AI Tools For Ecommerce

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

Concordancer

A concordancer is a computer program that automatically constructs a concordance—an alphabetised index of every occurrence of a word or phrase in a body of text, each entry displayed with its surrounding context. Concordancers are primary tools in corpus linguistics, lexicography, computer-assisted translation, and language teaching. The most common display format is the key word in context (KWIC) layout, in which each hit appears centred on a line with a fixed span of words to its left and right, enabling rapid scanning of usage patterns across many occurrences. == History == === Pre-computational concordances === The compilation of concordances predates computers by many centuries. Around 1230, the French Dominican cardinal Hugh of Saint-Cher directed a team of friars in assembling a concordance of the Latin Vulgate Bible, generally regarded as the first systematic concordance of any text. To help readers locate passages, Hugh divided each biblical chapter into lettered sections. Later milestones include a Hebrew Old Testament concordance compiled by Rabbi Mordecai Nathan (1448), Alexander Cruden's Complete Concordance to the Holy Scriptures (1737), and the manuscript Asaf ha-Mazkir, an unfinished concordance to the Babylonian Talmud compiled by Moses Rigotz around the turn of the 19th century. === First computer concordance === The first concordance produced with computing assistance was the Index Thomisticus, a comprehensive lexical index of the writings of and around Thomas Aquinas, totalling approximately 10.6 million Latin words. The Italian Jesuit priest Roberto Busa conceived the project in 1946 and secured the sponsorship of IBM in 1949 after a meeting with chairman Thomas J. Watson. Keypunch operators in Gallarate, Italy, encoded the texts onto punched cards from around 1950. IBM executive Paul Tasman developed the processing methods. The full 56-volume printed edition was completed around 1980, followed by a CD-ROM edition in 1989 and a web-accessible version in 2005. === The KWIC format === The key word in context (KWIC) display was formalised as a computational technique by Hans Peter Luhn, a researcher at IBM, in a 1960 paper in American Documentation. In KWIC output, each instance of the search term (the node word) is centred on a line with a fixed window of words to each side; sorting the resulting lines alphabetically by the immediately adjacent word reveals collocational and phraseological patterns at a glance. === COCOA === One of the first dedicated concordancing programs was COCOA (COunt and COncordance Generation on Atlas), created in 1965 by D. B. Russell at University College London and the Atlas Computer Laboratory in Harwell, Oxfordshire. Written in approximately 4,000 cards of FORTRAN, it processed text annotated with flat, non-hierarchical markup tags and could produce word counts and concordances in multiple languages. Within its first six months COCOA had been applied to texts in at least six languages. A second version designed for multiple mainframe platforms was distributed to British computing centres in the mid-1970s. Growing dissatisfaction with its interface and the eventual withdrawal of Atlas Laboratory support prompted British funding bodies to commission a successor program. === Oxford Concordance Program === The Oxford Concordance Program (OCP) was designed and written in FORTRAN by Susan Hockey and Ian Marriott at Oxford University Computing Services (OUCS) between 1979 and 1980 and first released in 1981. Hockey and Marriott acknowledged that OCP owed much to COCOA and the CLOC system at the University of Birmingham. OCP accepted COCOA-format markup to encode metadata such as author, act, scene, and line number, and was described by its authors as "a machine-independent text analysis program for producing word lists, indices and concordances in a variety of languages and alphabets." By the mid-1980s it had been licensed to approximately 240 institutions in 23 countries. A personal computer version, Micro-OCP, was developed for the IBM PC and sold by Oxford University Press from the late 1980s. Version 2 was rewritten in 1985–86 and documented in the same 1987 article by Hockey and co-author John Martin. === Personal computer era === The availability of affordable personal computers in the 1980s and 1990s enabled standalone concordancing applications that analysts could run locally without specialist computing facilities. MicroConcord, developed by Mike Scott and Tim Johns and published by Oxford University Press in 1993 for MS-DOS, was among the first concordancers designed specifically for classroom language teaching. WordSmith Tools, also developed by Mike Scott, was first released in 1996 and became one of the most widely used corpus analysis suites in academic linguistics research. Other tools from this era include TACT (University of Toronto, 1989), a suite of MS-DOS freeware programs for literary text analysis, and MonoConc, a Windows concordancer created by Michael Barlow. === Web-based concordancers === From the late 1990s onwards, web-based concordancers hosted on remote servers gave researchers browser access to large preloaded corpora without requiring local storage or processing. The Sketch Engine, developed by Adam Kilgarriff and Pavel Rychlý (Masaryk University), was launched commercially in July 2003 by Lexical Computing Limited and introduced word sketches—automatically generated one-page profiles of a word's typical grammatical relations and collocations. AntConc, created by Laurence Anthony at Waseda University, Tokyo, was first released in 2002 as freeware for Windows, macOS, and Linux. == Features == Modern concordancers typically offer a range of analytical functions beyond basic KWIC display. These commonly include: KWIC display with the node word centred and context words in aligned columns, sortable by the word one, two, or three positions to the left or right of the node (L1–L3 and R1–R3) Concordance plots, visualising the distribution of hits as marks along a scaled bar representing each text in the corpus Frequency and word lists, both alphabetical and ranked by frequency Collocation statistics, identifying words that co-occur with the search term more often than chance, quantified by measures such as mutual information, the t-score, or log-likelihood Keyword analysis, comparing word frequencies between a study corpus and a reference corpus to identify statistically distinctive items N-gram analysis, finding frequently recurring word sequences of a specified length Part-of-speech tagging integration, allowing searches filtered to particular grammatical categories Unicode support for multilingual text Bilingual and parallel concordancers additionally display aligned text in two or more languages side by side, enabling comparison of translation equivalents across language pairs. == Notable concordancers == === WordSmith Tools === Created by Mike Scott and first released in 1996, WordSmith Tools is a Windows corpus analysis suite that evolved from MicroConcord. Its three core modules are Concord (KWIC concordances), WordList (frequency and alphabetical word lists), and Keywords (statistical keyword identification relative to a reference corpus). Oxford University Press used WordSmith Tools for dictionary preparation work. Version 4.0 is freely available; later versions are sold by Lexical Analysis Software Limited. === AntConc === AntConc is a freeware, multiplatform concordancing toolkit created by Laurence Anthony, Professor of Applied Linguistics at Waseda University, Tokyo. First released in 2002 and formally described in a 2005 academic paper, it runs on Windows, macOS, and Linux. Its tools include a KWIC concordancer, a concordance plot for visualising distribution across texts, a collocates tool, a keyword list, and an n-gram analysis module. Because it is free and requires only plain text files, AntConc is widely used in linguistics courses and independent research worldwide. === Sketch Engine === The Sketch Engine is a corpus management and query system co-created by Adam Kilgarriff and Pavel Rychlý and launched in 2003 by Lexical Computing Limited. It provides browser-based access to over 800 corpora in more than 100 languages. Beyond concordance searching, it offers word sketches, collocation analysis, distributional thesaurus construction, keyword and terminology extraction, and diachronic analysis. It is used by major publishers including Macmillan and Oxford University Press for lexicographic research. A subset tool, SKELL (Sketch Engine for Language Learning), is freely accessible to individual learners. === Wmatrix === Wmatrix is a web-based corpus processing environment developed by Paul Rayson at the University Centre for Computer Corpus Research on Language (UCREL), Lancaster University. Alongside concordances and frequency lists, Wmatrix integrates CLAWS part-of-speech tagging and the USAS semantic tagger, enabling keyword analysis simultane
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How to Choose an AI Customer-support Bot

