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Sanad (government app)

Sanad (Arabic: سند) is the official digital identity and e-government services application of the Hashemite Kingdom of Jordan. Developed and managed by the Ministry of Digital Economy and Entrepreneurship, the app provides a unified platform for accessing a range of public services and personal records digitally. == Overview == Launched in February 2020, Sanad is part of Jordan's broader digital transformation strategy aimed at improving public service delivery and enhancing administrative efficiency. The app allows users to authenticate their identity digitally and access over 550 services from more than 50 government and private sector entities. == Features == Sanad provides a wide array of services, including: Viewing and managing official digital documents Applying for government services (e.g., jordanian passport issuance or renewal, health insurance) Accessing personal records (e.g., pension, property ownership) Digitally signing documents Paying utility bills and traffic fines Receiving and tracking official notifications The app is available on iOS, Android, and HarmonyOS platforms and supports both Arabic and English languages. == Digital Identity == A core feature of Sanad is the digital identity system, which enables secure login and authentication for all integrated services. Users must activate their digital identity at designated Sanad stations across Jordan to access the full suite of services. == Adoption and Impact == As of 2025, more than 1.6 million Jordanians have activated their digital identities through Sanad. The app has played a significant role in streamlining government interactions and reducing the need for in-person visits, especially during the COVID-19 pandemic. == Recent Developments == In 2025, the Ministry launched an updated version of the app with enhanced user experience and new services, including the e-passport issuance feature.
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Information behavior

Information behavior is a field of information science research that seeks to understand the way people search for and use information in various contexts. It can include information seeking and information retrieval, but it also aims to understand why people seek information and how they use it. The term 'information behavior' was coined by Thomas D. Wilson in 1982 and sparked controversy upon its introduction. The term has now been adopted and Wilson's model of information behavior is widely cited in information behavior literature. In 2000, Wilson defined information behavior as "the totality of human behavior in relation to sources and channels of information". A variety of theories of information behavior seek to understand the processes that surround information seeking. An analysis of the most cited publications on information behavior during the early 21st century shows its theoretical nature. Information behavior research can employ various research methodologies grounded in broader research paradigms from psychology, sociology and education. In 2003, a framework for information-seeking studies was introduced that aims to guide the production of clear, structured descriptions of research objects and positions information-seeking as a concept within information behavior. == Concepts of information behavior == === Information need === Information need is a concept introduced by Wilson. Understanding the information need of an individual involved three elements: Why the individual decides to look for information, What purpose the information they find will serve, and How the information is used once it is retrieved === Information-seeking behavior === Information-seeking behavior is a more specific concept of information behavior. It specifically focuses on searching, finding, and retrieving information. Information-seeking behavior research can focus on improving information systems or, if it includes information need, can also focus on why the user behaves the way they do. A review study on information search behavior of users highlighted that behavioral factors, personal factors, product/service factors and situational factors affect information search behavior. Information-seeking behavior can be more or less explicit on the part of users: users might seek to solve some task or to establish some piece of knowledge which can be found in the data in question, or alternatively the search process itself is part of the objective of the user, in use cases for exploring visual content or for familiarising oneself with the content of an information service. In the general case, information-seeking needs to be understood and analysed as a session rather than as a one-off transaction with a search engine, and in a broader context which includes user high-level intentions in addition to the immediate information need. === Information use === An information need is the recognition that a gap exists in one’s knowledge, prompting a desire to seek information to fill that gap. It often arises when a person encounters a problem or question they cannot resolve with their current understanding. === Information poverty and barriers === Introduced by Elfreda Chatman in 1987, information poverty is informed by the understanding that information is not equally accessible to all people. Information poverty does not describe a lack of information, but rather a worldview in which one's own experiences inside their own small world may create a distrust in the information provided by those outside their own lived experiences. == Metatheories == In Library and Information Science (LIS), a metatheory is described "a set of assumptions that orient and direct theorizing about a given phenomenon". Library and information science researchers have adopted a number of different metatheories in their research. A common concern among LIS researchers, and a prominent discussion in the field, is the broad spectrum of theories that inform the study of information behavior, information users, or information use. This variation has been noted as a cause of concern because it makes individual studies difficult to compare or synthesize if they are not guided by the same theory. This sentiment has been expressed in studies of information behavior literature from the early 1980s and more recent literature reviews have declared it necessary to refine their reviews to specific contexts or situations due to the sheer breadth of information behavior research available. Below are descriptions of some, but not all, metatheories that have guided LIS research. === Cognitivist approach === A cognitive approach to understanding information behavior is grounded in psychology. It holds the assumption that a person's thinking influences how they seek, retrieve, and use information. Researchers that approach information behavior with the assumption that it is influenced by cognition, seek to understand what someone is thinking while they engage in information behavior and how those thoughts influence their behavior. Wilson's attempt to understand information-seeking behavior by defining information need includes a cognitive approach. Wilson theorizes that information behavior is influenced by the cognitive need of an individual. By understanding the cognitive information need of an individual, we may gain insight into their information behavior. Nigel Ford takes a cognitive approach to information-seeking, focusing on the intellectual processes of information-seeking. In 2004, Ford proposed an information-seeking model using a cognitive approach that focuses on how to improve information retrieval systems and serves to establish information-seeking and information behavior as concepts in and of themselves, rather than synonymous terms. === Constructionist approach === The constructionist approach to information behavior has roots in the humanities and social sciences. It relies on social constructionism, which assumes that a person's information behavior is influenced by their experiences in society. In order to understand information behavior, constructionist researchers must first understand the social discourse that surrounds the behavior. The most popular thinker referenced in constructionist information behavior research is Michel Foucault, who famously rejected the concept of a universal human nature. The constructionist approach to information behavior research creates space for contextualizing the behavior based on the social experiences of the individual. One study that approaches information behavior research through the social constructionist approach is a study of the information behavior of a public library knitting group. The authors use a collectivist theory to frame their research, which denies the universality of information behavior and focuses on "understanding the ways that discourse communities collectively construct information needs, seeking, sources, and uses". === Constructivist approach === The constructivist approach is born out of education and sociology in which, "individuals are seen as actively constructing an understanding of their worlds, heavily influenced by the social world(s) in which they are operating". Constructivist approaches to information behavior research generally treat the individual's reality as constructed within their own mind rather than built by the society in which they live. The constructivist metatheory makes space for the influence of society and culture with social constructivism, "which argues that, while the mind constructs reality in its relationship to the world, this mental process is significantly informed by influences received from societal conventions, history and interaction with significant others". == Theories == A common concern among LIS researchers, and a prominent discussion in the field, is the broad spectrum of theories that inform LIS research. This variation has been noted as a cause of concern because it makes individual studies difficult to compare if they are not guided by the same theory. Recent studies have shown that the impact of these theories and theoretical models is very limited. LIS researchers have applied concepts and theories from many disciplines, including sociology, psychology, communication, organizational behavior, and computer science. === Wilson's theory of information behavior (1981) === The term was coined by Thomas D. Wilson in his 1981 paper, on the grounds that the current term, 'information needs' was unhelpful since 'need' could not be directly observed, while how people behaved in seeking information could be observed and investigated. However, there is increasing work in the information-searching field that is relating behaviors to underlying needs. In 2000, Wilson described information behavior as the totality of human behavior in relation to sources and channels of information, including both active and passive information-seeking, and information use. He described info
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List of algorithms

