AI For Business Guide

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

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  Frankenstein complex

  The Frankenstein complex is a term coined by Isaac Asimov in his robot series, referring to the fear of mechanical men. == History == Some of Asimov's science fiction short stories and novels predict that this suspicion will become strongest and most widespread in respect of "mechanical men" that most-closely resemble human beings (see android), but it is also present on a lower level against robots that are plainly electromechanical automatons. The "Frankenstein complex" is similar in many respects to Masahiro Mori's uncanny valley hypothesis. The name, "Frankenstein complex", is derived from the name of Victor Frankenstein in the 1818 novel Frankenstein; or, The Modern Prometheus by Mary Shelley. In Shelley's story, Frankenstein created an intelligent, somewhat superhuman being, but he finds that his creation is horrifying to behold and abandons it. This ultimately leads to Victor's death at the conclusion of a vendetta between himself and his creation. In much of his fiction, Asimov depicts the general attitude of the public towards robots as negative, with ordinary people fearing that robots will either replace them or dominate them, although dominance would not be allowed under the specifications of the Three Laws of Robotics, the first of which is: "A robot may not harm a human being or, through inaction, allow a human being to come to harm." However, Asimov's fictitious earthly public is not fully persuaded by this, and remains largely suspicious and fearful of robots. I, Robot's short story "Little Lost Robot" is about this "fear of robots". In Asimov's robot novels, the Frankenstein complex is a major problem for roboticists and robot manufacturers. They do all they can to reassure the public that robots are harmless, even though this sometimes involves hiding the truth because they think that the public would misunderstand it. The fear by the public and the response of the manufacturers is an example of the theme of paternalism, the dread of paternalism, and the conflicts that arise from it in Asimov's fiction. The same theme occurs in many later works of fiction featuring robots, although it is rarely referred to as such.

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  Information literacy

  The Association of College and Research Libraries defines information literacy as a "set of integrated abilities encompassing the reflective discovery of information, the understanding of how information is produced and valued and the use of information in creating new knowledge and participating ethically in communities of learning". In the United Kingdom, the Chartered Institute of Library and Information Professionals' definition also makes reference to knowing both "when" and "why" information is needed. The 1989 American Library Association (ALA) Presidential Committee on Information Literacy formally defined information literacy (IL) as attributes of an individual, stating that "to be information literate, a person must be able to recognize when information is needed and have the ability to locate, evaluate and use effectively the needed information". In 1990, academic Lori Arp published a paper asking, "Are information literacy instruction and bibliographic instruction the same?" Arp argued that neither term was particularly well defined by theoreticians or practitioners in the field. Further studies were needed to lessen the confusion and continue to articulate the parameters of the question. The Alexandria Proclamation of 2005 defined the term as a human rights issue: "Information literacy empowers people in all walks of life to seek, evaluate, use and create information effectively to achieve their personal, social, occupational and educational goals. It is a basic human right in a digital world and promotes social inclusion in all nations." The United States National Forum on Information Literacy defined information literacy as "the ability to know when there is a need for information, to be able to identify, locate, evaluate, and effectively use that information for the issue or problem at hand." Meanwhile, in the UK, the library professional body CILIP, define information literacy as "the ability to think critically and make balanced judgements about any information we find and use. It empowers us as citizens to develop informed views and to engage fully with society." A number of other efforts have been made to better define the concept and its relationship to other skills and forms of literacy. Other pedagogical outcomes related to information literacy include traditional literacy, computer literacy, research skills and critical thinking skills. Information literacy as a sub-discipline is an emerging topic of interest and counter measure among educators and librarians with the prevalence of misinformation, fake news, and disinformation. Scholars have argued that in order to maximize people's contributions to a democratic and pluralistic society, educators should be challenging governments and the business sector to support and fund educational initiatives in information literacy. == History == The phrase "information literacy" first appeared in print in a 1974 report written on behalf of the National Commission on Libraries and Information Science by Paul G. Zurkowski, who was at the time president of the Information Industry Association (now the Software and Information Industry Association). Zurkowski used the phrase to describe the "techniques and skills" learned by the information literate "for utilizing the wide range of information tools as well as primary sources in molding information solutions to their problems" and drew a relatively firm line between the "literates" and "information illiterates." The concept of information literacy appeared again in a 1976 paper by Lee Burchina presented at the Texas A&M University library's symposium. Burchina identified a set of skills needed to locate and use information for problem solving and decision making. In another 1976 article in Library Journal, M.R. Owens applied the concept to political information literacy and civic responsibility, stating, "All [people] are created equal but voters with information resources are in a position to make more intelligent decisions than citizens who are information illiterates. The application of information resources to the process of decision-making to fulfill civic responsibilities is a vital necessity." In a literature review published in an academic journal in 2020, Oral Roberts University professor Angela Sample cites several conceptual waves of information literacy definitions as defining information as a way of thinking, a set of skills, and a social practice. The introduction of these concepts led to the adoption of a mechanism called metaliteracy and the creation of threshold concepts and knowledge dispositions, which led to the creation of the ALA's Information Literacy Framework. The American Library Association's Presidential Committee on Information Literacy released a report on January 10, 1989. Titled as the Presidential Committee on Information Literacy: Final Report, the article outlines the importance of information literacy, opportunities to develop it, and the idea of an Information Age School. The recommendations of the Committee led to establishment of the National Forum on Information Literacy, a coalition of more than 90 national and international organizations. In 1998, the American Association of School Librarians and the Association for Educational Communications and Technology published Information Power: Building Partnerships for Learning, which further established specific goals for information literacy education, defining some nine standards in the categories of "information literacy," "independent learning," and "social responsibility." Also in 1998, the Presidential Committee on Information Literacy updated its final report. The report outlined six recommendations from the original report, and examined areas of challenge and progress. In 1999, the Society of College, National and University Libraries (SCONUL) in the UK published The Seven Pillars of Information Literacy to model the relationship between information skills and IT skills, and the idea of the progression of information literacy into the curriculum of higher education. In 2003, the National Forum on Information Literacy, along with UNESCO and the National Commission on Libraries and Information Science, sponsored an international conference in Prague. Representatives from twenty-three countries gathered to discuss the importance of information literacy in a global context. The resulting Prague Declaration described information literacy as a "key to social, cultural, and economic development of nations and communities, institutions and individuals in the 21st century" and declared its acquisition as "part of the basic human right of lifelong learning". In the United States specifically, information literacy was prioritized in 2009 during President Barack Obama's first term. In effort to stress the value information literacy has on everyday communication, he designated October as National Information Literacy Awareness Month in his released proclamation. In 2015, the Association of College and Research Libraries (ACRL) adopted the Framework for Information Literacy for Higher Education, which defines information literacy as "the set of integrated abilities encompassing the reflective discovery of information, the understanding of how information is produced and valued, and the use of information in creating new knowledge and participating ethically in communities of learning".Association of College and Research Libraries (2015-02-09). "Framework for Information Literacy for Higher Education". Association of College and Research Libraries. American Library Association. Retrieved 2026-02-17. == Presidential Committee on Information Literacy == The American Library Association's Presidential Committee on Information Literacy defined information literacy as the ability "to recognize when information is needed and have the ability to locate, evaluate, and use effectively the needed information" and highlighted information literacy as a skill essential for lifelong learning and the production of an informed and prosperous citizenry. The committee outlined six principal recommendations. Included were recommendations like "Reconsider the ways we have organized information institutionally, structured information access, and defined information's role in our lives at home in the community, and in the work place"; to promote "public awareness of the problems created by information illiteracy"; to develop a national research agenda related to information and its use; to ensure the existence of "a climate conducive to students' becoming information literate"; to include information literacy concerns in teacher education democracy. In the updated report, the committee ended with an invitation, asking the National Forum and regular citizens to recognize that "the result of these combined efforts will be a citizenry which is made up of effective lifelong learners who can always find the information needed for the issue or decision at hand. This new

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  BioCreative

  BioCreAtIvE (A critical assessment of text mining methods in molecular biology) consists in a community-wide effort for evaluating information extraction and text mining developments in the biological domain. It was preceded by the Knowledge Discovery and Data Mining (KDD) Challenge Cup for detection of gene mentions. == Community Challenges == === First edition (2004-2005) === Three main tasks were posed at the first BioCreAtIvE challenge: the entity extraction task, the gene name normalization task, and the functional annotation of gene products task. The data sets produced by this contest serve as a Gold Standard training and test set to evaluate and train Bio-NER tools and annotation extraction tools. === Second edition (2006-2007) === The second BioCreAtIvE challenge (2006-2007) had also 3 tasks: detection of gene mentions, extraction of unique idenfiers for genes and extraction information related to physical protein-protein interactions. It counted with participation of 44 teams from 13 countries. === Third edition (2011-2012) === The third edition of BioCreative included for the first time the InterActive Task (IAT), designed to evaluate the practical usability of text mining tools in real-world biocuration tasks. === Fifth edition (2016) === BioCreative V had 5 different tracks, including an interactive task (IAT) for usability of text mining systems and a track using the BioC format for curating information for BioGRID.

