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  N-World

  N-World is a 3D graphics package developed by Nichimen Graphics in the 1990s, for Silicon Graphics and Windows NT workstations. Intended primarily for video game content creation, it has polygon modeling tools, 2D and 3D paint, scripting, color reduction, and exporters for several popular game consoles. After its initial release on Windows NT, N-World was renamed Mirai. The winged edge 3D modeler in N-World inspired the development at Nichimen Graphics of Nendo, a standalone 3D modeler, which in turn inspired the open source modeler Wings 3D. == History == N-World originated with Symbolics, a computer manufacturer notable for producing Lisp-based systems in the 1980s. Among the software packages that were produced for Symbolics computers are S-Graphics, a 3D animation suite that includes modules for polygon modeling, dynamics, paint, and rendering — titled S-Geometry, S-Dynamics, S-Paint, and S-Render, respectively. In 1992, Japanese trading company Nichimen Corporation purchased the rights to S-Graphics, ported it to Silicon Graphics IRIX, and marketed it as N-World. N-World retains the Lisp-based underpinnings of its predecessor, but was targeted at interactive content producers, with features useful for game developers. It was priced at US$16,995 (equivalent to $34,100 in 2025) for the full suite, later reduced to $9,995 when ported to Windows NT in 1997. N-World was used to create graphics for many console games in the 1990s, specifically most of the Nintendo 64 games, like Super Mario 64 and Final Fantasy VII. It was superseded by Mirai in 1999. == Features == The N-World package, like its predecessor S-Graphics, is divided into several components: N-Geometry: 3D polygon-based modeling tools, including smoothing, "magnet" geometry editing, and instancing. N-Dynamics: Animation tools including scripting, curve-based animation, and skeletal animation. N-Render: Surfacing and rendering tools with ray tracing and materials output to various game console formats. N-Paint: 2D and 3D paint with mattes, effects, color reduction, and a visual VRAM editor for PlayStation. Game Tools: Utilities for game developers, including exporters for PlayStation, Nintendo 64, and Saturn consoles. == Credits == The following games were created using N-World. Rap Stars Online

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  AI: When a Robot Writes a Play