An algorithm is a fundamental set of rules or defined procedures that are typically designed and used to be a simpler way to solve a specific problem or a broad set of problems. Simply speaking, algorithms define different processes, sets of rules and regulations, or methodologies that are to be followed through in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations. With the increasing automation of services, more and more decisions are being made by algorithms. Some general examples are risk assessments, anticipatory policing, and pattern recognition technology. The following is a list of well-known algorithms. == Automated planning == == Combinatorial algorithms == === General combinatorial algorithms === Brent's algorithm: finds a cycle in function value iterations using only two iterators Floyd's cycle-finding algorithm: finds a cycle in function value iterations Gale–Shapley algorithm: solves the stable matching problem Pseudorandom number generators (uniformly distributed—see also List of pseudorandom number generators for other PRNGs with varying degrees of convergence and varying statistical quality): ACORN generator Blum Blum Shub Lagged Fibonacci generator Linear congruential generator Mersenne Twister === Graph algorithms === Blossom algorithm: algorithm for constructing maximum-cardinality matching on graphs. Coloring algorithm: algorithms for graph (vertex or edge) coloring (subject to constraints, e.g. proper coloring or list coloring) Hopcroft–Karp algorithm: convert a bipartite graph to a maximum-cardinality matching Hungarian algorithm: algorithm for finding a perfect matching Prüfer coding: conversion between a labeled tree and its Prüfer sequence Tarjan's off-line lowest common ancestors algorithm: computes lowest common ancestors for pairs of nodes in a tree Topological sort: finds linear order of nodes (e.g. jobs) based on their dependencies. ==== Graph drawing ==== Coin graph drawing algorithms for finite connected planar graphs (approximately computing the theoretical circle-packing given by the Koebe-Andreev-Thurston theorem). See also Fáry's theorem on straight-line drawings of planar graphs. Force-based algorithms (also known as force-directed algorithms or spring-based algorithms) Spectral layout ==== Network theory ==== Network analysis Link analysis Girvan–Newman algorithm: detect communities in complex systems Web link analysis Hyperlink-Induced Topic Search (HITS) (also known as Hubs and authorities) PageRank TrustRank Flow networks Dinic's algorithm: is a strongly polynomial algorithm for computing the maximum flow in a flow network. Edmonds–Karp algorithm: implementation of Ford–Fulkerson Ford–Fulkerson algorithm: computes the maximum flow in a graph Karger's algorithm: a Monte Carlo method to compute the minimum cut of a connected graph Push–relabel algorithm: computes a maximum flow in a graph ==== Routing for graphs ==== Edmonds' algorithm (also known as Chu–Liu/Edmonds' algorithm): find maximum or minimum branchings Euclidean minimum spanning tree: algorithms for computing the minimum spanning tree of a set of points in the plane Longest path problem: find a simple path of maximum length in a given graph Minimum spanning tree Borůvka's algorithm Kruskal's algorithm Prim's algorithm Reverse-delete algorithm Nonblocking minimal spanning switch say, for a telephone exchange Shortest path problem Bellman–Ford algorithm: computes shortest paths in a weighted graph (where some of the edge weights may be negative) Dijkstra's algorithm: computes shortest paths in a graph with non-negative edge weights Floyd–Warshall algorithm: solves the all pairs shortest path problem in a weighted, directed graph Johnson's algorithm: all pairs shortest path algorithm in sparse weighted directed graph Transitive closure problem: find the transitive closure of a given binary relation Traveling salesman problem Christofides algorithm Nearest neighbour algorithm Vehicle routing problem Clarke and Wright Saving algorithm Warnsdorff's rule: a heuristic method for solving the Knight's tour problem ==== Graph search ==== A: special case of best-first search that uses heuristics to improve speed B: a best-first graph search algorithm that finds the least-cost path from a given initial node to any goal node (out of one or more possible goals) Backtracking: abandons partial solutions when they are found not to satisfy a complete solution Beam search: is a heuristic search algorithm that is an optimization of best-first search that reduces its memory requirement Beam stack search: integrates backtracking with beam search Best-first search: traverses a graph in the order of likely importance using a priority queue Bidirectional search: find the shortest path from an initial vertex to a goal vertex in a directed graph Breadth-first search: traverses a graph level by level Brute-force search: an exhaustive and reliable search method, but computationally inefficient in many applications D: an incremental heuristic search algorithm Depth-first search: traverses a graph branch by branch Dijkstra's algorithm: a special case of A for which no heuristic function is used General Problem Solver: a seminal theorem-proving algorithm intended to work as a universal problem solver machine. Iterative deepening depth-first search (IDDFS): a state space search strategy Jump point search: an optimization to A which may reduce computation time by an order of magnitude using further heuristics Lexicographic breadth-first search (also known as Lex-BFS): a linear time algorithm for ordering the vertices of a graph SSS: state space search traversing a game tree in a best-first fashion similar to that of the A search algorithm Uniform-cost search: a tree search that finds the lowest-cost route where costs vary ==== Subgraphs ==== Cliques Bron–Kerbosch algorithm: a technique for finding maximal cliques in an undirected graph MaxCliqueDyn maximum clique algorithm: find a maximum clique in an undirected graph Strongly connected components Kosaraju's algorithm Path-based strong component algorithm Tarjan's strongly connected components algorithm Subgraph isomorphism problem === Sequence algorithms === ==== Approximate sequence matching ==== Bitap algorithm: fuzzy algorithm that determines if strings are approximately equal. Phonetic algorithms Daitch–Mokotoff Soundex: a Soundex refinement which allows matching of Slavic and Germanic surnames Double Metaphone: an improvement on Metaphone Match rating approach: a phonetic algorithm developed by Western Airlines Metaphone: an algorithm for indexing words by their sound, when pronounced in English NYSIIS: phonetic algorithm, improves on Soundex Soundex: a phonetic algorithm for indexing names by sound, as pronounced in English String metrics: computes a similarity or dissimilarity (distance) score between two pairs of text strings Damerau–Levenshtein distance: computes a distance measure between two strings, improves on Levenshtein distance Dice's coefficient (also known as the Dice coefficient): a similarity measure related to the Jaccard index Hamming distance: sum number of positions which are different Jaro–Winkler distance: is a measure of similarity between two strings Levenshtein edit distance: computes a metric for the amount of difference between two sequences Trigram search: search for text when the exact syntax or spelling of the target object is not precisely known ==== Selection algorithms ==== Introselect Quickselect ==== Sequence search ==== Linear search: locates an item in an unsorted sequence Selection algorithm: finds the kth largest item in a sequence Sorted lists Binary search algorithm: locates an item in a sorted sequence Eytzinger binary search: cache friendly binary search algorithm Fibonacci search technique: search a sorted sequence using a divide and conquer algorithm that narrows down possible locations with the aid of Fibonacci numbers Jump search (or block search): linear search on a smaller subset of the sequence Predictive search: binary-like search which factors in magnitude of search term versus the high and low values in the search. Sometimes called dictionary search or interpolated search. Uniform binary search: an optimization of the classic binary search algorithm Ternary search: a technique for finding the minimum or maximum of a function that is either strictly increasing and then strictly decreasing or vice versa ==== Sequence merging ==== k-way merge algorithm Simple merge algorithm Union (merge, with elements on the output not repeated) ==== Sequence permutations ==== Fisher–Yates shuffle (also known as the Knuth shuffle): randomly shuffle a finite set Heap's permutation generation algorithm: interchange elements to generate next permutation Schensted algorithm: constructs a pair of Young tableaux from a permutation Steinhaus–Johnson–Trotter algorithm (also known as the Johnson–Trotter algorithm):
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Explore-then-commit algorithm

