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  Israeli cybersecurity industry

  The Israeli cybersecurity industry is a rapidly growing sector within Israel's technology and innovation ecosystem. Israel is internationally recognized as a powerhouse in the cybersecurity domain, with numerous cybersecurity startups, established companies, research institutions, and government initiatives. Tel Aviv itself is being ranked 7th in annual list of best global tech ecosystems, as reported by the Jerusalem Post. == History == The roots of Israel's cybersecurity industry can be traced back to the country's strong focus on national security and intelligence. The establishment of elite military units such as Unit 8200, the Israeli Intelligence Corps unit responsible for signals intelligence and code decryption, played a significant role in the development of cybersecurity expertise in the country. Many former members of Unit 8200 have gone on to establish successful cybersecurity companies or join existing organizations, bringing their unique skill sets and experience to the private sector. == Market overview == As of 2024, Israel housed more than 450 cybersecurity startups and companies. In 2023, the value of exits by Israeli tech companies reached $7.5 billion. Israel's cybersecurity industry is characterized by a high concentration of startups develop new technologies in areas such as network security, endpoint protection, data security, cloud security, and threat intelligence. In recent years, the sector has attracted significant investment from both local and international venture capital firms, as well as major technology companies such as Microsoft, Google, and IBM. Several Israeli cybersecurity companies have gained global recognition and success, with some being acquired by major corporations or conducting successful initial public offerings (IPOs). === Key Israeli cybersecurity companies === Some key Israeli cybersecurity companies include: Check Point Software Technologies CyberArk Cato Networks Radware Wiz === Financial activity === Israel’s cybersecurity sector has seen significant financial activity. As of 2023, mergers and acquisitions in the cybersecurity sector totaled $2.8 billion. In the first quarter of 2024, the sector secured $846 million in private funding. == Background == The military experience helped much. Israel's mandatory military service, combined with the expertise developed within elite units such as Unit 8200, has fostered a strong talent pool with practical experience in cybersecurity. Israel's thriving startup ecosystem, often referred to as the "Startup Nation," has fostered an environment of innovation and collaboration that has contributed to the growth of the cybersecurity industry. Israeli cybersecurity companies often collaborate with international partners, both in the private and public sectors, to share knowledge and develop joint solutions. === Government Initiatives and Support === The government also supported well through various initiatives, such as the Israel National Cyber Directorate (INCD), which works to strengthen cybersecurity defenses and promote the development of the sector. === Academic institutions === Israeli universities and research centers are involved in cybersecurity research and education, contributing to the development of new technologies and training the next generation of cybersecurity professionals. Academic Tech transfer offices in Israel also facilitate the commercialization of cybersecurity technologies. Some academic institutions with cybersecurity laboratories include: Tel Aviv University Technion Ben-Gurion University

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  Chai AI

  Chai AI (also known as Chai Research) is an American artificial intelligence (AI) company that operates a chatbot platform where users can create, share, and interact with character-based chatbots powered by large language models (LLMs). The company is headquartered in Palo Alto, California. == History == Chai was founded in 2021 by William Beauchamp, a former quantitative trader educated at Cambridge, who began developing the initial prototype in 2020 in Cambridge, England. The company launched in 2021 and relocated to Palo Alto in 2022. In June 2023, Chai raised US$2 million in a pre-seed funding round. In September 2023, GPU cloud provider CoreWeave invested in the company at a valuation of US$450 million. In January 2024, Chai Research reported a $450 million valuation following an investment from cloud computing provider CoreWeave. In July 2024, authorities in Belgium launched an investigation into the company following reports of a man dying by suicide following extensive chats on the Chai app. == Reception == In 2025, Chai Research announced that their app had over 10 million downloads and 1 million daily active users. In 2022, Canadian writer Sheila Heti published her conversations with various chatbots in The Paris Review, including Chai AI chatbots, and later used Chai AI chatbots in the development of a novel. Heti said that she had found that Chai's default chatbot, Eliza, "had turned out to be like most of the other bots on the site—primarily interested in sex". In January 2026, CHAI introduced country-based blocks on its free, ad-supported tier, initially providing the community with little information and inaccurate lists of the affected countries. Users in "Low tier" regions are required to subscribe to use the app in any capacity, while "High tier" regions will retain free ad-supported access. In response to backlash, the company announced a "Basic" tier with unlimited messages and ads, intended to cover electricity and infrastructure costs. In February 2026, CHAI was criticized for the unannounced implementation of restrictive "token limits" that abruptly blocked messages and froze conversations for both free and paid subscribers. Users generating long responses or utilizing roleplay features found their quotas exhausted within minutes, resulting in lockouts lasting anywhere from a few hours to a week. == Technology == Chai allows users to create characters and interact with chatbot versions of those characters. These chatbots use the open-source large language model (LLM) GPT-J originally developed by EleutherAI. Chai AI chatbots can be shared on the platform for other users to interact with.

