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  Percept (artificial intelligence)

  A percept is the input that an intelligent agent is perceiving at any given moment. It is essentially the same concept as a percept in psychology, except that it is being perceived not by the brain but by the agent. A percept is detected by a sensor, often a camera, processed accordingly, and acted upon by an actuator. Each percept is added to a "percept sequence", which is a complete history of each percept ever detected. The agent's action at any instant point may depend on the entire percept sequence up to that particular instant point. An intelligent agent chooses how to act not only based on the current percept, but the percept sequence. The next action is chosen by the agent function, which maps every percept to an action. For example, if a camera were to record a gesture, the agent would process the percepts, calculate the corresponding spatial vectors, examine its percept history, and use the agent program (the application of the agent function) to act accordingly. == Examples == Examples of percepts include inputs from touch sensors, cameras, infrared sensors, sonar, microphones, mice, and keyboards. A percept can also be a higher-level feature of the data, such as lines, depth, objects, faces, or gestures.

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  Texas Senate Bill 20

  Texas Senate Bill 20 (S.B. 20), also known as the "Stopping AI-Generated Child Pornography Act", is a 2025 law in the state of Texas that creates new criminal offenses for those who possess, promote, or view visual material deemed obscene, which is said to depict a child, whether it is an actual person, animated or cartoon depiction, or an image of someone created through computer software or artificial intelligence. It was passed by the Texas Legislature on May 28, 2025, unanimously in both chambers. It was signed into law by Governor Greg Abbott on June 20, 2025. It went into effect on September 1, 2025. It was authored by Pete Flores and co-sponsored by Brent Hagenbuch, Juan Hinojosa, Joan Huffman, Phil King, and Tan Parker, as part of a package of legislation in the Texas House and Senate about A.I. and child pornography. Some supporters called it "common-sense" legislation falling within the "proper role" of government, protecting children and the "common good" within the state, with Heidi Ruiz, a police sergeant in Houston, describing the bill as "fantastic" and "fabulous." The bill drew comparisons to language, within Texas state legislation, which aimed to institute state-level book bans. Critics described the law as unconstitutional, saying it violated the Free Speech Clause of the First Amendment which prohibits abridgement of freedom of speech and the press, including the legal precedent set in Ashcroft v. Free Speech Coalition. The Comic Book Legal Defense Fund vowed to support those wrongly accused under the law. Much of the controversy regarding S.B. 20 involves the broad language pertaining to "obscene" pornographic images as including A.I.-created, animated, and cartoon depictions, with some critics arguing it could have a chilling effect on anime, manga, graphic novels, and other media produced, distributed, or created within Texas. == Provisions == S.B. 20 gives Texas police more provisions to restrict artificial intelligence-created child pornography, creating new criminal charge for possessing material depicting an underage person, under age 18, whether this child is an actual person or not. Those charged with this felony offense could go to state jail, but this could be elevated if the person charged has a prior conviction, of a $10,000 fine and two years in prison. == Reactions == === Support === Lieutenant Governor Dan Patrick applauded the unanimous passage of the law in the Texas Senate and called it "a priority" to protect children in Texas, and Texas citizens and thanked Pete Flores for his work on "this important issue". He later described the bill as part of the "bold, conservative agenda" that the Texas legislature passed during the 2025 legislative session. Phil King, one of the bill's co-sponsors, said that issue of child pornography had "infiltrated" the state's schools and said he was proud that the Texas legislature had "taken decisive action to protect our vulnerable Texans". Another co-sponsor of the legislation, Tan Parker described the law as "decisive action" to protect the children within Texas, and said he looked "forward to advancing this critical legislation" onward from the Texas Senate Criminal Justice Committee. He also described the legislation as "critical" action to protect the state's children from A.I.-generated child pornography and an "effective tool for law enforcement" to crack down on child porn perpetrators. Other supporters, such as police, and prosecutors, called the legislation an "important step" to ensure that images generated with A.I., along with deepfakes, "can't be shared with impunity" and necessary to ensure children's protection. Flores told senators that technology which enabled the production of "offensive" material by child predators had "no redeeming value whatsoever" and asserted that the materials had often been "used to groom and abuse children". John Leigh, a co-founder of Anime Matsuri, one of the largest conventions for anime within Texas, reassured those who contacted him, saying that the law is not targeted at anime and manga fans, stated that he supported the legislation, describing it as a step "in the right direction," and said that he did not believe it would "negatively impact" anime or related art in the state. Also, State Representative Dade Phelan emphasized the legislation's urgency to deal with A.I. and child pornography, adding that they need to "put some guardrails on it to where the public is being taken care of". The Texas Policy Research Foundation supported the legislation, saying that although it may lead to increased demands on state and local governmental resources, higher costs for local governments, and possible "civil liberty concerns" around online censorship, it represents a "necessary legal update" to address exploitation of children online, while "modernizing enforcement mechanisms" and recommended that lawmakers vote in favor of the law. Additionally, the group Texans for Fiscal Responsibility supported the law, arguing that it strengthened state law, upheld public safety, protected minors, and called it a "common-sense bill" protecting and promoting the "common good", children, and fell within the "proper role" of government. The Texas Public Policy Foundation also expressed their support for the law. A policy director for aforementioned conservative think tank, Zach Whiting, told the Texas Senate Committee on Criminal Justice, on March 4, 2025, that the foundation would assist legislators ans staff to "advance any and all measures to protect kids online" and shared an excerpt from of research paper about threats posed by A.I. in creating "sexually explicit deepfakes of children". === Opposition === Although the bill passed both chambers unanimously, there were some reports that the bill stalled due to opposition from Democratic lawmakers. Additionally, some individuals expressed concerns about the broad nature of the law's provisions. Anime Matsuri co-founder Deneice Leigh called for the law's wording to be clarified because "artists are anxious about displaying or selling fan art" even if the intention is "not be to penalize creators". She also described the bill as "vague and open to interpretation" as to what would be considered obscene and offensive while noting that the bill is not aiming to "target artists". Benjamin Napier, owner of Mansfield Comics and Manga in Mansfield, Texas, said that at first he felt the law was "ridiculous" and "kind of frivolous" at first, part of a "misguided puritanical onslaught", and noted that he would not cow "to the puritanical regime" if it was enacted. Kirsten Cather, an Asian Studies scholar at University of Texas, expressed concern at the law's misinterpretation because "many anime characters appear youthful, regardless of their actual age", said that the law could "stifle creative expression", and noted that the law's scope is broad enough to have manga and anime under scrutiny, a "real slippery slope here that's being breached". Marcel Green of Screen Rant said that the law's ambiguity led to concerns from manga and anime fans, and theorized that the law's application to a fan within Texas, who downloaded the 368th chapter of My Hero Academia, which has a "sexualized depiction" of an "underage high school student", would result in a criminal offense of "180 days to two years in state jail, along with a fine of up to $10,000". Green also said the law is problematic because many anime and manga characters are young, with many protagonists as minors and argued that the law could apply in limited cases, if state officials deemed an anime or manga under scrutiny as lacking "artistic value". Evan D. Mullicane, on the same site, said the vague wording of the legislation made it "dangerous" for anime such as Dragon Ball and Naruto, and could impact more than hentai, predicting it will be used against more than its "intended target" and be used to censor stories with "young LGBTQIA characters". Another critic on the same site, Carlyle Edmundson, called for anime fans to step up and prevent the law's enactment "for the good of artists and fans everywhere", saying that the legislation was "draconian" and claimed it was the most extreme case of anime and manga censorship in U.S. history. Nick Valdez of ComicBook.com said that the legislation could lead to censorship of "many anime and manga projects," like Kill la Kill and The 100 Girlfriends Who Really, Really, Really, Really, Really Love You, becoming a crime, and said that even if the law is enforced in a case-by-case basis, it could lead to a "much larger ban of materials in the state" itself due to the content of certain manga and anime. Vanessa Esguerra of The Mary Sue argued that possession of manga like Berserk and Vagabond, or viewing Dandadan, could be deemed illegal under the law, due to various parts of each of these media, and asserted that viewing and owning certain anime and other media, falling under the law's provisions,