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  Knuth–Eve algorithm

  In computer science, the Knuth–Eve algorithm is an algorithm for polynomial evaluation. It preprocesses the coefficients of the polynomial to reduce the number of multiplications required at runtime. Ideas used in the algorithm were originally proposed by Donald Knuth in 1962. His procedure opportunistically exploits structure in the polynomial being evaluated. In 1964, James Eve determined for which polynomials this structure exists, and gave a simple method of "preconditioning" polynomials (explained below) to endow them with that structure. == Algorithm == === Preliminaries === Consider an arbitrary polynomial p ∈ R [ x ] {\displaystyle p\in \mathbb {R} [x]} of degree n {\displaystyle n} . Assume that n ≥ 3 {\displaystyle n\geq 3} . Define m {\displaystyle m} such that: if n {\displaystyle n} is odd then n = 2 m + 1 {\displaystyle n=2m+1} , and if n {\displaystyle n} is even then n = 2 m + 2 {\displaystyle n=2m+2} . Unless otherwise stated, all variables in this article represent either real numbers or univariate polynomials with real coefficients. All operations in this article are done over R {\displaystyle \mathbb {R} } . Again, the goal is to create an algorithm that returns p ( x ) {\displaystyle p(x)} given any x {\displaystyle x} . The algorithm is allowed to depend on the polynomial p {\displaystyle p} itself, since its coefficients are known in advance. === Overview === ==== Key idea ==== Using polynomial long division, we can write p ( x ) = q ( x ) ⋅ ( x 2 − α ) + ( β x + γ ) , {\displaystyle p(x)=q(x)\cdot (x^{2}-\alpha )+(\beta x+\gamma ),} where x 2 − α {\displaystyle x^{2}-\alpha } is the divisor. Picking a value for α {\displaystyle \alpha } fixes both the quotient q {\displaystyle q} and the coefficients in the remainder β {\displaystyle \beta } and γ {\displaystyle \gamma } . The key idea is to cleverly choose α {\displaystyle \alpha } such that β = 0 {\displaystyle \beta =0} , so that p ( x ) = q ( x ) ⋅ ( x 2 − α ) + γ . {\displaystyle p(x)=q(x)\cdot (x^{2}-\alpha )+\gamma .} This way, no operations are needed to compute the remainder polynomial, since it's just a constant. We apply this procedure recursively to q {\displaystyle q} , expressing p ( x ) = ( ( q ( x ) ⋅ ( x 2 − α m ) + γ m ) ⋯ ) ⋅ ( x 2 − α 1 ) + γ 1 . {\displaystyle p(x)=\left(\left(q(x)\cdot (x^{2}-\alpha _{m})+\gamma _{m}\right)\cdots \right)\cdot (x^{2}-\alpha _{1})+\gamma _{1}.} After m {\displaystyle m} recursive calls, the quotient q {\displaystyle q} is either a linear or a quadratic polynomial. In this base case, the polynomial can be evaluated with (say) Horner's method. ==== "Preconditioning" ==== For arbitrary p {\displaystyle p} , it may not be possible to force β = 0 {\displaystyle \beta =0} at every step of the recursion. Consider the polynomials p e {\displaystyle p^{e}} and p o {\displaystyle p^{o}} with coefficients taken from the even and odd terms of p {\displaystyle p} respectively, so that p ( x ) = p e ( x 2 ) + x ⋅ p o ( x 2 ) . {\displaystyle p(x)=p^{e}(x^{2})+x\cdot p^{o}(x^{2}).} If every root of p o {\displaystyle p^{o}} is real, then it is possible to write p {\displaystyle p} in the form given above. Each α i {\displaystyle \alpha _{i}} is a different root of p o {\displaystyle p^{o}} , counting multiple roots as distinct. Furthermore, if at least n − 1 {\displaystyle n-1} roots of p {\displaystyle p} lie in one half of the complex plane, then every root of p o {\displaystyle p^{o}} is real. Ultimately, it may be necessary to "precondition" p {\displaystyle p} by shifting it — by setting p ( x ) ← p ( x + t ) {\displaystyle p(x)\gets p(x+t)} for some t {\displaystyle t} — to endow it with the structure that most of its roots lie in one half of the complex plane. At runtime, this shift has to be "undone" by first setting x ← x − t {\displaystyle x\gets x-t} . === Preprocessing step === The following algorithm is run once for a given polynomial p {\displaystyle p} . At this point, the values of x {\displaystyle x} that p {\displaystyle p} will be evaluated on are not known. ==== Better choice of t ==== While any t ≥ Re ( r 2 ) {\displaystyle t\geq {\text{Re}}(r_{2})} can work, it is possible to remove one addition during evaluation if t {\displaystyle t} is also chosen such that two roots of p ( x + t ) {\displaystyle p(x+t)} are symmetric about the origin. In that case, α 1 {\displaystyle \alpha _{1}} can be chosen such that the shifted polynomial has a factor of x 2 − α 1 {\displaystyle x^{2}-\alpha _{1}} , so γ 1 = 0 {\displaystyle \gamma _{1}=0} . It is always possible to find such a t {\displaystyle t} . One possible algorithm for choosing t {\displaystyle t} is: === Evaluation step === The following algorithm evaluates p {\displaystyle p} at some, now known, point x {\displaystyle x} . Assuming t {\displaystyle t} is chosen optimally, γ 1 = 0 {\displaystyle \gamma _{1}=0} . So, the final iteration of the loop can instead run y ← y ⋅ ( s − α i ) , {\displaystyle y\gets y\cdot (s-\alpha _{i}),} saving an addition. == Analysis == In total, evaluation using the Knuth–Eve algorithm for a polynomial of degree n {\displaystyle n} requires n {\displaystyle n} additions and ⌊ n / 2 ⌋ + 2 {\displaystyle \lfloor n/2\rfloor +2} multiplications, assuming t {\displaystyle t} is chosen optimally. No algorithm to evaluate a given polynomial of degree n {\displaystyle n} can use fewer than n {\displaystyle n} additions or fewer than ⌈ n / 2 ⌉ {\displaystyle \lceil n/2\rceil } multiplications during evaluation. This result assumes only addition and multiplication are allowed during both preprocessing and evaluation. The Knuth–Eve algorithm is not well-conditioned.

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  Symbaloo

  Symbaloo is a cloud-based site that allows users to organize and categorize web links in the form of buttons. Symbaloo works from a web browser and can be configured as a homepage, allowing users to create a personalized virtual desktop accessible from any device with an Internet connection. Symbaloo users, which must be previously registered, have a page with a grid of buttons that can be configured to link to a specific page. The site allows users to assign different colors to the buttons for easy visual classification. Symbaloo allows a single user to create different pages or screens with buttons. These screens called webmix are useful to separate topics and links can be shared with other users, making them public and sending the link via email. As of 2015 Symbaloo has 6 million users worldwide and mainly used as an online education resource. Symbaloo's slogan is "Start Simple".