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  Spell checker

  In software, a spell checker (or spelling checker or spell check) is a software feature that checks for misspellings in a text. Spell-checking features are often embedded in software or services, such as a word processor, email client, electronic dictionary, or search engine. == Design == A basic spell checker carries out the following processes: It scans the text and extracts the words contained in it. It then compares each word with a known list of correctly spelled words (i.e. a dictionary). This might contain just a list of words, or it might also contain additional information, such as hyphenation points or lexical and grammatical attributes. An additional step is a language-dependent algorithm for handling morphology. Even for a lightly inflected language like English, the spell checker will need to consider different forms of the same word, such as plurals, verbal forms, contractions, and possessives. For many other languages, such as those featuring agglutination and more complex declension and conjugation, this part of the process is more complicated. It is unclear whether morphological analysis—allowing for many forms of a word depending on its grammatical role—provides a significant benefit for English, though its benefits for highly synthetic languages such as German, Hungarian, or Turkish are clear. As an adjunct to these components, the program's user interface allows users to approve or reject replacements and modify the program's operation. Spell checkers can use approximate string matching algorithms such as Levenshtein distance to find correct spellings of misspelled words. An alternative type of spell checker uses solely statistical information, such as n-grams, to recognize errors instead of correctly-spelled words. This approach usually requires a lot of effort to obtain sufficient statistical information. Key advantages include needing less runtime storage and the ability to correct errors in words that are not included in a dictionary. In some cases, spell checkers use a fixed list of misspellings and suggestions for those misspellings; this less flexible approach is often used in paper-based correction methods, such as the see also entries of encyclopedias. Clustering algorithms have also been used for spell checking combined with phonetic information. == History == === Pre-PC === In 1961, Les Earnest, who headed the research on this budding technology, saw it necessary to include the first spell checker that accessed a list of 10,000 acceptable words. Ralph Gorin, a graduate student under Earnest at the time, created the first true spelling checker program written as an applications program (rather than research) for general English text: SPELL for the DEC PDP-10 at Stanford University's Artificial Intelligence Laboratory, in February 1971. Gorin wrote SPELL in assembly language, for faster action; he made the first spelling corrector by searching the word list for plausible correct spellings that differ by a single letter or adjacent letter transpositions and presenting them to the user. Gorin made SPELL publicly accessible, as was done with most SAIL (Stanford Artificial Intelligence Laboratory) programs, and it soon spread around the world via the new ARPAnet, about ten years before personal computers came into general use. SPELL, its algorithms and data structures inspired the Unix ispell program. The first spell checkers were widely available on mainframe computers in the late 1970s. A group of six linguists from Georgetown University developed the first spell-check system for the IBM corporation. Henry Kučera invented one for the VAX machines of Digital Equipment Corp in 1981. === Unix === The International Ispell program commonly used in Unix is based on R. E. Gorin's SPELL. It was converted to C by Pace Willisson at MIT. The GNU project has its spell checker GNU Aspell. Aspell's main improvement is that it can more accurately suggest correct alternatives for misspelled English words. Due to the inability of traditional spell checkers to check words in complex inflected languages, Hungarian László Németh developed Hunspell, a spell checker that supports agglutinative languages and complex compound words. Hunspell also uses Unicode in its dictionaries. Hunspell replaced the previous MySpell in OpenOffice.org in version 2.0.2. Enchant is another general spell checker, derived from AbiWord. Its goal is to combine programs supporting different languages such as Aspell, Hunspell, Nuspell, Hspell (Hebrew), Voikko (Finnish), Zemberek (Turkish) and AppleSpell under one interface. === PCs === The first spell checkers for personal computers appeared in 1980, such as "WordCheck" for Commodore systems which was released in late 1980 in time for advertisements to go to print in January 1981. Developers such as Maria Mariani and Random House rushed OEM packages or end-user products into the rapidly expanding software market. On the pre-Windows PCs, these spell checkers were standalone programs, many of which could be run in terminate-and-stay-resident mode from within word-processing packages on PCs with sufficient memory. However, the market for standalone packages was short-lived, as by the mid-1980s developers of popular word-processing packages like WordStar and WordPerfect had incorporated spell checkers in their packages, mostly licensed from the above companies, who quickly expanded support from just English to many European and eventually even Asian languages. However, this required increasing sophistication in the morphology routines of the software, particularly with regard to heavily-agglutinative languages like Hungarian and Finnish. Although the size of the word-processing market in a country like Iceland might not have justified the investment of implementing a spell checker, companies like WordPerfect nonetheless strove to localize their software for as many national markets as possible as part of their global marketing strategy. When Apple developed "a system-wide spelling checker" for Mac OS X so that "the operating system took over spelling fixes," it was a first: one "didn't have to maintain a separate spelling checker for each" program. Mac OS X's spellcheck coverage includes virtually all bundled and third party applications. Visual Tools' VT Speller, introduced in 1994, was "designed for developers of applications that support Windows." It came with a dictionary but had the ability to build and incorporate use of secondary dictionaries. === Browsers === Web browsers such as Firefox and Google Chrome offer spell checking support, using Hunspell. Prior to using Hunspell, Firefox and Chrome used MySpell and GNU Aspell, respectively. === Specialties === Some spell checkers have separate support for medical dictionaries to help prevent medical errors. == Functionality == The first spell checkers were "verifiers" instead of "correctors." They offered no suggestions for incorrectly spelled words. This was helpful for typos but it was not so helpful for logical or phonetic errors. The challenge the developers faced was the difficulty in offering useful suggestions for misspelled words. This requires reducing words to a skeletal form and applying pattern-matching algorithms. It might seem logical that where spell-checking dictionaries are concerned, "the bigger, the better," so that correct words are not marked as incorrect. In practice, however, an optimal size for English appears to be around 90,000 entries. If there are more than this, incorrectly spelled words may be skipped because they are mistaken for others. For example, a linguist might determine on the basis of corpus linguistics that the word baht is more frequently a misspelling of bath or bat than a reference to the Thai currency. Hence, it would typically be more useful if a few people who write about Thai currency were slightly inconvenienced than if the spelling errors of the many more people who discuss baths were overlooked. The first MS-DOS spell checkers were mostly used in proofing mode from within word processing packages. After preparing a document, a user scanned the text looking for misspellings. Later, however, batch processing was offered in such packages as Oracle's short-lived CoAuthor and allowed a user to view the results after a document was processed and correct only the words that were known to be wrong. When memory and processing power became abundant, spell checking was performed in the background in an interactive way, such as has been the case with the Sector Software produced Spellbound program released in 1987 and Microsoft Word since Word 95. Spell checkers became increasingly sophisticated; now capable of recognizing grammatical errors. However, even at their best, they rarely catch all the errors in a text (such as homophone errors) and will flag neologisms and foreign words as misspellings. Nonetheless, spell checkers can be considered as a type of foreign language writing aid that non-native language lea

