AI Headshot Generator

AI Headshot Generator — hands-on reviews, top picks, pricing, pros and cons and a practical how-to guide on Aizhi.

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  SWIG

  The Simplified Wrapper and Interface Generator (SWIG) is an open-source software tool used to connect computer programs or libraries written in C or C++ with scripting languages such as Lua, Perl, PHP, Python, R, Ruby, Tcl, and other language implementations like C#, Java, JavaScript, Go, D, OCaml, Octave, Scilab and Scheme. Output can also be in the form of XML. == Function == The aim is to allow the calling of native functions (that were written in C or C++) by other programming languages, passing complex data types to those functions, keeping memory from being inappropriately freed, inheriting object classes across languages, etc. The programmer writes an interface file containing a list of C/C++ functions to be made visible to an interpreter. SWIG will compile the interface file and generate code in regular C/C++ and the target programming language. SWIG will generate conversion code for functions with simple arguments; conversion code for complex types of arguments must be written by the programmer. The SWIG tool creates source code that provides the glue between C/C++ and the target language. Depending on the language, this glue comes in three forms: a shared library that an extant interpreter can link to as some form of extension module, or a shared library that can be linked to other programs compiled in the target language (for example, using Java Native Interface (JNI) in Java). a shared dynamic library source code that should be compiled and dynamically loaded (e.g. Node.js native extensions) SWIG is not used for calling interpreted functions by native code; this must be done by the programmer manually. == Example == SWIG wraps simple C declarations by creating an interface that closely matches the way in which the declarations would be used in a C program. For example, consider the following interface file: In this file, there are two functions sin() and strcmp(), a global variable Foo, and two constants STATUS and VERSION. When SWIG creates an extension module, these declarations are accessible as scripting language functions, variables, and constants respectively. In Python: == Purpose == There are two main reasons to embed a scripting engine in an existing C/C++ program: The program can then be customized far faster, via a scripting language instead of C/C++. The scripting engine may even be exposed to the end-user, so that they can automate common tasks by writing scripts. Even if the final product is not to contain the scripting engine, it may nevertheless be very useful for writing test scripts. There are several reasons to create dynamic libraries that can be loaded into extant interpreters, including: Provide access to a C/C++ library which has no equivalent in the scripting language. Write the whole program in the scripting language first, and after profiling, rewrite performance-critical code in C or C++. == History == SWIG is written in C and C++ and has been publicly available since February 1996. The initial author and main developer was David M. Beazley who developed SWIG while working as a graduate student at Los Alamos National Laboratory and the University of Utah and while on the faculty at the University of Chicago. Development is currently supported by an active group of volunteers led by William Fulton. SWIG has been released under a GNU General Public License. == Google Summer of Code == SWIG was a successful participant of Google Summer of Code in 2008, 2009, 2012. In 2008, SWIG got four slots. Haoyu Bai spent his summers on SWIG's Python 3.0 Backend, Jan Jezabek worked on Support for generating COM wrappers, Cheryl Foil spent her time on Comment 'Translator' for SWIG, and Maciej Drwal worked on a C backend. In 2009, SWIG again participated in Google Summer of Code. This time four students participated. Baozeng Ding worked on a Scilab module. Matevz Jekovec spent time on C++0x features. Ashish Sharma spent his summer on an Objective-C module, Miklos Vajna spent his time on PHP directors. In 2012, SWIG participated in Google Summer of Code. This time four out of five students successfully completed the project. Leif Middelschulte worked on a C target language module. Swati Sharma enhanced the Objective-C module. Neha Narang added the new module on JavaScript. Dmitry Kabak worked on source code documentation and Doxygen comments. == Alternatives == For Python, similar functionality is offered by SIP, Pybind11, and Boost's Boost.python library. == Projects using SWIG == ZXID (Apache License, Version 2.0) Symlabs SFIS (commercial) LLDB GNU Radio up to (including) version 3.8.x.x; later versions use Pybind11 Xapian TensorFlow Apache SINGA QuantLib Babeltrace

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  Best AI Clip Makers in 2026

  Trying to pick the best AI clip maker? An AI clip maker is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI clip maker 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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  Top 10 AI Text-to-video Tools Compared (2026)

  Trying to pick the best AI text-to-video tool? An AI text-to-video tool is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI text-to-video tool 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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  Corpus linguistics