Comparing the best AI customer-support bot? An AI customer-support bot is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI customer-support bot slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
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Georgetown–IBM experiment

The Georgetown–IBM experiment was an influential demonstration of machine translation, which was performed on January 7, 1954. Developed jointly by Georgetown University and IBM, the experiment involved completely automatic translation of more than sixty Russian sentences into English. == Background == Conceived and performed primarily in order to attract governmental and public interest and funding by showing the possibilities of machine translation, it was by no means a fully featured system: It had only six grammar rules and 250 lexical items in its vocabulary (of stems and endings). Words in the vocabulary were in the fields of politics, law, mathematics, chemistry, metallurgy, communications and military affairs. Vocabulary was punched onto punch cards. This complete dictionary was never fully shown (only the extended one from Garvin's article). Apart from general topics, the system was specialized in the domain of organic chemistry. The translation was carried out using an IBM 701 mainframe computer (launched in April 1953). The Georgetown-IBM experiment is the best-known result of the MIT conference in June 1952 to which all active researchers in the machine translation field were invited. At the conference, Duncan Harkin from US Department of Defense suggested that his department would finance a new machine translation project. Jerome Weisner supported the idea and offered finance from the Research Laboratory of Electronics at MIT. Leon Dostert had been invited to the project for his previous experience with the automatic correction of translations (back then 'mechanical translation'); his interpretation system had a strong impact on the Nuremberg War Crimes Tribunal. The linguistics part of the demonstration was carried out for the most part by linguist Paul Garvin who had also good knowledge of Russian. Over 60 Romanized Russian statements from a wide range of political, legal, mathematical, and scientific topics were entered into the machine by a computer operator who knew no Russian, and the resulting English translations appeared on a printer. The sentences to be translated were carefully selected. Many operations for the demonstration were fitted to specific words and sentences. In addition, there was no relational or sentence analysis which could recognize the sentence structure. The approach was mostly 'lexicographical' based on a dictionary where a specific word had a connection with specific rules and steps. == Algorithm == The algorithm first translates Russian words into numerical codes, then performs the following case-analysis on each numerical code to choose between possible English word translations, reorder the English words, or omit some English words. The flowchart of the algorithm is reproduced in (see Table 1 for the 6 rules). == Translation examples == How it analyzes Vyelyichyina ugla opryedyelyayetsya otnoshyenyiyem dlyini dugi k radyiusu (figure 2 of ). == Reception == Well publicized by journalists and perceived as a success, the experiment did encourage governments to invest in computational linguistics. The authors claimed that within three or five years, machine translation could well be a solved problem. However, the real progress was much slower, and after the ALPAC report in 1966, which found that the ten years of long research had failed to fulfill the expectations, funding was reduced dramatically. The demonstration was given widespread coverage in the foreign press, but only a small fraction of journalists drew attention to previous machine translation attempts.
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AI Image Generators: Free vs Paid (2026)

Looking for the best AI image generator? An AI image generator is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI image generator slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
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Programming tool