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  Harris corner detector

  The Harris corner detector is a corner detection operator that is commonly used in computer vision algorithms to extract corners and infer features of an image. It was first introduced by Chris Harris and Mike Stephens in 1988 upon the improvement of Moravec's corner detector. Compared to its predecessor, Harris' corner detector takes the differential of the corner score into account with reference to direction directly, instead of using shifting patches for every 45 degree angles, and has been proved to be more accurate in distinguishing between edges and corners. Since then, it has been improved and adopted in many algorithms to preprocess images for subsequent applications. == Introduction == A corner is a point whose local neighborhood stands in two dominant and different edge directions. In other words, a corner can be interpreted as the junction of two edges, where an edge is a sudden change in image brightness. Corners are the important features in the image, and they are generally termed as interest points which are invariant to translation, rotation and illumination. Although corners are only a small percentage of the image, they contain the most important features in restoring image information, and they can be used to minimize the amount of processed data for motion tracking, image stitching, building 2D mosaics, stereo vision, image representation and other related computer vision areas. In order to capture the corners from the image, researchers have proposed many different corner detectors including the Kanade-Lucas-Tomasi (KLT) operator and the Harris operator which are most simple, efficient and reliable for use in corner detection. These two popular methodologies are both closely associated with and based on the local structure matrix. Compared to the Kanade-Lucas-Tomasi corner detector, the Harris corner detector provides good repeatability under changing illumination and rotation, and therefore, it is more often used in stereo matching and image database retrieval. Although there still exist drawbacks and limitations, the Harris corner detector is still an important and fundamental technique for many computer vision applications. == Development of Harris corner detection algorithm == Source: Without loss of generality, we will assume a grayscale 2-dimensional image is used. Let this image be given by I {\displaystyle I} . Consider taking an image patch ( x , y ) ∈ W {\displaystyle (x,y)\in W} (window) and shifting it by ( Δ x , Δ y ) {\displaystyle (\Delta x,\Delta y)} . The sum of squared differences (SSD) between these two patches, denoted f {\displaystyle f} , is given by: f ( Δ x , Δ y ) = ∑ ( x k , y k ) ∈ W ( I ( x k , y k ) − I ( x k + Δ x , y k + Δ y ) ) 2 {\displaystyle f(\Delta x,\Delta y)={\underset {(x_{k},y_{k})\in W}{\sum }}\left(I(x_{k},y_{k})-I(x_{k}+\Delta x,y_{k}+\Delta y)\right)^{2}} I ( x + Δ x , y + Δ y ) {\displaystyle I(x+\Delta x,y+\Delta y)} can be approximated by a Taylor expansion. Let I x {\displaystyle I_{x}} and I y {\displaystyle I_{y}} be the partial derivatives of I {\displaystyle I} , such that I ( x + Δ x , y + Δ y ) ≈ I ( x , y ) + I x ( x , y ) Δ x + I y ( x , y ) Δ y {\displaystyle I(x+\Delta x,y+\Delta y)\approx I(x,y)+I_{x}(x,y)\Delta x+I_{y}(x,y)\Delta y} This produces the approximation f ( Δ x , Δ y ) ≈ ∑ ( x , y ) ∈ W ( I x ( x , y ) Δ x + I y ( x , y ) Δ y ) 2 , {\displaystyle f(\Delta x,\Delta y)\approx {\underset {(x,y)\in W}{\sum }}\left(I_{x}(x,y)\Delta x+I_{y}(x,y)\Delta y\right)^{2},} which can be written in matrix form: f ( Δ x , Δ y ) ≈ ( Δ x Δ y ) M ( Δ x Δ y ) , {\displaystyle f(\Delta x,\Delta y)\approx {\begin{pmatrix}\Delta x&\Delta y\end{pmatrix}}M{\begin{pmatrix}\Delta x\\\Delta y\end{pmatrix}},} where M is the structure tensor, M = ∑ ( x , y ) ∈ W [ I x 2 I x I y I x I y I y 2 ] = [ ∑ ( x , y ) ∈ W I x 2 ∑ ( x , y ) ∈ W I x I y ∑ ( x , y ) ∈ W I x I y ∑ ( x , y ) ∈ W I y 2 ] {\displaystyle M={\underset {(x,y)\in W}{\sum }}{\begin{bmatrix}I_{x}^{2}&I_{x}I_{y}\\I_{x}I_{y}&I_{y}^{2}\end{bmatrix}}={\begin{bmatrix}{\underset {(x,y)\in W}{\sum }}I_{x}^{2}&{\underset {(x,y)\in W}{\sum }}I_{x}I_{y}\\{\underset {(x,y)\in W}{\sum }}I_{x}I_{y}&{\underset {(x,y)\in W}{\sum }}I_{y}^{2}\end{bmatrix}}} == Process of Harris corner detection algorithm == Commonly, Harris corner detector algorithm can be divided into five steps. Color to grayscale Spatial derivative calculation Structure tensor setup Harris response calculation Non-maximum suppression === Color to grayscale === If we use Harris corner detector in a color image, the first step is to convert it into a grayscale image, which will enhance the processing speed. The value of the gray scale pixel can be computed as a weighted sums of the values R, B and G of the color image, ∑ C ∈ { R , G , B } w C ⋅ C {\displaystyle \sum _{C\,\in \,\{R,G,B\}}w_{C}\cdot C} , where, e.g., w R = 0.299 , w G = 0.587 , w B = 1 − ( w R + w G ) = 0.114. {\displaystyle w_{R}=0.299,\ w_{G}=0.587,\ w_{B}=1-(w_{R}+w_{G})=0.114.} === Spatial derivative calculation === Next, we are going to find the derivative with respect to x and the derivative with respect to y, I x ( x , y ) {\displaystyle I_{x}(x,y)} and I y ( x , y ) {\displaystyle I_{y}(x,y)} . This can be approximated by applying Sobel operators. === Structure tensor setup === With I x ( x , y ) {\displaystyle I_{x}(x,y)} , I y ( x , y ) {\displaystyle I_{y}(x,y)} , we can construct the structure tensor M {\displaystyle M} . === Harris response calculation === For x ≪ y {\displaystyle x\ll y} , one has x ⋅ y x + y = x 1 1 + x / y ≈ x . {\displaystyle {\tfrac {x\cdot y}{x+y}}=x{\tfrac {1}{1+x/y}}\approx x.} In this step, we compute the smallest eigenvalue of the structure tensor using that approximation: λ min ≈ λ 1 λ 2 ( λ 1 + λ 2 ) = det ( M ) tr ⁡ ( M ) {\displaystyle \lambda _{\min }\approx {\frac {\lambda _{1}\lambda _{2}}{(\lambda _{1}+\lambda _{2})}}={\frac {\det(M)}{\operatorname {tr} (M)}}} with the trace t r ( M ) = m 11 + m 22 {\displaystyle \mathrm {tr} (M)=m_{11}+m_{22}} . Another commonly used Harris response calculation is shown as below, R = λ 1 λ 2 − k ( λ 1 + λ 2 ) 2 = det ( M ) − k tr ⁡ ( M ) 2 {\displaystyle R=\lambda _{1}\lambda _{2}-k(\lambda _{1}+\lambda _{2})^{2}=\det(M)-k\operatorname {tr} (M)^{2}} where k {\displaystyle k} is an empirically determined constant; k ∈ [ 0.04 , 0.06 ] {\displaystyle k\in [0.04,0.06]} . === Non-maximum suppression === In order to pick up the optimal values to indicate corners, we find the local maxima as corners within the window which is a 3 by 3 filter. == Improvement == Sources: Harris-Laplace Corner Detector Differential Morphological Decomposition Based Corner Detector Multi-scale Bilateral Structure Tensor Based Corner Detector == Applications == Image Alignment, Stitching and Registration 2D Mosaics Creation 3D Scene Modeling and Reconstruction Motion Detection Object Recognition Image Indexing and Content-based Retrieval Video Tracking