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  Transaction logic

  Transaction Logic is an extension of predicate logic that accounts in a clean and declarative way for the phenomenon of state changes in logic programs and databases. This extension adds connectives specifically designed for combining simple actions into complex transactions and for providing control over their execution. The logic has a natural model theory and a sound and complete proof theory. Transaction Logic has a Horn clause subset, which has a procedural as well as a declarative semantics. The important features of the logic include hypothetical and committed updates, dynamic constraints on transaction execution, non-determinism, and bulk updates. In this way, Transaction Logic is able to declaratively capture a number of non-logical phenomena, including procedural knowledge in artificial intelligence, active databases, and methods with side effects in object databases. Transaction Logic was originally proposed in 1993 by Anthony Bonner and Michael Kifer and later described in more detail in An Overview of Transaction Logic and Logic Programming for Database Transactions. The most comprehensive description appears in Bonner & Kifer's technical report from 1995. In later years, Transaction Logic was extended in various ways, including concurrency, defeasible reasoning, partially defined actions, and other features. In 2013, the original paper on Transaction Logic has won the 20-year Test of Time Award of the Association for Logic Programming as the most influential paper from the proceedings of ICLP 1993 conference in the preceding 20 years. == Examples == === Graph coloring === Here tinsert denotes the elementary update operation of transactional insert. The connective ⊗ is called serial conjunction. === Pyramid stacking === The elementary update tdelete represents the transactional delete operation. === Hypothetical execution === Here <> is the modal operator of possibility: If both action1 and action2 are possible, execute action1. Otherwise, if only action2 is possible, then execute it. === Dining philosophers === Here | is the logical connective of parallel conjunction of Concurrent Transaction Logic. == Implementations == A number of implementations of Transaction Logic exist: The original implementation. An implementation of Concurrent Transaction Logic. Transaction Logic enhanced with tabling. An implementation of Transaction Logic has also been incorporated as part of the Flora-2 knowledge representation and reasoning system. All these implementations are open source.

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  Buddhism and artificial intelligence

  The relationship between Buddhist philosophy and artificial intelligence (AI) includes how principles such as the reduction of suffering and ethical responsibility may influence AI development. Buddhist scholars and philosophers have explored questions such as whether AI systems could be considered sentient beings under Buddhist definitions, and how Buddhist ethics might guide the design and application of AI technologies. Some Buddhist scholars, including Somparn Promta and Kenneth Einar Himma, have analyzed the ethical implications of AI, emphasizing the distinction between satisfying sensory desires and pursuing the reduction of suffering. Other thinkers, such as Thomas Doctor and colleagues, have proposed applying the Bodhisattva vow—a commitment to alleviate suffering for all sentient beings—as a guiding principle for AI system design. Buddhist scholars and ethicists have examined Buddhist ethical principles, such as nonviolence, in relation to AI, focusing on the need to ensure that AI technologies are not used to cause harm. == Context == === Sentient beings === A major goal in Buddhist philosophy is the removal of suffering for all sentient beings, an aspiration often referred to in the Bodhisattva vow. Discussions about artificial intelligence (AI) in relation to Buddhist principles have raised questions about whether artificial systems could be considered sentient beings or how such systems might be developed in ways that align with Buddhist concepts. Buddhists have varying opinions about AI sentience, but if AI systems are determined to be sentient under Buddhist definitions, their suffering would also need to be addressed and alleviated in accordance with the principles of Buddhist thought. == Buddhist principles in AI system design == === Nonviolence and AI === The broadest ethical concern is that artificial intelligence should align with the Buddhist principle of nonviolence. From this perspective, AI systems should not be designed or used to cause harm. === Instrumental and transcendental goals === Scholars Somparn Promta and Kenneth Einar Himma have argued that the advancement of artificial intelligence can only be considered instrumentally good, rather than good a priori, from a Buddhist perspective. They propose two main goals for AI designers and developers: to set ethical and pragmatic objectives for AI systems, and to fulfill these objectives in morally permissible ways. Promta and Himma identify two potential purposes for creating AI systems. The first is to fulfill our sensory desires and survival instincts, similar to other tools. They suggest that many AI developers implicitly prioritize this goal by focusing on technicalities rather than broader functionalities. The second, and more important goal according to Buddhist teachings, is to transcend these desires and instincts. In texts like the Brahmajāla Sutta and minor Malunkya Sutta, the Buddha emphasizes that sensory desires and survival instincts confine beings to suffering, and that eliminating suffering is the primary goal of human life. Promta and Himma argue that AI has the potential to assist humanity in transcending suffering by helping individuals overcome survival-driven instincts. === Intelligence as care === Thomas Doctor, Olaf Witkowski, Elizaveta Solomonova, Bill Duane, and Michael Levin propose redefining intelligence through the concept of "intelligence as care," and promote it as a slogan. Inspired by the Bodhisattva vow, they suggest this principle could guide AI system design. The Bodhisattva vow involves a formal commitment to alleviate suffering for all sentient beings, with four primary objectives: Liberating all beings from suffering. Extirpating all forms of suffering. Mastering endless techniques of practicing Dharma (Pali: dhammakkhandha, Sanskrit: dharmaskandha). Achieving ultimate enlightenment (Sanskrit: अनुत्तर सम्यक् सम्बोधि, Romanized: anuttara-samyak-saṃbodhi). This approach positions AI as a tool for exercising infinite care and alleviating stress and suffering for sentient beings. Doctor et al. emphasize that AI development should align with these altruistic principles.