Explore Then Commit (ETC) is an algorithm for the multi-armed bandit problem foc,used on finding the best trade-off between exploration and exploitation. == Multi-armed bandit problem == The multi-armed bandit problem is a sequential game where one player has to choose at each turn between K {\displaystyle K} actions (arms). Behind every arm a {\displaystyle a} is an unknown distribution ν a {\displaystyle \nu _{a}} that lies in a set D {\displaystyle {\mathcal {D}}} known by the player (for example, D {\displaystyle {\mathcal {D}}} can be the set of Gaussian distributions or Bernoulli distributions). At each turn t {\displaystyle t} the player chooses (pulls) an arm a t {\displaystyle a_{t}} , they then get an observation X t {\displaystyle X_{t}} of the distribution ν a t {\displaystyle \nu _{a_{t}}} . === Regret minimization === The goal is to minimize the regret at time T {\displaystyle T} that is defined as R T := ∑ a = 1 K Δ a E [ N a ( T ) ] {\displaystyle R_{T}:=\sum _{a=1}^{K}\Delta _{a}\mathbb {E} [N_{a}(T)]} where μ a := E [ ν a ] {\displaystyle \mu _{a}:=\mathbb {E} [\nu _{a}]} is the mean of arm a {\displaystyle a} μ ∗ := max a μ a {\displaystyle \mu ^{}:=\max _{a}\mu _{a}} is the highest mean Δ a := μ ∗ − μ a {\displaystyle \Delta _{a}:=\mu ^{}-\mu _{a}} N a ( t ) {\displaystyle N_{a}(t)} is the number of pulls of arm a {\displaystyle a} up to turn t {\displaystyle t} The player has to find an algorithm that chooses at each turn t {\displaystyle t} which arm to pull based on the previous actions and observations ( a s , X s ) s < t {\displaystyle (a_{s},X_{s})_{s Read more →
Transfer learning

Transfer learning (TL) is a technique in machine learning (ML) in which knowledge learned from a task is re-used in order to boost performance on a related task. For example, for image classification, knowledge gained while learning to recognize cars could be applied when trying to recognize trucks. This topic is related to the psychological literature on transfer of learning, although practical ties between the two fields are limited. Reusing or transferring information from previously learned tasks to new tasks has the potential to significantly improve learning efficiency. Since transfer learning makes use of training with multiple objective functions it is related to cost-sensitive machine learning and multi-objective optimization. == History == In 1976, Bozinovski and Fulgosi published a paper addressing transfer learning in neural network training. The paper gives a mathematical and geometrical model of the topic. In 1981, a report considered the application of transfer learning to a dataset of images representing letters of computer terminals, experimentally demonstrating positive and negative transfer learning. In 1992, Lorien Pratt formulated the discriminability-based transfer (DBT) algorithm. By 1998, the field had advanced to include multi-task learning, along with more formal theoretical foundations. Influential publications on transfer learning include the book Learning to Learn in 1998, a 2009 survey and a 2019 survey. Ng said in his NIPS 2016 tutorial that TL would become the next driver of machine learning commercial success after supervised learning. In the 2020 paper, "Rethinking Pre-Training and self-training", Zoph et al. reported that pre-training can hurt accuracy, and advocate self-training instead. == Definition == The definition of transfer learning is given in terms of domains and tasks. A domain D {\displaystyle {\mathcal {D}}} consists of: a feature space X {\displaystyle {\mathcal {X}}} and a marginal probability distribution P ( X ) {\displaystyle P(X)} , where X = { x 1 , . . . , x n } ∈ X {\displaystyle X=\{x_{1},...,x_{n}\}\in {\mathcal {X}}} . Given a specific domain, D = { X , P ( X ) } {\displaystyle {\mathcal {D}}=\{{\mathcal {X}},P(X)\}} , a task consists of two components: a label space Y {\displaystyle {\mathcal {Y}}} and an objective predictive function f : X → Y {\displaystyle f:{\mathcal {X}}\rightarrow {\mathcal {Y}}} . The function f {\displaystyle f} is used to predict the corresponding label f ( x ) {\displaystyle f(x)} of a new instance x {\displaystyle x} . This task, denoted by T = { Y , f ( x ) } {\displaystyle {\mathcal {T}}=\{{\mathcal {Y}},f(x)\}} , is learned from the training data consisting of pairs { x i , y i } {\displaystyle \{x_{i},y_{i}\}} , where x i ∈ X {\displaystyle x_{i}\in {\mathcal {X}}} and y i ∈ Y {\displaystyle y_{i}\in {\mathcal {Y}}} . Given a source domain D S {\displaystyle {\mathcal {D}}_{S}} and learning task T S {\displaystyle {\mathcal {T}}_{S}} , a target domain D T {\displaystyle {\mathcal {D}}_{T}} and learning task T T {\displaystyle {\mathcal {T}}_{T}} , where D S ≠ D T {\displaystyle {\mathcal {D}}_{S}\neq {\mathcal {D}}_{T}} , or T S ≠ T T {\displaystyle {\mathcal {T}}_{S}\neq {\mathcal {T}}_{T}} , transfer learning aims to help improve the learning of the target predictive function f T ( ⋅ ) {\displaystyle f_{T}(\cdot )} in D T {\displaystyle {\mathcal {D}}_{T}} using the knowledge in D S {\displaystyle {\mathcal {D}}_{S}} and T S {\displaystyle {\mathcal {T}}_{S}} . == Applications == Algorithms for transfer learning are available in Markov logic networks and Bayesian networks. Transfer learning has been applied to cancer subtype discovery, building utilization, general game playing, text classification, digit recognition, medical imaging and spam filtering. In 2020, it was discovered that, due to their similar physical natures, transfer learning is possible between electromyographic (EMG) signals from the muscles and classifying the behaviors of electroencephalographic (EEG) brainwaves, from the gesture recognition domain to the mental state recognition domain. It was noted that this relationship worked in both directions, showing that electroencephalographic can likewise be used to classify EMG. The experiments noted that the accuracy of neural networks and convolutional neural networks were improved through transfer learning both prior to any learning (compared to standard random weight distribution) and at the end of the learning process (asymptote). That is, results are improved by exposure to another domain. Moreover, the end-user of a pre-trained model can change the structure of fully-connected layers to improve performance.
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AlphaTensor