A programming tool or software development tool is a computer program that is used to develop another computer program, usually by helping the developer manage computer files. For example, a programmer may use a tool called a source code editor to edit source code files, and then a compiler to convert the source code into machine code files. They may also use build tools that automatically package executable program and data files into shareable packages or install kits. A set of tools that are run one after another, with each tool feeding its output to the next one, is called a toolchain. An integrated development environment (IDE) integrates the function of several tools into a single program. Usually, an IDE provides a source code editor as well as other built-in or plug-in tools that help with compiling, debugging, and testing. Whether a program is considered a development tool can be subjective. Some programs, such as the GNU compiler collection, are used exclusively for software development while others, such as Notepad, are not meant specifically for development but are nevertheless often used for programming. == Categories == Notable categories of development tools: Assembler – Converts assembly language into machine code Bug tracking system – Software application that records software bugs Build automation – Building software via an unattended fashion Code review software – Activity where one or more people check a program's code Compiler – Software that translates code from one programming language to another Compiler-compiler – Program that generates parsers or compilers, a.k.a. parser generator Debugger – Software for debugging a computer program Decompiler – Program translating executable to source code Disassembler – Computer program to translate machine language into assembly language Documentation generator – Automation technology for creating software documentation Graphical user interface builder – Software development tool Linker – Program that combines intermediate build files into an executable file Loader – Loads executable files into memory and prepares them for execution by the CPU. Memory debugger – Software memory problem finder Minifier – Removal of unnecessary characters in code without changing its functionality Pretty-printer – Formatting to make code or markup easier to readPages displaying short descriptions of redirect targets Performance profiler – Measuring the time or resources used by a section of a computer program Static code analyzer – Analysis of computer programs without executing themPages displaying short descriptions of redirect targets Source code editor – Text editor specializing in software codePages displaying short descriptions of redirect targets Source code generation – Type of computer programmingPages displaying short descriptions of redirect targets Version control system – Stores and tracks versions of files
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Language and Computers

Language and Computers: Studies in Practical Linguistics (ISSN 0921-5034) is a book series on corpus linguistics and related areas. As studies in linguistics, volumes in the series have, by definition, their foundations in linguistic theory; however, they are not concerned with theory for theory's sake, but always with a definite direct or indirect interest in the possibilities of practical application in the dynamic area where language and computers meet. The book series was founded in 1988, and is published by Brill|Rodopi. == Editors == Christian Mair Charles F. Meyer == Volumes == Volumes include: # 77. English Corpus Linguistics: Variation in Time, Space and Genre. Selected papers from ICAME 32., Edited by Gisle Andersen and Kristin Bech. ISBN 978-90-420-3679-6 E-ISBN 978-94-012-0940-3 # 76. English Corpus Linguistics: Crossing Paths., Edited by Merja Kytö. ISBN 978-90-420-3518-8 E-ISBN 978-94-012-0793-5 # 75. Corpus Linguistics and Variation in English.Theory and Description., Edited by Joybrato Mukherjee and Magnus Huber. ISBN 978-90-420-3495-2 E-ISBN 978-94-012-0771-3 # 74. English Corpus Linguistics: Looking back, Moving forward. Papers from the 30th International Conference on English Language Research on Computerized Corpora (ICAME 30), Lancaster, UK, 27–31 May 2009., Edited by Sebastian Hoffmann, Paul Rayson and Geoffrey Leech. ISBN 978-90-420-3466-2 E-ISBN 978-94-012-0747-8 #73. Corpus-based Studies in Language Use, Language Learning, and Language Documentation., Edited by John Newman, Harald Baayen and Sally Rice. ISBN 978-90-420-3401-3 E-ISBN 978-94-012-0688-4 #72. The Progressive in Modern English. A Corpus-Based Study of Grammaticalization and Related Changes., by Svenja Kranich. ISBN 978-90-420-3143-2 E-ISBN 978-90-420-3144-9 #71. Corpus-linguistic applications. Current studies, new directions, Edited by Stefan Th. Gries, Stefanie Wulff, and Mark Davies.. ISBN 978-90-420-2800-5 #70. A resource-light approach to morpho-syntactic tagging., by Anna Feldman and Jirka Hana. ISBN 978-90-420-2768-8 #69. Corpus Linguistics. Refinements and Reassessments., Edited by Antoinette Renouf and Andrew Kehoe. ISBN 978-90-420-2597-4 #68. Corpora: Pragmatics and Discourse. Papers from the 29th International Conference on English Language Research on Computerized Corpora (ICAME 29). Ascona, Switzerland, 14–18 May 2008., Edited by Andreas H. Jucker, Daniel Schreier and Marianne Hundt. ISBN 978-90-420-2592-9 #67. Modals and Quasi-modals in English., by Peter Collins. ISBN 978-90-420-2532-5 #66. Linking up contrastive and learner corpus research., Edited by Gaëtanelle Gilquin, Szilvia Papp and María Belén Díez-Bedmar. ISBN 978-90-420-2446-5 #64. Language, People, Numbers. Corpus Linguistics and Society., Edited by Andrea Gerbig and Oliver Mason. ISBN 978-90-420-2350-5 #63. Variation and change in the lexicon. A corpus-based analysis of adjectives in English ending in –ic and –ical. , by Mark Kaunisto. ISBN 978-90-420-2233-1 #62. Corpus Linguistics 25 Years on., Edited by Roberta Facchinetti. ISBN 978-90-420-2195-2 #61. Corpora in the Foreign Language Classroom. Selected papers from the Sixth International Conference on Teaching and Language Corpora (TaLC 6), Edited by Encarnación Hidalgo, Luis Quereda and Juan Santana. ISBN 978-90-420-2142-6 #60. Corpus Linguistics Beyond the Word. Corpus Research from Phrase to Discourse, Edited by Eileen Fitzpatrick. ISBN 978-90-420-2135-8 #59. Corpus Linguistics and the Web., Edited by Marianne Hundt, Nadja Nesselhauf and Carolin Biewer. ISBN 978-90-420-2128-0 #58. English mediopassive constructions. A cognitive, corpus-based study of their origin, spread, and current status, by Marianne Hundt. ISBN 978-90-420-2127-3 / ISBN 90-420-2127-6
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Is an AI Analytics Tool Worth It in 2026?