  AI: When a Robot Writes a Play (in Czech: AI: Když robot píše hru) is a 2021 experimental theatre play, where 90% of its script was automatically generated by artificial intelligence (the GPT-2 language model). The play is in Czech language, but an English version of the script also exists. == Creation == The play is the first result of the THEaiTRE research project, aiming to commemorate the centenary of the R.U.R. play by Karel Čapek by investigating to what extent artificial intelligence could be used to create theatre play scripts. The script of the play was created using the THEaiTRobot tool, based on the GPT-2 language model. First, the play dramaturge, David Košťák, described the initial setting of each scene in a few sentences, and wrote the first line for each character. Next, THEaiTRobot suggested a continuation of the script, which the dramaturge could use, reject, or use part of it and let the tool generate a new continuation. Another option was to manually insert another line or a scenic remark. The script was generated in English and was automatically translated to Czech by the state-of-the-art CUBBITT machine translation tool. The resulting script was then further post-edited by the dramaturge. The resulting script was made freely available for non-commercial use both in English and in Czech, with marked manually inserted texts and manual edits. The analysis shows that 90% of the English script is automatically generated, with 10% manually written or manually post-edited. In the Czech script, a larger amount of edits were made, but the analysis claims that these additional edits are corrections of errors of the automated translation and stylistic corrections which do not change the meaning of the lines as represented by the English script, but rather bring the Czech script closer to the English one. == Characters == The play contains 9 characters. The Robot appears in all the scenes, while each of the other characters appears in only one scene. Robot – The lead character, a male humanoid robot. Master – An old man, the creator of the Robot. Boy – A schoolboy. Masseuse – A sex worker in a brothel. Stranger – An engineer. Man. Psychologist. Administrator – A female clerk at an employment agency. Actress – A film actress and a model in a robot-like costume. == Plot == The play is composed of 8 scenes. It tells the story of a humanoid robot, who encounters 8 other characters and engages into various typically human situations and activities, related to death, love, sex, violence, etc. The individual scenes are not tightly linked, but there are some linking points, such as the central character of the robot or some repeated and developing themes, such as the robot's search for love. The scenes often contain some absurd turns and it is often hard to find sense in them. It is therefore a very complicated piece interpretationally, requiring the director and the actors to invest a lot of effort and creativity in finding a meaningful interpretation which would not deviate from the script. In the interpretation by Švanda theatre, who premiered the play and who also participated on the creation of the script, the scenes typically contain non-verbally expressed content which can add a lot to the meaning of the scene compared to what is contained in the actual script (as the script only contains the lines said by the characters). === Scene 1: Death === The play opens by the Robot parting with his dying Master. The Master gives the Robot several last lessons and talks with him about death, soul, and love. === Scene 2: Sense of Humour === In the second scene, the Robot meets a sad and angry Boy, who complains that he wants to go to school, that his girlfriend is crazy, that he wants to buy a car, etc. The Robot tries to help the Boy by giving him advice, but the Boy's reactions are quite negative and irritated. The Boy then repeatedly asks the Robot to tell him a joke; the Robot keeps refusing, but ultimately tells the following joke: When you are dead. When your children are dead. When your grandchildren are dead, I will be still alive. === Scene 3: Nightclub === The Robot wants to feel pleasure, so he goes to a "night club" (a brothel), where he meets a "Masseuse" (a prostitute). The Robot is initially "a bit cold", but eventually manages to enjoy the experience and falls in love with the Masseuse. In the Švanda theatre performance, the Robot and the Masseuse seem to have a sort of virtual sex without touching each other, reminiscent of the sex scene in Demolition Man. === Scene 4: Fear of the Dark === It is the night. The Robot is standing under a lamp, unable to move away from the light as he finds that he is afraid of the dark. He meets a Stranger, an engineer who tells him that robots don't have feelings and that people cannot be trusted, and keeps hurting him. In the Švanda theatre performance, the Man repeatedly zaps the Robot with some kind of electric pulse. === Scene 5: Killer Robot === A Man approaches the Robot and repeatedly asks him to kill him. Instead, the Robot sticks a finger into the Man's anus, which leads to an argument between the Man and the Robot. === Scene 6: Burn Out === The Robot meets a Psychologist, who keeps asking him lots of questions regarding his life, burnout feeling, love, relationships, and emotions. They also talk about the Robot using a device called emotion machine which helps him to get rid of stress. === Scene 7: Search for Job === The Robot comes to an employment agency. He meets an Administrator and asks her to help him find a job. He expresses the wish to become an actor, and talks about his experience as a clown. He reveals his name to be Troy McClure, which is a character from The Simpsons who is an actor. In the Švanda theatre performance, the Administrator starts to seduce the Robot once his name is revealed, which he keeps ignoring; the Administrator then becomes irritated. === Scene 8: Love at First Sight === The Robot meets a human Actress in a robotic costume and falls in love with her immediately. The Actress is first reluctant, but the Robot manages to seduce her and she also falls in love with him. The Robot tells her about a binary world, in which he lives and where he will also take her. Ultimately, the Actress agrees, and the whole play concludes by the Robot and the Actress promising each to other to always be together. In the Švanda theatre performance, the Robot does not have a physical body in this scene, we can only hear his voice and see a pulsating light (based on the line in the script where the Robot says: "I have no body. So I don't need to wear clothes. You can't see me, you only hear me."), and the Actress eventually also agrees to lose her physical body so that she can be with the Robot forever. == Theatrical performances == The play premiered on 26 February 2021 in Švanda Theatre in Prague, Czech Republic, directed by Daniel Hrbek. Due to the COVID-19 pandemic, the play was not played in front of a live audience, but it was broadcast online, in Czech language with English subtitles. The play was followed by a panel discussion by the project members and experts on artificial intelligence. The premiere was viewed by 13,498 spectators worldwide. A short trailer of the premiere is available on YouTube. In 2021, after the opening of the theatres in the Czech Republic to spectators, the play can be viewed at Švanda Theatre. The performance takes approximately 60 minutes, and is followed by a discussion of the creators with the audience. The derniere is planned for 4 February 2023. == Reception == The play received a number of reviews, both in its country of origin as well as internationally. It is praised as first of its kind, although some reviewers note the similarity to previous works, such as the musical Beyond the Fence, the play Lifestyle of the Richard and Family, or the short movie Sunspring; however, these works used less advanced technology, and either were very short (Sunspring) or necessitated a larger amount of human interventions. The reviewers note that the script is far from perfect, with many inconsistencies and nonsensical parts, and conclude that the technology is definitely not yet ready to replace human authors; however, some find some parts of the script frighteningly human-like. The amount of human intervention is a somewhat controversial topic, with some reviewers finding the human influence too large (especially in interpreting the script and putting the play on scene), while others feel that a greater amount of human intervention would have been favorable as this could greatly improve the quality of the play. The reviews also frequently comment on the amount of sex, violence and strong language in the play; this can be attributed to the method used for creating the script, where the GPT-2 language model reflects topics and language common in the human-written articles on the internet that were used to train the model. Furthermore, some r

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  Hindley–Milner type system