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  Ballin' (Mustard and Roddy Ricch song)

  "Ballin'" is a song by American record producer Mustard featuring American rapper Roddy Ricch. The track was released as the third single from Mustard's third studio album, Perfect Ten, on August 20, 2019, though it was available as early as the end of June 2019. The song and its accompanying video received acclaim from music critics, with Complex magazine naming it the Best Song of 2019. It peaked at number 11 on the Billboard Hot 100, marking Mustard's highest charting song in the US. The song received a nomination for Best Rap/Sung Performance at the 2020 Grammy Awards, making it the first time Ricch has been nominated for a Grammy and Mustard's first nomination as an artist. Later in 2019, the two released another collaboration, "High Fashion". == Background == Roddy Ricch revealed in an interview that the song was composed in late 2018, but Mustard wanted to keep it for his album, Perfect Ten, which he was still working on. The song was later included on the album, released in June 2019. Ricch said he knew the song was "hard enough" the first time he heard it, while Mustard proclaimed "this is going to be the one". == Composition and lyrics == "Ballin'" has a "rags to riches" theme. In its intro, the song samples girl group 702's 1997 top ten hit "Get It Together". The song features a "smooth, bouncy beat", with Roddy Ricch rapping about his come-up and ascent in the music industry. In the first verse, Ricch salutes fellow Los Angeles rapper, the late Nipsey Hussle and his girlfriend Lauren London: "I run these racks up with my queen like London and Nip". The line simultaneously references Ricch and Hussle's collaboration "Racks in the Middle", released earlier in 2019 as Hussle's last single before his death. Billboard's Heran Mamo noted that "in typical Hussle fashion", Roddy Ricch "narrates his life's hardships before delving into his newfound treasures". == Critical reception == The song was widely acclaimed by music critics. Charles Holmes of Rolling Stone magazine called it "a song of the year contender", while Complex and Billboard both named it as a "standout track" on the album. Pitchfork magazine included "Ballin'" in its list of The Best Rap Songs of 2019 and called it "the centerpiece of Mustard's underappreciated album Perfect Ten". Complex later named it the Best Song of 2019, calling it "a feel-good anthem so infectious you'll need antibiotics just to stop running it back". == Chart performance == "Ballin'" was at the time Mustard's highest charting song in the US, peaking at number 11 on the Billboard Hot 100. It was also Roddy Ricch's highest charting song, until he surpassed it a week later, with the release of his album track "The Box", which eventually reached number 1 on the chart. It reached number one on Billboard's Rhythmic Songs chart, becoming Mustard's second number one following "Pure Water" and Ricch's first number one. The song also topped the Rap Airplay chart. == Music video == The music video for the track was teased by Mustard on his Instagram page on September 29, 2019. The music video for the track was eventually released on October 2, 2019 to critical acclaim. The video features Mustard and Roddy Ricch driving a Lamborghini Aventador in Los Angeles, where they both are from, playing poker in a casino, and going to a strip club. This is contrasted with scenes in which Mustard and Roddy Ricch as children play cards with Monopoly money and playing with miniature toy Lamborghinis together, aspiring for wealth and luxury, representing how they went from "rags to riches". The video also pays tribute to rapper Nipsey Hussle, who had been killed a few months ago. == Live performances == On December 16, 2019, Roddy Ricch performed the song live, alongside an 8-piece orchestra, at Peppermint Club in Los Angeles for Audiomack's Trap Symphony series. Along with Mustard, he performed it at The Pop Out: Ken & Friends on June 19, 2024. == Other uses == The song can be heard on "Elyse's Skit", track 10 off Roddy Ricch's debut album Please Excuse Me for Being Antisocial. In the skit, which is an actual voicenote recording, the mother of a woman named Elyse sends her daughter a voicenote, with "Ballin'" playing in the background, while the mother proceeds to say "I can't get that damn song out my head", jokingly calling it "inappropriate music". Ricch called the skit "something natural". In 2023, AI covers of the song using models based on pop culture characters and real-world celebrities gained viral popularity. == Awards and nominations == 62nd Annual Grammy Awards == Charts == == Certifications ==

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  Timeline of algorithms

  The following timeline of algorithms outlines the development of algorithms (mainly "mathematical recipes") since their inception. == Antiquity == Before – writing about "recipes" (on cooking, rituals, agriculture and other themes) c. 1700–2000 BC – Egyptians develop earliest known algorithms for multiplying two numbers c. 1600 BC – Babylonians develop earliest known algorithms for factorization and finding square roots c. 300 BC – Euclid's algorithm c. 200 BC – the Sieve of Eratosthenes 263 AD – Gaussian elimination described by Liu Hui == Medieval Period == 628 – Chakravala method described by Brahmagupta c. 820 – Al-Khawarizmi described algorithms for solving linear equations and quadratic equations in his Algebra; the word algorithm comes from his name 825 – Al-Khawarizmi described the algorism, algorithms for using the Hindu–Arabic numeral system, in his treatise On the Calculation with Hindu Numerals, which was translated into Latin as Algoritmi de numero Indorum, where "Algoritmi", the translator's rendition of the author's name gave rise to the word algorithm (Latin algorithmus) with a meaning "calculation method" c. 850 – cryptanalysis and frequency analysis algorithms developed by Al-Kindi (Alkindus) in A Manuscript on Deciphering Cryptographic Messages, which contains algorithms on breaking encryptions and ciphers c. 1025 – Ibn al-Haytham (Alhazen), was the first mathematician to derive the formula for the sum of the fourth powers, and in turn, he develops an algorithm for determining the general formula for the sum of any integral powers c. 1400 – Ahmad al-Qalqashandi gives a list of ciphers in his Subh al-a'sha which include both substitution and transposition, and for the first time, a cipher with multiple substitutions for each plaintext letter; he also gives an exposition on and worked example of cryptanalysis, including the use of tables of letter frequencies and sets of letters which can not occur together in one word == Before 1940 == 1540 – Lodovico Ferrari discovered a method to find the roots of a quartic polynomial 1545 – Gerolamo Cardano published Cardano's method for finding the roots of a cubic polynomial 1614 – John Napier develops method for performing calculations using logarithms 1671 – Newton–Raphson method developed by Isaac Newton 1690 – Newton–Raphson method independently developed by Joseph Raphson 1706 – John Machin develops a quickly converging inverse-tangent series for π and computes π to 100 decimal places 1768 – Leonhard Euler publishes his method for numerical integration of ordinary differential equations in problem 85 of Institutiones calculi integralis 1789 – Jurij Vega improves Machin's formula and computes π to 140 decimal places, 1805 – FFT-like algorithm known by Carl Friedrich Gauss 1842 – Ada Lovelace writes the first algorithm for a computing engine 1903 – A fast Fourier transform algorithm presented by Carle David Tolmé Runge 1918 - Soundex 1926 – Borůvka's algorithm 1926 – Primary decomposition algorithm presented by Grete Hermann 1927 – Hartree–Fock method developed for simulating a quantum many-body system in a stationary state. 1934 – Delaunay triangulation developed by Boris Delaunay 1936 – Turing machine, an abstract machine developed by Alan Turing, with others developed the modern notion of algorithm. == 1940s == 1942 – A fast Fourier transform algorithm developed by G.C. Danielson and Cornelius Lanczos 1945 – Merge sort developed by John von Neumann 1947 – Simplex algorithm developed by George Dantzig == 1950s == 1950 – Hamming codes developed by Richard Hamming 1952 – Huffman coding developed by David A. Huffman 1953 – Simulated annealing introduced by Nicholas Metropolis 1954 – Radix sort computer algorithm developed by Harold H. Seward 1964 – Box–Muller transform for fast generation of normally distributed numbers published by George Edward Pelham Box and Mervin Edgar Muller. Independently pre-discovered by Raymond E. A. C. Paley and Norbert Wiener in 1934. 1956 – Kruskal's algorithm developed by Joseph Kruskal 1956 – Ford–Fulkerson algorithm developed and published by R. Ford Jr. and D. R. Fulkerson 1957 – Prim's algorithm developed by Robert Prim 1957 – Bellman–Ford algorithm developed by Richard E. Bellman and L. R. Ford, Jr. 1959 – Dijkstra's algorithm developed by Edsger Dijkstra 1959 – Shell sort developed by Donald L. Shell 1959 – De Casteljau's algorithm developed by Paul de Casteljau 1959 – QR factorization algorithm developed independently by John G.F. Francis and Vera Kublanovskaya 1959 – Rabin–Scott powerset construction for converting NFA into DFA published by Michael O. Rabin and Dana Scott == 1960s == 1960 – Karatsuba multiplication 1961 – CRC (Cyclic redundancy check) invented by W. Wesley Peterson 1962 – AVL trees 1962 – Quicksort developed by C. A. R. Hoare 1962 – Bresenham's line algorithm developed by Jack E. Bresenham 1962 – Gale–Shapley 'stable-marriage' algorithm developed by David Gale and Lloyd Shapley 1964 – Heapsort developed by J. W. J. Williams 1964 – multigrid methods first proposed by R. P. Fedorenko 1965 – Cooley–Tukey algorithm rediscovered by James Cooley and John Tukey 1965 – Levenshtein distance developed by Vladimir Levenshtein 1965 – Cocke–Younger–Kasami (CYK) algorithm independently developed by Tadao Kasami 1965 – Buchberger's algorithm for computing Gröbner bases developed by Bruno Buchberger 1965 – LR parsers invented by Donald Knuth 1966 – Dantzig algorithm for shortest path in a graph with negative edges 1967 – Viterbi algorithm proposed by Andrew Viterbi 1967 – Cocke–Younger–Kasami (CYK) algorithm independently developed by Daniel H. Younger 1968 – A graph search algorithm described by Peter Hart, Nils Nilsson, and Bertram Raphael 1968 – Risch algorithm for indefinite integration developed by Robert Henry Risch 1969 – Strassen algorithm for matrix multiplication developed by Volker Strassen == 1970s == 1970 – Dinic's algorithm for computing maximum flow in a flow network by Yefim (Chaim) A. Dinitz 1970 – Knuth–Bendix completion algorithm developed by Donald Knuth and Peter B. Bendix 1970 – BFGS method of the quasi-Newton class 1970 – Needleman–Wunsch algorithm published by Saul B. Needleman and Christian D. Wunsch 1972 – Edmonds–Karp algorithm published by Jack Edmonds and Richard Karp, essentially identical to Dinic's algorithm from 1970 1972 – Graham scan developed by Ronald Graham 1972 – Red–black trees and B-trees discovered 1973 – RSA encryption algorithm discovered by Clifford Cocks 1973 – Jarvis march algorithm developed by R. A. Jarvis 1973 – Hopcroft–Karp algorithm developed by John Hopcroft and Richard Karp 1974 – Pollard's p − 1 algorithm developed by John Pollard 1974 – Quadtree developed by Raphael Finkel and J.L. Bentley 1975 – Genetic algorithms popularized by John Holland 1975 – Pollard's rho algorithm developed by John Pollard 1975 – Aho–Corasick string matching algorithm developed by Alfred V. Aho and Margaret J. Corasick 1975 – Cylindrical algebraic decomposition developed by George E. Collins 1976 – Salamin–Brent algorithm independently discovered by Eugene Salamin and Richard Brent 1976 – Knuth–Morris–Pratt algorithm developed by Donald Knuth and Vaughan Pratt and independently by J. H. Morris 1977 – Boyer–Moore string-search algorithm for searching the occurrence of a string into another string. 1977 – RSA encryption algorithm rediscovered by Ron Rivest, Adi Shamir, and Len Adleman 1977 – LZ77 algorithm developed by Abraham Lempel and Jacob Ziv 1977 – multigrid methods developed independently by Achi Brandt and Wolfgang Hackbusch 1978 – LZ78 algorithm developed from LZ77 by Abraham Lempel and Jacob Ziv 1978 – Bruun's algorithm proposed for powers of two by Georg Bruun 1979 – Khachiyan's ellipsoid method developed by Leonid Khachiyan 1979 – ID3 decision tree algorithm developed by Ross Quinlan == 1980s == 1980 – Brent's Algorithm for cycle detection Richard P. Brendt 1981 – Quadratic sieve developed by Carl Pomerance 1981 – Smith–Waterman algorithm developed by Temple F. Smith and Michael S. Waterman 1983 – Simulated annealing developed by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi 1983 – Classification and regression tree (CART) algorithm developed by Leo Breiman, et al. 1984 – LZW algorithm developed from LZ78 by Terry Welch 1984 – Karmarkar's interior-point algorithm developed by Narendra Karmarkar 1984 – ACORN PRNG discovered by Roy Wikramaratna and used privately 1985 – Simulated annealing independently developed by V. Cerny 1985 – Car–Parrinello molecular dynamics developed by Roberto Car and Michele Parrinello 1985 – Splay trees discovered by Sleator and Tarjan 1986 – Blum Blum Shub proposed by L. Blum, M. Blum, and M. Shub 1986 – Push relabel maximum flow algorithm by Andrew Goldberg and Robert Tarjan 1986 – Barnes–Hut tree method developed by Josh Barnes and Piet Hut for fast approximate simulation of n-body problems 1987 – Fast multipole method developed by Leslie Greengard and Vladimir