  Corpus linguistics is an empirical method for the study of language by text corpus (plural corpora). Corpora are balanced, often stratified collections of authentic, "real world", text of speech or writing that aim to represent a given linguistic variety. Today, corpora are generally machine-readable data collections. Corpus linguistics proposes that a reliable analysis of a language is more feasible with corpora collected in the field—the natural context ("realia") of that language—with minimal experimental interference. Large collections of text, though corpora may also be small in terms of running words, allow linguists to run quantitative analyses on linguistic concepts that may be difficult to test in a qualitative manner. The text-corpus method uses the body of texts in any natural language to derive the set of abstract rules which govern that language. Those results can be used to explore the relationships between that subject language and other languages which have undergone a similar analysis. The first such corpora were manually derived from source texts, but now that work is automated. Corpora have not only been used for linguistics research, they have been increasingly used to compile dictionaries (starting with The American Heritage Dictionary of the English Language in 1969) and reference grammars, with A Comprehensive Grammar of the English Language, published in 1985, as a first. Experts in the field have differing views about the annotation of a corpus. These views range from John McHardy Sinclair, who advocates minimal annotation so texts speak for themselves, to the Survey of English Usage team (University College, London), who advocate annotation as allowing greater linguistic understanding through rigorous recording. == History == Some of the earliest efforts at grammatical description were based at least in part on corpora of particular religious or cultural significance. For example, Prātiśākhya literature described the sound patterns of Sanskrit as found in the Vedas, and Pāṇini's grammar of classical Sanskrit was based at least in part on analysis of that same corpus. Similarly, the early Arabic grammarians paid particular attention to the language of the Quran. In the Western European tradition, scholars prepared concordances to allow detailed study of the language of the Bible and other canonical texts. === English corpora === A landmark in modern corpus linguistics was the publication of Computational Analysis of Present-Day American English in 1967. Written by Henry Kučera and W. Nelson Francis, the work was based on an analysis of the Brown Corpus, which is a structured and balanced corpus of one million words of American English from the year 1961. The corpus comprises 2000 text samples, from a variety of genres. The Brown Corpus was the first computerized corpus designed for linguistic research. Kučera and Francis subjected the Brown Corpus to a variety of computational analyses and then combined elements of linguistics, language teaching, psychology, statistics, and sociology to create a rich and variegated opus. A further key publication was Randolph Quirk's "Towards a description of English Usage" in 1960 in which he introduced the Survey of English Usage. Quirk's corpus was the first modern corpus to be built with the purpose of representing the whole language. Shortly thereafter, Boston publisher Houghton-Mifflin approached Kučera to supply a million-word, three-line citation base for its new American Heritage Dictionary, the first dictionary compiled using corpus linguistics. The AHD took the innovative step of combining prescriptive elements (how language should be used) with descriptive information (how it actually is used). Other publishers followed suit. The British publisher Collins' COBUILD monolingual learner's dictionary, designed for users learning English as a foreign language, was compiled using the Bank of English. The Survey of English Usage Corpus was used in the development of one of the most important Corpus-based Grammars, which was written by Quirk et al. and published in 1985 as A Comprehensive Grammar of the English Language. The Brown Corpus has also spawned a number of similarly structured corpora: the LOB Corpus (1960s British English), Kolhapur (Indian English), Wellington (New Zealand English), Australian Corpus of English (Australian English), the Frown Corpus (early 1990s American English), and the FLOB Corpus (1990s British English). Other corpora represent many languages, varieties and modes, and include the International Corpus of English, and the British National Corpus, a 100 million word collection of a range of spoken and written texts, created in the 1990s by a consortium of publishers, universities (Oxford and Lancaster) and the British Library. For contemporary American English, work has stalled on the American National Corpus, but the 400+ million word Corpus of Contemporary American English (1990–present) is now available through a web interface. The first computerized corpus of transcribed spoken language was constructed in 1971 by the Montreal French Project, containing one million words, which inspired Shana Poplack's much larger corpus of spoken French in the Ottawa-Hull area. === Multilingual corpora === In the 1990s, many of the notable early successes on statistical methods in natural-language programming (NLP) occurred in the field of machine translation, due especially to work at IBM Research. These systems were able to take advantage of existing multilingual textual corpora that had been produced by the Parliament of Canada and the European Union as a result of laws calling for the translation of all governmental proceedings into all official languages of the corresponding systems of government. There are corpora in non-European languages as well. For example, the National Institute for Japanese Language and Linguistics in Japan has built a number of corpora of spoken and written Japanese. Sign language corpora have also been created using video data. === Ancient languages corpora === Besides these corpora of living languages, computerized corpora have also been made of collections of texts in ancient languages. An example is the Andersen-Forbes database of the Hebrew Bible, developed since the 1970s, in which every clause is parsed using graphs representing up to seven levels of syntax, and every segment tagged with seven fields of information. The Quranic Arabic Corpus is an annotated corpus for the Classical Arabic language of the Quran. This is a recent project with multiple layers of annotation including morphological segmentation, part-of-speech tagging, and syntactic analysis using dependency grammar. The Digital Corpus of Sanskrit (DCS) is a "Sandhi-split corpus of Sanskrit texts with full morphological and lexical analysis... designed for text-historical research in Sanskrit linguistics and philology." === Corpora from specific fields === Besides pure linguistic inquiry, researchers had begun to apply corpus linguistics to other academic and professional fields, such as the emerging sub-discipline of Law and Corpus Linguistics, which seeks to understand legal texts using corpus data and tools. The DBLP Discovery Dataset concentrates on computer science, containing relevant computer science publications with sentient metadata such as author affiliations, citations, or study fields. A more focused dataset was introduced by NLP Scholar, a combination of papers of the ACL Anthology and Google Scholar metadata. Corpora can also aid in translation efforts or in teaching foreign languages. == Methods == Corpus linguistics has generated a number of research methods, which attempt to trace a path from data to theory. Wallis and Nelson (2001) first introduced what they called the 3A perspective: Annotation, Abstraction and Analysis. Annotation consists of the application of a scheme to texts. Annotations may include structural markup, part-of-speech tagging, parsing, and numerous other representations. Abstraction consists of the translation (mapping) of terms in the scheme to terms in a theoretically motivated model or dataset. Abstraction typically includes linguist-directed search but may include e.g., rule-learning for parsers. Analysis consists of statistically probing, manipulating and generalising from the dataset. Analysis might include statistical evaluations, optimisation of rule-bases or knowledge discovery methods. Most lexical corpora today are part-of-speech-tagged (POS-tagged). However even corpus linguists who work with 'unannotated plain text' inevitably apply some method to isolate salient terms. In such situations annotation and abstraction are combined in a lexical search. The advantage of publishing an annotated corpus is that other users can then perform experiments on the corpus (through corpus managers). Linguists with other interests and differing perspectives than the originators' can exploit this work. By sharing data