Curious about the best AI analytics tool? An AI analytics tool is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI analytics tool slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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Models of DNA evolution

A number of different Markov models of DNA sequence evolution have been proposed. These substitution models differ in terms of the parameters used to describe the rates at which one nucleotide replaces another during evolution. These models are frequently used in molecular phylogenetic analyses. In particular, they are used during the calculation of likelihood of a tree (in Bayesian and maximum likelihood approaches to tree estimation) and they are used to estimate the evolutionary distance between sequences from the observed differences between the sequences. == Introduction == These models are phenomenological descriptions of the evolution of DNA as a string of four discrete states. These Markov models do not explicitly depict the mechanism of mutation nor the action of natural selection. Rather they describe the relative rates of different changes. For example, mutational biases and purifying selection favoring conservative changes are probably both responsible for the relatively high rate of transitions compared to transversions in evolving sequences. However, the Kimura (K80) model described below only attempts to capture the effect of both forces in a parameter that reflects the relative rate of transitions to transversions. Evolutionary analyses of sequences are conducted on a wide variety of time scales. Thus, it is convenient to express these models in terms of the instantaneous rates of change between different states (the Q matrices below). If we are given a starting (ancestral) state at one position, the model's Q matrix and a branch length expressing the expected number of changes to have occurred since the ancestor, then we can derive the probability of the descendant sequence having each of the four states. The mathematical details of this transformation from rate-matrix to probability matrix are described in the mathematics of substitution models section of the substitution model page. By expressing models in terms of the instantaneous rates of change we can avoid estimating a large numbers of parameters for each branch on a phylogenetic tree (or each comparison if the analysis involves many pairwise sequence comparisons). The models described on this page describe the evolution of a single site within a set of sequences. They are often used for analyzing the evolution of an entire locus by making the simplifying assumption that different sites evolve independently and are identically distributed. This assumption may be justifiable if the sites can be assumed to be evolving neutrally. If the primary effect of natural selection on the evolution of the sequences is to constrain some sites, then models of among-site rate-heterogeneity can be used. This approach allows one to estimate only one matrix of relative rates of substitution, and another set of parameters describing the variance in the total rate of substitution across sites. == DNA evolution as a continuous-time Markov chain == === Continuous-time Markov chains === Continuous-time Markov chains have the usual transition matrices which are, in addition, parameterized by time, t {\displaystyle t} . Specifically, if E 1 , E 2 , E 3 , E 4 {\displaystyle E_{1},E_{2},E_{3},E_{4}} are the states, then the transition matrix P ( t ) = ( P i j ( t ) ) {\displaystyle P(t)={\big (}P_{ij}(t){\big )}} where each individual entry, P i j ( t ) {\displaystyle P_{ij}(t)} refers to the probability that state E i {\displaystyle E_{i}} will change to state E j {\displaystyle E_{j}} in time t {\displaystyle t} . Example: We would like to model the substitution process in DNA sequences (i.e. Jukes–Cantor, Kimura, etc.) in a continuous-time fashion. The corresponding transition matrices will look like: P ( t ) = ( p A A ( t ) p A G ( t ) p A C ( t ) p A T ( t ) p G A ( t ) p G G ( t ) p G C ( t ) p G T ( t ) p C A ( t ) p C G ( t ) p C C ( t ) p C T ( t ) p T A ( t ) p T G ( t ) p T C ( t ) p T T ( t ) ) {\displaystyle P(t)={\begin{pmatrix}p_{\mathrm {AA} }(t)&p_{\mathrm {AG} }(t)&p_{\mathrm {AC} }(t)&p_{\mathrm {AT} }(t)\\p_{\mathrm {GA} }(t)&p_{\mathrm {GG} }(t)&p_{\mathrm {GC} }(t)&p_{\mathrm {GT} }(t)\\p_{\mathrm {CA} }(t)&p_{\mathrm {CG} }(t)&p_{\mathrm {CC} }(t)&p_{\mathrm {CT} }(t)\\p_{\mathrm {TA} }(t)&p_{\mathrm {TG} }(t)&p_{\mathrm {TC} }(t)&p_{\mathrm {TT} }(t)\end{pmatrix}}} where the top-left and bottom-right 2 × 2 blocks correspond to transition probabilities and the top-right and bottom-left 2 × 2 blocks corresponds to transversion probabilities. Assumption: If at some time t 0 {\displaystyle t_{0}} , the Markov chain is in state E i {\displaystyle E_{i}} , then the probability that at time t 0 + t {\displaystyle t_{0}+t} , it will be in state E j {\displaystyle E_{j}} depends only upon i {\displaystyle i} , j {\displaystyle j} and t {\displaystyle t} . This then allows us to write that probability as p i j ( t ) {\displaystyle p_{ij}(t)} . Theorem: Continuous-time transition matrices satisfy: P ( t + τ ) = P ( t ) P ( τ ) {\displaystyle P(t+\tau )=P(t)P(\tau )} Note: There is here a possible confusion between two meanings of the word transition. (i) In the context of Markov chains, transition is the general term for the change between two states. (ii) In the context of nucleotide changes in DNA sequences, transition is a specific term for the exchange between either the two purines (A ↔ G) or the two pyrimidines (C ↔ T) (for additional details, see the article about transitions in genetics). By contrast, an exchange between one purine and one pyrimidine is called a transversion. === Deriving the dynamics of substitution === Consider a DNA sequence of fixed length m evolving in time by base replacement. Assume that the processes followed by the m sites are Markovian independent, identically distributed and that the process is constant over time. For a particular site, let E = { A , G , C , T } {\displaystyle {\mathcal {E}}=\{A,\,G,\,C,\,T\}} be the set of possible states for the site, and p ( t ) = ( p A ( t ) , p G ( t ) , p C ( t ) , p T ( t ) ) {\displaystyle \mathbf {p} (t)=(p_{A}(t),\,p_{G}(t),\,p_{C}(t),\,p_{T}(t))} their respective probabilities at time t {\displaystyle t} . For two distinct x , y ∈ E {\displaystyle x,y\in {\mathcal {E}}} , let μ x y {\displaystyle \mu _{xy}\ } be the transition rate from state x {\displaystyle x} to state y {\displaystyle y} . Similarly, for any x {\displaystyle x} , let the total rate of change from x {\displaystyle x} be μ x = ∑ y ≠ x μ x y . {\displaystyle \mu _{x}=\sum _{y\neq x}\mu _{xy}\,.} The changes in the probability distribution p A ( t ) {\displaystyle p_{A}(t)} for small increments of time Δ t {\displaystyle \Delta t} are given by p A ( t + Δ t ) = p A ( t ) − p A ( t ) μ A Δ t + ∑ x ≠ A p x ( t ) μ x A Δ t . {\displaystyle p_{A}(t+\Delta t)=p_{A}(t)-p_{A}(t)\mu _{A}\Delta t+\sum _{x\neq A}p_{x}(t)\mu _{xA}\Delta t\,.} In other words, (in frequentist language), the frequency of A {\displaystyle A} 's at time t + Δ t {\displaystyle t+\Delta t} is equal to the frequency at time t {\displaystyle t} minus the frequency of the lost A {\displaystyle A} 's plus the frequency of the newly created A {\displaystyle A} 's. Similarly for the probabilities p G ( t ) {\displaystyle p_{G}(t)} , p C ( t ) {\displaystyle p_{C}(t)} and p T ( t ) {\displaystyle p_{T}(t)} . These equations can be written compactly as p ( t + Δ t ) = p ( t ) + p ( t ) Q Δ t , {\displaystyle \mathbf {p} (t+\Delta t)=\mathbf {p} (t)+\mathbf {p} (t)Q\Delta t\,,} where Q = ( − μ A μ A G μ A C μ A T μ G A − μ G μ G C μ G T μ C A μ C G − μ C μ C T μ T A μ T G μ T C − μ T ) {\displaystyle Q={\begin{pmatrix}-\mu _{A}&\mu _{AG}&\mu _{AC}&\mu _{AT}\\\mu _{GA}&-\mu _{G}&\mu _{GC}&\mu _{GT}\\\mu _{CA}&\mu _{CG}&-\mu _{C}&\mu _{CT}\\\mu _{TA}&\mu _{TG}&\mu _{TC}&-\mu _{T}\end{pmatrix}}} is known as the rate matrix. Note that, by definition, the sum of the entries in each row of Q {\displaystyle Q} is equal to zero. It follows that p ′ ( t ) = p ( t ) Q . {\displaystyle \mathbf {p} '(t)=\mathbf {p} (t)Q\,.} For a stationary process, where Q {\displaystyle Q} does not depend on time t, this differential equation can be solved. First, P ( t ) = exp ⁡ ( t Q ) , {\displaystyle P(t)=\exp(tQ),} where exp ⁡ ( t Q ) {\displaystyle \exp(tQ)} denotes the exponential of the matrix t Q {\displaystyle tQ} . As a result, p ( t ) = p ( 0 ) P ( t ) = p ( 0 ) exp ⁡ ( t Q ) . {\displaystyle \mathbf {p} (t)=\mathbf {p} (0)P(t)=\mathbf {p} (0)\exp(tQ)\,.} === Ergodicity === If the Markov chain is irreducible, i.e. if it is always possible to go from a state x {\displaystyle x} to a state y {\displaystyle y} (possibly in several steps), then it is also ergodic. As a result, it has a unique stationary distribution π = { π x , x ∈ E } {\displaystyle {\boldsymbol {\pi }}=\{\pi _{x},\,x\in {\mathcal {E}}\}} , where π x {\displaystyle \pi _{x}} corresponds to the proportion of time spent in state x {\displaystyle x} after the Markov chain has run for an infinite amount of time. In DNA evo
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Digital image

