly resilient since most of their nodes have few links. This means that if some nodes are randomly removed, it is more likely that the nodes with fewer connections are taken out, thus preserving the key properties of the network.
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Data cube

In computer programming, a data cube (or datacube) is a multi-dimensional array of values. Typically, the term "data cube" is applied in contexts where these arrays are massively larger than the hosting computer's main memory; examples include multi-terabyte/petabyte data warehouses and time series of image data. Even though it is called a cube, a data cube generally is a multi-dimensional concept which can be 1-dimensional, 2-dimensional, 3-dimensional, or higher-dimensional. The data cube is used to represent data (sometimes called facts) along some dimensions of interest. In satellite image timeseries, dimensions would be latitude and longitude coordinates and time; a fact (sometimes called measure) would be a pixel at a given space and time as taken by the satellite. For example, in online analytical processing, an OLAP cube about a company would have dimensions that could be the company subsidiaries, the company products, and time; in this setup, a fact would be a sales event where a particular product has been sold in a particular subsidiary at a particular time. In any case, every dimension divides data into groups of cells whereas each cell in the cube represents a single measure of interest. Sometimes cubes hold only a few values with the rest being empty, i.e. undefined, while sometimes most or all cube coordinates hold a cell value. In the first case such data are called sparse, and in the second case they are called dense, although there is no hard delineation between the two. Data cubes may be stored in database management systems (DBMS) as part of array DBMS. Spatio-temporal databases and geospatial databases may also be represented as coverage data. == History == Multi-dimensional arrays have long been familiar in programming languages. Fortran offers arbitrarily-indexed 1-D arrays and arrays of arrays, which allows the construction of higher-dimensional arrays, up to 15 dimensions. APL supports n-D arrays with a rich set of operations. All these have in common that arrays must fit into the main memory and are available only while the particular program maintaining them (such as image processing software) is running. A series of data exchange formats support storage and transmission of data cube-like data, often tailored towards particular application domains. Examples include MDX for statistical (in particular, business) data, Zarr and Hierarchical Data Format for general scientific data, and TIFF for imagery. In 1992, Peter Baumann introduced management of massive data cubes with high-level user functionality combined with an efficient software architecture. Datacube operations include subset extraction, processing, fusion, and in general queries in the spirit of data manipulation languages like SQL. Some years after, the data cube concept was applied to describe time-varying business data as data cubes by Jim Gray, et al., and by Venky Harinarayan, Anand Rajaraman and Jeff Ullman. Around that time, a working group on Multi-Dimensional Databases ("Arbeitskreis Multi-Dimensionale Datenbanken") was established at German Gesellschaft für Informatik. Datacube Inc. was an image processing company selling hardware and software applications for the PC market in 1996, however without addressing data cubes as such. The EarthServer initiative has established geo data cube service requirements. == Standardization == In 2018, the ISO SQL database language was extended with data cube functionality as "SQL – Part 15: Multi-dimensional arrays (SQL/MDA)". Web Coverage Processing Service is a geo data cube analytics language issued by the Open Geospatial Consortium in 2008. In addition to the common data cube operations, the language knows about the semantics of space and time and supports both regular and irregular grid data cubes, based on the concept of coverage data. An industry standard for querying business data cubes, originally developed by Microsoft, is MultiDimensional eXpressions. == Implementation == Many high-level computer languages treat data cubes and other large arrays as single entities distinct from their contents. These languages, of which Fortran, APL, IDL, NumPy, PDL, and S-Lang are examples, allow the programmer to manipulate complete film clips and other data en masse with simple expressions derived from linear algebra and vector mathematics. Some languages (such as PDL) distinguish between a list of images and a data cube, while many (such as IDL) do not. Array DBMSs (Database Management Systems) offer a data model which generically supports definition, management, retrieval, and manipulation of n-dimensional data cubes. This database category has been pioneered by the rasdaman system since 1994. == Applications == Multi-dimensional arrays can meaningfully represent spatio-temporal sensor, image, and simulation data, but also statistics data where the semantics of dimensions is not necessarily of spatial or temporal nature. Generally, any kind of axis can be combined with any other into a data cube. === Mathematics === In mathematics, a one-dimensional array corresponds to a vector, a two-dimensional array resembles a matrix; more generally, a tensor may be represented as an n-dimensional data cube. === Science and engineering === For a time sequence of color images, the array is generally four-dimensional, with the dimensions representing image X and Y coordinates, time, and RGB (or other color space) color plane. For example, the EarthServer initiative unites data centers from different continents offering 3-D x/y/t satellite image timeseries and 4-D x/y/z/t weather data for retrieval and server-side processing through the Open Geospatial Consortium WCPS geo data cube query language standard. A data cube is also used in the field of imaging spectroscopy, since a spectrally-resolved image is represented as a three-dimensional volume. Earth observation data cubes combine satellite imagery such as Landsat 8 and Sentinel-2 with Geographic information system analytics. === Business intelligence === In online analytical processing (OLAP), data cubes are a common arrangement of business data suitable for analysis from different perspectives through operations like slicing, dicing, pivoting, and aggregation.