  A Hindley–Milner (HM) type system is a classical type system for the lambda calculus with parametric polymorphism. It is also known as Damas–Milner or Damas–Hindley–Milner. It was first described by J. Roger Hindley and later rediscovered by Robin Milner. Luis Damas contributed a close formal analysis and proof of the method in his PhD thesis. Among HM's more notable properties are its completeness and its ability to infer the most general type of a given program without programmer-supplied type annotations or other hints. Algorithm W is an efficient type inference method in practice and has been successfully applied on large code bases, although it has a high theoretical complexity. HM is preferably used for functional programming languages. It was first implemented as part of the type system of the programming language ML. Since then, HM has been extended in various ways, most notably with type class constraints like those in Haskell. == Introduction == As a type inference method, Hindley–Milner is able to deduce the types of variables, expressions and functions from programs written in an entirely untyped style. Being scope sensitive, it is not limited to deriving the types only from a small portion of source code, but rather from complete programs or modules. Being able to cope with parametric types, too, it is core to the type systems of many functional programming languages. It was first applied in this manner in the ML programming language. The origin is the type inference algorithm for the simply typed lambda calculus that was devised by Haskell Curry and Robert Feys in 1958. In 1969, J. Roger Hindley extended this work and proved that their algorithm always inferred the most general type. In 1978, Robin Milner, independently of Hindley's work, provided an equivalent algorithm, Algorithm W. In 1982, Luis Damas finally proved that Milner's algorithm is complete and extended it to support systems with polymorphic references. === Monomorphism vs. polymorphism === In the simply typed lambda calculus, types T are either atomic type constants or function types of form T → T {\displaystyle T\rightarrow T} . Such types are monomorphic. Typical examples are the types used in arithmetic values: 3 : N u m b e r a d d 3 4 : N u m b e r a d d : N u m b e r → N u m b e r → N u m b e r {\displaystyle {\begin{array}{ll}3&:{\mathtt {Number}}\\{\mathtt {add}}\ 3\ 4&:{\mathtt {Number}}\\{\mathtt {add}}&:{\mathtt {Number}}\rightarrow {\mathtt {Number}}\rightarrow {\mathtt {Number}}\end{array}}} Contrary to this, the untyped lambda calculus is neutral to typing at all, and many of its functions can be meaningfully applied to all type of arguments. The trivial example is the identity function i d ≡ λ x . x {\displaystyle {\mathtt {id}}\equiv \lambda x.x} which simply returns whatever value it is applied to. Less trivial examples include parametric types like lists. While polymorphism in general means that operations accept values of more than one type, the polymorphism used here is parametric. One finds the notation of type schemes in the literature, too, emphasizing the parametric nature of the polymorphism. Additionally, constants may be typed with (quantified) type variables. For example, the following type schemes quantify universally over α {\displaystyle \alpha } , meaning that they are true for all possible α {\displaystyle \alpha } : c o n s : ∀ α . α → L i s t α → L i s t α n i l : ∀ α . L i s t α i d : ∀ α . α → α {\displaystyle {\begin{array}{ll}{\mathtt {cons}}&:\forall \alpha .\alpha \rightarrow {\mathtt {List}}\ \alpha \rightarrow {\mathtt {List}}\ \alpha \\{\mathtt {nil}}&:\forall \alpha .{\mathtt {List}}\ \alpha \\{\mathtt {id}}&:\forall \alpha .\alpha \rightarrow \alpha \end{array}}} Polymorphic types can become monomorphic by consistent substitution of their variables. Examples of monomorphic instances are: i d ′ : S t r i n g → S t r i n g n i l ′ : L i s t N u m b e r {\displaystyle {\begin{array}{ll}{\mathtt {id}}'&:{\mathtt {String}}\rightarrow {\mathtt {String}}\\{\mathtt {nil}}'&:{\mathtt {List}}\ {\mathtt {Number}}\end{array}}} More generally, types are polymorphic when they contain type variables, while types without them are monomorphic. Contrary to the type systems used for example in Pascal (1970) or C (1972), which only support monomorphic types, HM is designed with emphasis on parametric polymorphism. The successors of the languages mentioned, like C++ (1985), focused on different types of polymorphism, namely subtyping in connection with object-oriented programming and overloading. While subtyping is incompatible with HM, a variant of systematic overloading is available in the HM-based type system of Haskell. === Let-polymorphism === When extending the type inference for the simply-typed lambda calculus towards polymorphism, one has to decide whether assigning a polymorphic type not only as type of an expression, but also as the type of a λ-bound variable is admissible. This would allow the generic identity type to be assigned to the variable 'id' in: (λ id . ... (id 3) ... (id "text") ... ) (λ x . x) Allowing this gives rise to the polymorphic lambda calculus; however, type inference in this system is not decidable. Instead, HM distinguishes variables that are immediately bound to an expression from more general λ-bound variables, calling the former let-bound variables, and allows polymorphic types to be assigned only to these. This leads to let-polymorphism where the above example takes the form let id = λ x . x in ... (id 3) ... (id "text") ... which can be typed with a polymorphic type for 'id'. As indicated, the expression syntax is extended to make the let-bound variables explicit, and by restricting the type system to allow only let-bound variable to have polymorphic types, while the parameters in lambda-abstractions must get a monomorphic type, type inference becomes decidable. == Overview == The remainder of this article proceeds as follows: The HM type system is defined. This is done by describing a deduction system that makes precise what expressions have what type, if any. From there, it works towards an implementation of the type inference method. After introducing a syntax-driven variant of the above deductive system, it sketches an efficient implementation (algorithm J), appealing mostly to the reader's metalogical intuition. Because it remains open whether algorithm J indeed realises the initial deduction system, a less efficient implementation (algorithm W), is introduced and its use in a proof is hinted. Finally, further topics related to the algorithm are discussed. The same description of the deduction system is used throughout, even for the two algorithms, to make the various forms in which the HM method is presented directly comparable. == The Hindley–Milner type system == The type system can be formally described by syntax rules that fix a language for the expressions, types, etc. The presentation here of such a syntax is not too formal, in that it is written down not to study the surface grammar, but rather the depth grammar, and leaves some syntactical details open. This form of presentation is usual. Building on this, typing rules are used to define how expressions and types are related. As before, the form used is a bit liberal. === Syntax === The expressions to be typed are exactly those of the lambda calculus extended with a let-expression as shown in the adjacent table. Parentheses can be used to disambiguate an expression. The application is left-binding and binds stronger than abstraction or the let-in construct. Types are syntactically split into two groups, monotypes and polytypes. ==== Monotypes ==== Monotypes always designate a particular type. Monotypes τ {\displaystyle \tau } are syntactically represented as terms. Examples of monotypes include type constants like i n t {\displaystyle {\mathtt {int}}} or s t r i n g {\displaystyle {\mathtt {string}}} , and parametric types like M a p ( S e t s t r i n g ) i n t {\displaystyle {\mathtt {Map\ (Set\ string)\ int}}} . The latter types are examples of applications of type functions, for example, from the set { M a p 2 , S e t 1 , s t r i n g 0 , i n t 0 , → 2 } {\displaystyle \{{\mathtt {Map^{2},\ Set^{1},\ string^{0},\ int^{0}}},\ \rightarrow ^{2}\}} , where the superscript indicates the number of type parameters. The complete set of type functions C {\displaystyle C} is arbitrary in HM, except that it must contain at least → 2 {\displaystyle \rightarrow ^{2}} , the type of functions. It is often written in infix notation for convenience. For example, a function mapping integers to strings has type i n t → s t r i n g {\displaystyle {\mathtt {int}}\rightarrow {\mathtt {string}}} . Again, parentheses can be used to disambiguate a type expression. The application binds stronger than the infix arrow, which is right-binding. Type variables are admitted as monotypes. Monotypes are not to be confused with monomorphic types, which exc