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  Behavior selection algorithm

  In artificial intelligence, a behavior selection algorithm, or action selection algorithm, is an algorithm that selects appropriate behaviors or actions for one or more intelligent agents. In game artificial intelligence, it selects behaviors or actions for one or more non-player characters. Common behavior selection algorithms include: Finite-state machines Hierarchical finite-state machines Decision trees Behavior trees Hierarchical task networks Hierarchical control systems Utility systems Dialogue tree (for selecting what to say) == Related concepts == In application programming, run-time selection of the behavior of a specific method is referred to as the strategy design pattern.

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  Caspio

  Caspio, Inc. is an American software company providing a low-code platform for building cloud-based business applications. Founded in 2000 by Frank Zamani, the company is headquartered in Sunnyvale, California, with operations in Poland, the Philippines, and Spain. Caspio’s platform allows organizations to create online database applications and workflow tools without extensive coding. == History == Caspio was founded by Frank Zamani in 2000. The company initially focused on simplifying custom cloud applications and reducing development time and cost as compared to traditional software development. Caspio released the first version of its platform, Caspio Bridge, in 2001. In 2014, Caspio released a HIPAA-Compliant Edition of its low-code application development platform. Caspio also released an EU General Data Protection Regulation (GDPR) Compliance Edition of its low-code application development platform in 2016. Caspio's second European Software Development Center opened in Kraków, Poland in 2017. In 2019, Forrester Research listed Caspio and three other platforms in its highest of four ranked tiers of twelve low-code platforms for business developers based on rankings of offerings and strategy at that time. Caspio also opened data centers in Montreal, Canada and India in 2020.

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  Documentation science

  Documentation science is the study of the recording and retrieval of information. It includes methods for storing, retrieving, and sharing of information captured on physical as well as digital documents. This field is closely linked to the fields of library science and information science but has its own theories and practices. The term documentation science was coined by Belgian lawyer and peace activist Paul Otlet. He is considered to be the forefather of information science. He along with Henri La Fontaine laid the foundations of documentation science as a field of study. Professionals in this field are called documentalists. Over the years, documentation science has grown to become a large and important field of study. Evolving from traditional practices like archiving and retrieval to modern theories about the nature of documents, novel methods for organizing digital information, and applications in libraries, research, healthcare, business, and technology and more. This field continues to evolve in the digital age. == Developments in documentation science == 1895: The International Institute of Bibliography (originally Institut International de Bibliographie, IIB) was established on 12 September 1895, in Brussels, Belgium by Paul Otlet and Henri La Fontaine. It aimed to catalog all recorded knowledge using a universal classification system now known as the Universal Decimal Classification (UDC). 1931: International Institute of Bibliography (originally Institut International de Bibliographie, IIB) was renamed The International Institute for Documentation, (Institut International de Documentation, IID). 1934: Paul Otlet envisioned a “radiated library,” a global network of interconnected documents accessible from anywhere via telecommunication. This early idea is now seen as a forerunner of the internet. 1937: American Documentation Institute was founded (1968 nameshift to American Society for Information Science). 1951: Suzanne Briet published Qu'est-ce que la documentation? where she proposed that “a document is evidence in support of a fact,” expanding the definition to include objects such as animals in zoos when they are part of a scientific study. This was a significant theoretical shift in defining documents. 1965-1990: Documentation departments were established, for example, large research libraries, online computer retrieval systems and more. The persons doing the searches were called documentalists. But with the appearance of first CD-ROM databases in the mid-1980s and later the internet in 1990s, these intermediary searches decreased and most such departments closed or merged with other departments. 1996: "Dokvit", Documentation Studies, was established in 1996 at the University of Tromsø in Norway. 2001: The Document Academy was established. It is an international network that celebrates documentation. It was conducted by The Program of Documentation Studies, University of Tromsø, Norway and The School of Information Management and Systems, UC Berkeley. 2003: The first Document Research Conference (DOCAM), a series of conferences made by the Document Academy. DOCAM '03 (2003) was held 13–15 August 2003 at The School of Information Management and Systems (SIMS) at the University of California, Berkeley. 2007: Michael Buckland, Ronald Day, and Birger Hjørland expanded the theoretical foundations of documentation science. They researched and explored documents to be social artifacts, the role of ideology in classification, and how documents influenced knowledge systems. 2010s: The concept of post-documentation or “documentality” began in the 2010s, which focused on how digital traces (e.g., tweets, logs) function as documents without traditional physical form. This led to new thinking in document theory. 2016–present: The Document Academy's DOCAM conferences have continued, offering ongoing developments in the theory and practice of documentation. Themes include affect, memory, activism, and born-digital records. 2017: The journal Information Research published special issues addressing “document theory,” including views on documentation in virtual environments and digital archives. 2020–present: The growth of research data management (RDM) and open science has made documentation practices central to data sharing, metadata standards, and reproducibility in scientific work. == Theoretical foundations == Documentation science has some deep theories that explain what a document is, how people use documents, and how they are organized. These concepts were introduced by scholars who have not only studied libraries, but also philosophy, language, and social sciences. Suzanne Briet described a document as “any material form of evidence” that is made to be used as proof or to share information. An antelope in a zoo, for example, can be a document because it is being studied, classified, and described. Documents are not just things or materials but are also shaped by society. Michael Buckland noted that documents have meaning only when people agree they are useful or valid as information. He explained a document becomes a document when someone decides to use it as evidence. Ronald Day wrote about how documentation is not neutral, it can be influenced by power, ideology, and politics. He claimed that classification systems, like how libraries organize books, are not just technical tools. They also show what kinds of knowledge are seen as more important than others. In recent years, new theories have been introduced, like “documentality” by Maurizio Ferraris. He proposed that a document does not have to be a paper or file, it can also be something digital like a tweet, a database entry, or a log file, as long as it leaves a trace that can be looked at later. This theory helps explain modern digital documents. == Methodologies and practice == Documentation science includes many methods that help people collect, organize, store, and find information. These practices are used in libraries, archives, research labs, companies, and now also in online systems. === Collecting and creating documents === In the past, documentation work included gathering books, articles, reports, and other printed materials. People created records of these materials manually, using catalog cards, indexes, or bibliographies. Paul Otlet’s work with the Universal Bibliographic Repertory is one example. He created millions of card entries to organize knowledge from around the world. Today, documents are not only created by humans. Computers and machines also generate documents, like log files, metadata, and sensor data. These need new tools and methods for collection and management. === Organizing information === Organizing documents has always been a foundational element of documentation science. Methods like classification (dividing things into groups) and indexing (making lists of topics or keywords) help individuals find what they need. A widely used system is the Universal Decimal Classification (UDC) developed by Otlet and La Fontaine. Another is the Library of Congress Classification (LCC) used in the majority of U.S. libraries. Indexing can be performed by humans or by software programs that read the text and add tags to documents. Metadata is also used to describe documents. Metadata is “data about data” like the title, author, date, and subject of a document. Standards like Dublin Core are used in digital libraries to keep metadata consistent. === Retrieval and access === One of the main objectives of documentation is helping users find the right document. This is called information retrieval. In the past, this meant using catalog drawers or printed indexes. Today, people use search engines, databases, and digital libraries. Modern retrieval tools use Boolean logic, ranking algorithms, and sometimes machine learning to show the most useful results first. This is part of what is studied in both documentation science and information retrieval. === Preservation and archiving === Documents require long-term storage. This is called preservation of documents. Printed documents can be damaged by light, pests, or even time on the other hand digital documents can be deemed worthless if formats become outdated or storage facilities fail. Archivists use methods like migration, which includes moving files to new formats, and emulation, which replicates obsolete systems, to preserve materials. These methods and tools are ever changing as new technologies develop. But the main objective of documentation has remained the same, which is to keep information safe, organized, and easy to find. == Documentation in the digital age == With the expansion of the internet, computers, and cloud storage, documents are no longer just books, papers, or reports. They can now be emails, tweets, videos, websites, databases, or even log files created by machines. === Born-digital documents === Many documents today are created directly in digital form. These are called born-digit