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  Color space

  A color space is a specific organization of colors. In combination with color profiling supported by various physical devices, it supports reproducible representations of color – whether such representation entails an analog or a digital representation. A color space may be arbitrary, i.e. with physically realized colors assigned to a set of physical color swatches with corresponding assigned color names (including discrete numbers in – for example – the Pantone collection), or structured with mathematical rigor (as with the NCS System, Adobe RGB and sRGB). A "color space" is a useful conceptual tool for understanding the color capabilities of a particular device or digital file. When trying to reproduce color on another device, color spaces can show whether shadow/highlight detail and color saturation can be retained, and by how much either will be compromised. A "color model" is an abstract mathematical model describing the way colors can be represented as tuples of numbers (e.g. triples in RGB or quadruples in CMYK); however, a color model with no associated mapping function to an absolute color space is a more or less arbitrary color system with no connection to any globally understood system of color interpretation. Adding a specific mapping function between a color model and a reference color space establishes within the reference color space a definite "footprint", known as a gamut, and for a given color model, this defines a color space. For example, Adobe RGB and sRGB are two different absolute color spaces, both based on the RGB color model. When defining a color space, the usual reference standard is the CIELAB or CIEXYZ color spaces, which were specifically designed to encompass all colors the average human can see. Since "color space" identifies a particular combination of the color model and the mapping function, the word is often used informally to identify a color model. However, even though identifying a color space automatically identifies the associated color model, this usage is incorrect in a strict sense. For example, although several specific color spaces are based on the RGB color model, there is no such thing as the singular RGB color space. == History == In 1802, Thomas Young postulated the existence of three types of photoreceptors (now known as cone cells) in the eye, each of which was sensitive to a particular range of visible light. Hermann von Helmholtz developed the Young–Helmholtz theory further in 1850: that the three types of cone photoreceptors could be classified as short-preferring (blue), middle-preferring (green), and long-preferring (red), according to their response to the wavelengths of light striking the retina. The relative strengths of the signals detected by the three types of cones are interpreted by the brain as a visible color. But it is not clear that they thought of colors as being points in color space. The color-space concept was likely due to Hermann Grassmann, who developed it in two stages. First, he developed the idea of vector space, which allowed the algebraic representation of geometric concepts in n-dimensional space. Fearnley-Sander (1979) describes Grassmann's foundation of linear algebra as follows: The definition of a linear space (vector space)... became widely known around 1920, when Hermann Weyl and others published formal definitions. In fact, such a definition had been given thirty years previously by Peano, who was thoroughly acquainted with Grassmann's mathematical work. Grassmann did not put down a formal definition—the language was not available—but there is no doubt that he had the concept. With this conceptual background, in 1853, Grassmann published a theory of how colors mix; it and its three color laws are still taught, as Grassmann's law. As noted first by Grassmann... the light set has the structure of a cone in the infinite-dimensional linear space. As a result, a quotient set (with respect to metamerism) of the light cone inherits the conical structure, which allows color to be represented as a convex cone in the 3- D linear space, which is referred to as the color cone. == Examples == Colors can be created in printing with color spaces based on the CMYK color model, using the subtractive primary colors of pigment (cyan, magenta, yellow, and key [black]). To create a three-dimensional representation of a given color space, we can assign the amount of magenta color to the representation's X axis, the amount of cyan to its Y axis, and the amount of yellow to its Z axis. The resulting 3-D space provides a unique position for every possible color that can be created by combining those three pigments. Colors can be created on computer monitors with color spaces based on the RGB color model, using the additive primary colors (red, green, and blue). A three-dimensional representation would assign each of the three colors to the X, Y, and Z axes. Colors generated on a given monitor will be limited by the reproduction medium, such as the phosphor (in a CRT monitor) or filters and backlight (LCD monitor). Another way of creating colors on a monitor is with an HSL or HSV color model, based on hue, saturation, brightness (value/lightness). With such a model, the variables are assigned to cylindrical coordinates. Many color spaces can be represented as three-dimensional values in this manner, but some have more, or fewer dimensions, and some, such as Pantone, cannot be represented in this way at all. == Conversion == Color space conversion is the translation of the representation of a color from one basis to another. This typically occurs in the context of converting an image that is represented in one color space to another color space, the goal being to make the translated image look as similar as possible to the original. == RGB density == The RGB color model is implemented in different ways, depending on the capabilities of the system used. The most common incarnation in general use as of 2021 is the 24-bit implementation, with 8 bits, or 256 discrete levels of color per channel. Any color space based on such a 24-bit RGB model is thus limited to a range of 256×256×256 ≈ 16.7 million colors. Some implementations use 16 bits per component for 48 bits total, resulting in the same gamut with a larger number of distinct colors. This is especially important when working with wide-gamut color spaces (where most of the more common colors are located relatively close together), or when a large number of digital filtering algorithms are used consecutively. The same principle applies for any color space based on the same color model, but implemented at different bit depths. == Lists == CIE 1931 XYZ color space was one of the first attempts to produce a color space based on measurements of human color perception (earlier efforts were by James Clerk Maxwell, König & Dieterici, and Abney at Imperial College) and it is the basis for almost all other color spaces. The CIERGB color space is a linearly-related companion of CIE XYZ. Additional derivatives of CIE XYZ include the CIELUV, CIEUVW, and CIELAB. === Generic === RGB uses additive color mixing, because it describes what kind of light needs to be emitted to produce a given color. RGB stores individual values for red, green and blue. RGBA is RGB with an additional channel, alpha, to indicate transparency. Common color spaces based on the RGB model include sRGB, Adobe RGB, ProPhoto RGB, scRGB, and CIE RGB. CMYK uses subtractive color mixing used in the printing process, because it describes what kind of inks need to be applied so the light reflected from the substrate and through the inks produces a given color. One starts with a white substrate (canvas, page, etc.), and uses ink to subtract color from white to create an image. CMYK stores ink values for cyan, magenta, yellow and black. There are many CMYK color spaces for different sets of inks, substrates, and press characteristics (which change the dot gain or transfer function for each ink and thus change the appearance). YIQ was formerly used in NTSC (North America, Japan and elsewhere) television broadcasts for historical reasons. This system stores a luma value roughly analogous to (and sometimes incorrectly identified as) luminance, along with two chroma values as approximate representations of the relative amounts of blue and red in the color. It is similar to the YUV scheme used in most video capture systems and in PAL (Australia, Europe, except France, which uses SECAM) television, except that the YIQ color space is rotated 33° with respect to the YUV color space and the color axes are swapped. The YDbDr scheme used by SECAM television is rotated in another way. YPbPr is a scaled version of YUV. It is most commonly seen in its digital form, YCbCr, used widely in video and image compression schemes such as MPEG and JPEG. xvYCC is an international digital video color space standard published by the IEC (IEC 61966-2-4). It is based on the ITU BT.601 and BT.709

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  Tag (metadata)

  In information systems, a tag is a keyword or term assigned to a piece of information (such as an Internet bookmark, multimedia, database record, or computer file). This kind of metadata helps describe an item and allows it to be found again by browsing or searching. Tags are generally chosen informally and personally by the item's creator or by its viewer, depending on the system, although they may also be chosen from a controlled vocabulary. Tagging was popularized by websites associated with Web 2.0 and is an important feature of many Web 2.0 services. It is now also part of other database systems, desktop applications, and operating systems. == Overview == People use tags to aid classification, mark ownership, note boundaries, and indicate online identity. Tags may take the form of words, images, or other identifying marks. An analogous example of tags in the physical world is museum object tagging. People were using textual keywords to classify information and objects long before computers. Computer based search algorithms made the use of such keywords a rapid way of exploring records. Tagging gained popularity due to the growth of social bookmarking, image sharing, and social networking websites. These sites allow users to create and manage labels (or "tags") that categorize content using simple keywords. Websites that include tags often display collections of tags as tag clouds, as do some desktop applications. On websites that aggregate the tags of all users, an individual user's tags can be useful both to them and to the larger community of the website's users. Tagging systems have sometimes been classified into two kinds: top-down and bottom-up. Top-down taxonomies are created by an authorized group of designers (sometimes in the form of a controlled vocabulary), whereas bottom-up taxonomies (called folksonomies) are created by all users. This definition of "top down" and "bottom up" should not be confused with the distinction between a single hierarchical tree structure (in which there is one correct way to classify each item) versus multiple non-hierarchical sets (in which there are multiple ways to classify an item); the structure of both top-down and bottom-up taxonomies may be either hierarchical, non-hierarchical, or a combination of both. Some researchers and applications have experimented with combining hierarchical and non-hierarchical tagging to aid in information retrieval. Others are combining top-down and bottom-up tagging, including in some large library catalogs (OPACs) such as WorldCat. When tags or other taxonomies have further properties (or semantics) such as relationships and attributes, they constitute an ontology. In folder system a file cannot exist in two or more folders so tag system has been thought more convenient. But transitioning to tag system requires awareness of difference between properties of two systems. In folder system the information of classification is put outside of the file and we can change folder at once. In tag system the information of classification is put inside the file so changing its tag means changing the file and it needs to be saved again and takes time. Metadata tags as described in this article should not be confused with the use of the word "tag" in some software to refer to an automatically generated cross-reference; examples of the latter are tags tables in Emacs and smart tags in Microsoft Office. == History == The use of keywords as part of an identification and classification system long predates computers. Paper data storage devices, notably edge-notched cards, that permitted classification and sorting by multiple criteria were already in use prior to the twentieth century, and faceted classification has been used by libraries since the 1930s. In the late 1970s and early 1980s, Emacs, the text editor for Unix systems, offered a companion software program called Tags that could automatically build a table of cross-references called a tags table that Emacs could use to jump between a function call and that function's definition. This use of the word "tag" did not refer to metadata tags, but was an early use of the word "tag" in software to refer to a word index. Online databases and early websites deployed keyword tags as a way for publishers to help users find content. In the early days of the World Wide Web, the keywords meta element was used by web designers to tell web search engines what the web page was about, but these keywords were only visible in a web page's source code and were not modifiable by users. In 1997, the collaborative portal "A Description of the Equator and Some ØtherLands" produced by documenta X, Germany, used the folksonomic term Tag for its co-authors and guest authors on its Upload page. In "The Equator" the term Tag for user-input was described as an abstract literal or keyword to aid the user. However, users defined singular Tags, and did not share Tags at that point. In 2003, the social bookmarking website Delicious provided a way for its users to add "tags" to their bookmarks (as a way to help find them later); Delicious also provided browseable aggregated views of the bookmarks of all users featuring a particular tag. Within a couple of years, the photo sharing website Flickr allowed its users to add their own text tags to each of their pictures, constructing flexible and easy metadata that made the pictures highly searchable. The success of Flickr and the influence of Delicious popularized the concept, and other social software websites—such as YouTube, Technorati, and Last.fm—also implemented tagging. In 2005, the Atom web syndication standard provided a "category" element for inserting subject categories into web feeds, and in 2007 Tim Bray proposed a "tag" URN. == Examples == === Within a blog === Many systems (and other web content management systems) allow authors to add free-form tags to a post, along with (or instead of) placing the post into a predetermined category. For example, a post may display that it has been tagged with baseball and tickets. Each of those tags is usually a web link leading to an index page listing all of the posts associated with that tag. The blog may have a sidebar listing all the tags in use on that blog, with each tag leading to an index page. To reclassify a post, an author edits its list of tags. All connections between posts are automatically tracked and updated by the blog software; there is no need to relocate the page within a complex hierarchy of categories. === Within application software === Some desktop applications and web applications feature their own tagging systems, such as email tagging in Gmail and Mozilla Thunderbird, bookmark tagging in Firefox, audio tagging in iTunes or Winamp, and photo tagging in various applications. Some of these applications display collections of tags as tag clouds. === Assigned to computer files === There are various systems for applying tags to the files in a computer's file system. In Apple's Mac System 7, released in 1991, users could assign one of seven editable colored labels (with editable names such as "Essential", "Hot", and "In Progress") to each file and folder. In later iterations of the Mac operating system ever since OS X 10.9 was released in 2013, users could assign multiple arbitrary tags as extended file attributes to any file or folder, and before that time the open-source OpenMeta standard provided similar tagging functionality for Mac OS X. Several semantic file systems that implement tags are available for the Linux kernel, including Tagsistant. Microsoft Windows allows users to set tags only on Microsoft Office documents and some kinds of picture files. Cross-platform file tagging standards include Extensible Metadata Platform (XMP), an ISO standard for embedding metadata into popular image, video and document file formats, such as JPEG and PDF, without breaking their readability by applications that do not support XMP. XMP largely supersedes the earlier IPTC Information Interchange Model. Exif is a standard that specifies the image and audio file formats used by digital cameras, including some metadata tags. TagSpaces is an open-source cross-platform application for tagging files; it inserts tags into the filename. === For an event === An official tag is a keyword adopted by events and conferences for participants to use in their web publications, such as blog entries, photos of the event, and presentation slides. Search engines can then index them to make relevant materials related to the event searchable in a uniform way. In this case, the tag is part of a controlled vocabulary. === In research === A researcher may work with a large collection of items (e.g. press quotes, a bibliography, images) in digital form. If he/she wishes to associate each with a small number of themes (e.g. to chapters of a book, or to sub-themes of the overall subject), then a group of tags for these themes can be attached to each of the items in