AlphaTensor is an artificial intelligence system developed by DeepMind for discovering efficient matrix multiplication algorithms using reinforcement learning. Introduced in 2022, the system was based on AlphaZero and formulated the search for matrix multiplication algorithms as a single-player game called TensorGame. AlphaTensor was designed to search for new ways to multiply matrices with fewer scalar multiplication operations. Matrix multiplication is a fundamental operation in linear algebra, numerical analysis, scientific computing, computer graphics, and machine learning. The system discovered thousands of matrix multiplication algorithms, including algorithms that rediscovered known human-designed methods and others that improved on previously known results for particular matrix sizes and mathematical settings. == Background == Matrix multiplication is one of the basic operations in numerical computing. The standard algorithm for multiplying two square matrices has cubic time complexity, while faster algorithms such as the Strassen algorithm reduce the number of multiplication operations by using more complex algebraic decompositions. Finding optimal matrix multiplication algorithms can be difficult because it involves searching through a large space of possible tensor decompositions. AlphaTensor approached this problem by representing algorithm discovery as TensorGame, in which each move corresponds to an operation that reduces a tensor representing matrix multiplication. The goal of the game is to find a low-rank decomposition of the matrix multiplication tensor, corresponding to an efficient multiplication algorithm. == Development == AlphaTensor was developed by DeepMind and described in a paper published in Nature in October 2022. The system built on the reinforcement-learning approach used in AlphaZero, which had previously been applied to games such as Go, chess, and shogi. Unlike those games, TensorGame involved a very large search space, requiring changes to the AlphaZero-style search method and neural network architecture. DeepMind released source code and discovered algorithms associated with the publication through a public GitHub repository. == Results == AlphaTensor discovered matrix multiplication algorithms over both standard arithmetic and finite fields. One widely reported result was a method for multiplying 4 × 4 matrices over the field with two elements using 47 multiplication operations, improving on the 49 operations required by applying Strassen's algorithm recursively in that setting. The system also found algorithms optimized for particular computer hardware, including algorithms designed for graphics processing units and Tensor Processing Units. DeepMind stated that some of the hardware-specific algorithms improved practical execution time compared with commonly used algorithms on the tested hardware. == Significance == AlphaTensor was described as an example of using machine learning not only to apply existing algorithms, but to assist in discovering new ones. The work was connected to broader research in algorithm discovery, automated machine learning, program synthesis, and computational complexity theory, especially the open problem of determining the optimal complexity of matrix multiplication. AlphaTensor later became part of a broader group of Google DeepMind systems for algorithm and mathematical discovery, alongside systems such as AlphaDev and AlphaEvolve.
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Algorism

Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist. This positional notation system has largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude, such as Roman numerals, and in some cases required a device such as an abacus. == Etymology == The word algorism comes from the name Al-Khwārizmī (c. 780–850), a Persian mathematician, astronomer, geographer and scholar in the House of Wisdom in Baghdad, whose name means "the native of Khwarezm", which is now in modern-day Uzbekistan. He wrote a treatise in Arabic language in the 9th century, which was translated into Latin in the 12th century under the title Algoritmi de numero Indorum. This title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name. Al-Khwarizmi was the most widely read mathematician in Europe in the late Middle Ages, primarily through his other book, the Algebra. In late medieval Latin, algorismus, the corruption of his name, simply meant the "decimal number system" that is still the meaning of modern English algorism. During the 17th century, the French form for the word – but not its meaning – was changed to algorithm, following the model of the word logarithm, this form alluding to the ancient Greek arithmos = number. English adopted the French very soon afterwards, but it wasn't until the late 19th century that "algorithm" took on the meaning that it has in modern English. In English, it was first used about 1230 and then by Chaucer in 1391. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu. It begins thus: Haec algorismus ars praesens dicitur, in qua / Talibus Indorum fruimur bis quinque figuris. which translates as: This present art, in which we use those twice five Indian figures, is called algorismus. The word algorithm also derives from algorism, a generalization of the meaning to any set of rules specifying a computational procedure. Occasionally algorism is also used in this generalized meaning, especially in older texts. == History == Starting with the integer arithmetic developed in India using base 10 notation, Al-Khwārizmī along with other mathematicians in medieval Islam, documented new arithmetic methods and made many other contributions to decimal arithmetic (see the articles linked below). These included the concept of the decimal fractions as an extension of the notation, which in turn led to the notion of the decimal point. This system was popularized in Europe by Leonardo of Pisa, now known as Fibonacci.
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Magic state distillation