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  Human image synthesis

  Human image synthesis is technology that can be applied to make believable and even photorealistic renditions of human-likenesses, moving or still. It has effectively existed since the early 2000s. Many films using computer generated imagery have featured synthetic images of human-like characters digitally composited onto the real or other simulated film material. Towards the end of the 2010s deep learning artificial intelligence has been applied to synthesize images and video that look like humans, without need for human assistance, once the training phase has been completed, whereas the old school 7D-route required massive amounts of human work. == Timeline of human image synthesis == In 1971 Henri Gouraud made the first CG geometry capture and representation of a human face. Modeling was his wife Sylvie Gouraud. The 3D model was a simple wire-frame model and he applied the Gouraud shader he is most known for to produce the first known representation of human-likeness on computer. The 1972 short film A Computer Animated Hand by Edwin Catmull and Fred Parke was the first time that computer-generated imagery was used in film to simulate moving human appearance. The film featured a computer simulated hand and face (watch film here). The 1976 film Futureworld reused parts of A Computer Animated Hand on the big screen. The 1983 music video for song Musique Non-Stop by German band Kraftwerk aired in 1986. Created by the artist Rebecca Allen, it features non-realistic looking, but clearly recognizable computer simulations of the band members. The 1994 film The Crow was the first film production to make use of digital compositing of a computer simulated representation of a face onto scenes filmed using a body double. Necessity was the muse as the actor Brandon Lee portraying the protagonist was tragically killed accidentally on-stage. In 1999 Paul Debevec et al. of USC captured the reflectance field of a human face with their first version of a light stage. They presented their method at the SIGGRAPH 2000 In 2003 audience debut of photo realistic human-likenesses in the 2003 films The Matrix Reloaded in the burly brawl sequence where up-to-100 Agent Smiths fight Neo and in The Matrix Revolutions where at the start of the end showdown Agent Smith's cheekbone gets punched in by Neo leaving the digital look-alike unnaturally unhurt. The Matrix Revolutions bonus DVD documents and depicts the process in some detail and the techniques used, including facial motion capture and limbal motion capture, and projection onto models. In 2003 The Animatrix: Final Flight of the Osiris a state-of-the-art want-to-be human likenesses not quite fooling the watcher made by Square Pictures. In 2003 digital likeness of Tobey Maguire was made for movies Spider-man 2 and Spider-man 3 by Sony Pictures Imageworks. In 2005 the Face of the Future project was an established. by the University of St Andrews and Perception Lab, funded by the EPSRC. The website contains a "Face Transformer", which enables users to transform their face into any ethnicity and age as well as the ability to transform their face into a painting (in the style of either Sandro Botticelli or Amedeo Modigliani). This process is achieved by combining the user's photograph with an average face. In 2009 Debevec et al. presented new digital likenesses, made by Image Metrics, this time of actress Emily O'Brien whose reflectance was captured with the USC light stage 5 Motion looks fairly convincing contrasted to the clunky run in the Animatrix: Final Flight of the Osiris which was state-of-the-art in 2003 if photorealism was the intention of the animators. In 2009 a digital look-alike of a younger Arnold Schwarzenegger was made for the movie Terminator Salvation though the end result was critiqued as unconvincing. Facial geometry was acquired from a 1984 mold of Schwarzenegger. In 2010 Walt Disney Pictures released a sci-fi sequel entitled Tron: Legacy with a digitally rejuvenated digital look-alike of actor Jeff Bridges playing the antagonist CLU. In SIGGGRAPH 2013 Activision and USC presented a real-time "Digital Ira" a digital face look-alike of Ari Shapiro, an ICT USC research scientist, utilizing the USC light stage X by Ghosh et al. for both reflectance field and motion capture. The end result both precomputed and real-time rendering with the modernest game GPU shown here and looks fairly realistic. In 2014 The Presidential Portrait by USC Institute for Creative Technologies in conjunction with the Smithsonian Institution was made using the latest USC mobile light stage wherein President Barack Obama had his geometry, textures and reflectance captured. In 2014 Ian Goodfellow et al. presented the principles of a generative adversarial network. GANs made the headlines in early 2018 with the deepfakes controversies. For the 2015 film Furious 7 a digital look-alike of actor Paul Walker who died in an accident during the filming was done by Weta Digital to enable the completion of the film. In 2016 techniques which allow near real-time counterfeiting of facial expressions in existing 2D video have been believably demonstrated. In 2016 a digital look-alike of Peter Cushing was made for the Rogue One film where its appearance would appear to be of same age as the actor was during the filming of the original 1977 Star Wars film. In SIGGRAPH 2017 an audio driven digital look-alike of upper torso of Barack Obama was presented by researchers from University of Washington. It was driven only by a voice track as source data for the animation after the training phase to acquire lip sync and wider facial information from training material consisting 2D videos with audio had been completed. Late 2017 and early 2018 saw the surfacing of the deepfakes controversy where porn videos were doctored using deep machine learning so that the face of the actress was replaced by the software's opinion of what another persons face would look like in the same pose and lighting. In 2018 Game Developers Conference Epic Games and Tencent Games demonstrated "Siren", a digital look-alike of the actress Bingjie Jiang. It was made possible with the following technologies: CubicMotion's computer vision system, 3Lateral's facial rigging system and Vicon's motion capture system. The demonstration ran in near real time at 60 frames per second in the Unreal Engine 4. In 2018 at the World Internet Conference in Wuzhen the Xinhua News Agency presented two digital look-alikes made to the resemblance of its real news anchors Qiu Hao (Chinese language) and Zhang Zhao (English language). The digital look-alikes were made in conjunction with Sogou. Neither the speech synthesis used nor the gesturing of the digital look-alike anchors were good enough to deceive the watcher to mistake them for real humans imaged with a TV camera. In September 2018 Google added "involuntary synthetic pornographic imagery" to its ban list, allowing anyone to request the search engine block results that falsely depict them as "nude or in a sexually explicit situation." In February 2019 Nvidia open sources StyleGAN, a novel generative adversarial network. Right after this Phillip Wang made the website ThisPersonDoesNotExist.com with StyleGAN to demonstrate that unlimited amounts of often photo-realistic looking facial portraits of no-one can be made automatically using a GAN. Nvidia's StyleGAN was presented in a not yet peer reviewed paper in late 2018. At the June 2019 CVPR the MIT CSAIL presented a system titled "Speech2Face: Learning the Face Behind a Voice" that synthesizes likely faces based on just a recording of a voice. It was trained with massive amounts of video of people speaking. Since 1 July 2019 Virginia has criminalized the sale and dissemination of unauthorized synthetic pornography, but not the manufacture., as § 18.2–386.2 titled 'Unlawful dissemination or sale of images of another; penalty.' became part of the Code of Virginia. The law text states: "Any person who, with the intent to coerce, harass, or intimidate, maliciously disseminates or sells any videographic or still image created by any means whatsoever that depicts another person who is totally nude, or in a state of undress so as to expose the genitals, pubic area, buttocks, or female breast, where such person knows or has reason to know that he is not licensed or authorized to disseminate or sell such videographic or still image is guilty of a Class 1 misdemeanor.". The identical bills were House Bill 2678 presented by Delegate Marcus Simon to the Virginia House of Delegates on 14 January 2019 and three-day later an identical Senate bill 1736 was introduced to the Senate of Virginia by Senator Adam Ebbin. Since 1 September 2019 Texas senate bill SB 751 amendments to the election code came into effect, giving candidates in elections a 30-day protection period to the elections during which making and distributing digital look-alikes or synthetic fakes of the candidates is an offense. Th