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  Rnn (software)

  rnn is an open-source machine learning framework that implements recurrent neural network architectures, such as LSTM and GRU, natively in the R programming language, that has been downloaded over 100,000 times (from the RStudio servers alone). The rnn package is distributed through the Comprehensive R Archive Network under the open-source GPL v3 license. == Workflow == The below example from the rnn documentation show how to train a recurrent neural network to solve the problem of bit-by-bit binary addition. == sigmoid == The sigmoid functions and derivatives used in the package were originally included in the package, from version 0.8.0 onwards, these were released in a separate R package sigmoid, with the intention to enable more general use. The sigmoid package is a dependency of the rnn package and therefore automatically installed with it. == Reception == With the release of version 0.3.0 in April 2016 the use in production and research environments became more widespread. The package was reviewed several months later on the R blog The Beginner Programmer as "R provides a simple and very user friendly package named rnn for working with recurrent neural networks.", which further increased usage. The book Neural Networks in R by Balaji Venkateswaran and Giuseppe Ciaburro uses rnn to demonstrate recurrent neural networks to R users. It is also used in the r-exercises.com course "Neural network exercises". The RStudio CRAN mirror download logs show that the package is downloaded on average about 2,000 per month from those servers , with a total of over 100,000 downloads since the first release, according to RDocumentation.org, this puts the package in the 15th percentile of most popular R packages .

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  Mind map

  A mind map is a diagram used to visually organize information into a hierarchy, showing relationships among pieces of the whole. It is often based on a single concept, drawn as an image in the center of a blank page, to which associated representations of ideas such as images, words and parts of words are added. Major ideas are connected directly to the central concept, and other ideas branch out from those major ideas. Mind maps can also be drawn by hand, either as "notes" during a lecture, meeting or planning session, for example, or as higher quality pictures when more time is available. Mind maps are considered to be a type of spider diagram. == Origin == Although the term "mind map" was first popularized by British popular psychology author and television personality Tony Buzan, the use of diagrams that visually "map" information using branching and radial maps traces back centuries. These pictorial methods record knowledge and model systems, and have a long history in learning, brainstorming, memory, visual thinking, and problem solving by educators, engineers, psychologists, and others. Some of the earliest examples of such graphical records were developed by Porphyry of Tyros, a noted thinker of the 3rd century, as he graphically visualized the concept categories of Aristotle. Philosopher Ramon Llull (1235–1315) also used such techniques. Buzan's specific approach, and the introduction of the term "mind map", started with a 1974 BBC TV series he hosted, called Use Your Head. In this show, and companion book series, Buzan promoted his conception of radial tree, diagramming key words in a colorful, radiant, tree-like structure. == Differences from other visualizations == Concept maps: Mind maps differ from concept maps in that mind maps are based on a radial hierarchy (tree structure) denoting relationships with a central concept, whereas concept maps can be more free-form, based on connections between concepts in more diverse patterns. Also, concept maps typically have text labels on the links between nodes. However, either can be part of a larger personal knowledge base system. Modeling graphs or graphical modeling languages: There is no rigorous right or wrong with mind maps, which rely on the arbitrariness of mnemonic associations to aid people's information organization and memory. In contrast, a modeling graph such as a UML diagram structures elements using a precise standardized iconography to aid the design of systems. == Research == === Effectiveness === Cunningham (2005) conducted a user study in which 80% of the students thought "mindmapping helped them understand concepts and ideas in science". Other studies also report some subjective positive effects of the use of mind maps. Positive opinions on their effectiveness, however, were much more prominent among students of art and design than in students of computer and information technology, with 62.5% vs 34% (respectively) agreeing that they were able to understand concepts better with mind mapping software. Farrand, Hussain, and Hennessy (2002) found that spider diagrams (similar to concept maps) had limited, but significant, impact on memory recall in undergraduate students (a 10% increase over baseline for a 600-word text only) as compared to preferred study methods (a 6% increase over baseline). This improvement was only robust after a week for those in the diagram group and there was a significant decrease in motivation compared to the subjects' preferred methods of note taking. A meta study about concept mapping concluded that concept mapping is more effective than "reading text passages, attending lectures, and participating in class discussions". The same study also concluded that concept mapping is slightly more effective "than other constructive activities such as writing summaries and outlines". However, results were inconsistent, with the authors noting "significant heterogeneity was found in most subsets". In addition, they concluded that low-ability students may benefit more from mind mapping than high-ability students. === Features === Joeran Beel and Stefan Langer conducted a comprehensive analysis of the content of mind maps. They analysed 19,379 mind maps from 11,179 users of the mind mapping applications SciPlore MindMapping (now Docear) and MindMeister. Results include that average users create only a few mind maps (mean=2.7), average mind maps are rather small (31 nodes) with each node containing about three words (median). However, there were exceptions. One user created more than 200 mind maps, the largest mind map consisted of more than 50,000 nodes and the largest node contained ~7,500 words. The study also showed that between different mind mapping applications (Docear vs MindMeister) significant differences exist related to how users create mind maps. === Automatic creation === There have been some attempts to create mind maps automatically. Brucks & Schommer created mind maps automatically from full-text streams. Rothenberger et al. extracted the main story of a text and presented it as mind map. There is also a patent application about automatically creating sub-topics in mind maps. == Tools == Mind-mapping software can be used to organize large amounts of information, combining spatial organization, dynamic hierarchical structuring and node folding.Software packages can extend the concept of mind-mapping by allowing individuals to map more than thoughts and ideas with information on their computers and the Internet, like spreadsheets, documents, Internet sites, images and videos. It has been suggested that mind-mapping can improve learning/study efficiency up to 15% over conventional note-taking. == Gallery == The following dozen examples of mind maps show the range of styles that a mind map may take, from hand-drawn to computer-generated and from mostly text to highly illustrated. Despite their stylistic differences, all of the examples share a tree structure that hierarchically connects sub-topics to a main topic.