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  Recording format

  A recording format is a format for encoding data for storage on a storage medium. The format can be container information such as sectors on a disk, or user/audience information (content) such as analog stereo audio. Multiple levels of encoding may be achieved in one format. For example, a text encoded page may contain HTML and XML encoding, combined in a plain text file format, using either EBCDIC or ASCII character encoding, on a UDF digitally formatted disk. In electronic media, the primary format is the encoding that requires hardware to interpret (decode) data; while secondary encoding is interpreted by secondary signal processing methods, usually computer software. == Recording container formats == A container format is a system for dividing physical storage space or virtual space for data. Data space can be divided evenly by a system of measurement, or divided unevenly with meta data. A grid may divide physical or virtual space with physical or virtual (dividers) borders, evenly or unevenly. Just as a physical container (such as a file cabinet) is divided by physical borders (such as drawers and file folders), data space is divided by virtual borders. Meta data such as a unit of measurement, address, or meta tags act as virtual borders in a container format. A template may be considered an abstract format for containing a solution as well as the content itself. Systems of measurement Metric system Geographic coordinate system Page grid Film formats Audio data format Video tape format Disk format File format Meta data Text formatting Template Data structure == Raw content formats == A raw content format is a system of converting data to displayable information. Raw content formats may either be recorded in secondary signal processing methods such as a software container format (e.g. digital audio, digital video) or recorded in the primary format. A primary raw content format may be directly observable (e.g. image, sound, motion, smell, sensation) or physical data which only requires hardware to display it, such as a phonographic needle and diaphragm or a projector lamp and magnifying glass.

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  Line detection

  In image processing, line detection is an algorithm that takes a collection of n edge points and finds all the lines on which these edge points lie. The most popular line detectors are the Hough transform and convolution-based techniques. == Hough transform == The Hough transform can be used to detect lines and the output is a parametric description of the lines in an image, for example ρ = r cos(θ) + c sin(θ). If there is a line in a row and column based image space, it can be defined ρ, the distance from the origin to the line along a perpendicular to the line, and θ, the angle of the perpendicular projection from the origin to the line measured in degrees clockwise from the positive row axis. Therefore, a line in the image corresponds to a point in the Hough space. The Hough space for lines has therefore these two dimensions θ and ρ, and a line is represented by a single point corresponding to a unique set of these parameters. The Hough transform can then be implemented by choosing a set of values of ρ and θ to use. For each pixel (r, c) in the image, compute r cos(θ) + c sin(θ) for each values of θ, and place the result in the appropriate position in the (ρ, θ) array. At the end, the values of (ρ, θ) with the highest values in the array will correspond to strongest lines in the image == Convolution-based technique == In a convolution-based technique, the line detector operator consists of a convolution masks tuned to detect the presence of lines of a particular width n and a θ orientation. Here are the four convolution masks to detect horizontal, vertical, oblique (+45 degrees), and oblique (−45 degrees) lines in an image. a) Horizontal mask(R1) (b) Vertical (R3) (C) Oblique (+45 degrees)(R2) (d) Oblique (−45 degrees)(R4) In practice, masks are run over the image and the responses are combined given by the following equation: R(x, y) = max(|R1 (x, y)|, |R2 (x, y)|, |R3 (x, y)|, |R4 (x, y)|) If R(x, y) > T, then discontinuity As can be seen below, if mask is overlay on the image (horizontal line), multiply the coincident values, and sum all these results, the output will be the (convolved image). For example, (−1)(0)+(−1)(0)+(−1)(0) + (2)(1) +(2)(1)+(2)(1) + (−1)(0)+(−1)(0)+(−1)(0) = 6 pixels on the second row, second column in the (convolved image) starting from the upper left corner of the horizontal lines. page 82 == Example == These masks above are tuned for light lines against a dark background, and would give a big negative response to dark lines against a light background. == Code example == The code was used to detect only the vertical lines in an image using Matlab and the result is below. The original image is the one on the top and the result is below it. As can be seen on the picture on the right, only the vertical lines were detected