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  Regular language

  In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expression engines, which are augmented with features that allow the recognition of non-regular languages). Alternatively, a regular language can be defined as a language recognised by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after American mathematician Stephen Cole Kleene). In the Chomsky hierarchy, regular languages are the languages generated by Type-3 grammars. == Formal definition == The collection of regular languages over an alphabet Σ is defined recursively as follows: The empty language ∅ is a regular language. For each a ∈ Σ (a belongs to Σ), the singleton language {a} is a regular language. If A is a regular language, A (Kleene star) is a regular language. Due to this, the empty string language {ε} is also regular. If A and B are regular languages, then A ∪ B (union) and A • B (concatenation) are regular languages. No other languages over Σ are regular. See Regular expression § Formal language theory for syntax and semantics of regular expressions. == Examples == All finite languages are regular; in particular the empty string language {ε} = ∅ is regular. Other typical examples include the language consisting of all strings over the alphabet {a, b} which contain an even number of as, or the language consisting of all strings of the form: several as followed by several bs. A simple example of a language that is not regular is the set of strings {anbn | n ≥ 0}. Intuitively, it cannot be recognized with a finite automaton, since a finite automaton has finite memory and it cannot remember the exact number of a's. Techniques to prove this fact rigorously are given below. == Equivalent formalisms == A regular language satisfies the following equivalent properties: it is the language of a regular expression (by the above definition) it is the language accepted by a nondeterministic finite automaton (NFA) it is the language accepted by a deterministic finite automaton (DFA) it can be generated by a regular grammar it is the language accepted by an alternating finite automaton it is the language accepted by a two-way finite automaton it can be generated by a prefix grammar it can be accepted by a read-only Turing machine it can be defined in monadic second-order logic (Büchi–Elgot–Trakhtenbrot theorem) it is recognized by some finite syntactic monoid M, meaning it is the preimage {w ∈ Σ | f(w) ∈ S} of a subset S of a finite monoid M under a monoid homomorphism f : Σ → M from the free monoid on its alphabet the number of equivalence classes of its syntactic congruence is finite. (This number equals the number of states of the minimal deterministic finite automaton accepting L.) Properties 10. and 11. are purely algebraic approaches to define regular languages; a similar set of statements can be formulated for a monoid M ⊆ Σ. In this case, equivalence over M leads to the concept of a recognizable language. Some authors use one of the above properties different from "1." as an alternative definition of regular languages. Some of the equivalences above, particularly those among the first four formalisms, are called Kleene's theorem in textbooks. Precisely which one (or which subset) is called such varies between authors. One textbook calls the equivalence of regular expressions and NFAs ("1." and "2." above) "Kleene's theorem". Another textbook calls the equivalence of regular expressions and DFAs ("1." and "3." above) "Kleene's theorem". Two other textbooks first prove the expressive equivalence of NFAs and DFAs ("2." and "3.") and then state "Kleene's theorem" as the equivalence between regular expressions and finite automata (the latter said to describe "recognizable languages"). A linguistically oriented text first equates regular grammars ("4." above) with DFAs and NFAs, calls the languages generated by (any of) these "regular", after which it introduces regular expressions which it terms to describe "rational languages", and finally states "Kleene's theorem" as the coincidence of regular and rational languages. Other authors simply define "rational expression" and "regular expressions" as synonymous and do the same with "rational languages" and "regular languages". Apparently, the term regular originates from a 1951 technical report where Kleene introduced regular events and explicitly welcomed "any suggestions as to a more descriptive term". Noam Chomsky, in his 1959 seminal article, used the term regular in a different meaning at first (referring to what is called Chomsky normal form today), but noticed that his finite state languages were equivalent to Kleene's regular events. == Closure properties == The regular languages are closed under various operations, that is, if the languages K and L are regular, so is the result of the following operations: the set-theoretic Boolean operations: union K ∪ L, intersection K ∩ L, and complement L, hence also relative complement K − L. the regular operations: K ∪ L, concatenation ⁠ K ∘ L {\displaystyle K\circ L} ⁠, and Kleene star L. the trio operations: string homomorphism, inverse string homomorphism, and intersection with regular languages. As a consequence they are closed under arbitrary finite state transductions, like quotient K / L with a regular language. Even more, regular languages are closed under quotients with arbitrary languages: If L is regular then L / K is regular for any K. the reverse (or mirror image) LR. Given a nondeterministic finite automaton to recognize L, an automaton for LR can be obtained by reversing all transitions and interchanging starting and finishing states. This may result in multiple starting states; ε-transitions can be used to join them. == Decidability properties == Given two deterministic finite automata A and B, it is decidable whether they accept the same language. As a consequence, using the above closure properties, the following problems are also decidable for arbitrarily given deterministic finite automata A and B, with accepted languages LA and LB, respectively: Containment: is LA ⊆ LB ? Disjointness: is LA ∩ LB = {} ? Emptiness: is LA = {} ? Universality: is LA = Σ ? Membership: given a ∈ Σ, is a ∈ LB ? For regular expressions, the universality problem is NP-complete already for a singleton alphabet. For larger alphabets, that problem is PSPACE-complete. If regular expressions are extended to allow also a squaring operator, with "A2" denoting the same as "AA", still just regular languages can be described, but the universality problem has an exponential space lower bound, and is in fact complete for exponential space with respect to polynomial-time reduction. For a fixed finite alphabet, the theory of the set of all languages – together with strings, membership of a string in a language, and for each character, a function to append the character to a string (and no other operations) – is decidable, and its minimal elementary substructure consists precisely of regular languages. For a binary alphabet, the theory is called S2S. == Complexity results == In computational complexity theory, the complexity class of all regular languages is sometimes referred to as REGULAR or REG and equals DSPACE(O(1)), the decision problems that can be solved in constant space (the space used is independent of the input size). REGULAR ≠ AC0, since it (trivially) contains the parity problem of determining whether the number of 1 bits in the input is even or odd and this problem is not in AC0. On the other hand, REGULAR does not contain AC0, because the nonregular language of palindromes, or the nonregular language { 0 n 1 n : n ∈ N } {\displaystyle \{0^{n}1^{n}:n\in \mathbb {N} \}} can both be recognized in AC0. If a language is not regular, it requires a machine with at least Ω(log log n) space to recognize (where n is the input size). In other words, DSPACE(o(log log n)) equals the class of regular languages. In practice, most nonregular problems are studied in a setting with at least logarithmic space, as this is the amount of space required to store a pointer into the input tape. == Location in the Chomsky hierarchy == To locate the regular languages in the Chomsky hierarchy, one notices that every regular language is context-free. The converse is not true: for example, the language consisting of all strings having the same number of as as bs is context-free but not regular. To prove that a language is not regular, one often uses the Myhill–Nerode theorem and the pumping lemma. Other approaches include using the closure properties of regular languages or quantifying Kolmogorov complexity. Important subclasses of regular languages include: Finite languages, those containing only a finite number of words. These are regular la

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  Top 10 AI Marketing Tools Compared (2026)

  Comparing the best AI marketing tool? An AI marketing tool 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 marketing tool 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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  Michael I. Jordan