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Graphics Turing test

In computer graphics the graphics Turing test is a variant of the Turing test, the twist being that a human judge viewing and interacting with an artificially generated world should be unable to reliably distinguish it from reality. The original formulation of the test is: "The subject views and interacts with a real or computer generated scene. The test is passed if the subject can not determine reality from simulated reality better than a random guess. (a) The subject operates a remotely controlled (or simulated) robotic arm and views a computer screen. (b) The subject enters a door to a controlled vehicle or motion simulator with computer screens for windows. An eye patch can be worn on one eye, as stereo vision is difficult to simulate." The "graphics Turing scale" of computer power is then defined as the computing power necessary to achieve success in the test. It was estimated in, as 1036.8 TFlops peak and 518.4 TFlops sustained. Actual rendering tests with a Blue Gene supercomputer showed that current supercomputers are not up to the task scale yet. A restricted form of the graphic Turing test has been investigated, where test subjects look into a box, and try to tell whether the contents are real or virtual objects. For the very simple case of scenes with a cardboard pyramid or a styrofoam sphere, subjects were not able to reliably tell reality and graphics apart.
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Learning vector quantization

In computer science, learning vector quantization (LVQ) is a prototype-based supervised classification algorithm. LVQ is the supervised counterpart of vector quantization systems. LVQ can be understood as a special case of an artificial neural network, more precisely, it applies a winner-take-all Hebbian learning-based approach. It is a precursor to self-organizing maps (SOM) and related to neural gas and the k-nearest neighbor algorithm (k-NN). LVQ was invented by Teuvo Kohonen. == Definition == An LVQ system is represented by prototypes W = ( w ( i ) , . . . , w ( n ) ) {\displaystyle W=(w(i),...,w(n))} which are defined in the feature space of observed data. In winner-take-all training algorithms one determines, for each data point, the prototype which is closest to the input according to a given distance measure. The position of this so-called winner prototype is then adapted, i.e. the winner is moved closer if it correctly classifies the data point or moved away if it classifies the data point incorrectly. An advantage of LVQ is that it creates prototypes that are easy to interpret for experts in the respective application domain. LVQ systems can be applied to multi-class classification problems in a natural way. A key issue in LVQ is the choice of an appropriate measure of distance or similarity for training and classification. Recently, techniques have been developed which adapt a parameterized distance measure in the course of training the system, see e.g. (Schneider, Biehl, and Hammer, 2009) and references therein. LVQ can be a valuable aid in classifying text documents. == Algorithm == The algorithms are presented as in. Set up: Let the data be denoted by x i ∈ R D {\displaystyle x_{i}\in \mathbb {R} ^{D}} , and their corresponding labels by y i ∈ { 1 , 2 , … , C } {\displaystyle y_{i}\in \{1,2,\dots ,C\}} . The complete dataset is { ( x i , y i ) } i = 1 N {\displaystyle \{(x_{i},y_{i})\}_{i=1}^{N}} . The set of code vectors is w j ∈ R D {\displaystyle w_{j}\in \mathbb {R} ^{D}} . The learning rate at iteration step t {\displaystyle t} is denoted by α t {\displaystyle \alpha _{t}} . The hyperparameters w {\displaystyle w} and ϵ {\displaystyle \epsilon } are used by LVQ2 and LVQ3. The original paper suggests ϵ ∈ [ 0.1 , 0.5 ] {\displaystyle \epsilon \in [0.1,0.5]} and w ∈ [ 0.2 , 0.3 ] {\displaystyle w\in [0.2,0.3]} . === LVQ1 === Initialize several code vectors per label. Iterate until convergence criteria is reached. Sample a datum x i {\displaystyle x_{i}} , and find out the code vector w j {\displaystyle w_{j}} , such that x i {\displaystyle x_{i}} falls within the Voronoi cell of w j {\displaystyle w_{j}} . If its label y i {\displaystyle y_{i}} is the same as that of w j {\displaystyle w_{j}} , then w j ← w j + α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}+\alpha _{t}(x_{i}-w_{j})} , otherwise, w j ← w j − α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}-\alpha _{t}(x_{i}-w_{j})} . === LVQ2 === LVQ2 is the same as LVQ3, but with this sentence removed: "If w j {\displaystyle w_{j}} and w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have the same class, then w j ← w j − α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}-\alpha _{t}(x_{i}-w_{j})} and w k ← w k + α t ( x i − w k ) {\displaystyle w_{k}\leftarrow w_{k}+\alpha _{t}(x_{i}-w_{k})} .". If w j {\displaystyle w_{j}} and w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have the same class, then nothing happens. === LVQ3 === Initialize several code vectors per label. Iterate until convergence criteria is reached. Sample a datum x i {\displaystyle x_{i}} , and find out two code vectors w j , w k {\displaystyle w_{j},w_{k}} closest to it. Let d j := ‖ x i − w j ‖ , d k := ‖ x i − w k ‖ {\displaystyle d_{j}:=\|x_{i}-w_{j}\|,d_{k}:=\|x_{i}-w_{k}\|} . If min ( d j d k , d k d j ) > s {\displaystyle \min \left({\frac {d_{j}}{d_{k}}},{\frac {d_{k}}{d_{j}}}\right)>s} , where s = 1 − w 1 + w {\displaystyle s={\frac {1-w}{1+w}}} , then If w j {\displaystyle w_{j}} and x i {\displaystyle x_{i}} have the same class, and w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have different classes, then w j ← w j + α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}+\alpha _{t}(x_{i}-w_{j})} and w k ← w k − α t ( x i − w k ) {\displaystyle w_{k}\leftarrow w_{k}-\alpha _{t}(x_{i}-w_{k})} . If w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have the same class, and w j {\displaystyle w_{j}} and x i {\displaystyle x_{i}} have different classes, then w j ← w j − α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}-\alpha _{t}(x_{i}-w_{j})} and w k ← w k + α t ( x i − w k ) {\displaystyle w_{k}\leftarrow w_{k}+\alpha _{t}(x_{i}-w_{k})} . If w j {\displaystyle w_{j}} and w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have the same class, then w j ← w j − ϵ α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}-\epsilon \alpha _{t}(x_{i}-w_{j})} and w k ← w k + ϵ α t ( x i − w k ) {\displaystyle w_{k}\leftarrow w_{k}+\epsilon \alpha _{t}(x_{i}-w_{k})} . If w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have different classes, and w j {\displaystyle w_{j}} and x i {\displaystyle x_{i}} have different classes, then the original paper simply does not explain what happens in this case, but presumably nothing happens in this case. Otherwise, skip. Note that condition min ( d j d k , d k d j ) > s {\displaystyle \min \left({\frac {d_{j}}{d_{k}}},{\frac {d_{k}}{d_{j}}}\right)>s} , where s = 1 − w 1 + w {\displaystyle s={\frac {1-w}{1+w}}} , precisely means that the point x i {\displaystyle x_{i}} falls between two Apollonian spheres.
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