Magic state distillation is a method for creating more accurate quantum states from multiple noisy ones, which is important for building fault tolerant quantum computers. It has also been linked to quantum contextuality, a concept thought to contribute to quantum computers' power. The technique was first proposed by Emanuel Knill in 2004, and further analyzed by Sergey Bravyi and Alexei Kitaev the same year. Thanks to the Gottesman–Knill theorem, it is known that some quantum operations (operations in the Clifford group) can be perfectly simulated in polynomial time on a classical computer. In order to achieve universal quantum computation, a quantum computer must be able to perform operations outside this set. Magic state distillation achieves this, in principle, by concentrating the usefulness of imperfect resources, represented by mixed states, into states that are conducive for performing operations that are difficult to simulate classically. A variety of qubit magic state distillation routines and distillation routines for qubits with various advantages have been proposed. == Stabilizer formalism == The Clifford group consists of a set of n {\displaystyle n} -qubit operations generated by the gates {H, S, CNOT} (where H is Hadamard and S is [ 1 0 0 i ] {\displaystyle {\begin{bmatrix}1&0\\0&i\end{bmatrix}}} ) called Clifford gates. The Clifford group generates stabilizer states which can be efficiently simulated classically, as shown by the Gottesman–Knill theorem. This set of gates with a non-Clifford operation is universal for quantum computation. == Magic states == Magic states are purified from n {\displaystyle n} copies of a mixed state ρ {\displaystyle \rho } . These states are typically provided via an ancilla to the circuit. A magic state for the π / 6 {\displaystyle \pi /6} rotation operator is | M ⟩ = cos ⁡ ( β / 2 ) | 0 ⟩ + e i π 4 sin ⁡ ( β / 2 ) | 1 ⟩ {\displaystyle |M\rangle =\cos(\beta /2)|0\rangle +e^{i{\frac {\pi }{4}}}\sin(\beta /2)|1\rangle } where β = arccos ⁡ ( 1 3 ) {\displaystyle \beta =\arccos \left({\frac {1}{\sqrt {3}}}\right)} . A non-Clifford gate can be generated by combining (copies of) magic states with Clifford gates. Since a set of Clifford gates combined with a non-Clifford gate is universal for quantum computation, magic states combined with Clifford gates are also universal. == Purification algorithm for distilling |M〉 == The first magic state distillation algorithm, invented by Sergey Bravyi and Alexei Kitaev, is as follows. Input: Prepare 5 imperfect states. Output: An almost pure state having a small error probability. repeat Apply the decoding operation of the five-qubit error correcting code and measure the syndrome. If the measured syndrome is | 0000 ⟩ {\displaystyle |0000\rangle } , the distillation attempt is successful. else Get rid of the resulting state and restart the algorithm. until The states have been distilled to the desired purity.
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LiveChat

LiveChat is an AI customer service software with chatbot, online chat, help desk software, and web analytics capabilities. LiveChat is used by over 76,000 companies. It was first launched in 2002 and is offered via a SaaS (software as a service) business model by Text. Organizations use LiveChat as a single point of contact to manage customer service and online sales activities with a single program. == Product == LiveChat is proprietary software. LiveChat's website chat widget can be embedded on customers' websites as a small chat box, often displayed in the bottom right corner of the web browser. It can be used to conduct chats, share files and save transcripts. The agent application is used by company employees to respond to questions asked by the customers. This is available through both web-based application, desktop applications, and mobile apps. Web chat sessions can be initiated by the visiting customer, or by the agent, either manually or automatically by the LiveChat system when the visitor meets the predefined criteria (i.e. searched keyword, time on website, encountered error, etc.). LiveChat's system attempts to identify the best prospects visiting a website based on data gathered from past purchasing decisions. Other features include real-time website traffic monitoring, built-in ticketing system and agents' efficiency analytics. LiveChat is available in 48 languages. == Research and reception == Reviewing LiveChat's usefulness for online learning in 2020, psychologist Jaclyn Broadbent said "LiveChat occurs as a real-time conversation, it can be time-consuming for staff and disruptive to other tasks." However, using it has resulted in reduced communication traffic from other channels, such as the discussion boards or email. As a teacher, the best time to be available on LiveChat is when you are doing other administrative jobs." Since 2014 LiveChat has been publishing Customer Service Report - an annual study of customer satisfaction and analysis of online business communication trends. It includes research of thousands of companies and millions of customer service email and live support interactions.
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Information scientist

The term information scientist developed in the latter part of the twentieth century by Wm. Hovey Smith to describe an individual, usually with a relevant subject degree (such as one in Information and Computer Science - CIS) or high level of subject knowledge, providing focused information to scientific and technical research staff in industry. It is a role quite distinct from and complementary to that of a librarian. Developments in end-user searching, together with some convergence between the roles of librarian and information scientist, have led to a diminution in its use in this context, and the term information officer or information professional (information specialist) are also now used. The term was, and is, also used for an individual carrying out research in information science. Brian C. Vickery mentions that the Institute of Information Scientists (IIS) was established in London during 1958 and lists the criteria put forward by this institute "Criteria for Information Science" (appendix 1) as well as his own "Areas of study in information science" (appendix 2). The IIS merged with the Library Association in 2002 to form the Chartered Institute of Library and Information Professionals (CILIP). == Notable Information Scientists == See also Award of Merit - Association for Information Science and Technology Marcia Bates David Blair (information technologist) Samuel C. Bradford Michael Buckland John M. Carroll Blaise Cronin Emilia Currás Brenda Dervin Eugene Garfield Paul B. Kantor Frederick Wilfrid Lancaster Calvin Mooers Tefko Saracevic Linda C. Smith Robert Saxton Taylor Brian Campbell Vickery Thomas D. Wilson == Additional reading == Ellis, David and Merete Haugan. (1997) "Modelling the information seeking patterns of engineers and research scientists in an industrial environment" (Journal of Documentation, Volume 53(4): pp. 384–403) Poole, Alex H. (2024). "'There's a big difference between going through life with the wind at your back, and going through life leaning into the wind': Feminism in Post-World War II Information Science". Proceedings of the Association for Information Science and Technology. 61: 300–313. doi:10.1002/pra2.1029. Vickery, Brian Campbell (1988) "Essays presented to B. C. Vickery" (Journal of Documentation, Volume 44, pp. 199–283). Vickery, B. & Vickery, A. (1987) Information Science in theory and practice (London: Bowker-Saur, pp. 361–369)
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Agentic commerce