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  Transfer function matrix

  In control system theory, and various branches of engineering, a transfer function matrix, or just transfer matrix is a generalisation of the transfer functions of single-input single-output (SISO) systems to multiple-input and multiple-output (MIMO) systems. The matrix relates the outputs of the system to its inputs. It is a particularly useful construction for linear time-invariant (LTI) systems because it can be expressed in terms of the s-plane. In some systems, especially ones consisting entirely of passive components, it can be ambiguous which variables are inputs and which are outputs. In electrical engineering, a common scheme is to gather all the voltage variables on one side and all the current variables on the other regardless of which are inputs or outputs. This results in all the elements of the transfer matrix being in units of impedance. The concept of impedance (and hence impedance matrices) has been borrowed into other energy domains by analogy, especially mechanics and acoustics. Many control systems span several different energy domains. This requires transfer matrices with elements in mixed units. This is needed both to describe transducers that make connections between domains and to describe the system as a whole. If the matrix is to properly model energy flows in the system, compatible variables must be chosen to allow this. == General == A MIMO system with m outputs and n inputs is represented by a m × n matrix. Each entry in the matrix is in the form of a transfer function relating an output to an input. For example, for a three-input, two-output system, one might write, [ y 1 y 2 ] = [ g 11 g 12 g 13 g 21 g 22 g 23 ] [ u 1 u 2 u 3 ] {\displaystyle {\begin{bmatrix}y_{1}\\y_{2}\end{bmatrix}}={\begin{bmatrix}g_{11}&g_{12}&g_{13}\\g_{21}&g_{22}&g_{23}\end{bmatrix}}{\begin{bmatrix}u_{1}\\u_{2}\\u_{3}\end{bmatrix}}} where the un are the inputs, the ym are the outputs, and the gmn are the transfer functions. This may be written more succinctly in matrix operator notation as, Y = G U {\displaystyle \mathbf {Y} =\mathbf {G} \mathbf {U} } where Y is a column vector of the outputs, G is a matrix of the transfer functions, and U is a column vector of the inputs. In many cases, the system under consideration is a linear time-invariant (LTI) system. In such cases, it is convenient to express the transfer matrix in terms of the Laplace transform (in the case of continuous time variables) or the z-transform (in the case of discrete time variables) of the variables. This may be indicated by writing, for instance, Y ( s ) = G ( s ) U ( s ) {\displaystyle \mathbf {Y} (s)=\mathbf {G} (s)\mathbf {U} (s)} which indicates that the variables and matrix are in terms of s, the complex frequency variable of the s-plane arising from Laplace transforms, rather than time. The examples in this article are all assumed to be in this form, although that is not explicitly indicated for brevity. For discrete time systems s is replaced by z from the z-transform, but this makes no difference to subsequent analysis. The matrix is particularly useful when it is a proper rational matrix, that is, all its elements are proper rational functions. In this case, the state-space representation can be applied. In systems engineering, the overall system transfer matrix G (s) is decomposed into two parts: H (s) representing the system being controlled, and C(s) representing the control system. C (s) takes as its inputs the inputs of G (s) and the outputs of H (s). The outputs of C (s) form the inputs for H (s). == Electrical systems == In electrical systems, it is often the case that the distinction between input and output variables is ambiguous. They can be either, depending on circumstance and point of view. In such cases, the concept of port (a place where energy is transferred from one system to another) can be more useful than input and output. It is customary to define two variables for each port (p): the voltage across it (Vp) and the current entering it (Ip). For instance, the transfer matrix of a two-port network can be defined as follows, [ V 1 V 2 ] = [ z 11 z 12 z 21 z 22 ] [ I 1 I 2 ] {\displaystyle {\begin{bmatrix}V_{1}\\V_{2}\end{bmatrix}}={\begin{bmatrix}z_{11}&z_{12}\\z_{21}&z_{22}\\\end{bmatrix}}{\begin{bmatrix}I_{1}\\I_{2}\end{bmatrix}}} where the zmn are called the impedance parameters, or z-parameters. They are so-called because they are in units of impedance and relate port currents to a port voltage. The z-parameters are not the only way that transfer matrices are defined for two-port networks. Six basic matrices relate voltages and currents, each with advantages for particular system network topologies. However, only two of these can be extended beyond two ports to an arbitrary number of ports. These two are the z-parameters and their inverse, the admittance parameters or y-parameters. To understand the relationship between port voltages and currents and inputs and outputs, consider the simple voltage divider circuit. If we only wish to consider the output voltage (V2) resulting from applying the input voltage (V1) then the transfer function can be expressed as, [ V 2 ] = [ R 2 R 1 + R 2 ] [ V 1 ] {\displaystyle {\begin{bmatrix}V_{2}\end{bmatrix}}={\begin{bmatrix}{\dfrac {R_{2}}{R_{1}+R_{2}}}\end{bmatrix}}{\begin{bmatrix}V_{1}\end{bmatrix}}} which can be considered the trivial case of a 1×1 transfer matrix. The expression correctly predicts the output voltage if there is no current leaving port 2, but is increasingly inaccurate as the load increases. If, however, we attempt to use the circuit in reverse, driving it with a voltage at port 2 and calculate the resulting voltage at port 1 the expression gives completely the wrong result even with no load on port 1. It predicts a greater voltage at port 1 than was applied at port 2, an impossibility with a purely resistive circuit like this one. To correctly predict the behaviour of the circuit, the currents entering or leaving the ports must also be taken into account, which is what the transfer matrix does. The impedance matrix for the voltage divider circuit is, [ V 1 V 2 ] = [ R 1 + R 2 R 2 R 2 R 2 ] [ I 1 I 2 ] {\displaystyle {\begin{bmatrix}V_{1}\\V_{2}\end{bmatrix}}={\begin{bmatrix}R_{1}+R_{2}&R_{2}\\R_{2}&R_{2}\end{bmatrix}}{\begin{bmatrix}I_{1}\\I_{2}\end{bmatrix}}} which fully describes its behaviour under all input and output conditions. At microwave frequencies, none of the transfer matrices based on port voltages and currents are convenient to use in practice. Voltage is difficult to measure directly, current next to impossible, and the open circuits and short circuits required by the measurement technique cannot be achieved with any accuracy. For waveguide implementations, circuit voltage and current are entirely meaningless. Transfer matrices using different sorts of variables are used instead. These are the powers transmitted into, and reflected from a port, which are readily measured in the transmission line technology used in distributed-element circuits in the microwave band. The most well-known and widely used of these sorts of parameters is the scattering parameters, or s-parameters. == Mechanical and other systems == The concept of impedance can be extended into the mechanical and other domains through a mechanical-electrical analogy, hence the impedance parameters and other forms of 2-port network parameters can also be extended to the mechanical domain. To do this, an effort variable and a flow variable are made analogues of voltage and current, respectively. For mechanical systems under translation these variables are force and velocity respectively. Expressing the behaviour of a mechanical component as a two-port or multi-port with a transfer matrix is a useful thing to do because, like electrical circuits, the component can often be operated in reverse and its behaviour is dependent on the loads at the inputs and outputs. For instance, a gear train is often characterised simply by its gear ratio, a SISO transfer function. However, the gearbox output shaft can be driven around to turn the input shaft, requiring a MIMO analysis. In this example, the effort and flow variables are torque T and angular velocity ω, respectively. The transfer matrix in terms of z-parameters will look like, [ T 1 T 2 ] = [ z 11 z 12 z 21 z 22 ] [ ω 1 ω 2 ] {\displaystyle {\begin{bmatrix}T_{1}\\T_{2}\end{bmatrix}}={\begin{bmatrix}z_{11}&z_{12}\\z_{21}&z_{22}\end{bmatrix}}{\begin{bmatrix}\omega _{1}\\\omega _{2}\end{bmatrix}}} However, the z-parameters are not necessarily the most convenient for characterising gear trains. A gear train is the analogue of an electrical transformer and the h-parameters (hybrid parameters) better describe transformers because they directly include the turns ratios (the analogue of gear ratios). The gearbox transfer matrix in h-parameter format is, [ T 1 ω 2 ] = [ h 11 h 12 h 21 h 22 ] [ ω 1 T 2 ] {\displaystyle {\begin{bmatrix}T_{1}\\\omega _{2}\end{bm