A digital image is an image composed of picture elements, also known as pixels, each with finite, discrete quantities of numeric representation for its intensity or gray level that is an output from its two-dimensional functions fed as input by its spatial coordinates denoted with x, y on the x-axis and y-axis, respectively. An image can be vector or raster type. By itself, the term "digital image" usually refers to raster images or bitmapped images (as opposed to vector images). == Raster == Raster images have a finite set of digital values, called picture elements or pixels. The digital image contains a fixed number of rows and columns of pixels. Pixels are the smallest individual element in an image, holding quantized values that represent the brightness of a given color at any specific point. Typically, the pixels are stored in computer memory as a raster image or raster map, a two-dimensional array of small integers. These values are often transmitted or stored in a compressed form. Raster images can be created by a variety of input devices and techniques, such as digital cameras, scanners, coordinate-measuring machines, seismographic profiling, airborne radar, and more. They can also be synthesized from arbitrary non-image data, such as mathematical functions or three-dimensional geometric models; the latter being a major sub-area of computer graphics. The field of digital image processing is the study of algorithms for their transformation. === Raster file formats === Most users come into contact with raster images through digital cameras, which use any of several image file formats. Some digital cameras give access to almost all the data captured by the camera, using a raw image format. The Universal Photographic Imaging Guidelines (UPDIG) suggests these formats be used when possible since raw files produce the best quality images. These file formats allow the photographer and the processing agent the greatest level of control and accuracy for output. Their use is inhibited by the prevalence of proprietary information (trade secrets) for some camera makers, but there have been initiatives such as OpenRAW to influence manufacturers to release these records publicly. An alternative may be Digital Negative (DNG), a proprietary Adobe product described as "the public, archival format for digital camera raw data". Although this format is not yet universally accepted, support for the product is growing, and increasingly professional archivists and conservationists, working for respectable organizations, variously suggest or recommend DNG for archival purposes. == Vector == Vector images resulted from mathematical geometry (vector). In mathematical terms, a vector consists of both a magnitude, or length, and a direction. Often, both raster and vector elements will be combined in one image; for example, in the case of a billboard with text (vector) and photographs (raster). Example of vector file types are EPS, PDF, and AI. == Image viewing == Image viewer software displayed on images. Web browsers can display standard internet images formats including JPEG, GIF and PNG. Some can show SVG format which is a standard W3C format. In the past, when the Internet was still slow, it was common to provide "preview" images that would load and appear on the website before being replaced by the main image (to give a preliminary impression). Now Internet is fast enough and this preview image is seldom used. Some scientific images can be very large (for instance, the 46 gigapixel size image of the Milky Way, about 194 GB in size). Such images are difficult to download and are usually browsed online through more complex web interfaces. Some viewers offer a slideshow utility to display a sequence of images. == History == Early digital fax machines such as the Bartlane cable picture transmission system preceded digital cameras and computers by decades. The first picture to be scanned, stored, and recreated in digital pixels was displayed on the Standards Eastern Automatic Computer (SEAC) at NIST. The advancement of digital imagery continued in the early 1960s, alongside development of the space program and in medical research. Projects at the Jet Propulsion Laboratory, MIT, Bell Labs and the University of Maryland, among others, used digital images to advance satellite imagery, wirephoto standards conversion, medical imaging, videophone technology, character recognition, and photo enhancement. Rapid advances in digital imaging began with the introduction of MOS integrated circuits in the 1960s and microprocessors in the early 1970s, alongside progress in related computer memory storage, display technologies, and data compression algorithms. The invention of computerized axial tomography (CAT scanning), using x-rays to produce a digital image of a "slice" through a three-dimensional object, was of great importance to medical diagnostics. As well as origination of digital images, digitization of analog images allowed the enhancement and restoration of archaeological artifacts and began to be used in fields as diverse as nuclear medicine, astronomy, law enforcement, defence and industry. Advances in microprocessor technology paved the way for the development and marketing of charge-coupled devices (CCDs) for use in a wide range of image capture devices and gradually displaced the use of analog film and tape in photography and videography towards the end of the 20th century. The computing power necessary to process digital image capture also allowed computer-generated digital images to achieve a level of refinement close to photorealism. === Digital image sensors === The first semiconductor image sensor was the CCD, developed by Willard S. Boyle and George E. Smith at Bell Labs in 1969. While researching MOS technology, they realized that an electric charge was the analogy of the magnetic bubble and that it could be stored on a tiny MOS capacitor. As it was fairly straightforward to fabricate a series of MOS capacitors in a row, they connected a suitable voltage to them so that the charge could be stepped along from one to the next. The CCD is a semiconductor circuit that was later used in the first digital video cameras for television broadcasting. Early CCD sensors suffered from shutter lag. This was largely resolved with the invention of the pinned photodiode (PPD). It was invented by Nobukazu Teranishi, Hiromitsu Shiraki and Yasuo Ishihara at NEC in 1980. It was a photodetector structure with low lag, low noise, high quantum efficiency and low dark current. In 1987, the PPD began to be incorporated into most CCD devices, becoming a fixture in consumer electronic video cameras and then digital still cameras. Since then, the PPD has been used in nearly all CCD sensors and then CMOS sensors. The NMOS active-pixel sensor (APS) was invented by Olympus in Japan during the mid-1980s. This was enabled by advances in MOS semiconductor device fabrication, with MOSFET scaling reaching smaller micron and then sub-micron levels. The NMOS APS was fabricated by Tsutomu Nakamura's team at Olympus in 1985. The CMOS active-pixel sensor (CMOS sensor) was later developed by Eric Fossum's team at the NASA Jet Propulsion Laboratory in 1993. By 2007, sales of CMOS sensors had surpassed CCD sensors. === Digital image compression === An important development in digital image compression technology was the discrete cosine transform (DCT), a lossy compression technique first proposed by Nasir Ahmed in 1972. DCT compression is used in JPEG, which was introduced by the Joint Photographic Experts Group in 1992. JPEG compresses images down to much smaller file sizes, and has become the most widely used image file format on the Internet. == Mosaic == In digital imaging, a mosaic is a combination of non-overlapping images, arranged in some tessellation. Gigapixel images are an example of such digital image mosaics. Satellite imagery are often mosaicked to cover Earth regions. Interactive viewing is provided by virtual-reality photography.
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Marti Hearst