  Michael Irwin Jordan (born February 25, 1956) is an American scientist, professor at the University of California, Berkeley, research scientist at the Inria Paris, and researcher in machine learning, statistics, and artificial intelligence. Jordan was elected a member of the National Academy of Engineering in 2010 for contributions to the foundations and applications of machine learning. He is one of the leading figures in machine learning, and in 2016 Science reported him as the world's most influential computer scientist. In 2022, Jordan won the inaugural World Laureates Association Prize in Computer Science or Mathematics, "for fundamental contributions to the foundations of machine learning and its application." == Education == Jordan received a Bachelor of Science magna cum laude in psychology from the Louisiana State University in 1978, a Master of Science in mathematics from Arizona State University in 1980, and a Doctor of Philosophy in cognitive science from the University of California, San Diego in 1985. At UC San Diego, Jordan was a student of David Rumelhart and a member of the Parallel Distributed Processing (PDP) Group in the 1980s. == Career and research == Jordan is the Pehong Chen Distinguished Professor at the University of California, Berkeley, where his appointment is split across EECS and Statistics. He was a professor at the Department of Brain and Cognitive Sciences at MIT from 1988 to 1998. In the 1980s Jordan started developing recurrent neural networks as a cognitive model. In recent years, his work is less driven from a cognitive perspective and more from the background of traditional statistics. Jordan popularised Bayesian networks in the machine learning community and is known for pointing out links between machine learning and statistics. He was also prominent in the formalisation of variational methods for approximate inference and the popularisation of the expectation–maximization algorithm in machine learning. === Resignation from Machine Learning === In 2001, Jordan and others resigned from the editorial board of the journal Machine Learning. In a public letter, they argued for less restrictive access and pledged support for a new open access journal, the Journal of Machine Learning Research, which was created by Leslie Kaelbling to support the evolution of the field of machine learning. === Honors and awards === Jordan has received numerous awards, including a best student paper award (with X. Nguyen and M. Wainwright) at the International Conference on Machine Learning (ICML 2004), a best paper award (with R. Jacobs) at the American Control Conference (ACC 1991), the ACM-AAAI Allen Newell Award, the IEEE Neural Networks Pioneer Award, and an NSF Presidential Young Investigator Award. In 2002 he was named an AAAI Fellow "for significant contributions to reasoning under uncertainty, machine learning, and human motor control." In 2004 he was named an IMS Fellow "for contributions to graphical models and machine learning." In 2005 he was named an IEEE Fellow "for contributions to probabilistic graphical models and neural information processing systems." In 2007 he was named an ASA Fellow. In 2010 he was named a Cognitive Science Society Fellow and named an ACM Fellow "for contributions to the theory and application of machine learning." In 2012 he was named a SIAM Fellow "for contributions to machine learning, in particular variational approaches to statistical inference." In 2014 he was named an International Society for Bayesian Analysis Fellow "for his outstanding research contributions at the interface of statistics, computer sciences and probability, for his leading role in promoting Bayesian methods in machine learning, engineering and other fields, and for his extensive service to ISBA in many roles." Jordan is a member of the National Academy of Sciences, a member of the National Academy of Engineering and a member of the American Academy of Arts and Sciences. He has been named a Neyman Lecturer and a Medallion Lecturer by the Institute of Mathematical Statistics. He received the David E. Rumelhart Prize in 2015 and the ACM/AAAI Allen Newell Award in 2009. He also won the 2020 IEEE John von Neumann Medal. In 2016, Jordan was identified as the "most influential computer scientist", based on an analysis of the published literature by the Semantic Scholar project. In 2019, Jordan argued that the artificial intelligence revolution hasn't happened yet and that the AI revolution required a blending of computer science with statistics. In 2022, Jordan was awarded the inaugural World Laureates Association Prize by non-governmental and non-profit international organization World Laureates Association, for fundamental contributions to the foundations of machine learning and its application. For 2024 he received the BBVA Foundation Frontiers of Knowledge Award in the category of "Information and Communication Technologies".

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  Kleene star

  In formal language theory, the Kleene star (or Kleene operator or Kleene closure) refers to two related unary operations, that can be applied either to an alphabet of symbols or to a formal language, a set of strings (finite sequences of symbols). The Kleene star operator on an alphabet V generates the set V of all finite-length strings over V, that is, finite sequences whose elements belong to V; in mathematics, it is more commonly known as the free monoid construction. The Kleene star operator on a language L generates another language L, the set of all strings that can be obtained as a concatenation of zero or more members of L. In both cases, repetitions are allowed. The Kleene star operators are named after American mathematician Stephen Cole Kleene, who first introduced and widely used it to characterize automata for regular expressions. == Of an alphabet == Given an alphabet V {\displaystyle V} , define V 0 = { ε } {\displaystyle V^{0}=\{\varepsilon \}} (the set consists only of the empty string), V 1 = V , {\displaystyle V^{1}=V,} and define recursively the set V i + 1 = { w v : w ∈ V i and v ∈ V } {\displaystyle V^{i+1}=\{wv:w\in V^{i}{\text{ and }}v\in V\}} for each i > 0 , {\displaystyle i>0,} where w v {\displaystyle wv} denotes the string obtained by appending the single character v {\displaystyle v} to the end of w {\displaystyle w} . Here, V i {\displaystyle V^{i}} can be understood to be the set of all strings of length exactly i {\displaystyle i} , with characters from V {\displaystyle V} . The definition of Kleene star on V {\displaystyle V} is V ∗ = ⋃ i ≥ 0 V i = V 0 ∪ V 1 ∪ V 2 ∪ V 3 ∪ V 4 ∪ ⋯ . {\displaystyle V^{}=\bigcup _{i\geq 0}V^{i}=V^{0}\cup V^{1}\cup V^{2}\cup V^{3}\cup V^{4}\cup \cdots .} == Of a language == Given a language L {\displaystyle L} (any finite or infinite set of strings), define L 0 = { ε } {\displaystyle L^{0}=\{\varepsilon \}} (the language consisting only of the empty string), L 1 = L , {\displaystyle L^{1}=L,} and define recursively the set L i + 1 = { w v : w ∈ L i and v ∈ L } {\displaystyle L^{i+1}=\{wv:w\in L^{i}{\text{ and }}v\in L\}} for each i > 0 , {\displaystyle i>0,} where w v {\displaystyle wv} denotes the string obtained by concatenating w {\displaystyle w} and v {\displaystyle v} . Here, L i {\displaystyle L^{i}} can be understood to be the set of all strings that can be obtained by concatenating exactly i {\displaystyle i} strings from L {\displaystyle L} , allowing repetitions. The definition of Kleene star on L {\displaystyle L} is L ∗ = ⋃ i ≥ 0 L i = L 0 ∪ L 1 ∪ L 2 ∪ L 3 ∪ L 4 ∪ ⋯ . {\displaystyle L^{}=\bigcup _{i\geq 0}L^{i}=L^{0}\cup L^{1}\cup L^{2}\cup L^{3}\cup L^{4}\cup \cdots .} == Kleene plus == In some formal language studies, (e.g. AFL theory) a variation on the Kleene star operation called the Kleene plus is used. The Kleene plus omits the V 0 {\displaystyle V^{0}} or L 0 {\displaystyle L^{0}} term in the above unions. In other words, the Kleene plus on V {\displaystyle V} is V + = ⋃ i ≥ 1 V i = V 1 ∪ V 2 ∪ V 3 ∪ ⋯ , {\displaystyle V^{+}=\bigcup _{i\geq 1}V^{i}=V^{1}\cup V^{2}\cup V^{3}\cup \cdots ,} or V + = V ∗ V . {\displaystyle V^{+}=V^{}V.} == Examples == Example of Kleene star applied to a set of strings: {"ab","c"} = { ε, "ab", "c", "abab", "abc", "cab", "cc", "ababab", "ababc", "abcab", "abcc", "cabab", "cabc", "ccab", "ccc", ...}. Example of Kleene star applied to a set of strings without the prefix property: {"a","ab","b"} = { ε, "a", "ab", "b", "aa", "aab", "aba", "abab", "abb", "ba", "bab", "bb", ...};In this example, the string "aab" can be obtained in two different ways. The Sardinas-Patterson algorithm can be used to check for a given V whether any member of V can be obtained in more than one way. Example of Kleene and Kleene plus applied to a set of characters (following the C programming language convention where a character is denoted by single quotes and a string is denoted by double quotes): {'a', 'b', 'c'} = { ε, "a", "b", "c", "aa", "ab", "ac", "ba", "bb", "bc", "ca", "cb", "cc", "aaa", "aab", ...}. {'a', 'b', 'c'}+ = { "a", "b", "c", "aa", "ab", "ac", "ba", "bb", "bc", "ca", "cb", "cc", "aaa", "aab", ...}. == Properties == If V {\displaystyle V} is any finite or countably infinite set of characters, then V ∗ {\displaystyle V^{}} is a countably infinite set. As a result, each formal language over a finite or countably infinite alphabet Σ {\displaystyle \Sigma } is countable, since it is a subset of the countably infinite set Σ ∗ {\displaystyle \Sigma ^{}} . ( L ∗ ) ∗ = L ∗ {\displaystyle (L^{})^{}=L^{}} , which means that the Kleene star operator is an idempotent unary operator, as ( L ∗ ) i = L ∗ {\displaystyle (L^{})^{i}=L^{}} for every i ≥ 1 {\displaystyle i\geq 1} . V ∗ = { ε } {\displaystyle V^{}=\{\varepsilon \}} , if V {\displaystyle V} is the empty set ∅. For the version of the Kleene star operator on languages, L ∗ = { ε } {\displaystyle L^{}=\{\varepsilon \}} when L {\displaystyle L} is either the empty set ∅ or the singleton set { ε } {\displaystyle \{\varepsilon \}} . == Generalization == Strings form a monoid with concatenation as the binary operation and ε the identity element. In addition to strings, the Kleene star is defined for any monoid. More precisely, let (M, ⋅) be a monoid, and S ⊆ M. Then S is the smallest submonoid of M containing S; that is, S contains the neutral element of M, the set S, and is such that if x,y ∈ S, then x⋅y ∈ S. Furthermore, the Kleene star is generalized by including the -operation (and the union) in the algebraic structure itself by the notion of complete star semiring.