Agentic commerce (also referred to as agent-based commerce) describes an emerging form of e-commerce in which autonomous artificial intelligence (AI) agents independently execute purchasing and payment processes on behalf of users or organizations. Unlike conventional digital commerce systems, which require direct human interaction at key decision points, agentic commerce systems are designed to search for products or services, evaluate options, make purchasing decisions, and complete payments without real-time human involvement. An emerging development within the broader fields of e-commerce, fintech, and artificial intelligence; agentic commerce combines advances in generative AI, autonomous agents, application programming interfaces (APIs), and digital payment infrastructures to direct transactions with no direct human interaction. == Characteristics == A defining feature of agentic commerce is the delegation of end-to-end commercial activities to software agents. These agents typically operate according to predefined user preferences, rules, or constraints, such as price limits, quality criteria, delivery times, or preferred payment methods. Based on these parameters, an agent can autonomously perform tasks including product discovery, price comparison, contract selection, order placement, and payment execution. In contrast to decision-support systems, which provide recommendations to human users, agentic commerce systems are designed to act independently. Human involvement may be limited to initial configuration, periodic supervision, or exception handling. == Comparison with traditional and AI-assisted commerce == Traditional e-commerce requires users to manually browse products, select offers, and authorize payments. Generative AI systems used in commerce commonly assist users by answering questions or suggesting options, and do not complete transactions autonomously. Agentic commerce differs in that decision-making authority is partially or fully transferred to AI agents. As a result, the conventional customer journey, characterized by conscious decision points, may be replaced by continuous, automated micro-decisions performed by software. == Applications and business use cases == Potential applications of agentic commerce include recurring purchases, subscription management, business-to-business procurement, inventory replenishment, and price monitoring. In such contexts, transactions are often predictable and standardized, making them suitable for automation. From a business perspective, agentic commerce systems may be used to optimize supply chains, manage inventory levels, negotiate prices algorithmically, or execute transactions across multiple platforms. Enterprises adopting the new technology include retailers Walmart, Home Depot, Wayfair and Urban Outfitters, and ad tech DSPs, including Google Ads, Amazon, and Yahoo. Chinese tech firms are using apps to provide full-service shopping and payment tools. These includes Alibaba, Tencent, and ByteDance who are currently developing AI powered shopping apps. The Qwen AI chatbot allows users to complete transactions directly within its interface. US firms are still leading in developing AI models but integration is slower due to privacy restrictions. == Payments and technical infrastructure == Agentic commerce relies on digital payment systems capable of supporting automated, machine-initiated transactions, including API-based payment processing, tokenization, real-time authorization, and continuous risk monitoring. Typical user interfaces, such as shopping carts, may be replaced by backend integrations between AI agents, merchants, and payment service providers. For example, Iike 2025, Alibaba launched Alipay AI Pay, which grew and began operating as an application for different retailers. In December 2025, Alipay teamed up with Rokid to enable developers to integrate AI payments into AI agents on Rokid's Lingzhu platform. In January 2025, Alipay unveiled the Agentic Commerce Trust Protocol in partnership with Alibaba's consumer AI applications, such as the Qwen App and Taobao Instant Commerce. Qwen adopted the platform first, connecting it to Taobao Instant Commerce and Alipay AI Pay. Users could use Qwen's agentic feature to place food and drink orders within the application instead of having to click outside to an external browser. For merchants, participation in agentic commerce may require products and services to be presented in structured, machine-readable formats to ensure discoverability and interoperability with autonomous agents. == Universal Commerce Protocol (UCP) == In January 2026, Google announced the Universal Commerce Protocol (UCP), an open-source web standard intended to enable interoperability between AI agents and retail systems across the shopping journey, from discovery and checkout to post-purchase support. UCP makes use of REST, JSON-RPC transports, and support for Agent Payments Protocol (AP2), Agent2Agent (A2A), and Model Context Protocol (MCP). == Legal, regulatory, and security considerations == The use of autonomous agents in commerce raises legal and regulatory questions, particularly regarding authorization, liability, consumer protection, and fraud prevention. Existing payment and contract frameworks are generally based on human decision-makers, and their applicability to autonomous agents remains an area of active discussion. Open issues include responsibility for unauthorized or erroneous transactions, mechanisms for dispute resolution, standards for agent authentication, and compliance with data protection and financial regulations. Continuous, automated transaction patterns may also require new approaches to security and risk assessment. Traditional fraud models centered on identity verification may be insufficient for agentic commerce, and that merchants may need intent-based detection methods using machine learning and behavioral analysis to distinguish legitimate AI agents from malicious automation. === Governance frameworks === The deployment of autonomous AI agents in commercial environments has prompted the development of dedicated governance frameworks. These aim to define operational boundaries, decision authority, oversight mechanisms, and accountability structures for agentic systems. The Agentic Commerce Framework (ACF), created in 2025 by Vincent Dorange, is a governance standard that structures the deployment of autonomous AI agents around four founding principles (Decision Sovereignty, Governance by Design, Ultimate Human Control, Traceable Accountability), four operational layers, and 18 governance KPIs. In January 2026, Singapore's Infocomm Media Development Authority (IMDA) published the Model AI Governance Framework for Agentic AI, extending its existing AI governance guidelines to address agent-specific risks including delegation chains and multi-agent coordination. The Cloud Security Alliance (CSA) has also proposed an Agentic Trust Framework applying zero-trust principles to AI agent governance. == Ecosystem and implementation == The adoption of agentic commerce typically requires changes in commerce architecture, data modeling, identity and permissions, and API-based orchestration of checkout and post-purchase workflows. Management consultancies have identified agentic commerce as a structural evolution of digital commerce, emphasizing the role of AI-driven agents in automating discovery, decision-making, and transaction processes across commerce systems. McKinsey & Company has described agentic commerce as a significant shift in how consumers interact with brands and how enterprises design their commerce operating models. In Europe, this ecosystem also includes digital commerce consultancies specializing in the adoption of agentic commerce. Consulting firms such as Horrea support brands in understanding and implementing the technological and organizational shifts associated with agentic commerce. == Market development and outlook == Agentic commerce is generally regarded as an early-stage development. Industry analysts have projected that AI-driven agents could account for a small but growing share of digital payment transactions within the coming years. Due to the scale of global digital commerce, even limited adoption could represent substantial transaction volumes. Analysts expect that by 2029, AI agents could handle between 1% and 4% of all digital payment transactions. With a projected total transaction volume of over $36 trillion a year, even a small share translates into a market worth up to $1.47 trillion. According to a McKinsey study from October 2025, agentic commerce projects that by 2030, the U.S. business-to-consumer retail market alone could see up to $1 trillion in revenue orchestrated through agentic commerce. On a global scale, the opportunity could range from $3 trillion to $5 trillion. Early experiments and pilot projects have demonstrated both the potential and current limitations of the
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Savepoint