Marti Alice Hearst is a professor in the School of Information at the University of California, Berkeley. She did early work in corpus-based computational linguistics, including some of the first work in automating sentiment analysis, and word sense disambiguation. She invented an algorithm that became known as "Hearst patterns" which applies lexico-syntactic patterns to recognize hyponymy (ISA) relations with high accuracy in large text collections, including an early application of it to WordNet; this algorithm is widely used in commercial text mining applications including ontology learning. Hearst also developed early work in automatic segmentation of text into topical discourse boundaries, inventing a now well-known approach called TextTiling. Hearst's research is on user interfaces for search engine technology and big data analytics. She did early work in user interfaces and information visualization for search user interfaces, inventing the TileBars query term visualization. Her Flamenco research project investigated and developed the now widely used faceted navigation approach for searching and browsing web sites and information collections. She wrote the first academic book on the topic of Search User Interfaces (Cambridge University Press, 2009). Hearst is an Edge Foundation contributing author and a member of the Usage panel of the American Heritage Dictionary of the English Language. Hearst received her B.A., M.S., and Ph.D. in computer science, all from Berkeley. In 2013 she became a fellow of the Association for Computing Machinery. She became a member of the CHI Academy in 2017, and has previously served as president of the Association for Computational Linguistics and on the advisory council of NSF's CISE Directorate. Additionally, she has been a member of the Web Board for CACM, the Usage Panel for the American Heritage Dictionary, the Edge.org panel of experts, the research staff at Xerox PARC, and the boards of ACM Transactions on the Web, Computational Linguistics, ACM Transactions on Information Systems, and IEEE Intelligent Systems. Hearst has received an NSF CAREER award, an IBM Faculty Award, and an Okawa Foundation Fellowship. Her work on user interfaces has had a profound impact on the industry, earning Hearst two Google Research Awards and four Excellence in Teaching Awards.} She has also led projects worth over $3.5M in research grants. Hearst’s publications date back to 1990, when ‘A Hybrid Approach to Restricted Text Interpretation’ was published in Stanford University’s AAAI Spring Symposium on Text Based Intelligent Systems in March of that year.
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Heikki Mannila