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  Interviewer effect

  The interviewer effect (also called interviewer variance or interviewer error) is the distortion of response to an interviewer-administered data collection effort which results from differential reactions to the social style and personality of interviewers or to their presentation of particular questions. The use of fixed-wording questions is one method of reducing interviewer bias. Anthropological research and case-studies are also affected by the problem, which is exacerbated by the self-fulfilling prophecy, when the researcher is also the interviewer it is also any effect on data gathered from interviewing people that is caused by the behavior or characteristics (real or perceived) of the interviewer. Interviewer effects can also be associated with the characteristics of the interviewer, such as race. Whether black respondents are interviewed by white interviewers or black interviewers has a strong impact on their responses to both attitude questions and behavioral ones. In the latter case, for example, if black respondents are interviewed by black interviewers in pre-election surveys, they are more likely to actually vote in the upcoming election than if they are interviewed by white interviewers. Furthermore, the race of the interviewer can also affect answers to factual questions that might take the form of a test of how informed the respondent is. Black respondents in a survey of political knowledge, for example, get fewer correct answers to factual questions about politics when interviewed by white interviewers than when interviewed by black interviewers. This is consistent with the research literature on stereotype threat, which finds diminished test performance of potentially stigmatised groups when the interviewer or test supervisor is from a perceived higher status group. Interviewer effects can be mitigated somewhat by randomly assigning subjects to different interviewers, or by using tools such as computer-assisted telephone interviewing (CATI).

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  Algorithmic paradigm

  An algorithmic paradigm or algorithm design paradigm is a generic model or framework which underlies the design of a class of algorithms. An algorithmic paradigm is an abstraction higher than the notion of an algorithm, just as an algorithm is an abstraction higher than a computer program. == List of well-known paradigms == === General === Backtracking Branch and bound Brute-force search Divide and conquer Dynamic programming Greedy algorithm Recursion Prune and search === Parameterized complexity === Kernelization Iterative compression === Computational geometry === Sweep line algorithms Rotating calipers Randomized incremental construction

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  World Congress of Universal Documentation

  The World Congress of Universal Documentation was held from 16 to 21 August 1937 in Paris, France. Delegates from 45 countries met to discuss means by which all of the world's information, in print, in manuscript, and in other forms, could be efficiently organized and made accessible. == The Congress in the history of information science == The Congress, held at the Trocadéro under "the auspices" of the Institut International de Bibliographie, was "the apotheosis" of a general movement in the 1930s towards the classification of the growing mass of information and the improvement of access to that information. For the first time in the history of information science, technological means were beginning to catch up with theoretical ends, and the discussions at the conference reflected that fact. Its participation in the Congress was one of the first projects of the American Documentation Institute (ADI). Participants in the conference discussed what has been more recently called "a continuously updated hypertext encyclopedia." Joseph Reagle sees many of the ideas considered at the conference as forerunners of some of the key goals and norms of Wikipedia. == Microfilm == The main resolution adopted by the congress proposed that microfilm be used to make information universally available. Watson Davis, chairman of the American delegation and president of the ADI, stated that the volume of information being produced created difficult problems of access and preservation, but that these could be solved by the use of microfilm. In his address to the Congress, Davis said: Most immediate and practical to put into operation is the microfilming of material in libraries upon demand. It will become fashionable and economical to send a potential book borrower a little strip of microfilm for his permanent possession instead of the book and then badgering him to return it before he has had a chance to use it effectively. I believe that reading machines for microfilm will become as common as typewriters in studies and laboratories. If the principal libraries and information centers of the world will cooperate in such "bibliofilm services," as they are called, if they exchange orders and have essentially uniform methods, forms for ordering, standard microfilm format and production methods and comparable if not uniform prices, the resources of any library will be placed at the disposal of any scholar or scientist anywhere in the world. All the libraries cooperating will merge into one world library without loss of identity or individuality. The world's documentation will become available to even the most isolated and individualistic scholar. The Congress included two separate exhibits on microfilm. One was of the equipment used at the Bibliothèque nationale de France and the other, coordinated by Herman H. Fussler of the University of Chicago, consisting of "an entire microfilm laboratory," complete with cameras, a darkroom, and various kinds of reading machines. Emanuel Goldberg presented a paper on an early copying camera he had invented. Other resolutions passed by the Congress concerned uniform standards for the preparation of articles, for classifying books and other documents, for indexing newspapers and periodicals, and for cooperation between libraries. == H. G. Wells == In his address to the Congress, H. G. Wells said that he thought that his idea of the "world brain" was a precursor to the ideas other delegates were proposing, and explicitly linked the projects being discussed to the work of the encyclopédistes: I am speaking of a process of mental organization throughout the world which I believe to be as inevitable as anything can be in human affairs. All the distresses and horrors of the present time are fundamentally intellectual. The world has to pull its mind together, and this [Congress] is the beginning of its efforts. Civilization is a Phoenix. It perishes in flames and even as it dies it is born again. This synthesis of knowledge upon which you are working is the necessary beginning of a new world. It is good to be meeting here in Paris where the first encyclopedia of power was made. It would be impossible to overrate our debt to Diderot and his associates. == Other participants == Participants in the Congress included authors, librarians, scholars, archivists, scientists, and editors. Some of the notable people in attendance not mentioned above were:

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  DAvE (Infineon)

  DAVE, or Digital Application Virtual Engineer, is a software development and code generation tool for microcontroller applications created in C/C++. == Versions == === Version 4 (beta) === The successor of the Eclipse-based development environment for C/C++ and/or graphical user interface (GUI) based development using application software (apps). It generates code for the latest XMC1xxx and XMC4xxx microcontrollers using ARM Cortex-M processors. DAVE software development kit (SDK) is a free integrated development environment to set up its own apps for DAVE. === Version 3 === Automatic code generation is based on the use of case-oriented, configurable, and tested software (SW) components, called DAVE Apps. They are comparable to executable and configurable application notes that can be downloaded from the web. The environment is based on Eclipse. Ordinary program development using C/C++ is also available. The targets for this development are XMC1xxx and XMC4xxx microcontrollers that use Cortex-M processors. === Previous versions === This version targets 32-bit microcontroller units (MCUs) (Infineon TriCore AUDO family), 16-bit MCUs (C166, XC166, XE166, and XC2000 family), and 8-bit MCUs (XC800 family) from Infineon. After the initial setup, the configuration wizard appears and gives an overview of the hardware peripherals, control units, and modules. The microcontroller application can be created by selecting the desired functions. At this step, module-specific functions must be selected for module initializing and control. Finally, the application source files will be generated by DAVE and embedded in a project in the selected development environment, where the code can still be modified or added to an extant project. == DAVE-related software == Infineon also developed additional software that can be used in conjunction with DAVE for specific microcontroller families or additional hardware: DAVE Bench for XC800 is a platform providing free development tools for Infineon's 8-bit microcontroller family, based on the Open Source Eclipse architecture. DAVE Drive is a GUI-based software tool that allows application developers to create embedded software for the control of brushless synchronous three-phase motors. == Alternative software == The Infineon MCUs are directly supported by several commercial products, depending on the selected MCU target. An embedded programming library for MATLAB exists. As a free alternative to DAVE, the developer can use the Keil Microcontroller Development Kit (MDK) Version 5. Code for the XMX1000 series up to 128 kB can be developed this way without purchasing a license from Keil.

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  Communication-avoiding algorithm

  Communication-avoiding algorithms minimize movement of data within a memory hierarchy for improving its running-time and energy consumption. These minimize the total of two costs (in terms of time and energy): arithmetic and communication. Communication, in this context refers to moving data, either between levels of memory or between multiple processors over a network. It is much more expensive than arithmetic. == Formal theory == === Two-level memory model === A common computational model in analyzing communication-avoiding algorithms is the two-level memory model: There is one processor and two levels of memory. Level 1 memory is infinitely large. Level 0 memory ("cache") has size M {\displaystyle M} . In the beginning, input resides in level 1. In the end, the output resides in level 1. Processor can only operate on data in cache. The goal is to minimize data transfers between the two levels of memory. === Matrix multiplication === Corollary 6.2: More general results for other numerical linear algebra operations can be found in. The following proof is from. == Motivation == Consider the following running-time model: Measure of computation = Time per FLOP = γ Measure of communication = No. of words of data moved = β ⇒ Total running time = γ·(no. of FLOPs) + β·(no. of words) From the fact that β >> γ as measured in time and energy, communication cost dominates computation cost. Technological trends indicate that the relative cost of communication is increasing on a variety of platforms, from cloud computing to supercomputers to mobile devices. The report also predicts that gap between DRAM access time and FLOPs will increase 100× over coming decade to balance power usage between processors and DRAM. Energy consumption increases by orders of magnitude as we go higher in the memory hierarchy. United States president Barack Obama cited communication-avoiding algorithms in the FY 2012 Department of Energy budget request to Congress: New Algorithm Improves Performance and Accuracy on Extreme-Scale Computing Systems. On modern computer architectures, communication between processors takes longer than the performance of a floating-point arithmetic operation by a given processor. ASCR researchers have developed a new method, derived from commonly used linear algebra methods, to minimize communications between processors and the memory hierarchy, by reformulating the communication patterns specified within the algorithm. This method has been implemented in the TRILINOS framework, a highly-regarded suite of software, which provides functionality for researchers around the world to solve large scale, complex multi-physics problems. == Objectives == Communication-avoiding algorithms are designed with the following objectives: Reorganize algorithms to reduce communication across all memory hierarchies. Attain the lower-bound on communication when possible. The following simple example demonstrates how these are achieved. === Matrix multiplication example === Let A, B and C be square matrices of order n × n. The following naive algorithm implements C = C + A B: for i = 1 to n for j = 1 to n for k = 1 to n C(i,j) = C(i,j) + A(i,k) B(k,j) Arithmetic cost (time-complexity): n2(2n − 1) for sufficiently large n or O(n3). Rewriting this algorithm with communication cost labelled at each step for i = 1 to n {read row i of A into fast memory} - n2 reads for j = 1 to n {read C(i,j) into fast memory} - n2 reads {read column j of B into fast memory} - n3 reads for k = 1 to n C(i,j) = C(i,j) + A(i,k) B(k,j) {write C(i,j) back to slow memory} - n2 writes Fast memory may be defined as the local processor memory (CPU cache) of size M and slow memory may be defined as the DRAM. Communication cost (reads/writes): n3 + 3n2 or O(n3) Since total running time = γ·O(n3) + β·O(n3) and β >> γ the communication cost is dominant. The blocked (tiled) matrix multiplication algorithm reduces this dominant term: ==== Blocked (tiled) matrix multiplication ==== Consider A, B and C to be n/b-by-n/b matrices of b-by-b sub-blocks where b is called the block size; assume three b-by-b blocks fit in fast memory. for i = 1 to n/b for j = 1 to n/b {read block C(i,j) into fast memory} - b2 × (n/b)2 = n2 reads for k = 1 to n/b {read block A(i,k) into fast memory} - b2 × (n/b)3 = n3/b reads {read block B(k,j) into fast memory} - b2 × (n/b)3 = n3/b reads C(i,j) = C(i,j) + A(i,k) B(k,j) - {do a matrix multiply on blocks} {write block C(i,j) back to slow memory} - b2 × (n/b)2 = n2 writes Communication cost: 2n3/b + 2n2 reads/writes << 2n3 arithmetic cost Making b as large possible: 3b2 ≤ M we achieve the following communication lower bound: 31/2n3/M1/2 + 2n2 or Ω (no. of FLOPs / M1/2) == Previous approaches for reducing communication == Most of the approaches investigated in the past to address this problem rely on scheduling or tuning techniques that aim at overlapping communication with computation. However, this approach can lead to an improvement of at most a factor of two. Ghosting is a different technique for reducing communication, in which a processor stores and computes redundantly data from neighboring processors for future computations. Cache-oblivious algorithms represent a different approach introduced in 1999 for fast Fourier transforms, and then extended to graph algorithms, dynamic programming, etc. They were also applied to several operations in linear algebra as dense LU and QR factorizations. The design of architecture specific algorithms is another approach that can be used for reducing the communication in parallel algorithms, and there are many examples in the literature of algorithms that are adapted to a given communication topology.