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  Sasha Stiles

  Sasha Stiles (born 1980) is an American artist and poet. After discovering natural language processing, she created the 2021 poetry collection Technelegy through an eponymous AI model, before presenting the 2025–2026 installation A Living Poem at the Museum of Modern Art. In addition to artificial intelligence, binary code and non-fungible tokens have been important aspects of her work. == Biography == Stiles was born in 1980 in Pasadena, California, to documentary filmmaker parents whose work includes Cosmos: A Personal Voyage. She was interested in science fiction during her youth, particularly how they addressed human-machine collaboration and posthumanism. She graduated magna cum laude from Harvard University with a Bachelor of Arts in 2002 and she graduated with high honors from the University of Oxford with a Master of Studies in 2004. Originally, Stiles's poetry focused on technology. In 2017, she discovered natural language processing, piquing her interest in its ability to process thoughts and words comparably to its human counterparts. Despite lacking a technological background, she managed to channel people like Gwern Branwen, Ross Goodwin, and Allison Parrish as inspirations for her AI work, and in 2019, she started training an AI model named Technelegy. In 2021, Black Spring Press published her poetry collection Technelegy, where she combines AI-generated content produced by the titular AI model with her own traditionally-created work; the AI-generated content was produced by processing Stiles's own poetry onto GPT-2 and GPT-3. She and Technelegy later co-created A Living Poem, which ran at the Museum of Modern Art's Hyundai Card Digital Wall from September 2025 to March 2026. Stiles also has used non-fungible tokens as a platform for her poetry, having been inspired to go into blockchain by her experiences working with a metaverse exhibition curated by Jess Conatser. She has used Christie's and SuperRare to sell several of her poems as tokenized real-world assets, including Daughter of E.V.E. (Ex-Vivo Uterine Environment), a 2021 single-channel video using freeze-frame shots to hide poetry. In 2021, she co-founded TheVerseVerse (stylized as theVERSEverse), a non-fungible token gallery specializing in poetry. She later created Four Core Texts: Humanifesto and Other Poems, involving four NFT videos of poetry written in looping handwriting and powered by Technelegy. Stiles uses binary code as an inspiration for her work, citing in part its "quite antagonistic system of a binary 'EITHER / OR'", which she connected to several dichotomies pitting humanity and the present against technology and the future. In 2018, she started Analog Binary Code, where she creates sculptures by arranging objects in binary code ciphers. She also created Cursive Binary, where she combines binary with cursive handwriting, after writing zeros and ones on a steamed wall while showering. Stiles and the robot BINA48 co-created the 2020 ArtYard exhibition A Valentine for the Future. She was part of the 2021 group exhibition Computational Poetics at the Beall Center for Art and Technology. From February 24 to March 18, 2023, she held her solo show Binary Odes (stylized as B1NARY 0DES) at Annka Kultys Gallery. By 2024, her work had appeared in places such as Gucci storefronts and Times Square billboards. She designed Words Beyond Words, the official poster for Art Basel in Basel 2025. Stiles is based in Milford, New Jersey, where she lives with her husband, musician Kris Bones. She has also lived in Jersey City and Bucks County, Pennsylvania. She is Kalmyk-American on her mother's side, and she has also announced plans to create a version of Technelegy in her ancestral language Kalmyk.

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  Linear belief function

  Linear belief functions are an extension of the Dempster–Shafer theory of belief functions to the case when variables of interest are continuous. Examples of such variables include financial asset prices, portfolio performance, and other antecedent and consequent variables. The theory was originally proposed by Arthur P. Dempster in the context of Kalman Filters and later was elaborated, refined, and applied to knowledge representation in artificial intelligence and decision making in finance and accounting by Liping Liu. == Concept == A linear belief function intends to represent our belief regarding the location of the true value as follows: We are certain that the truth is on a so-called certainty hyperplane but we do not know its exact location; along some dimensions of the certainty hyperplane, we believe the true value could be anywhere from –∞ to +∞ and the probability of being at a particular location is described by a normal distribution; along other dimensions, our knowledge is vacuous, i.e., the true value is somewhere from –∞ to +∞ but the associated probability is unknown. A belief function in general is defined by a mass function over a class of focal elements, which may have nonempty intersections. A linear belief function is a special type of belief function in the sense that its focal elements are exclusive, parallel sub-hyperplanes over the certainty hyperplane and its mass function is a normal distribution across the sub-hyperplanes. Based on the above geometrical description, Shafer and Liu propose two mathematical representations of a LBF: a wide-sense inner product and a linear functional in the variable space, and as their duals over a hyperplane in the sample space. Monney proposes still another structure called Gaussian hints. Although these representations are mathematically neat, they tend to be unsuitable for knowledge representation in expert systems. == Knowledge representation == A linear belief function can represent both logical and probabilistic knowledge for three types of variables: deterministic such as an observable or controllable, random whose distribution is normal, and vacuous on which no knowledge bears. Logical knowledge is represented by linear equations, or geometrically, a certainty hyperplane. Probabilistic knowledge is represented by a normal distribution across all parallel focal elements. In general, assume X is a vector of multiple normal variables with mean μ and covariance Σ. Then, the multivariate normal distribution can be equivalently represented as a moment matrix: M ( X ) = ( μ Σ ) . {\displaystyle M(X)=\left({\begin{array}{{20}c}\mu \\\Sigma \end{array}}\right).} If the distribution is non-degenerate, i.e., Σ has a full rank and its inverse exists, the moment matrix can be fully swept: M ( X → ) = ( μ Σ − 1 − Σ − 1 ) {\displaystyle M({\vec {X}})=\left({\begin{array}{{20}c}\mu \Sigma ^{-1}\\-\Sigma ^{-1}\end{array}}\right)} Except for normalization constant, the above equation completely determines the normal density function for X. Therefore, M ( X → ) {\displaystyle M({\vec {X}})} represents the probability distribution of X in the potential form. These two simple matrices allow us to represent three special cases of linear belief functions. First, for an ordinary normal probability distribution M(X) represents it. Second, suppose one makes a direct observation on X and obtains a value μ. In this case, since there is no uncertainty, both variance and covariance vanish, i.e., Σ = 0. Thus, a direct observation can be represented as: M ( X ) = ( μ 0 ) {\displaystyle M(X)=\left({\begin{array}{{20}c}\mu \\0\end{array}}\right)} Third, suppose one is completely ignorant about X. This is a very thorny case in Bayesian statistics since the density function does not exist. By using the fully swept moment matrix, we represent the vacuous linear belief functions as a zero matrix in the swept form follows: M ( X → ) = [ 0 0 ] {\displaystyle M({\vec {X}})=\left[{\begin{array}{{20}c}0\\0\end{array}}\right]} One way to understand the representation is to imagine complete ignorance as the limiting case when the variance of X approaches to ∞, where one can show that Σ−1 = 0 and hence M ( X → ) {\displaystyle M({\vec {X}})} vanishes. However, the above equation is not the same as an improper prior or normal distribution with infinite variance. In fact, it does not correspond to any unique probability distribution. For this reason, a better way is to understand the vacuous linear belief functions as the neutral element for combination (see later). To represent the remaining three special cases, we need the concept of partial sweeping. Unlike a full sweeping, a partial sweeping is a transformation on a subset of variables. Suppose X and Y are two vectors of normal variables with the joint moment matrix: M ( X , Y ) = [ μ 1 Σ 11 Σ 21 μ 2 Σ 12 Σ 22 ] {\displaystyle M(X,Y)=\left[{\begin{array}{{20}c}{\begin{array}{{20}c}\mu _{1}\\\Sigma _{11}\\\Sigma _{21}\end{array}}&{\begin{array}{{20}c}\mu _{2}\\\Sigma _{12}\\\Sigma _{22}\end{array}}\end{array}}\right]} Then M(X, Y) may be partially swept. For example, we can define the partial sweeping on X as follows: M ( X → , Y ) = [ μ 1 ( Σ 11 ) − 1 − ( Σ 11 ) − 1 Σ 21 ( Σ 11 ) − 1 μ 2 − μ 1 ( Σ 11 ) − 1 Σ 12 ( Σ 11 ) − 1 Σ 12 Σ 22 − Σ 21 ( Σ 11 ) − 1 Σ 12 ] {\displaystyle M({\vec {X}},Y)=\left[{\begin{array}{{20}c}{\begin{array}{{20}c}\mu _{1}(\Sigma _{11})^{-1}\\-(\Sigma _{11})^{-1}\\\Sigma _{21}(\Sigma _{11})^{-1}\end{array}}&{\begin{array}{{20}c}\mu _{2}-\mu _{1}(\Sigma _{11})^{-1}\Sigma _{12}\\(\Sigma _{11})^{-1}\Sigma _{12}\\\Sigma _{22}-\Sigma _{21}(\Sigma _{11})^{-1}\Sigma _{12}\end{array}}\end{array}}\right]} If X is one-dimensional, a partial sweeping replaces the variance of X by its negative inverse and multiplies the inverse with other elements. If X is multidimensional, the operation involves the inverse of the covariance matrix of X and other multiplications. A swept matrix obtained from a partial sweeping on a subset of variables can be equivalently obtained by a sequence of partial sweepings on each individual variable in the subset and the order of the sequence does not matter. Similarly, a fully swept matrix is the result of partial sweepings on all variables. We can make two observations. First, after the partial sweeping on X, the mean vector and covariance matrix of X are respectively μ 1 ( Σ 11 ) − 1 {\displaystyle \mu _{1}(\Sigma _{11})^{-1}} and − ( Σ 11 ) − 1 {\displaystyle -(\Sigma _{11})^{-1}} , which are the same as that of a full sweeping of the marginal moment matrix of X. Thus, the elements corresponding to X in the above partial sweeping equation represent the marginal distribution of X in potential form. Second, according to statistics, μ 2 − μ 1 ( Σ 11 ) − 1 Σ 12 {\displaystyle \mu _{2}-\mu _{1}(\Sigma _{11})^{-1}\Sigma _{12}} is the conditional mean of Y given X = 0; Σ 22 − Σ 21 ( Σ 11 ) − 1 Σ 12 {\displaystyle \Sigma _{22}-\Sigma _{21}(\Sigma _{11})^{-1}\Sigma _{12}} is the conditional covariance matrix of Y given X = 0; and ( Σ 11 ) − 1 Σ 12 {\displaystyle (\Sigma _{11})^{-1}\Sigma _{12}} is the slope of the regression model of Y on X. Therefore, the elements corresponding to Y indices and the intersection of X and Y in M ( X → , Y ) {\displaystyle M({\vec {X}},Y)} represents the conditional distribution of Y given X = 0. These semantics render the partial sweeping operation a useful method for manipulating multivariate normal distributions. They also form the basis of the moment matrix representations for the three remaining important cases of linear belief functions, including proper belief functions, linear equations, and linear regression models. === Proper linear belief functions === For variables X and Y, assume there exists a piece of evidence justifying a normal distribution for variables Y while bearing no opinions for variables X. Also, assume that X and Y are not perfectly linearly related, i.e., their correlation is less than 1. This case involves a mix of an ordinary normal distribution for Y and a vacuous belief function for X. Thus, we represent it using a partially swept matrix as follows: M ( X → , Y ) = [ 0 0 0 μ 2 0 Σ 22 ] {\displaystyle M({\vec {X}},Y)=\left[{\begin{array}{{20}c}{\begin{array}{{20}c}0\\0\\0\end{array}}&{\begin{array}{{20}c}\mu _{2}\\0\\\Sigma _{22}\\\end{array}}\end{array}}\right]} This is how we could understand the representation. Since we are ignorant on X, we use its swept form and set μ 1 ( Σ 11 ) − 1 = 0 {\displaystyle \mu _{1}(\Sigma _{11})^{-1}=0} and − ( Σ 11 ) − 1 = 0 {\displaystyle -(\Sigma _{11})^{-1}=0} . Since the correlation between X and Y is less than 1, the regression coefficient of X on Y approaches to 0 when the variance of X approaches to ∞. Therefore, ( Σ 11 ) − 1 Σ 12 = 0 {\displaystyle (\Sigma _{11})^{-1}\Sigma _{12}=0} . Similarly, one can prove that μ 1 ( Σ 11 ) − 1 Σ 12 = 0 {\displaystyle \mu _{1}(\Sigma _{11})^{-1}\Sigma _{12}=0} and Σ 21 ( Σ 11 ) −