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  Berlekamp–Rabin algorithm

  In number theory, Berlekamp's root finding algorithm, also called the Berlekamp–Rabin algorithm, is the probabilistic method of finding roots of polynomials over the field F p {\displaystyle \mathbb {F} _{p}} with p {\displaystyle p} elements. The method was discovered by Elwyn Berlekamp in 1970 as an auxiliary to the algorithm for polynomial factorization over finite fields. The algorithm was later modified by Rabin for arbitrary finite fields in 1979. The method was also independently discovered before Berlekamp by other researchers. == History == The method was proposed by Elwyn Berlekamp in his 1970 work on polynomial factorization over finite fields. His original work lacked a formal correctness proof and was later refined and modified for arbitrary finite fields by Michael Rabin. In 1986 René Peralta proposed a similar algorithm for finding square roots in F p {\displaystyle \mathbb {F} _{p}} . In 2000 Peralta's method was generalized for cubic equations. == Statement of problem == Let p {\displaystyle p} be an odd prime number. Consider the polynomial f ( x ) = a 0 + a 1 x + ⋯ + a n x n {\textstyle f(x)=a_{0}+a_{1}x+\cdots +a_{n}x^{n}} over the field F p ≃ Z / p Z {\displaystyle \mathbb {F} _{p}\simeq \mathbb {Z} /p\mathbb {Z} } of remainders modulo p {\displaystyle p} . The algorithm should find all λ {\displaystyle \lambda } in F p {\displaystyle \mathbb {F} _{p}} such that f ( λ ) = 0 {\textstyle f(\lambda )=0} in F p {\displaystyle \mathbb {F} _{p}} . == Algorithm == === Randomization === Let f ( x ) = ( x − λ 1 ) ( x − λ 2 ) ⋯ ( x − λ n ) {\textstyle f(x)=(x-\lambda _{1})(x-\lambda _{2})\cdots (x-\lambda _{n})} . Finding all roots of this polynomial is equivalent to finding its factorization into linear factors. To find such factorization it is sufficient to split the polynomial into any two non-trivial divisors and factorize them recursively. To do this, consider the polynomial f z ( x ) = f ( x − z ) = ( x − λ 1 − z ) ( x − λ 2 − z ) ⋯ ( x − λ n − z ) {\textstyle f_{z}(x)=f(x-z)=(x-\lambda _{1}-z)(x-\lambda _{2}-z)\cdots (x-\lambda _{n}-z)} where z {\displaystyle z} is some element of F p {\displaystyle \mathbb {F} _{p}} . If one can represent this polynomial as the product f z ( x ) = p 0 ( x ) p 1 ( x ) {\displaystyle f_{z}(x)=p_{0}(x)p_{1}(x)} then in terms of the initial polynomial it means that f ( x ) = p 0 ( x + z ) p 1 ( x + z ) {\displaystyle f(x)=p_{0}(x+z)p_{1}(x+z)} , which provides needed factorization of f ( x ) {\displaystyle f(x)} . === Classification of === F p {\displaystyle \mathbb {F} _{p}} elements Due to Euler's criterion, for every monomial ( x − λ ) {\displaystyle (x-\lambda )} exactly one of following properties holds: The monomial is equal to x {\displaystyle x} if λ = 0 {\displaystyle \lambda =0} , The monomial divides g 0 ( x ) = ( x ( p − 1 ) / 2 − 1 ) {\textstyle g_{0}(x)=(x^{(p-1)/2}-1)} if λ {\displaystyle \lambda } is quadratic residue modulo p {\displaystyle p} , The monomial divides g 1 ( x ) = ( x ( p − 1 ) / 2 + 1 ) {\textstyle g_{1}(x)=(x^{(p-1)/2}+1)} if λ {\displaystyle \lambda } is quadratic non-residual modulo p {\displaystyle p} . Thus if f z ( x ) {\displaystyle f_{z}(x)} is not divisible by x {\displaystyle x} , which may be checked separately, then f z ( x ) {\displaystyle f_{z}(x)} is equal to the product of greatest common divisors gcd ( f z ( x ) ; g 0 ( x ) ) {\displaystyle \gcd(f_{z}(x);g_{0}(x))} and gcd ( f z ( x ) ; g 1 ( x ) ) {\displaystyle \gcd(f_{z}(x);g_{1}(x))} . === Berlekamp's method === The property above leads to the following algorithm: Explicitly calculate coefficients of f z ( x ) = f ( x − z ) {\displaystyle f_{z}(x)=f(x-z)} , Calculate remainders of x , x 2 , x 2 2 , x 2 3 , x 2 4 , … , x 2 ⌊ log 2 ⁡ p ⌋ {\textstyle x,x^{2},x^{2^{2}},x^{2^{3}},x^{2^{4}},\ldots ,x^{2^{\lfloor \log _{2}p\rfloor }}} modulo f z ( x ) {\displaystyle f_{z}(x)} by squaring the current polynomial and taking remainder modulo f z ( x ) {\displaystyle f_{z}(x)} , Using exponentiation by squaring and polynomials calculated on the previous steps calculate the remainder of x ( p − 1 ) / 2 {\textstyle x^{(p-1)/2}} modulo f z ( x ) {\textstyle f_{z}(x)} , If x ( p − 1 ) / 2 ≢ ± 1 ( mod f z ( x ) ) {\textstyle x^{(p-1)/2}\not \equiv \pm 1{\pmod {f_{z}(x)}}} then gcd {\displaystyle \gcd } mentioned below provide a non-trivial factorization of f z ( x ) {\displaystyle f_{z}(x)} , Otherwise all roots of f z ( x ) {\displaystyle f_{z}(x)} are either residues or non-residues simultaneously and one has to choose another z {\displaystyle z} . If f ( x ) {\displaystyle f(x)} is divisible by some non-linear primitive polynomial g ( x ) {\displaystyle g(x)} over F p {\displaystyle \mathbb {F} _{p}} then when calculating gcd {\displaystyle \gcd } with g 0 ( x ) {\displaystyle g_{0}(x)} and g 1 ( x ) {\displaystyle g_{1}(x)} one will obtain a non-trivial factorization of f z ( x ) / g z ( x ) {\displaystyle f_{z}(x)/g_{z}(x)} , thus algorithm allows to find all roots of arbitrary polynomials over F p {\displaystyle \mathbb {F} _{p}} . === Modular square root === Consider equation x 2 ≡ a ( mod p ) {\textstyle x^{2}\equiv a{\pmod {p}}} having elements β {\displaystyle \beta } and − β {\displaystyle -\beta } as its roots. Solution of this equation is equivalent to factorization of polynomial f ( x ) = x 2 − a = ( x − β ) ( x + β ) {\textstyle f(x)=x^{2}-a=(x-\beta )(x+\beta )} over F p {\displaystyle \mathbb {F} _{p}} . In this particular case problem it is sufficient to calculate only gcd ( f z ( x ) ; g 0 ( x ) ) {\displaystyle \gcd(f_{z}(x);g_{0}(x))} . For this polynomial exactly one of the following properties will hold: GCD is equal to 1 {\displaystyle 1} which means that z + β {\displaystyle z+\beta } and z − β {\displaystyle z-\beta } are both quadratic non-residues, GCD is equal to f z ( x ) {\displaystyle f_{z}(x)} which means that both numbers are quadratic residues, GCD is equal to ( x − t ) {\displaystyle (x-t)} which means that exactly one of these numbers is quadratic residue. In the third case GCD is equal to either ( x − z − β ) {\displaystyle (x-z-\beta )} or ( x − z + β ) {\displaystyle (x-z+\beta )} . It allows to write the solution as β = ( t − z ) ( mod p ) {\textstyle \beta =(t-z){\pmod {p}}} . === Example === Assume we need to solve the equation x 2 ≡ 5 ( mod 11 ) {\textstyle x^{2}\equiv 5{\pmod {11}}} . For this we need to factorize f ( x ) = x 2 − 5 = ( x − β ) ( x + β ) {\displaystyle f(x)=x^{2}-5=(x-\beta )(x+\beta )} . Consider some possible values of z {\displaystyle z} : Let z = 3 {\displaystyle z=3} . Then f z ( x ) = ( x − 3 ) 2 − 5 = x 2 − 6 x + 4 {\displaystyle f_{z}(x)=(x-3)^{2}-5=x^{2}-6x+4} , thus gcd ( x 2 − 6 x + 4 ; x 5 − 1 ) = 1 {\displaystyle \gcd(x^{2}-6x+4;x^{5}-1)=1} . Both numbers 3 ± β {\displaystyle 3\pm \beta } are quadratic non-residues, so we need to take some other z {\displaystyle z} . Let z = 2 {\displaystyle z=2} . Then f z ( x ) = ( x − 2 ) 2 − 5 = x 2 − 4 x − 1 {\displaystyle f_{z}(x)=(x-2)^{2}-5=x^{2}-4x-1} , thus gcd ( x 2 − 4 x − 1 ; x 5 − 1 ) ≡ x − 9 ( mod 11 ) {\textstyle \gcd(x^{2}-4x-1;x^{5}-1)\equiv x-9{\pmod {11}}} . From this follows x − 9 = x − 2 − β {\textstyle x-9=x-2-\beta } , so β ≡ 7 ( mod 11 ) {\displaystyle \beta \equiv 7{\pmod {11}}} and − β ≡ − 7 ≡ 4 ( mod 11 ) {\textstyle -\beta \equiv -7\equiv 4{\pmod {11}}} . A manual check shows that, indeed, 7 2 ≡ 49 ≡ 5 ( mod 11 ) {\textstyle 7^{2}\equiv 49\equiv 5{\pmod {11}}} and 4 2 ≡ 16 ≡ 5 ( mod 11 ) {\textstyle 4^{2}\equiv 16\equiv 5{\pmod {11}}} . == Correctness proof == The algorithm finds factorization of f z ( x ) {\displaystyle f_{z}(x)} in all cases except for ones when all numbers z + λ 1 , z + λ 2 , … , z + λ n {\displaystyle z+\lambda _{1},z+\lambda _{2},\ldots ,z+\lambda _{n}} are quadratic residues or non-residues simultaneously. According to theory of cyclotomy, the probability of such an event for the case when λ 1 , … , λ n {\displaystyle \lambda _{1},\ldots ,\lambda _{n}} are all residues or non-residues simultaneously (that is, when z = 0 {\displaystyle z=0} would fail) may be estimated as 2 − k {\displaystyle 2^{-k}} where k {\displaystyle k} is the number of distinct values in λ 1 , … , λ n {\displaystyle \lambda _{1},\ldots ,\lambda _{n}} . In this way even for the worst case of k = 1 {\displaystyle k=1} and f ( x ) = ( x − λ ) n {\displaystyle f(x)=(x-\lambda )^{n}} , the probability of error may be estimated as 1 / 2 {\displaystyle 1/2} and for modular square root case error probability is at most 1 / 4 {\displaystyle 1/4} . == Complexity == Let a polynomial have degree n {\displaystyle n} . We derive the algorithm's complexity as follows: Due to the binomial theorem ( x − z ) k = ∑ i = 0 k ( k i ) ( − z ) k − i x i {\textstyle (x-z)^{k}=\sum \limits _{i=0}^{k}{\binom {k}{i}}(-z)^{k-i}x^{i}} , we may transition from f ( x ) {\displaystyle f(x)} to f ( x − z ) {\displaystyle f(x-z)} in O ( n 2 ) {\displaystyle O(n^{2})} time. Polynomial multiplication a

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  Vinberg's algorithm

  In mathematics, Vinberg's algorithm is an algorithm, introduced by Ernest Borisovich Vinberg, for finding a fundamental domain of a hyperbolic reflection group. Conway (1983) used Vinberg's algorithm to describe the automorphism group of the 26-dimensional even unimodular Lorentzian lattice II25,1 in terms of the Leech lattice. == Description of the algorithm == Let Γ < I s o m ( H n ) {\displaystyle \Gamma <\mathrm {Isom} (\mathbb {H} ^{n})} be a hyperbolic reflection group. Choose any point v 0 ∈ H n {\displaystyle v_{0}\in \mathbb {H} ^{n}} ; we shall call it the basic (or initial) point. The fundamental domain P 0 {\displaystyle P_{0}} of its stabilizer Γ v 0 {\displaystyle \Gamma _{v_{0}}} is a polyhedral cone in H n {\displaystyle \mathbb {H} ^{n}} . Let H 1 , . . . , H m {\displaystyle H_{1},...,H_{m}} be the faces of this cone, and let a 1 , . . . , a m {\displaystyle a_{1},...,a_{m}} be outer normal vectors to it. Consider the half-spaces H k − = { x ∈ R n , 1 | ( x , a k ) ≤ 0 } . {\displaystyle H_{k}^{-}=\{x\in \mathbb {R} ^{n,1}|(x,a_{k})\leq 0\}.} There exists a unique fundamental polyhedron P {\displaystyle P} of Γ {\displaystyle \Gamma } contained in P 0 {\displaystyle P_{0}} and containing the point v 0 {\displaystyle v_{0}} . Its faces containing v 0 {\displaystyle v_{0}} are formed by faces H 1 , . . . , H m {\displaystyle H_{1},...,H_{m}} of the cone P 0 {\displaystyle P_{0}} . The other faces H m + 1 , . . . {\displaystyle H_{m+1},...} and the corresponding outward normals a m + 1 , . . . {\displaystyle a_{m+1},...} are constructed by induction. Namely, for H j {\displaystyle H_{j}} we take a mirror such that the root a j {\displaystyle a_{j}} orthogonal to it satisfies the conditions (1) ( v 0 , a j ) < 0 {\displaystyle (v_{0},a_{j})<0} ; (2) ( a i , a j ) ≤ 0 {\displaystyle (a_{i},a_{j})\leq 0} for all i < j {\displaystyle i Read more →