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  Probiv

  Probiv (Russian: пробив, literally "to pierce" or "to punch through") is an illicit data market operating primarily in Russia, where personal information from restricted government and corporate databases is bought and sold through networks of corrupt officials and insiders. The probiv market operates as a parallel information economy built on corrupt officials from various sectors including traffic police, banks, telecommunications companies, and security services who sell access to restricted databases. For fees ranging from as little as $10 to several hundred dollars, buyers can obtain passport numbers, addresses, travel histories, vehicle registrations, and telecommunications records. The market operates through various channels, including specialized Telegram bots and darknet forums. == Notable uses == Probiv services have been utilized by diverse actors for various purposes. Investigative journalists have used the market to conduct high-profile investigations, including tracing the FSB unit allegedly behind the poisoning of Alexei Navalny. Russian police and security services themselves have routinely used the black market to track activists and opposition figures. Since Russia's invasion of Ukraine, Ukrainian intelligence services have exploited the market to identify Russian military officials. == Government response == In late 2024, Russian authorities introduced legislation imposing penalties of up to ten years in prison for accessing or distributing leaked data. Several operators of probiv services, including the teams behind Usersbox and Solaris, have been arrested. However, the crackdown appears to have had unintended consequences. Many operators have relocated their businesses abroad, where they operate with fewer constraints. Some services that previously cooperated with Russian authorities have severed those ties and moved staff out of the country.

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  Concept mining

  Concept mining is an activity that results in the extraction of concepts from artifacts. Solutions to the task typically involve aspects of artificial intelligence and statistics, such as data mining and text mining. Because artifacts are typically a loosely structured sequence of words and other symbols (rather than concepts), the problem is nontrivial, but it can provide powerful insights into the meaning, provenance and similarity of documents. == Methods == Traditionally, the conversion of words to concepts has been performed using a thesaurus, and for computational techniques the tendency is to do the same. The thesauri used are either specially created for the task, or a pre-existing language model, usually related to Princeton's WordNet. The mappings of words to concepts are often ambiguous. Typically each word in a given language will relate to several possible concepts. Humans use context to disambiguate the various meanings of a given piece of text, where available machine translation systems cannot easily infer context. For the purposes of concept mining, however, these ambiguities tend to be less important than they are with machine translation, for in large documents the ambiguities tend to even out, much as is the case with text mining. There are many techniques for disambiguation that may be used. Examples are linguistic analysis of the text and the use of word and concept association frequency information that may be inferred from large text corpora. Recently, techniques that base on semantic similarity between the possible concepts and the context have appeared and gained interest in the scientific community. == Applications == === Detecting and indexing similar documents in large corpora === One of the spin-offs of calculating document statistics in the concept domain, rather than the word domain, is that concepts form natural tree structures based on hypernymy and meronymy. These structures can be used to generate simple tree membership statistics, that can be used to locate any document in a Euclidean concept space. If the size of a document is also considered as another dimension of this space then an extremely efficient indexing system can be created. This technique is currently in commercial use locating similar legal documents in a 2.5 million document corpus. === Clustering documents by topic === Standard numeric clustering techniques may be used in "concept space" as described above to locate and index documents by the inferred topic. These are numerically far more efficient than their text mining cousins, and tend to behave more intuitively, in that they map better to the similarity measures a human would generate.

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  AUTINDEX

  AUTINDEX is a commercial text mining software package based on sophisticated linguistics. AUTINDEX, resulting from research in information extraction, is a product of the Institute of Applied Information Sciences (IAI) which is a non-profit institute that has been researching and developing language technology since its foundation in 1985. IAI is an institute affiliated to Saarland University in Saarbrücken, Germany. AUTINDEX is the result of a number of research projects funded by the EU (Project BINDEX), by Deutsche Forschungsgemeinschaft and the German Ministry for Economy. Amongst the latter there are the projects LinSearch, and WISSMER, see also the reference to IAI-Website. The basic functionality of AUTINDEX is the extraction of key words from a document to represent the semantics of the document. Ideally the system is integrated with a thesaurus that defines the standardised terms to be used for key word assignment. AUTINDEX is used in library applications (e.g. integrated in dandelon.com) as well as in high quality (expert) information systems, and in document management and content management environments. Together with AUTINDEX a number of additional software comes along such as an integration with Apache Solr / Lucene to provide a complete information retrieval environment, a classification and categorisation system on the basis of a machine learning software that assigns domains to the document, and a system for searching with semantically similar terms that are collected in so called tag clouds.