A savepoint is a way of implementing subtransactions (also known as nested transactions) within a relational database management system by indicating a point within a transaction that can be "rolled back to" without affecting any work done in the transaction before the savepoint was created. Multiple savepoints can exist within a single transaction. Savepoints are useful for implementing complex error recovery in database applications. If an error occurs in the midst of a multiple-statement transaction, the application may be able to recover from the error (by rolling back to a savepoint) without needing to abort the entire transaction. A savepoint can be declared by issuing a SAVEPOINT name statement. All changes made after a savepoint has been declared can be undone by issuing a ROLLBACK TO SAVEPOINT name command. Issuing RELEASE SAVEPOINT name will cause the named savepoint to be discarded, but will not otherwise affect anything. Issuing the commands ROLLBACK or COMMIT will also discard any savepoints created since the start of the main transaction. Savepoints are defined in the SQL standard and are supported by all established SQL relational databases, including PostgreSQL, Oracle Database, Microsoft SQL Server, MySQL, IBM Db2, SQLite (since 3.6.8), Firebird, H2 Database Engine, and Informix (since version 11.50xC3).
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Region Based Convolutional Neural Networks

Region-based Convolutional Neural Networks (R-CNN) are a family of machine learning models for computer vision, and specifically object detection and localization. The original goal of R-CNN was to take an input image and produce a set of bounding boxes as output, where each bounding box contains an object and also the category (e.g. car or pedestrian) of the object. In general, R-CNN architectures perform selective search over feature maps outputted by a CNN. R-CNN has been extended to perform other computer vision tasks, such as: tracking objects from a drone-mounted camera, locating text in an image, and enabling object detection in Google Lens. Mask R-CNN is also one of seven tasks in the MLPerf Training Benchmark, which is a competition to speed up the training of neural networks. == History == The following covers some of the versions of R-CNN that have been developed. November 2013: R-CNN. April 2015: Fast R-CNN. June 2015: Faster R-CNN. March 2017: Mask R-CNN. December 2017: Cascade R-CNN is trained with increasing Intersection over Union (IoU, also known as the Jaccard index) thresholds, making each stage more selective against nearby false positives. June 2019: Mesh R-CNN adds the ability to generate a 3D mesh from a 2D image. == Architecture == For review articles see. === Selective search === Given an image (or an image-like feature map), selective search (also called Hierarchical Grouping) first segments the image by the algorithm in (Felzenszwalb and Huttenlocher, 2004), then performs the following: Input: (colour) image Output: Set of object location hypotheses L Segment image into initial regions R = {r1, ..., rn} using Felzenszwalb and Huttenlocher (2004) Initialise similarity set S = ∅ foreach Neighbouring region pair (ri, rj) do Calculate similarity s(ri, rj) S = S ∪ s(ri, rj) while S ≠ ∅ do Get highest similarity s(ri, rj) = max(S) Merge corresponding regions rt = ri ∪ rj Remove similarities regarding ri: S = S \ s(ri, r∗) Remove similarities regarding rj: S = S \ s(r∗, rj) Calculate similarity set St between rt and its neighbours S = S ∪ St R = R ∪ rt Extract object location boxes L from all regions in R === R-CNN === With R-CNN, prediction follows a two-step process. A preprocessing selective search step generates a large set of candidate objects (typically as many as 2000), known as regions of interest (ROI). These are forwarded to a CNN, which predicts an object class score and bounding box estimate, independently for each ROI. Importantly, the ROIs are heavily filtered to remove excess candidates. This is achieved using two mechanism. Filtering begins by removing ROIs assigned to the background category. This is a specialized category, which is scored by the CNN alongside other categories. An unfortunate reality is that remaining ROIs typically suffer from heavy duplication. Namely, multiple ROIs that cover same objects in the image are all assigned non-background categories. This is resolved by a heuristic non-maximum suppression (NMS) step. === Fast R-CNN === While the original R-CNN independently computed the neural network features on each of as many as two thousand regions of interest, Fast R-CNN runs the neural network once on the whole image. At the end of the network is a ROIPooling module, which slices out each ROI from the network's output tensor, reshapes it, and classifies it. As in the original R-CNN, the Fast R-CNN uses selective search to generate its region proposals. === Faster R-CNN === While Fast R-CNN used selective search to generate ROIs, Faster R-CNN integrates the ROI generation into the neural network itself. === Mask R-CNN === While previous versions of R-CNN focused on object detections, Mask R-CNN adds instance segmentation. Mask R-CNN also replaced ROIPooling with a new method called ROIAlign, which can represent fractions of a pixel.
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Living lab