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  Ave!Comics

  Ave!Comics Production is a privately owned French company editing comics on smartphones, tablets and computers. It was founded in 2008 and it is a subsidiary of Aquafadas, a software development company in digital publishing owned by Kobo Inc. AveComics is a comic book store for digital comic books that can be used on computers, tablets, and smartphones.(iOS, Android) Readers can buy and read comic books, manga and graphic novels in French, English and Spanish. AveComics uses a technology created by Aquafadas for comics transformation, distribution and reading, based around its AVE format. The AveComics application was also a finalist in the BlackBerry Innovation Awards 2009, in the "Entertainment" category. == Company history == Aquafadas, a company working on creative software for Flash, HTML5, photo, and video editing, created the application MyComics to allow the reading of comics on mobile in 2006. This application was made available in 2008, to enable the reading and storing of comics on iPhone and iPod Touch. A reading system adapted to low resolution screens was also available. In October of the same year, the company launched a comics library on both devices, in partnership with the Angoulême International Comics Festival, Fnac and SNCF. This library included the official selection of the festival, and was downloaded over 150 000 times. In December 2008 "The Adventures of Lucky Luke n°3", at Lucky Comics was published on both devices. The comic made a 50 000 € turnover. In April 2009, "Les Blondes" 10th volume was the top-selling comic for 10 months on the AppStore. After, in August 2009, the AveComics application was launched on iPhone, iPod Touch and BlackBerry. The company's website was launched in September when more than 100 titles were available on smartphones and computers. == Catalogue == AveComics works with over 80 international publishers including Glénat, Marsu Productions, Delcourt, Casterman, Soleil, Ubisoft, Les Humanoïdes Associés and Mad Fabrik. Comics such as "Assassin's Creed", "Talisman", "Titeuf", and "Seoul District" are sold by the company. == Award == Grand Prix Software Venture Capital - Senate 2008.

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  Knowledge graph

  In knowledge representation and reasoning, a knowledge graph is a knowledge base that uses a graph-structured data model or topology to represent and operate on data. Knowledge graphs are often used to store interlinked descriptions of entities – objects, events, situations or abstract concepts – while also encoding the free-form semantics or relationships underlying these entities. Since the development of the Semantic Web, knowledge graphs have often been associated with linked open data projects, focusing on the connections between concepts and entities. They are also historically associated with and used by search engines such as Google, Bing, and Yahoo; knowledge engines and question-answering services such as WolframAlpha, Apple's Siri, and Amazon Alexa; and social networks such as LinkedIn and Facebook. Recent developments in data science and machine learning, particularly in graph neural networks, representation learning, and machine learning, have broadened the scope of knowledge graphs beyond their traditional use in search engines and recommender systems. They are increasingly used in scientific research, with notable applications in fields such as genomics, proteomics, and systems biology. == History == The term was coined as early as 1972 by the Austrian linguist Edgar W. Schneider, in a discussion of how to build modular instructional systems for courses. In the late 1980s, the University of Groningen and University of Twente jointly began a project called Knowledge Graphs, focusing on the design of semantic networks with edges restricted to a limited set of relations, to facilitate algebras on the graph. In subsequent decades, the distinction between semantic networks and knowledge graphs was blurred. Some early knowledge graphs were topic-specific. In 1985, Wordnet was founded, capturing semantic relationships between words and meanings – an application of this idea to language itself. In 2005, Marc Wirk founded Geonames to capture relationships between different geographic names and locales and associated entities. In 1998, Andrew Edmonds of Science in Finance Ltd in the UK created a system called ThinkBase that offered fuzzy-logic based reasoning in a graphical context. In 2007, both DBpedia and Freebase were founded as graph-based knowledge repositories for general-purpose knowledge. DBpedia focused exclusively on data extracted from Wikipedia, while Freebase also included a range of public datasets. Neither described themselves as a 'knowledge graph' but developed and described related concepts. In 2012, Google introduced their Knowledge Graph, building on DBpedia and Freebase among other sources. They later incorporated RDFa, Microdata, JSON-LD content extracted from indexed web pages, including the CIA World Factbook, Wikidata, and Wikipedia. Entity and relationship types associated with this knowledge graph have been further organized using terms from the schema.org vocabulary. The Google Knowledge Graph became a complement to string-based search within Google, and its popularity online brought the term into more common use. Since then, several large multinationals have advertised their use of knowledge graphs, further popularising the term. These include Facebook, LinkedIn, Airbnb, Microsoft, Amazon, Uber and eBay. In 2019, IEEE combined its annual international conferences on "Big Knowledge" and "Data Mining and Intelligent Computing" into the International Conference on Knowledge Graph. The development of large language models expanded interest in knowledge graphs as a way to structure information from unstructured text, with advances in language processing enabling their automatic or semi-automatic generation and expansion. The term knowledge graph has since broadened to include the dynamically constructed and adaptive graph structures, which support retrieval, reasoning, and summarization in generative systems. Microsoft Research's GraphRAG (2024) exemplified this development by integrating LLM-generated graphs into retrieval-augmented generation. == Definitions == There is no single commonly accepted definition of a knowledge graph. Most definitions view the topic through a Semantic Web lens and include these features: Flexible relations among knowledge in topical domains: A knowledge graph (i) defines abstract classes and relations of entities in a schema, (ii) mainly describes real world entities and their interrelations, organized in a graph, (iii) allows for potentially interrelating arbitrary entities with each other, and (iv) covers various topical domains. General structure: A network of entities, their semantic types, properties, and relationships. To represent properties, categorical or numerical values are often used. Supporting reasoning over inferred ontologies: A knowledge graph acquires and integrates information into an ontology and applies a reasoner to derive new knowledge. There are, however, many knowledge graph representations for which some of these features are not relevant. For those knowledge graphs, this simpler definition may be more useful: A digital structure that represents knowledge as concepts and the relationships between them (facts). A knowledge graph can include an ontology that allows both humans and machines to understand and reason about its contents. === Implementations === In addition to the above examples, the term has been used to describe open knowledge projects such as YAGO and Wikidata; federations like the Linked Open Data cloud; a range of commercial search tools, including Yahoo's semantic search assistant Spark, Google's Knowledge Graph, and Microsoft's Satori; and the LinkedIn and Facebook entity graphs. The term is also used in the context of note-taking software applications that allow a user to build a personal knowledge graph. The popularization of knowledge graphs and their accompanying methods have led to the development of graph databases such as Neo4j, GraphDB and AgensGraph. These graph databases allow users to easily store data as entities and their interrelationships, and facilitate operations such as data reasoning, node embedding, and ontology development on knowledge bases. In contrast, virtual knowledge graphs do not store information in specialized databases. They rely on an underlying relational database or data lake to answer queries on the graph. Such a virtual knowledge graph system must be properly configured in order to answer the queries correctly. This specific configuration is done through a set of mappings that define the relationship between the elements of the data source and the structure and ontology of the virtual knowledge graph. == Using a knowledge graph for reasoning over data == A knowledge graph formally represents semantics by describing entities and their relationships. Knowledge graphs may make use of ontologies as a schema layer. By doing this, they allow logical inference for retrieving implicit knowledge rather than only allowing queries requesting explicit knowledge. In order to allow the use of knowledge graphs in various machine learning tasks, several methods for deriving latent feature representations of entities and relations have been devised. These knowledge graph embeddings allow them to be connected to machine learning methods that require feature vectors like word embeddings. This can complement other estimates of conceptual similarity. Models for generating useful knowledge graph embeddings are commonly the domain of graph neural networks (GNNs). GNNs are deep learning architectures that comprise edges and nodes, which correspond well to the entities and relationships of knowledge graphs. The topology and data structures afforded by GNNs provide a convenient domain for semi-supervised learning, wherein the network is trained to predict the value of a node embedding (provided a group of adjacent nodes and their edges) or edge (provided a pair of nodes). These tasks serve as fundamental abstractions for more complex tasks such as knowledge graph reasoning and alignment. === Entity alignment === As new knowledge graphs are produced across a variety of fields and contexts, the same entity will inevitably be represented in multiple graphs. However, because no single standard for the construction or representation of knowledge graph exists, resolving which entities from disparate graphs correspond to the same real world subject is a non-trivial task. This task is known as knowledge graph entity alignment, and is an active area of research. Strategies for entity alignment generally seek to identify similar substructures, semantic relationships, shared attributes, or combinations of all three between two distinct knowledge graphs. Entity alignment methods use these structural similarities between generally non-isomorphic graphs to predict which nodes correspond to the same entity. In 2023, researchers found success in using large language models (LLMs) in the task of entity alignment. This was in particul

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  Dependency network (graphical model)