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  Lingoes

  Lingoes is a dictionary and machine translation app. Lingoes was created in China. Lingoes is often compared to its competitor Babylon because of similarities in their GUI, functionalities and most importantly being freeware. == Features and expandability == Dictionaries and encyclopedias can be installed on Lingoes in the form of new add-ons to extend its functionality. Add-ons for Wikipedia, Baidu Baike, Longman Dictionary of Contemporary English, Merriam-Webster's Collegiate Dictionary, WordNet, MacMillan English Dictionary, Collins English Dictionary and other cross-English dictionaries (e.g. Arabic, French or German) are available in Lingoes' official website. The program has the ability to pronounce words and install additional text-to-speech engines available for download also through Lingoes' website. Lingoes also offers a whole-text translation ability using online translation service providers like Google Translate, Yahoo! Babel Fish Translation, SYSTRAN, Cross-Language, Click2Translate, and others. Lingoes offers to translate a text via a mouse-over popup, or by double-clicking the selected text. Additional tools, termed as appendices in the program, include a currency converter, weights and measure units converter and international time zones converter. Additional ones, such as the periodic table of elements, a scientific calculator, Traditional Chinese and Simplified Chinese conversion utility or a Base64 encoding utility, can be added through the website.

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  Cobham's theorem

  Cobham's theorem is a theorem in combinatorics on words that has important connections with number theory, notably transcendental numbers, and automata theory. Informally, the theorem gives the condition for the members of a set S of natural numbers written in bases b1 and base b2 to be recognised by finite automata. Specifically, consider bases b1 and b2 such that they are not powers of the same integer. Cobham's theorem states that S written in bases b1 and b2 is recognised by finite automata if and only if S differs by a finite set from a finite union of arithmetic progressions. The theorem was proved by Alan Cobham in 1969 and has since given rise to many extensions and generalisations. == Definitions == Let n > 0 {\displaystyle n>0} be an integer. The representation of a natural number n {\textstyle n} in base b {\textstyle b} is the sequence of digits n 0 n 1 ⋯ n h {\displaystyle n_{0}n_{1}\cdots n_{h}} such that n = n 0 + n 1 b + ⋯ + n h b h {\displaystyle n=n_{0}+n_{1}b+\cdots +n_{h}b^{h}} where 0 ≤ n 0 , n 1 , … , n h < b {\displaystyle 0\leq n_{0},n_{1},\ldots ,n_{h} 0 {\displaystyle n_{h}>0} . The word n 0 n 1 ⋯ n h {\displaystyle n_{0}n_{1}\cdots n_{h}} is often denoted ⟨ n ⟩ b {\displaystyle \langle n\rangle _{b}} , or more simply, n b {\displaystyle n_{b}} . A set of natural numbers S is recognisable in base b {\textstyle b} or more simply b {\textstyle b} -recognisable or b {\textstyle b} -automatic if the set { n b ∣ n ∈ S } {\displaystyle \{n_{b}\mid n\in S\}} of the representations of its elements in base b {\displaystyle b} is a language recognisable by a finite automaton on the alphabet { 0 , 1 , … , b − 1 } {\displaystyle \{0,1,\ldots ,b-1\}} . Two positive integers k {\displaystyle k} and ℓ {\displaystyle \ell } are multiplicatively independent if there are no non-negative integers p {\displaystyle p} and q {\displaystyle q} such that k p = ℓ q {\displaystyle k^{p}=\ell ^{q}} . For example, 2 and 3 are multiplicatively independent, but 8 and 16 are not since 8 4 = 16 3 {\displaystyle 8^{4}=16^{3}} . Two integers are multiplicatively dependent if and only if they are powers of a same third integer. == Problem statements == === Original problem statement === More equivalent statements of the theorem have been given. The original version by Cobham is the following: Another way to state the theorem is by using automatic sequences. Cobham himself calls them "uniform tag sequences." The following form is found in Allouche and Shallit's book:We can show that the characteristic sequence of a set of natural numbers S recognisable by finite automata in base k is a k-automatic sequence and that conversely, for all k-automatic sequences u {\displaystyle u} and all integers 0 ≤ i < k {\displaystyle 0\leq i 1 {\displaystyle \alpha >1} is the dominant eigenvalue of the matrix of morphism f {\displaystyle f} , namely, the matrix M ( f ) = ( m x , y ) x ∈ B , y ∈ A {\displaystyle M(f)=(m_{x,y})_{x\in B,y\in A}} , where m x , y {\displaystyle m_{x,y}} is the number of occurrences of the letter x {\displaystyle x} in the word f ( y ) {\displaystyle f(y)} . A set S of natural numbers is α {\displaystyle \alpha } -recognisable if its characteristic sequence s {\displaystyle s} is α {\displaystyle \alpha } -substitutive. A last definition: a Perron number is an algebraic number z > 1 {\displaystyle z>1} such that all its conjugates belong to the disc { z ′ ∈ C , | z ′ | < z } {\displaystyle \{z'\in \mathbb {C} ,|z'| Read more →