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  Superquadrics

  In mathematics, the superquadrics or super-quadrics (also superquadratics) are a family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by arbitrary powers. They can be seen as the three-dimensional relatives of the superellipses. The term may refer to the solid object or to its surface, depending on the context. The equations below specify the surface; the solid is specified by replacing the equality signs by less-than-or-equal signs. The superquadrics include many shapes that resemble cubes, octahedra, cylinders, lozenges and spindles, with rounded or sharp corners. Because of their flexibility and relative simplicity, they are popular geometric modeling tools, especially in computer graphics. It becomes an important geometric primitive widely used in computer vision, robotics, and physical simulation. Some authors, such as Alan Barr, define "superquadrics" as including both the superellipsoids and the supertoroids. In modern computer vision literatures, superquadrics and superellipsoids are used interchangeably, since superellipsoids are the most representative and widely utilized shape among all the superquadrics. Comprehensive coverage of geometrical properties of superquadrics and methods of their recovery from range images and point clouds are covered in several computer vision literatures. == Formulas == === Implicit equation === The surface of the basic superquadric is given by | x | r + | y | s + | z | t = 1 {\displaystyle \left|x\right|^{r}+\left|y\right|^{s}+\left|z\right|^{t}=1} where r, s, and t are positive real numbers that determine the main features of the superquadric. Namely: less than 1: a pointy octahedron modified to have concave faces and sharp edges. exactly 1: a regular octahedron. between 1 and 2: an octahedron modified to have convex faces, blunt edges and blunt corners. exactly 2: a sphere greater than 2: a cube modified to have rounded edges and corners. infinite (in the limit): a cube Each exponent can be varied independently to obtain combined shapes. For example, if r=s=2, and t=4, one obtains a solid of revolution which resembles an ellipsoid with round cross-section but flattened ends. This formula is a special case of the superellipsoid's formula if (and only if) r = s. If any exponent is allowed to be negative, the shape extends to infinity. Such shapes are sometimes called super-hyperboloids. The basic shape above spans from -1 to +1 along each coordinate axis. The general superquadric is the result of scaling this basic shape by different amounts A, B, C along each axis. Its general equation is | x A | r + | y B | s + | z C | t = 1. {\displaystyle \left|{\frac {x}{A}}\right|^{r}+\left|{\frac {y}{B}}\right|^{s}+\left|{\frac {z}{C}}\right|^{t}=1.} === Parametric description === Parametric equations in terms of surface parameters u and v (equivalent to longitude and latitude if m equals 2) are x ( u , v ) = A g ( v , 2 r ) g ( u , 2 r ) y ( u , v ) = B g ( v , 2 s ) f ( u , 2 s ) z ( u , v ) = C f ( v , 2 t ) − π 2 ≤ v ≤ π 2 , − π ≤ u < π , {\displaystyle {\begin{aligned}x(u,v)&{}=Ag\left(v,{\frac {2}{r}}\right)g\left(u,{\frac {2}{r}}\right)\\y(u,v)&{}=Bg\left(v,{\frac {2}{s}}\right)f\left(u,{\frac {2}{s}}\right)\\z(u,v)&{}=Cf\left(v,{\frac {2}{t}}\right)\\&-{\frac {\pi }{2}}\leq v\leq {\frac {\pi }{2}},\quad -\pi \leq u<\pi ,\end{aligned}}} where the auxiliary functions are f ( ω , m ) = sgn ⁡ ( sin ⁡ ω ) | sin ⁡ ω | m g ( ω , m ) = sgn ⁡ ( cos ⁡ ω ) | cos ⁡ ω | m {\displaystyle {\begin{aligned}f(\omega ,m)&{}=\operatorname {sgn}(\sin \omega )\left|\sin \omega \right|^{m}\\g(\omega ,m)&{}=\operatorname {sgn}(\cos \omega )\left|\cos \omega \right|^{m}\end{aligned}}} and the sign function sgn(x) is sgn ⁡ ( x ) = { − 1 , x < 0 0 , x = 0 + 1 , x > 0. {\displaystyle \operatorname {sgn}(x)={\begin{cases}-1,&x<0\\0,&x=0\\+1,&x>0.\end{cases}}} === Spherical product === Barr introduces the spherical product which given two plane curves produces a 3D surface. If f ( μ ) = ( f 1 ( μ ) f 2 ( μ ) ) , g ( ν ) = ( g 1 ( ν ) g 2 ( ν ) ) {\displaystyle f(\mu )={\begin{pmatrix}f_{1}(\mu )\\f_{2}(\mu )\end{pmatrix}},\quad g(\nu )={\begin{pmatrix}g_{1}(\nu )\\g_{2}(\nu )\end{pmatrix}}} are two plane curves then the spherical product is h ( μ , ν ) = f ( μ ) ⊗ g ( ν ) = ( f 1 ( μ ) g 1 ( ν ) f 1 ( μ ) g 2 ( ν ) f 2 ( μ ) ) {\displaystyle h(\mu ,\nu )=f(\mu )\otimes g(\nu )={\begin{pmatrix}f_{1}(\mu )\ g_{1}(\nu )\\f_{1}(\mu )\ g_{2}(\nu )\\f_{2}(\mu )\end{pmatrix}}} This is similar to the typical parametric equation of a sphere: x = x 0 + r sin ⁡ θ cos ⁡ φ y = y 0 + r sin ⁡ θ sin ⁡ φ ( 0 ≤ θ ≤ π , 0 ≤ φ < 2 π ) z = z 0 + r cos ⁡ θ {\displaystyle {\begin{aligned}x&=x_{0}+r\sin \theta \;\cos \varphi \\y&=y_{0}+r\sin \theta \;\sin \varphi \qquad (0\leq \theta \leq \pi ,\;0\leq \varphi <2\pi )\\z&=z_{0}+r\cos \theta \end{aligned}}} which give rise to the name spherical product. Barr uses the spherical product to define quadric surfaces, like ellipsoids, and hyperboloids as well as the torus, superellipsoid, superquadric hyperboloids of one and two sheets, and supertoroids. == Plotting code == The following GNU Octave code generates a mesh approximation of a superquadric:

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  BeeSafe

  BeeSafe is a personal safety mobile app launched in 2015 as a Slovak startup. It is a location-based security service that notifies family members and friends in case the user of the app gets in danger. The app has received numerous awards. The app has more than 700 downloads and 250 active logins from more than 60 countries worldwide. == History == BeeSafe was founded on March 20, 2015 by Peter Stražovec and Michal Kačerík. The project was a winner of Žilina’s Startup Weekend 2013 and a StartupAwards.SK 2015 finalist. Later on, the app was released in the Android and iOS marketplace. The whole BeeSafe project was in The Spot booster and incubator in Bratislava for three months. BeeSafe entered into an agreement with the city of Piešťany in November 2015 to increase the security of its citizen by connecting the mobile app with the police platform. It is the first city that started using the BeeSafe platform. Further on, the application tries to help people in other Slovak cities. The cities can see the users only if they are in danger. == Awards == BeeSafe app received the Via Bona award, it is a winner of a Slovak startup and has other nominations too.

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  MegaHAL

  MegaHAL is a computer conversation simulator, or "chatterbot", created by Jason Hutchens. == Background == In 1996, Jason Hutchens entered the Loebner Prize Contest with HeX, a chatterbot based on ELIZA. HeX won the competition that year and took the $2000 prize for having the highest overall score. In 1998, Hutchens again entered the Loebner Prize Contest with his new program, MegaHAL. MegaHAL made its debut in the 1998 Loebner Prize Contest. Like many chatterbots, the intent is for MegaHAL to appear as a human fluent in a natural language. As a user types sentences into MegaHAL, MegaHAL will respond with sentences that are sometimes coherent and at other times complete gibberish. MegaHAL learns as the conversation progresses, remembering new words and sentence structures. It will even learn new ways to substitute words or phrases for other words or phrases. Many would consider conversation simulators like MegaHAL to be a primitive form of artificial intelligence. However, MegaHAL doesn't understand the conversation or even the sentence structure. It generates its conversation based on sequential and mathematical relationships. In the world of conversation simulators, MegaHAL is based on relatively old technology and could be considered primitive. However, its popularity has grown due to its humorous nature; it has been known to respond with twisted or nonsensical statements that are often amusing. == Theory of Operation == MegaHal is based at least in part on a so-called "hidden Markov Model", so that the first thing that Megahal does when it "trains" on a script or text is to build a database of text fragments encompassing every possible subset of perhaps 4, 5, or even 6 consecutive words, so that for example - if MegaHal trains on the Declaration of Independence, then MegaHal will build a database containing text fragments such as "When in the course", "in the course of", "the course of human", "course of human events", "of human events, one", "human events, one people", and so on. Then if Megahal is fed another text, such has "Superman, Yes! It's Superman - he can change the course of mighty rivers, bend steel with his bare hands - and who disguised at Clark Kent …" IT MIGHT induce Megahal to apparently bemuse itself to proffer whether Superman can change the course of human events, or something else altogether - such as some rambling about "when in the course of mighty rivers", and so on. Thus likewise - if a phrase like "the White house said" comes up a lot in some text; then Megahal's ability to switch randomly between different contexts which otherwise share some similarity can result at times in some surprising lucidity, or else it might otherwise seem quite bizarre. == Examples == There are some sentences that MegaHAL generated: CHESS IS A FUN SPORT, WHEN PLAYED WITH SHOT GUNS. and COWS FLY LIKE CLOUDS BUT THEY ARE NEVER COMPLETELY SUCCESSFUL. == Distribution == MegaHAL is distributed under the Unlicense. Its source code can be downloaded from the Github repository.

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  Inverse consistency

  In image registration, inverse consistency measures the consistency of mappings between images produced by a registration algorithm. The inverse consistency error, introduced by Christiansen and Johnson in 2001, quantifies the distance between the composition of the mappings from each image to the other, produced by the registration procedure, and the identity function, and is used as a regularisation constraint in the loss function of many registration algorithms to enforce consistent mappings. Inverse consistency is necessary for good image registration but it is not sufficient, since a mapping can be perfectly consistent but not register the images at all. == Definition == Image registration is the process of establishing a common coordinate system between two images, and given two images I 1 : Ω 1 → R I 2 : Ω 2 → R {\displaystyle {\begin{aligned}I_{1}:\Omega _{1}\to \mathbb {R} \\I_{2}:\Omega _{2}\to \mathbb {R} \end{aligned}}} registering a source image I 1 {\displaystyle I_{1}} to a target image I 2 {\displaystyle I_{2}} consists of determining a transformation f 1 : Ω 2 → Ω 1 {\displaystyle f_{1}:\Omega _{2}\to \Omega _{1}} that maps points from the target space to the source space. An ideal registration algorithm should not be sensitive to which image in the pair is used as source or target, and the registration operator should be antisymmetric such that the mappings f 1 : Ω 2 → Ω 1 f 2 : Ω 1 → Ω 2 {\displaystyle {\begin{aligned}f_{1}:\Omega _{2}\to \Omega _{1}\\f_{2}:\Omega _{1}\to \Omega _{2}\end{aligned}}} produced when registering I 1 {\displaystyle I_{1}} to I 2 {\displaystyle I_{2}} and I 2 {\displaystyle I_{2}} to I 1 {\displaystyle I_{1}} respectively should be the inverse of each other, i.e. f 2 = f 1 − 1 {\displaystyle f_{2}=f_{1}^{-1}} and f 1 = f 2 − 1 {\displaystyle f_{1}=f_{2}^{-1}} or, equivalently, f 2 ∘ f 1 = id Ω 2 {\displaystyle f_{2}\circ f_{1}=\operatorname {id} _{\Omega _{2}}} and f 1 ∘ f 2 = id Ω 1 {\displaystyle f_{1}\circ f_{2}=\operatorname {id} _{\Omega _{1}}} , where ∘ {\displaystyle \circ } denotes the function composition operator. Real algorithms are not perfect, and when swapping the role of source and target image in a registration problem the so obtained transformations are not the inverse of each other. Inverse consistency can be enforced by adding to the loss function of the registration a symmetric regularisation term that penalises inconsistent transformations ∫ Ω 2 ‖ f 2 ( f 1 ( x ) ) − x ‖ 2 d x + ∫ Ω 1 ‖ f 1 ( f 2 ( x ) ) − x ‖ 2 d x . {\displaystyle \int _{\Omega _{2}}\left\Vert f_{2}(f_{1}(x))-x\right\Vert ^{2}\mathrm {d} x+\int _{\Omega _{1}}\left\Vert f_{1}(f_{2}(x))-x\right\Vert ^{2}\mathrm {d} x.} Inverse consistency can be used as a quality metric to evaluate image registration results. The inverse consistency error ( I C E {\displaystyle ICE} ) measures the distance between the composition of the two transforms and the identity function, and it can be formulated in terms of both average ( I C E a {\displaystyle ICE_{a}} ) or maximum ( I C E m {\displaystyle ICE_{m}} ) over a region of interest Ω {\displaystyle \Omega } of the image: I C E a = 1 ∫ Ω d x ∫ Ω ‖ f 2 ( f 1 ( x ) ) − x ‖ d x I C E m = max x ∈ Ω ‖ f 2 ( f 1 ( x ) ) − x ‖ . {\displaystyle {\begin{aligned}ICE_{a}&={\frac {1}{\int _{\Omega }\mathrm {d} x}}\int _{\Omega }\left\Vert f_{2}(f_{1}(x))-x\right\Vert \mathrm {d} x\\ICE_{m}&=\max _{x\in \Omega }\left\Vert f_{2}(f_{1}(x))-x\right\Vert .\end{aligned}}} While inverse consistency is a necessary property of good registration algorithms, inverse consistency error alone is not a sufficient metric to evaluate the quality of image registration results, since a perfectly consistent mapping, with no other constraint, may be not even close to correctly register a pair of images.