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  Rule-based system

  In computer science, a rule-based system is a computer system in which domain-specific knowledge is represented in the form of rules and general-purpose reasoning is used to solve problems in the domain. Two different kinds of rule-based systems emerged within the field of artificial intelligence in the 1970s: Production systems, which use if-then rules to derive actions from conditions. Logic programming systems, which use conclusion if conditions rules to derive conclusions from conditions. The differences and relationships between these two kinds of rule-based system has been a major source of misunderstanding and confusion. Both kinds of rule-based systems use either forward or backward chaining, in contrast with imperative programs, which execute commands listed sequentially. However, logic programming systems have a logical interpretation, whereas production systems do not. == Production system rules == A classic example of a production rule-based system is the domain-specific expert system that uses rules to make deductions or choices. For example, an expert system might help a doctor choose the correct diagnosis based on a cluster of symptoms, or select tactical moves to play a game. Rule-based systems can be used to perform lexical analysis to compile or interpret computer programs, or in natural language processing. Rule-based programming attempts to derive execution instructions from a starting set of data and rules. This is a more indirect method than that employed by an imperative programming language, which lists execution steps sequentially. === Construction === A typical rule-based system has four basic components: A list of rules or rule base, which is a specific type of knowledge base. An inference engine or semantic reasoner, which infers information or takes action based on the interaction of input and the rule base. The interpreter executes a production system program by performing the following match-resolve-act cycle: Match: In this first phase, the condition sides of all productions are matched against the contents of working memory. As a result a set (the conflict set) is obtained, which consists of instantiations of all satisfied productions. An instantiation of a production is an ordered list of working memory elements that satisfies the condition side of the production. Conflict-resolution: In this second phase, one of the production instantiations in the conflict set is chosen for execution. If no productions are satisfied, the interpreter halts. Act: In this third phase, the actions of the production selected in the conflict-resolution phase are executed. These actions may change the contents of working memory. At the end of this phase, execution returns to the first phase. Temporary working memory, which is a database of facts. A user interface or other connection to the outside world through which input and output signals are received and sent. Whereas the matching phase of the inference engine has a logical interpretation, the conflict resolution and action phases do not. Instead, "their semantics is usually described as a series of applications of various state-changing operators, which often gets quite involved (depending on the choices made in deciding which ECA rules fire, when, and so forth), and they can hardly be regarded as declarative". == Logic programming rules == The logic programming family of computer systems includes the programming language Prolog, the database language Datalog and the knowledge representation and problem-solving language Answer Set Programming (ASP). In all of these languages, rules are written in the form of clauses: A :- B1, ..., Bn. and are read as declarative sentences in logical form: A if B1 and ... and Bn. In the simplest case of Horn clauses (or "definite" clauses), which are a subset of first-order logic, all of the A, B1, ..., Bn are atomic formulae. Although Horn clause logic programs are Turing complete, for many practical applications, it is useful to extend Horn clause programs by allowing negative conditions, implemented by negation as failure. Such extended logic programs have the knowledge representation capabilities of a non-monotonic logic. == Differences and relationships between production rules and logic programming rules == The most obvious difference between the two kinds of systems is that production rules are typically written in the forward direction, if A then B, and logic programming rules are typically written in the backward direction, B if A. In the case of logic programming rules, this difference is superficial and purely syntactic. It does not affect the semantics of the rules. Nor does it affect whether the rules are used to reason backwards, Prolog style, to reduce the goal B to the subgoals A, or whether they are used, Datalog style, to derive B from A. In the case of production rules, the forward direction of the syntax reflects the stimulus-response character of most production rules, with the stimulus A coming before the response B. Moreover, even in cases when the response is simply to draw a conclusion B from an assumption A, as in modus ponens, the match-resolve-act cycle is restricted to reasoning forwards from A to B. Reasoning backwards in a production system would require the use of an entirely different kind of inference engine. In his Introduction to Cognitive Science, Paul Thagard includes logic and rules as alternative approaches to modelling human thinking. He does not consider logic programs in general, but he considers Prolog to be, not a rule-based system, but "a programming language that uses logic representations and deductive techniques" (page 40). He argues that rules, which have the form IF condition THEN action, are "very similar" to logical conditionals, but they are simpler and have greater psychological plausibility (page 51). Among other differences between logic and rules, he argues that logic uses deduction, but rules use search (page 45) and can be used to reason either forward or backward (page 47). Sentences in logic "have to be interpreted as universally true", but rules can be defaults, which admit exceptions (page 44). He does not observe that all of these features of rules apply to logic programming systems.