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  Bob Coecke

  Bob Coecke (born 23 July 1968) is a Belgian theoretical physicist and logician. He was Professor of Quantum foundations, Logics, and Structures at Oxford University until 2020. He was Chief Scientist at quantum computing company Quantinuum, until 2025 and founded a startup called Relational Intelligence in 2026. He is also Distinguished Visiting Research Chair at the Perimeter Institute for Theoretical Physics, and Emeritus Fellow at Wolfson College, Oxford. He pioneered categorical quantum mechanics (entry 18M40 in Mathematics Subject Classification 2020), Quantum Picturalism, ZX-calculus, DisCoCat model for natural language,, quantum natural language processing (QNLP) and quantum education through the book Quantum in Pictures. He is a founder of the Quantum Physics and Logic community and the Applied Category Theory communities and conference series, and of the journal Compositionality. Coecke is also a composer and musician, who has been called a pioneer of industrial music, and is also one of the pioneers of employing quantum computers in music. == Education and career == Coecke obtained his doctorate in sciences at the Vrije Universiteit Brussel in 1996, and performed postdoctoral work in the Theoretical Physics Group of Imperial College, London in the Category Theory Group of the Mathematics and Statistics Department at McGill University in Montreal, in the Department of Pure Mathematics and Mathematical Statistics of Cambridge University, and in the Department of Computer Science, University of Oxford. He was an EPSRC Advanced Research Fellow at the Department of Computer Science, University of Oxford, where he became Lecturer in Quantum Computer Science in 2007, and jointly with Samson Abramsky built and headed the Quantum Group. In July 2011, he was nominated professor of Quantum Foundations, Logics and Structures at Oxford University, with retroactive effect as of October 2010. He was a Governing Body Fellow of Wolfson College, Oxford since 2007, where he now is an Emeritus Fellow. In January 2019, Coecke became Senior Scientific Advisor of Cambridge Quantum Computing, and in January 2021 he resigned from his Professorship at Oxford, to become Chief Scientist of Cambridge Quantum Computing. After the merger of Cambridge Quantum Computing with Honeywell Quantum Systems, he stayed on as Chief Scientist of the joint entity Quantinuum until 2025. In January 2023 he also became Distinguished Visiting Research Chair at the Perimeter Institute for Theoretical Physics. == Work == Coecke's research focuses on the foundations of physics, more particularly category theory, logic, and diagrammatic reasoning, with application to quantum informatics, quantum gravity, and NLP. He has pioneered categorical quantum mechanics together with Samson Abramsky, and spearheaded the development of a diagrammatic quantum formalism based on Penrose graphical notation, on which he wrote a textbook entitled Picturing Quantum Processes with Aleks Kissinger. With Ross Duncan he pioneered ZX-calculus. He pioneered the DisCoCat model for natural language, with Stephen Clark and Mehrnoosh Sadrzadeh. He also pioneered quantum natural language processing (QNLP), with Will Zeng, and colleagues at Cambridge Quantum Computing. == Music == Coecke is also a musician, performing and recording since the eighties. He retrospectively has been named a pioneer of industrial music. His band, Black Tish, "used cutting edge sampling techniques for the time, a host of synth and sound loops and metal-style guitars to create a heavy rock/electronica fusion unlike anything heard before", and "bridge the gap between the pure experimental nature of bands like Throbbing Gristle and Einstürzende Neubauten and the (comparatively) more radio accessible Ministry or Nine Inch Nails". Coecke is also one of the pioneers of employing quantum computers in music. == Selected publications == Textbooks Bob Coecke, Aleks Kissinger:Picturing Quantum Processes. A First Course in Quantum Theory and Diagrammatic Reasoning, Cambridge University Press, 2017, ISBN 978-1316219317 Bob Coecke, Stefano Gogioso:Quantum in Pictures, Quantinuum, 2022, ISBN 978-1-7392147-1-5 Books (as editor) Bob Coecke, David Moore, Alexander Wilce (eds.): Current Research in Operational Quantum Logic: Algebras, Categories, Languages, Fundamental Theories of Physics, Kluwer Academic, 2010, ISBN 978-9048154371 Bob Coecke (ed.): New Structures for Physics, Lecture Notes in Physics 813, Springer, 2011, ISBN 978-3642128202 Articles Bob Coecke: Kindergarten quantum mechanics, arXiv:quant-ph/0510032 Samson Abramsky, Bob Coecke: A categorical semantics of quantum protocols, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004, pp. 415–425 Bob Coecke, Ross Duncan: Interacting quantum observables, Automata, Languages and Programming, pp. 298–310, 2008 Konstantinos Meichanetzidis, Alexis Toumi, Giovanni de Felice, Bob Coecke: Grammar-Aware Question-Answering on Quantum Computers, arXiv:2012.03756 Bob Coecke: The Mathematics of Text Structure, arXiv:1904.03478 Will Zeng, Bob Coecke: Quantum Algorithms for Compositional Natural Language Processing, arXiv:1608.01406 Bob Coecke, Tobias Fritz, Robert Spekkens: A mathematical theory of resources, arXiv:1409.5531 Bob Coecke: An Alternative Gospel of structure: order, composition, processes, arxiv:1307.4038 Bob Coecke, Mehrnoosh Sadrzadeh, Steven Clark: Mathematical Foundations for a Compositional Distributional Model of Meaning, arXiv:1003.4394 Bob Coecke: Quantum Picturalism, arXiv:0908.1787 Software articles Eduardo Reck Miranda, Richie Yeung, Anna Pearson, Konstantinos Meichanetzidis, Bob Coecke: A quantum natural language processing approach to musical intelligence, arXiv:2111.06741 Dimitri Kartsaklis, Ian Fan, Richie Yeung, Anna Pearson, Robin Lorenz, Alexis Toumi, Giovanni de Felice, Konstantinos Meichanetzidis, Stephen Clark, Bob Coecke: lambeq: An efficient high-level python library for quantum NLP, arXiv:2110.04236 Giovanni de Felice, Alexis Toumi, Bob Coecke: Discopy: monoidal categories in Python, arXiv:2111.06741