  Dependency networks (DNs) are graphical models, similar to Markov networks, wherein each vertex (node) corresponds to a random variable and each edge captures dependencies among variables. Unlike Bayesian networks, DNs may contain cycles. Each node is associated to a conditional probability table, which determines the realization of the random variable given its parents. == Markov blanket == In a Bayesian network, the Markov blanket of a node is the set of parents and children of that node, together with the children's parents. The values of the parents and children of a node evidently give information about that node. However, its children's parents also have to be included in the Markov blanket, because they can be used to explain away the node in question. In a Markov random field, the Markov blanket for a node is simply its adjacent (or neighboring) nodes. In a dependency network, the Markov blanket for a node is simply the set of its parents. == Dependency network versus Bayesian networks == Dependency networks have advantages and disadvantages with respect to Bayesian networks. In particular, they are easier to parameterize from data, as there are efficient algorithms for learning both the structure and probabilities of a dependency network from data. Such algorithms are not available for Bayesian networks, for which the problem of determining the optimal structure is NP-hard. Nonetheless, a dependency network may be more difficult to construct using a knowledge-based approach driven by expert-knowledge. == Dependency networks versus Markov networks == Consistent dependency networks and Markov networks have the same representational power. Nonetheless, it is possible to construct non-consistent dependency networks, i.e., dependency networks for which there is no compatible valid joint probability distribution. Markov networks, in contrast, are always consistent. == Definition == A consistent dependency network for a set of random variables X = ( X 1 , … , X n ) {\textstyle \mathbf {X} =(X_{1},\ldots ,X_{n})} with joint distribution p ( x ) {\displaystyle p(\mathbf {x} )} is a pair ( G , P ) {\displaystyle (G,P)} where G {\displaystyle G} is a cyclic directed graph, where each of its nodes corresponds to a variable in X {\displaystyle \mathbf {X} } , and P {\displaystyle P} is a set of conditional probability distributions. The parents of node X i {\displaystyle X_{i}} , denoted P a i {\displaystyle \mathbf {Pa_{i}} } , correspond to those variables P a i ⊆ ( X 1 , … , X i − 1 , X i + 1 , … , X n ) {\displaystyle \mathbf {Pa_{i}} \subseteq (X_{1},\ldots ,X_{i-1},X_{i+1},\ldots ,X_{n})} that satisfy the following independence relationships p ( x i ∣ p a i ) = p ( x i ∣ x 1 , … , x i − 1 , x i + 1 , … , x n ) = p ( x i ∣ x − x i ) . {\displaystyle p(x_{i}\mid \mathbf {pa_{i}} )=p(x_{i}\mid x_{1},\ldots ,x_{i-1},x_{i+1},\ldots ,x_{n})=p(x_{i}\mid \mathbf {x} -{x_{i}}).} The dependency network is consistent in the sense that each local distribution can be obtained from the joint distribution p ( x ) {\displaystyle p(\mathbf {x} )} . Dependency networks learned using large data sets with large sample sizes will almost always be consistent. A non-consistent network is a network for which there is no joint probability distribution compatible with the pair ( G , P ) {\displaystyle (G,P)} . In that case, there is no joint probability distribution that satisfies the independence relationships subsumed by that pair. == Structure and parameters learning == Two important tasks in a dependency network are to learn its structure and probabilities from data. Essentially, the learning algorithm consists of independently performing a probabilistic regression or classification for each variable in the domain. It comes from observation that the local distribution for variable X i {\displaystyle X_{i}} in a dependency network is the conditional distribution p ( x i | x − x i ) {\displaystyle p(x_{i}|\mathbf {x} -{x_{i}})} , which can be estimated by any number of classification or regression techniques, such as methods using a probabilistic decision tree, a neural network or a probabilistic support-vector machine. Hence, for each variable X i {\displaystyle X_{i}} in domain X {\displaystyle X} , we independently estimate its local distribution from data using a classification algorithm, even though it is a distinct method for each variable. Here, we will briefly show how probabilistic decision trees are used to estimate the local distributions. For each variable X i {\displaystyle X_{i}} in X {\displaystyle \mathbf {X} } , a probabilistic decision tree is learned where X i {\displaystyle X_{i}} is the target variable and X − X i {\displaystyle \mathbf {X} -X_{i}} are the input variables. To learn a decision tree structure for X i {\displaystyle X_{i}} , the search algorithm begins with a singleton root node without children. Then, each leaf node in the tree is replaced with a binary split on some variable X j {\displaystyle X_{j}} in X − X i {\displaystyle \mathbf {X} -X_{i}} , until no more replacements increase the score of the tree. == Probabilistic Inference == A probabilistic inference is the task in which we wish to answer probabilistic queries of the form p ( y ∣ z ) {\displaystyle p(\mathbf {y\mid z} )} , given a graphical model for X {\displaystyle \mathbf {X} } , where Y {\displaystyle \mathbf {Y} } (the 'target' variables) Z {\displaystyle \mathbf {Z} } (the 'input' variables) are disjoint subsets of X {\displaystyle \mathbf {X} } . One of the alternatives for performing probabilistic inference is using Gibbs sampling. A naive approach for this uses an ordered Gibbs sampler, an important difficulty of which is that if either p ( y ∣ z ) {\displaystyle p(\mathbf {y\mid z} )} or p ( z ) {\displaystyle p(\mathbf {z} )} is small, then many iterations are required for an accurate probability estimate. Another approach for estimating p ( y ∣ z ) {\displaystyle p(\mathbf {y\mid z} )} when p ( z ) {\displaystyle p(\mathbf {z} )} is small is to use modified ordered Gibbs sampler, where Z = z {\displaystyle \mathbf {Z=z} } is fixed during Gibbs sampling. It may also happen that y {\displaystyle \mathbf {y} } is rare, e.g. when Y {\displaystyle \mathbf {Y} } has many variables. So, the law of total probability along with the independencies encoded in a dependency network can be used to decompose the inference task into a set of inference tasks on single variables. This approach comes with the advantage that some terms may be obtained by direct lookup, thereby avoiding some Gibbs sampling. You can see below an algorithm that can be used for obtain p ( y | z ) {\displaystyle p(\mathbf {y|z} )} for a particular instance of y ∈ Y {\displaystyle \mathbf {y} \in \mathbf {Y} } and z ∈ Z {\displaystyle \mathbf {z} \in \mathbf {Z} } , where Y {\displaystyle \mathbf {Y} } and Z {\displaystyle \mathbf {Z} } are disjoint subsets. Algorithm 1: U := Y {\displaystyle \mathbf {U:=Y} } ( the unprocessed variables ) P := Z {\displaystyle \mathbf {P:=Z} } ( the processed and conditioning variables ) p := z {\displaystyle \mathbf {p:=z} } ( the values for P {\displaystyle \mathbf {P} } ) While U ≠ ∅ {\displaystyle \mathbf {U} \neq \emptyset } : Choose X i ∈ U {\displaystyle X_{i}\in \mathbf {U} } such that X i {\displaystyle X_{i}} has no more parents in U {\displaystyle U} than any variable in U {\displaystyle U} If all the parents of X {\displaystyle X} are in P {\displaystyle \mathbf {P} } p ( x i | p ) := p ( x i | p a i ) {\displaystyle p(x_{i}|\mathbf {p} ):=p(x_{i}|\mathbf {pa_{i}} )} Else Use a modified ordered Gibbs sampler to determine p ( x i | p ) {\displaystyle p(x_{i}|\mathbf {p} )} U := U − X i {\displaystyle \mathbf {U:=U} -X_{i}} P := P + X i {\displaystyle \mathbf {P:=P} +X_{i}} p := p + x i {\displaystyle \mathbf {p:=p} +x_{i}} Returns the product of the conditionals p ( x i | p ) {\displaystyle p(x_{i}|\mathbf {p} )} == Applications == In addition to the applications to probabilistic inference, the following applications are in the category of Collaborative Filtering (CF), which is the task of predicting preferences. Dependency networks are a natural model class on which to base CF predictions, once an algorithm for this task only needs estimation of p ( x i = 1 | x − x i = 0 ) {\displaystyle p(x_{i}=1|\mathbf {x} -{x_{i}}=0)} to produce recommendations. In particular, these estimates may be obtained by a direct lookup in a dependency network. Predicting what movies a person will like based on his or her ratings of movies seen; Predicting what web pages a person will access based on his or her history on the site; Predicting what news stories a person is interested in based on other stories he or she read; Predicting what product a person will buy based on products he or she has already purchased and/or dropped into his or her shopping basket. Another class of useful applications for dependency networks is related to data visualization, that is

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