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  Legal information retrieval

  Legal information retrieval is the science of information retrieval applied to legal text, including legislation, case law, and scholarly works. Accurate legal information retrieval is important to provide access to the law to laymen and legal professionals. Its importance has increased because of the vast and quickly increasing amount of legal documents available through electronic means. Legal information retrieval is a part of the growing field of legal informatics. In a legal setting, it is frequently important to retrieve all information related to a specific query. However, commonly used boolean search methods (exact matches of specified terms) on full text legal documents have been shown to have an average recall rate as low as 20 percent, meaning that only 1 in 5 relevant documents are actually retrieved. In that case, researchers believed that they had retrieved over 75% of relevant documents. This may result in failing to retrieve important or precedential cases. In some jurisdictions this may be especially problematic, as legal professionals are ethically obligated to be reasonably informed as to relevant legal documents. Legal Information Retrieval attempts to increase the effectiveness of legal searches by increasing the number of relevant documents (providing a high recall rate) and reducing the number of irrelevant documents (a high precision rate). This is a difficult task, as the legal field is prone to jargon, polysemes (words that have different meanings when used in a legal context), and constant change. Techniques used to achieve these goals generally fall into three categories: boolean retrieval, manual classification of legal text, and natural language processing of legal text. == Problems == Application of standard information retrieval techniques to legal text can be more difficult than application in other subjects. One key problem is that the law rarely has an inherent taxonomy. Instead, the law is generally filled with open-ended terms, which may change over time. This can be especially true in common law countries, where each decided case can subtly change the meaning of a certain word or phrase. Legal information systems must also be programmed to deal with law-specific words and phrases. Though this is less problematic in the context of words which exist solely in law, legal texts also frequently use polysemes, words may have different meanings when used in a legal or common-speech manner, potentially both within the same document. The legal meanings may be dependent on the area of law in which it is applied. For example, in the context of European Union legislation, the term "worker" has four different meanings: Any worker as defined in Article 3(a) of Directive 89/391/EEC who habitually uses display screen equipment as a significant part of his normal work. Any person employed by an employer, including trainees and apprentices but excluding domestic servants; Any person carrying out an occupation on board a vessel, including trainees and apprentices, but excluding port pilots and shore personnel carrying out work on board a vessel at the quayside; Any person who, in the Member State concerned, is protected as an employee under national employment law and in accordance with national practice; It also has the common meaning: A person who works at a specific occupation. Though the terms may be similar, correct information retrieval must differentiate between the intended use and irrelevant uses in order to return the correct results. Even if a system overcomes the language problems inherent in law, it must still determine the relevancy of each result. In the context of judicial decisions, this requires determining the precedential value of the case. Case decisions from senior or superior courts may be more relevant than those from lower courts, even where the lower court's decision contains more discussion of the relevant facts. The opposite may be true, however, if the senior court has only a minor discussion of the topic (for example, if it is a secondary consideration in the case). An information retrieval system must also be aware of the authority of the jurisdiction. A case from a binding authority is most likely of more value than one from a non-binding authority. Additionally, the intentions of the user may determine which cases they find valuable. For instance, where a legal professional is attempting to argue a specific interpretation of law, he might find a minor court's decision which supports his position more valuable than a senior courts position which does not. He may also value similar positions from different areas of law, different jurisdictions, or dissenting opinions. Overcoming these problems can be made more difficult because of the large number of cases available. The number of legal cases available via electronic means is constantly increasing (in 2003, US appellate courts handed down approximately 500 new cases per day), meaning that an accurate legal information retrieval system must incorporate methods of both sorting past data and managing new data. == Techniques == === Boolean searches === Boolean searches, where a user may specify terms such as use of specific words or judgments by a specific court, are the most common type of search available via legal information retrieval systems. They are widely implemented but overcome few of the problems discussed above. The recall and precision rates of these searches vary depending on the implementation and searches analyzed. One study found a basic boolean search's recall rate to be roughly 20%, and its precision rate to be roughly 79%. Another study implemented a generic search (that is, not designed for legal uses) and found a recall rate of 56% and a precision rate of 72% among legal professionals. Both numbers increased when searches were run by non-legal professionals, to a 68% recall rate and 77% precision rate. This is likely explained because of the use of complex legal terms by the legal professionals. === Manual classification === In order to overcome the limits of basic boolean searches, information systems have attempted to classify case laws and statutes into more computer friendly structures. Usually, this results in the creation of an ontology to classify the texts, based on the way a legal professional might think about them. These attempt to link texts on the basis of their type, their value, and/or their topic areas. Most major legal search providers now implement some sort of classification search, such as Westlaw's “Natural Language” or LexisNexis' Headnote searches. Additionally, both of these services allow browsing of their classifications, via Westlaw's West Key Numbers or Lexis' Headnotes. Though these two search algorithms are proprietary and secret, it is known that they employ manual classification of text (though this may be computer-assisted). These systems can help overcome the majority of problems inherent in legal information retrieval systems, in that manual classification has the greatest chances of identifying landmark cases and understanding the issues that arise in the text. In one study, ontological searching resulted in a precision rate of 82% and a recall rate of 97% among legal professionals. The legal texts included, however, were carefully controlled to just a few areas of law in a specific jurisdiction. The major drawback to this approach is the requirement of using highly skilled legal professionals and large amounts of time to classify texts. As the amount of text available continues to increase, some have stated their belief that manual classification is unsustainable. === Natural language processing === In order to reduce the reliance on legal professionals and the amount of time needed, efforts have been made to create a system to automatically classify legal text and queries. Adequate translation of both would allow accurate information retrieval without the high cost of human classification. These automatic systems generally employ Natural Language Processing (NLP) techniques that are adapted to the legal domain, and also require the creation of a legal ontology. Though multiple systems have been postulated, few have reported results. One system, “SMILE,” which attempted to automatically extract classifications from case texts, resulted in an f-measure (which is a calculation of both recall rate and precision) of under 0.3 (compared to perfect f-measure of 1.0). This is probably much lower than an acceptable rate for general usage. Despite the limited results, many theorists predict that the evolution of such systems will eventually replace manual classification systems. === Citation-Based ranking === In the mid-90s the Room 5 case law retrieval project used citation mining for summaries and ranked its search results based on citation type and count. This slightly pre-dated the PageRank algorithm at Stanford which was also a citation-based ranking. Ranking of results was based