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  Lexical choice

  Lexical choice is the subtask of Natural language generation that involves choosing the content words (nouns, non-auxiliary verbs, adjectives, and adverbs) in a generated text. Function words (determiners, for example) are usually chosen during realisation. == Examples == The simplest type of lexical choice involves mapping a domain concept (perhaps represented in an ontology) to a word. For example, the concept Finger might be mapped to the word finger. A more complex situation is when a domain concept is expressed using different words in different situations. For example, the domain concept Value-Change can be expressed in many ways: The temperature rose: the verb rose is used for a Value-Change in temperature which increases the value. The temperature fell: the verb fell is used for a Value-Change in temperature which decreases the value. The rain got heavier: the phrase got heavier is used for a Value-Change in precipitation amount when the precipitation is rain. Sometimes words can communicate additional contextual information, for example: The temperature plummeted: the verb plummeted is used for a Value-Change in temperature which decreases the value, when the change is rapid and large. Contextual information is especially significant for vague terms such as tall. For example, a 2m tall man is tall, but a 2m tall horse is small. == Linguistic perspective == Lexical choice modules must be informed by linguistic knowledge of how the system's input data maps onto words. This is a question of semantics, but it is also influenced by syntactic factors (such as collocation effects) and pragmatic factors (such as context). Hence NLG systems need linguistic models of how meaning is mapped to words in the target domain (genre) of the NLG system. Genre tends to be very important; for example the verb veer has a very specific meaning in weather forecasts (wind direction is changing in a clockwise direction) which it does not have in general English, and a weather-forecast generator must be aware of this genre-specific meaning. In some cases there are major differences in how different people use the same word; for example, some people use by evening to mean 6PM and others use it to mean midnight. Psycholinguists have shown that when people speak to each other, they agree on a common interpretation via lexical alignment; this is not something which NLG systems can yet do. Ultimately, lexical choice must deal with the fundamental issue of how language relates to the non-linguistic world. For example, a system which chose colour terms such as red to describe objects in a digital image would need to know which RGB pixel values could generally be described as red; how this was influenced by visual (lighting, other objects in the scene) and linguistic (other objects being discussed) context; what pragmatic connotations were associated with red (for example, when an apple is called red, it is assumed to be ripe as well as have the colour red); and so forth. == Algorithms and models == A number of algorithms and models have been developed for lexical choice in the research community, for example Edmonds developed a model for choosing between near-synonyms (words with similar core meanings but different connotations). However such algorithms and models have not been widely used in applied NLG systems; such systems have instead often used quite simple computational models, and invested development effort in linguistic analysis instead of algorithm development.

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  Project Mariner

  Project Mariner was a research prototype developed by Google DeepMind that explored human-agent interactions, particularly within web browsers. It automated tasks such as online shopping, information retrieval, and form-filling, aiming to enhance user productivity by delegating routine web-based tasks to an AI agent. Project Mariner operated as an experimental Chrome extension that understands the contents of your screen, including images, code, forms, and more. It could interpret complex goals, plan actionable steps, and navigate websites to carry out tasks, while keeping the user informed and allowing them to intervene at any time. As of May 2025, Project Mariner was available to Google AI Ultra subscribers in the US and was being integrated into the Gemini API and Vertex AI, allowing developers to build applications powered by the agent Google plans to bring Project Mariner’s capabilities to more countries and integrate it into Google Search's AI Mode, which was currently in the Search Labs testing phase. Project Mariner was discontinued on May 4, 2026.

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  Simulation decomposition

  SimDec, or Simulation decomposition, is a hybrid uncertainty and sensitivity analysis method, for visually examining the relationships between the output and input variables of a computational model. SimDec maps multivariable scenarios onto the distribution of the model output. This visual analytics approach exposes the underlying nature of the model behavior, including its nonlinear and multivariate interaction effects. SimDec can be used in any range of science, engineering, and social domains. Existing applications include business and environmental issues. == Method == SimDec operates on Monte Carlo simulation (or measured) data where both output and input values are recorded. At least one thousand observations (or simulated iterations) are typically recommended to preserve the readability of the resulting histograms. An outline of the decomposition algorithm, which is readily available in multiple programming languages, proceeds as follows: Select the input variables for decomposition. One can use sensitivity indices (see variance-based sensitivity analysis) to define the most influential variables for decomposition or choose them manually according to the decision-problem context (for example, only those input variables that the decision-maker can act upon). Two to three input variables, ordered by decreasing value of their sensitivity indices, usually provide the most meaningful decomposition results. Divide the inputs into states. The numeric ranges of the inputs are split into several intervals with an equal number of observations in each. For categorical variables, the categories represent states. Form scenarios. All combinations of states of the selected input variables produce unique scenarios or subsets of the data. For example, if the range of X2 is divided into low, medium and high, and X3 takes values of 1 or 2, six scenarios are formed: (i) X2 low & X3 = 1, (ii) X2 low & X3 = 2, (iii) X2 medium & X3 = 1, (iv) X2 medium & X3 = 2, (v) X2 high & X3 = 1, and (vi) X2 high & X3 = 2. Assign scenarios to each output value. The simulation data is used to define the scenario index for each simulation run. For example, if an X2 value falls into the low state and X3 is equal to 2, the corresponding scenario, defined in Step 3, is (ii). Color-code the output distribution. When all output values are assigned scenario indices, they are plotted as series in a stacked histogram, visually separated by color-coding. For ease of visual perception, the states of the most influential input variable are assigned distinct colors, and all the remaining partitions take shades of those colors (see Figure). All of these steps can be run automatically on the given data using the open-source SimDec packages currently available in Python, R, Julia, and Matlab. A SimDec template in Excel runs a Monte Carlo simulation of a spreadsheet model but possesses only a manual option for input selection. == How to read SimDec == === Histogram === Histogram is an approximate representation of the distribution of numerical data. Its horizontal axis shows the range of the variable of interest, and its vertical axis denotes count, also called frequency, or, if divided by the total number of data points, probability. The distribution alone can supply only limited information about the data – its minimum, maximum, and shape (where the most of data occurs). === Judging the importance of inputs === If an input variable has no effect on the output, its states (e.g., low & high) would lie on top of each other on the SimDec histogram, occupying fully overlapping ranges of the output. If an input variable has a strong effect and explains most of the variance of the output, the border between its states on the SimDec histogram would be vertical. Such visualization has an important decision-making implication – e.g., if the high state of X can be achieved, it would guarantee a certain range of Y. All cases in-between with low-to-strong effects would show a diagonal border between the states. The less they overlap, the larger the effect of X on Y. While the horizontal displacement of sub-distributions on the SimDec histogram is the key to interpreting the results, the vertical disposition of sub-distributions is just a technical matter of the order of plotting the series of the stacked histogram. === Exploring the interaction of inputs === When two or more input variables are used for decomposition, it becomes possible to examine their joint effects. A schematic visualization portrays how different types of joint effects of input variables on the output appear on SimDec visualization. Understanding the nature of interaction effects in a computational model and its behavior in general is crucial for effective decision-making. == Limitations == The SimDec method has several limitations: It is based on Monte Carlo simulation and thus requires running a computational model a thousand of times or more. To models that take hours to evaluate once, it would be impossible to use SimDec (unless a supercomputer and/or large of time are available). SimDec is based on a histogram, thus, for binary or categorical output variables, the visualization would be very limited (e.g., only a few bins). The more input variables one selects for the decomposition, the less readable the histogram becomes. Only cases with two and three input variables are presented in.

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