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  Avid DS

  Avid DS (which was called Avid DS Nitris until early 2008) is a high-end offline and finishing system comprising a non-linear editing system and visual effects software. It was developed by Softimage (this company was owned by Microsoft at the time of DS v1.0's launch before being acquired from Microsoft by Avid Technology, Inc. shortly thereafter) in Montreal. DS was discontinued on September 30, 2013 with support ending on the same date the following year. == Software == DS was called ‘Digital Studio’ in development. It was envisioned to be a complete platform for video/audio work. The first previews of the system were on the SGI platform, but this version was never released. The system was rewritten on Windows NT with different video hardware platforms (Matrox DigiSuite or Play Trinity running on a NetPower system) before the final system was released on Intergraph/StudioZ hardware in January 1998. After its acquisition by Avid, DS was always positioned as a high end video finishing tool. However, many users found it to be uniquely soup-to-nuts in its capabilities. From version 1.0 of the product, it competed with products like Autodesk Smoke, Quantel and Avid Symphony. The toolset in DS offered video timeline editing, an object-oriented vector-based paint tool, 2D layer compositing, sample based audio and starting with version 3.01 of the product, a 3D environment. Originally, a subset of the Softimage|XSI 3D software was planned to become part of the DS toolset, both were built on the same software foundation, but over time the code bases divided between the applications and the integration never happened. While the first version of the DS still lacked a few key features (no 3D, poor keying, no real-time effects), it had some significant features compared to the competing products at the time. It offered a large number of built in effects. Avid OMF import was available, positioning Softimage DS as a strong finishing tool for then typical off-line Avid systems. Lastly the integration of the toolset of Softimage DS was beyond what other product offered. A Softimage DS user could quickly go from editing, to paint, to compositing with a few mouse clicks all inside the same interface. Some of the lacking features were quickly resolved, within months of version 1.0 a new chroma keyer was released. Early versions of the software (up thru 4.0) added additional key features. Development continued with one of the first uncompressed HD editing systems (version 4.01) and an attempt to make the system more friendly to Media Composer editors in version 6. In later versions (v7.5 on beyond) DS was criticized for slow development of compositing tools, mainly lack of a new 3D environment and better tracking tools. Many DS users felt that Avid had not been giving DS the attention that it deserved. On July 7, 2013, Avid sent out an email marking the end of life of the DS product. "To Our Avid DS customers, We are writing to inform you that Avid will be realigning our business strategy to focus on a core suite of products to best leverage our developmental and creative resources. As part of this transition, we will be ceasing future development of Avid DS with a final sale date of September 30th, 2013" == Hardware == Up until version 10.5, DS was sold as a turn-key system; the software was not available without purchasing CPU, I/O and storage hardware from Avid. Beginning with 10.5, customers were able to configure their own systems using widely available components, based on recommended system requirements. In turn-key systems, there were many hardware refreshes over time. StudioZ single stream: Intergraph TDZ-425 with 30 minutes of uncompressed SCSI storage. CPUs at the time were Pentium II/300 MHz. StudioZ dual stream: Intergraph TDZ-2000 GT1 with one hour of fibre channel storage. CPUs on first systems were Pentium II/400 MHz, but last shipping systems had Pentium III/1 GHz. DS was one of the first applications to show that real-time effects could be processed with just the CPUs of the system, not requiring special video cards with real-time effect hardware. Equinox: Developed by Avid, it was one of the first uncompressed HD video cards available. Systems were available on CPUs from Pentium III/1 GHz to Pentium 4/2.8 GHz. Storage was typically SCSI, but fibre channel was also supported. Nitris DNA: Developed by Avid, the Nitris hardware was probably the largest hardware update to the system since it was released. 10-bit HD and SD support was standard. Real-time down and cross convert. This was the only hardware for DS that had on-board effect processing. This allowed a system at the time to play back dual-stream uncompressed HD effects in real-time at 16-bit precision. This was also the first hardware from Avid to support the DNxHD codec. Starting with Pentium 4, Intel Core Xeons were supported. SCSI storage was primarily used. AJA Video Systems: First available as a 4:4:4 option to be used in conjunction with Nitris hardware. Final-generation DS systems used the AJA Video Systems Kona 3 (Xena 2K) card as the only I/O for the system. The last systems shipped with two Intel Core Xeon 6-core processors. SAS is the recommended storage for these systems. == History ==

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  Barbara Di Eugenio

  Barbara Di Eugenio is an Italian-American computer scientist, the Collegiate Warren S. McCulloch Professor of Computer Science at the University of Illinois Chicago. Her research focuses on natural language processing and its applications to human–computer interaction, educational technology, and artificial intelligence in healthcare. == Education and career == Di Eugenio is originally from Turin. After an undergraduate education in Italy, she completed her Ph.D. in computer and information science in 1993 at the University of Pennsylvania. Her dissertation, Understanding Natural Language Instructions: A Computational Approach to Purpose Clauses, was supervised by Bonnie Webber. She became a faculty member at the University of Illinois Chicago in 1999, and at that time was the only woman faculty member in the Department of Electrical Engineering and Computer Science. == Recognition == In 2022, Di Eugenio received the Zenith Award of the Association for Women in Science. She was named as a Fellow of the Association for Computational Linguistics in 2023, "for outstanding contributions to natural language generation; intelligent tutoring systems; discourse; intercoder agreement; and applying multimodal interactive systems to health".

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  Pachinko allocation

  In machine learning and natural language processing, the pachinko allocation model (PAM) is a topic model. Topic models are a suite of algorithms to uncover the hidden thematic structure of a collection of documents. The algorithm improves upon earlier topic models such as latent Dirichlet allocation (LDA) by modeling correlations between topics in addition to the word correlations which constitute topics. PAM provides more flexibility and greater expressive power than latent Dirichlet allocation. While first described and implemented in the context of natural language processing, the algorithm may have applications in other fields such as bioinformatics. The model is named for pachinko machines—a game popular in Japan, in which metal balls bounce down around a complex collection of pins until they land in various bins at the bottom. == History == Pachinko allocation was first described by Wei Li and Andrew McCallum in 2006. The idea was extended with hierarchical Pachinko allocation by Li, McCallum, and David Mimno in 2007. In 2007, McCallum and his colleagues proposed a nonparametric Bayesian prior for PAM based on a variant of the hierarchical Dirichlet process (HDP). The algorithm has been implemented in the MALLET software package published by McCallum's group at the University of Massachusetts Amherst. == Model == PAM connects words in V and topics in T with an arbitrary directed acyclic graph (DAG), where topic nodes occupy the interior levels and the leaves are words. The probability of generating a whole corpus is the product of the probabilities for every document: P ( D | α ) = ∏ d P ( d | α ) {\displaystyle P(\mathbf {D} |\alpha )=\prod _{d}P(d|\alpha )}

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