Heikki Olavi Mannila (born 4 January 1960 in Espoo) is a Finnish computer scientist, the president of the Academy of Finland. Mannila earned his Ph.D. in 1985 from the University of Helsinki under the supervision of Esko Ukkonen and for many years he was a professor at the University of Helsinki himself. From 2004 to 2008 he was Academy Professor at the Academy of Finland. He became Vice President for Academic Affairs at Aalto University in 2009, and was appointed by the Finnish government as president of the Academy of Finland for a term lasting from 2012 to 2017. The appointment was renewed for the period 2017–2022. Mannila is known for his research in data mining, and has published highly cited papers on association rule learning and sequence mining. With David Hand and Padhraic Smyth, he is the co-author of the book Principles of Data Mining (MIT Press, 2001). Heikki Mannila is son to the professor Elina Haavio-Mannila.
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The Best Free AI Paragraph Rewriter for Beginners

Shopping for the best AI paragraph rewriter? An AI paragraph rewriter is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI paragraph rewriter slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
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JAX (software)

JAX is a Python library for accelerator-oriented array computation and program transformation, designed for high-performance numerical computing and large-scale machine learning. It is developed by Google with contributions from Nvidia and other community contributors. It is described as bringing together a modified version of the automatic differentiation system autograd and OpenXLA's XLA (Accelerated Linear Algebra). It is designed to follow the structure and workflow of NumPy as closely as possible and works with various existing frameworks such as TensorFlow and PyTorch. The primary features of JAX are: Providing a unified NumPy-like interface to computations that run on CPU, GPU, or TPU, in local or distributed settings. Built-in Just-In-Time (JIT) compilation via OpenXLA, an open-source machine learning compiler ecosystem. Efficient evaluation of gradients via its automatic differentiation transformations. Automatic vectorization to efficiently map functions over arrays representing batches of inputs. == Libraries using Jax == Flax Equinox Optax
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Corinna Cortes

Corinna Cortes (born 31 March 1961) is a Danish computer scientist known for her contributions to machine learning. She is a Vice President at Google Research in New York City. Cortes is an ACM Fellow and a recipient of the Paris Kanellakis Award for her work on theoretical foundations of support vector machines. == Early life and education == Corinna Cortes was born in 1961 in Denmark. Cortes received her Master of Science degree in physics from University of Copenhagen in 1989. She received her PhD in computer science from the University of Rochester in 1993 for research supervised by Randal C. Nelson. == Career and research == Cortes joined AT&T Bell Labs as a researcher in 1993. Since 2003, she has served as Vice President of Google Research, New York City, and since 2011, as adjunct professor at the UCPH Department of Computer Science. She is serves as an editorial board member of the journal Machine Learning. Cortes' research covers a wide range of topics in machine learning, including support vector machines (SVM) and data mining. SVM is one of the most frequently used algorithms in machine learning, which is used in many practical applications, including medical diagnosis and weather forecasting. At AT&T, Cortes was a contributor to the design of Hancock programming language. === Awards and honours === In 2008, she jointly with Vladimir Vapnik received the Paris Kanellakis Award for the development of a highly effective algorithm for supervised learning known as support vector machines (SVM). She was named an ACM Fellow in 2023 for theoretical and practical contributions to machine learning, industrial leadership and service to the field. == Personal life == Corinna has two children and is also a competitive runner.
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Paola Velardi