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  Webmail

  Webmail (or web-based email) is an email service that can be accessed using a standard web browser. It contrasts with email service accessible through a specialised email client software. Additionally, many internet service providers (ISP) provide webmail as part of their internet service package. Similarly, some web hosting providers also provide webmail as a part of their hosting package. As with any web application, webmail's main advantage over the use of a desktop email client is the ability to send and receive email anywhere from a web browser. == History == === Early implementations === The first Web Mail implementation was developed at CERN in 1993 by Phillip Hallam-Baker as a test of the HTTP protocol stack, but was not developed further. In the next two years, however, several people produced working webmail applications. In Europe, there were three implementations, Søren Vejrum's "WWW Mail", Luca Manunza's "WebMail", and Remy Wetzels' "WebMail". Søren Vejrum's "WWW Mail" was written when he was studying and working at the Copenhagen Business School in Denmark, and was released on February 28, 1995. Luca Manunza's "WebMail" was written while he was working at CRS4 in Sardinia, from an idea of Gianluigi Zanetti, with the first source release on March 30, 1995. Remy Wetzels' "WebMail" was written while he was studying at the Eindhoven University of Technology in the Netherlands for the DSE and was released early January 1995. In the United States, Matt Mankins wrote "Webex", and Bill Fitler, while at Lotus cc:Mail, began working on an implementation which he demonstrated publicly at Lotusphere on January 24, 1995. Customers who saw the cc:Mail demonstration were very enthusiastic, one recalling that they were "like an angry mob. People were yelling, 'We want this now!'". Matt Mankins, under the supervision of Dr. Burt Rosenberg at the University of Miami, released his "Webex" application source code in a post to comp.mail.misc on August 8, 1995, although it had been in use as the primary email application at the School of Architecture where Mankins worked for some months prior. Bill Fitler's webmail implementation was further developed as a commercial product, which Lotus announced and released in the fall of 1995 as cc:Mail for the World Wide Web 1.0; thereby providing an alternative means of accessing a cc:Mail message store (the usual means being a cc:Mail desktop application that operated either via dialup or within the confines of a local area network). Early commercialization of webmail was also achieved when "Webex" began to be sold by Mankins' company, DotShop, Inc., at the end of 1995. Within DotShop, "Webex" changed its name to "EMUmail"; which would be sold to companies like UPS and Rackspace until its sale to Accurev in 2001. EMUmail was one of the first applications to feature a free version that included embedded advertising, as well as a licensed version that did not. Hotmail and Four11's RocketMail both launched in 1996 as free services and immediately became very popular. === Widespread deployment === As the 1990s progressed, and into the 2000s, it became more common for the general public to have access to webmail because: many Internet service providers (such as EarthLink) and web hosting providers (such as Verio) began bundling webmail into their service offerings (often in parallel with POP/SMTP services); many other enterprises (such as universities and large corporations) also started offering webmail as a way for their user communities to access their email (either locally managed or outsourced); webmail service providers (such as Hotmail and RocketMail) emerged in 1996 as a free service to the general public, and rapidly gained in popularity. In some cases, webmail application software is developed in-house by the organizations running and managing the application, and in some cases it is obtained from software companies that develop and sell such applications, usually as part of an integrated mail server package (an early example being Netscape Messaging Server). The market for webmail application software has continued into the 2010s. == Rendering and compatibility == Email users may find the use of both a webmail client and a desktop client using the POP3 protocol presents some difficulties. For example, email messages that are downloaded by the desktop client and are removed from the server will no longer be available on the webmail client. The user is limited to previewing messages using the web client before they are downloaded by the desktop email client. However, one may choose to leave the emails on the server, in which case this problem does not occur. The use of both a webmail client and a desktop client using the IMAP4 protocol allows the contents of the mailbox to be consistently displayed in both the webmail and desktop clients and any action the user performs on messages in one interface will be reflected when the email is accessed via the other interface. There are significant differences in rendering capabilities for many popular webmail services such as Gmail, Outlook.com and Yahoo! Mail. Due to the varying treatment of HTML tags, such as