The concept of the living lab has been defined in multiple ways. A definition from the European Network of Living Labs (ENoLL) is used most widely, describing them as "user-centred open innovation ecosystems” that integrate research and innovation through co-creation in real-world environments.[1] Emerging at the intersection of ambient intelligence research and user experience methodologies in the late 1990s, the concept was pioneered at the Massachusetts Institute of Technology (MIT) as a way to study human interaction with new technologies in natural settings. Over time, living labs have evolved beyond their origins as controlled research environments, becoming dynamic platforms for participatory design, collaborative experimentation, and iterative innovation across various domains, including urban development, healthcare, sustainability, and digital technology. Characterized by principles such as real-world experimentation, active user involvement, and multi-stakeholder collaboration, living labs enable the continuous adaptation and validation of solutions in everyday contexts. Today, they are implemented globally, supported by networks like the European Network of Living Labs (ENoLL), and increasingly recognized as vital tools for addressing local and global transformation agendas. == Background == The term "living lab" has emerged in parallel from the ambient intelligence (AmI) research communities context and from the discussion on experience and application research (EAR). The emergence of the term is based on the concept of user experience and ambient intelligence. The term dates back to the late 1990s when Professor William J. Mitchell, Kent Larson, and Alex (Sandy) Pentland at the Massachusetts Institute of Technology were credited with first exploring the concept of a living laboratory. It was first associated with MIT's Media Lab as a concept for studying real-life contexts, where they described a living lab as a controlled environment designed to test new information and communication technology (ICT) innovations in a simulated home setting. This was also when some of the key characteristics often assigned to living labs today began to take shape. They argued that a living lab represents a user-centric research methodology for sensing, prototyping, validating and refining complex solutions in multiple and evolving real-life contexts. Research on living labs has expanded since the 1990s, especially in the 2010s, with growing interest in co-creation and participatory design. Particularly in Europe, the living lab evolved into a model that focused on studying user interactions with technology in real-world environments. This shift was influenced by earlier experiences in participatory design and social experiments with ICT. As interest grew, the term began to encompass a broader array of initiatives and projects, leading to variations in its interpretation and implementation. Today, living labs are used in various fields, such as technology, healthcare, and urban sustainability, showing a transition from a narrow focus on their role as controlled environments to a more wide-ranging understanding of collaborative innovation addressing real societal challenges, while also being referred to with various descriptions and definitions available from different sources. == Description == The ENoLL definition that refers to living labs as "user-centred open innovation ecosystems” that integrate research and innovation through co-creation in real-world environments is the most widely accepted description of living labs in academic literature. In simple terms, living labs can be described as an organization or experimental space, that can be both virtually or physically located, bringing different stakeholders from research, business, government, and citizens together to design and test solutions to be implemented in a real world environment. A common definition for the living lab term still does not exist to this day, which is due to the fact that living labs are interpreted and implemented across different contexts and can cover a wide range of activities and organizations, leading to different understandings of how living labs should function. Living labs also often operate in various territorial contexts (e.g. city, agglomeration, region, campus), and can vary in their methodological approach integrating concurrent research and innovation processes within a public-private-people partnership. Despite these variations, common characteristics include user-centricity, real-world experimentation, multi-stakeholder collaboration, and iterative innovation processes. The systematic user co-creation approach refers to integrating research and innovation processes through the co-creation, exploration, experimentation and evaluation of innovative ideas, scenarios, concepts and related technological artefacts in real life use cases. Such use cases involve user communities, not only as observed subjects but also as a source of creation. This approach allows all involved stakeholders to concurrently consider both the global performance of a product or service and its potential adoption by users. This consideration may be made at the earlier stage of research and development and through all elements of the product life-cycle, from design up to recycling. User-centred research methods, such as action research, community informatics, contextual design, user-centered design, participatory design, empathic design, emotional design, and other usability methods, already exist but fail to sufficiently empower users for co-creating into open development environments. More recently, the Web 2.0 has demonstrated the positive impact of involving user communities in new product development (NPD) such as mass collaboration projects (e.g. crowdsourcing, Wisdom of Crowds) in collectively creating new contents and applications. Real-world experimentation emphasizes conducting activities in real-life settings to ensure that the results of the projects and solutions are applicable to actual market conditions. Multi-stakeholder collaboration refers to an approach that involved various stakeholders, such as users, businesses, researchers, and government entities, working together towards a common goal. This is an important characteristics of living lab because collaboration of these diverse groups allows for exchange of ideas and perspectives, which are thought to enhance innovation processes. Iterative innovation processes involve a cyclical method of developing products or services, where stages such as research, development, testing, and implementation are revisited multiple times based on feedback and evaluation. This process allows for continuous improvement of the innovation, product, or service being developed. In particular, the ongoing involvement of the user creates feedback mechanisms that are ultimately key to successful development and implementation of products and services. A living lab is not similar to a testbed as its philosophy is to turn users, from being traditionally considered as observed subjects for testing modules against requirements, into value creation in contributing to the co-creation and exploration of emerging ideas, breakthrough scenarios, innovative concepts and related artefacts. Hence, a living lab rather constitutes an experiential environment, which could be compared to the concept of experiential learning, where users are immersed in a creative social space for designing and experiencing their own future. Living labs could also be used by policy makers and users/citizens for designing, exploring, experiencing and refining new policies and regulations in real-life scenarios for evaluating their potential impacts before their implementations. == European Network of Living Labs (ENoLL) == The European Network of Living Labs (ENoLL) is an international, non-profit, independent association of certified living labs, which popularized the living lab concept in the aim to increase user involvement in innovation. Formed in November 2006 under the guidance of the Finnish European Presidency, ENoLL is composed of a variety of stakeholders, including municipalities and research institutes, businesses, and users. Its primary role is to support the collaboration among living labs across Europe and includes many living labs focused on user-driven innovation across sectors. ENoLL focuses on facilitating knowledge exchange, joint actions and project partnerships among its historically labelled +/- 500 members, influencing EU policies, promoting living labs and enabling their implementation worldwide. ENoLL serves as a platform for linking living labs around the globe, which enables knowledge sharing and collaborative learning among diverse cultural environments. Membership to the platform is open to organizations worldwide, and ENoLL has expanded beyond Europe to include global members. ENoLL follows an application and accreditation pro
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Irish logarithm

The Irish logarithm was a system of number manipulation invented by Percy Ludgate for machine multiplication. The system used a combination of mechanical cams as lookup tables and mechanical addition to sum pseudo-logarithmic indices to produce partial products, which were then added to produce results. The technique is similar to Zech logarithms (also known as Jacobi logarithms), but uses a system of indices original to Ludgate. == Concept == Ludgate's algorithm compresses the multiplication of two single decimal numbers into two table lookups (to convert the digits into indices), the addition of the two indices to create a new index which is input to a second lookup table that generates the output product. Because both lookup tables are one-dimensional, and the addition of linear movements is simple to implement mechanically, this allows a less complex mechanism than would be needed to implement a two-dimensional 10×10 multiplication lookup table. Ludgate stated that he deliberately chose the values in his tables to be as small as he could make them; given this, Ludgate's tables can be simply constructed from first principles, either via pen-and-paper methods, or a systematic search using only a few tens of lines of program code. They do not correspond to either Zech logarithms, Remak indexes or Korn indexes. == Pseudocode == The following is an implementation of Ludgate's Irish logarithm algorithm in the Python programming language: Table 1 is taken from Ludgate's original paper; given the first table, the contents of Table 2 can be trivially derived from Table 1 and the definition of the algorithm. Note since that the last third of the second table is entirely zeros, this could be exploited to further simplify a mechanical implementation of the algorithm.
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