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  Ontology (information science)

  In information science, an ontology encompasses a representation, formal naming, and definitions of the categories, properties, and relations between the concepts, data, or entities that pertain to one, many, or all domains of discourse. More simply, an ontology is a way of showing the properties of a subject area and how they are related, by defining a set of terms and relational expressions that represent the entities in that subject area. The field which studies ontologies so conceived is sometimes referred to as applied ontology. Every academic discipline or field, in creating its terminology, thereby lays the groundwork for an ontology. Each uses ontological assumptions to frame explicit theories, research and applications. Improved ontologies may improve problem solving within that domain, interoperability of data systems, and discoverability of data. Translating research papers within every field is a problem made easier when experts from different countries maintain a controlled vocabulary of jargon between each of their languages. For instance, the definition and ontology of economics is a primary concern in Marxist economics, but also in other subfields of economics. An example of economics relying on information science occurs in cases where a simulation or model is intended to enable economic decisions, such as determining what capital assets are at risk and by how much (see risk management). What ontologies in both information science and philosophy have in common is the attempt to represent entities, including both objects and events, with all their interdependent properties and relations, according to a system of categories. In both fields, there is considerable work on problems of ontology engineering (e.g., Quine and Kripke in philosophy, Sowa and Guarino in information science), and debates concerning to what extent normative ontology is possible (e.g., foundationalism and coherentism in philosophy, BFO and Cyc in artificial intelligence). Applied ontology is considered by some as a successor to prior work in philosophy. However many current efforts are more concerned with establishing controlled vocabularies of narrow domains than with philosophical first principles, or with questions such as the mode of existence of fixed essences or whether enduring objects (e.g., perdurantism and endurantism) may be ontologically more primary than processes. Artificial intelligence has retained considerable attention regarding applied ontology in subfields like natural language processing within machine translation and knowledge representation, but ontology editors are being used often in a range of fields, including biomedical informatics and industry. Such efforts often use ontology editing tools such as Protégé. == Ontology in philosophy == Ontology is a branch of philosophy and intersects areas such as metaphysics, epistemology, and philosophy of language, as it considers how knowledge, language, and perception relate to the nature of reality. Metaphysics deals with questions like "what exists?" and "what is the nature of reality?". One of five traditional branches of philosophy, metaphysics is concerned with exploring existence through properties, entities and relations such as those between particulars and universals, intrinsic and extrinsic properties, or essence and existence. Metaphysics has been an ongoing topic of discussion since recorded history. == Etymology == The compound word ontology combines onto-, from the Greek ὄν, on (gen. ὄντος, ontos), i.e. "being; that which is", which is the present participle of the verb εἰμί, eimí, i.e. "to be, I am", and -λογία, -logia, i.e. "logical discourse", see classical compounds for this type of word formation. While the etymology is Greek, the oldest extant record of the word itself, the Neo-Latin form ontologia, appeared in 1606 in the work Ogdoas Scholastica by Jacob Lorhard (Lorhardus) and in 1613 in the Lexicon philosophicum by Rudolf Göckel (Goclenius). The first occurrence in English of ontology as recorded by the OED (Oxford English Dictionary, online edition, 2008) came in Archeologia Philosophica Nova or New Principles of Philosophy (1663) by Gideon Harvey. == Formal ontology == Since the mid-1970s, researchers in the field of artificial intelligence (AI) have recognized that knowledge engineering is the key to building large and powerful AI systems. AI researchers argued that they could create new ontologies as computational models that enable certain kinds of automated reasoning, which was only marginally successful. In the 1980s, the AI community began to use the term ontology to refer to both a theory of a modeled world and a component of knowledge-based systems. In particular, David Powers introduced the word ontology to AI to refer to real world or robotic grounding, publishing in 1990 literature reviews emphasizing grounded ontology in association with the call for papers for a AAAI Summer Symposium Machine Learning of Natural Language and Ontology, with an expanded version published in SIGART Bulletin and included as a preface to the proceedings. Some researchers, drawing inspiration from philosophical ontologies, viewed computational ontology as a kind of applied philosophy. In 1993, the widely cited web page and paper "Toward Principles for the Design of Ontologies Used for Knowledge Sharing" by Tom Gruber used ontology as