Paola Velardi (born in Rome, April 26, 1955) is a full professor of computer science at Sapienza University in Rome, Italy. Her research encompasses Artificial Intelligence and specifically, natural language processing, machine learning business intelligence and semantic web. Velardi is one of the hundred female scientists included in the database "100esperte.it" (translated from Italian with "100 female experts"). This online, open database champions the recognition of top-rated female scientists in Science, Technology, Engineering and Mathematics (STEM) areas. Among her prestigious appointments and honors, her inclusion stands out —alongside 45 other international female scientists from the past, present, and future— in the Women in Science pavilion of UNESCO’s Virtual Science Museum. == Research == Paola Velardi's research activity has focused, since the early 1980s, on Artificial Intelligence, with a particular emphasis on natural language processing (NLP), Machine learning, and data mining. Her scientific contributions have evolved over time, following the sector's primary paradigms: Semantic Web and Ontologies: She is known for her pioneering work on semantic disambiguation and automated ontology learning, collaborating on the development of systems such as OntoLearn. Social Computing and Predictive Analysis: She has conducted research on extracting information from social media for epidemiological monitoring (syndromic surveillance) and for the identification of opinion leaders. In the educational field, she has developed machine learning models to predict the risk of student dropout. AI for Health and Elder Monitoring: She has coordinated projects to support frailty in the elderly, developing systems based on ambient intelligence and wearables to detect clinical and behavioral anomalies. She has also contributed to models for analyzing behavioral changes through dynamic clustering. Generative AI and Finance: More recently, her research has expanded into the use of generative AI and deep learning for finance, including benchmark studies on price trend prediction based on Limit Order Books (LOB) and the development of diffusion models for realistic market simulation (the TRADES project). According to Google Scholar bibliometrics updated until December 2025, Velardi's scientific publications have been cited more than 8100 times. Her h-index was 42. She has published more than 200 papers in international journals and conference proceedings. Some of her publications have been published in top rated journals such as Artificial Intelligence, Computational Linguistics, Knowledge-Based Systems, IEEE Transactions on Data and Knowledge Engineering , IEEE Transactions on Pattern Analysis and Machine Intelligence, IEEE Transactions on Computers, IEEE Transactions on Software Engineering , Data Mining and Knowledge Discovery, and Journal of Web Semantics. == Education and previous employments == Velardi graduated in electronic engineering from Sapienza University in 1978. From 1978 to 1983, she worked for the Ugo Bordoni Foundation, a research institution focusing on ICT and working under the supervision of the Italian Ministry of Economic Development. In 1983, she was a visiting scholar at Stanford University. During this period she became passionate about Artificial Intelligence, which will remain her area of research throughout her career. From 1984 to 1986, she came back to her natal city and worked as a researcher for IBM. From 1986 to 1996 she was an associate professor in the engineering faculty of Polytechnic University of the Marches (Ancona, Italy). Starting in November 1996, she taught in and did research for the Department of Computer Science at the Sapienza University. Velardi was the head of Bachelor and Master Programs in Computer Science at Sapienza University from 2010 to 2013 and from 2015 to 2016. == Current employment == Since November 2001, Velardi has been a full professor in the department of computer science ("Dipartimento di Informatica" in Italian) at Sapienza University in Rome, Italy. Since 2013, she has been the coordinator of the Distance Learning Degree in Computer Science at Sapienza University. As of today, Velardi is a Senior Associate at the Institute of Cognitive Sciences and Technologies (ISTC) of the CNR. == Recognition == Velardi is one of the hundred female scientists included in the database "100esperte.it" (translated from Italian with "100 female experts"). This database lists top Italian female STEM scientists. Six out of one hundred scientists in the 100esperte's database are computer scientists like Velardi. Velardi is in the list of the top Italian scientists. A top scientist appearing in the Top-Italian-Scientists database is a scientist whose h-index is greater than 30. In March 2017, she was given an IBM Faculty Award for her research on social recommender systems. In December 2018, Velardi was included in the list of the 50 most influential Italian women in science and technology by Inspiring Fifty, a non-profit that aims to increase diversity in STEM by making female role models in tech more visible. In September 2019 she was the local co-organizer and Program Chair of the 6th ACM Celebration of Women in Computing. In November 2019 Velardi received the Standout Woman Award International at the seat of the Italian Parliament in Montecitorio. == Causes == Velardi aims at debunking the myth of computer science as a man-oriented and "inflexible" discipline. She is the founder of the project "NERD? Non e' roba per donne?" (translated from Italian: "NERD? Is it not stuff for women?"). This project was launched by Velardi in 2012 in the Department of Computer Science at Sapienza University. Since 2013 the project has been carried out in partnership with IBM Italy, which later created a spin-off of the project. The goal of the project is two-fold: (1) conveying computer science as creative, interdisciplinary and problem-solving-oriented science, and (2) encouraging young female students in studying computer science by, for instance, developing apps for smartphones. She has been the program chair of the 19th ACM celebration of Women in Computing. She is the creator and coordinator of the G4GRETA, an educational project that involves students of the third and fourth grades of Rome and Lazio. The project combines the development of IT skills with the themes of environmental sustainability and soft skills (teambuilding, pitching, social networking, etc.) Velardi is also involved in scientific dissemination. In 2020 and 2021 she cooperated with RaiCultura, the cultural division of RAI, the national broadcasting company.
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