a technical term in computer science closely related to earlier idea of semantic networks and taxonomies. Gruber introduced the term as a specification of a conceptualization: An ontology is a description (like a formal specification of a program) of the concepts and relationships that can formally exist for an agent or a community of agents. This definition is consistent with the usage of ontology as set of concept definitions, but more general. And it is a different sense of the word than its use in philosophy. Attempting to distance ontologies from taxonomies and similar efforts in knowledge modeling that rely on classes and inheritance, Gruber stated (1993): Ontologies are often equated with taxonomic hierarchies of classes, class definitions, and the subsumption relation, but ontologies need not be limited to these forms. Ontologies are also not limited to conservative definitions, that is, definitions in the traditional logic sense that only introduce terminology and do not add any knowledge about the world (Enderton, 1972). To specify a conceptualization, one needs to state axioms that do constrain the possible interpretations for the defined terms. Recent experimental ontology frameworks have also explored resonance-based AI-human co-evolution structures, such as IAMF (Illumination AI Matrix Framework), OntoMotoOS (a meta-operating system concept for ethical and ontological AI–human co-evolution), and PSRT (Phase-Structural Reality Theory across multi-scale ontological layers). Though not yet widely adopted in academic discourse, such models propose phased approaches to ethical harmonization and structural emergence. As refinement of Gruber's definition Feilmayr and Wöß (2016) stated: "An ontology is a formal, explicit specification of a shared conceptualization that is characterized by high semantic expressiveness required for increased complexity." == Formal ontology components == Contemporary ontologies share many structural similarities, regardless of the language in which they are expressed. Most ontologies describe individuals (instances), classes (concepts), attributes and relations. === Types === ==== Domain ontology ==== A domain ontology (or domain-specific ontology) represents concepts which belong to a realm of the world, such as biology or politics. Each domain ontology typically models domain-specific definitions of terms. For example, the word card has many different meanings. An ontology about the domain of poker would model the "playing card" meaning of the word, while an ontology about the domain of computer hardware would model the "punched card" and "video card" meanings. Since domain ontologies are written by different people, they represent concepts in very specific and unique ways, and are often incompatible within the same project. As systems that rely on domain ontologies expand, they often need to merge domain ontologies by hand-tuning each entity or using a combination of software merging and hand-tuning. This presents a challenge to the ontology designer. Different ontologies in the same domain arise due to different languages, different intended usage of the ontologies, and different perceptions of the domain (based on cultural background, education, ideology, etc.). At present, merging ontologies that are not developed from a common upper ontology is a largely manual process and therefore time-consuming and expensive. Domain ontologies that use the same upper ontology to provide a set of basic elements with which to specify the meanings of the domain ontology entities can be merged with less effo

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  Metadirectory

  A metadirectory system provides for the flow of data between one or more directory services and databases in order to maintain synchronization of that data. It is an important part of identity management systems. The data being synchronized typically are collections of entries that contain user profiles and possibly authentication or policy information. Most metadirectory deployments synchronize data into at least one LDAP-based directory server, to ensure that LDAP-based applications such as single sign-on and portal servers have access to recent data, even if the data is mastered in a non-LDAP data source. Metadirectory products support filtering and transformation of data in transit. Most identity management suites from commercial vendors include a metadirectory product, or a user provisioning product.

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  Artisse AI

  Artisse AI is a Hong Kong-based technology company founded by William Wu. The company developed a mobile photography application using generative artificial intelligence to transform selfies into high-quality, personalized images. The app allows users to visualize themselves in various scenarios, outfits, and hairstyles, and they can adjust lighting and ambiance to match their preferences. The app launched in 2023 across multiple markets, including the United States, United Kingdom, Japan, South Korea, Canada, and Australia. By January 2024, users had generated over 5 million images. That same month, the company secured $6.7 million in seed funding to support product development and marketing. == History == Artisse was originally founded in South Korea in 2022 by William Wu. The early concept was connected to a virtual idol initiative developed in collaboration with a K-pop agency, intended to support Wu's blockchain gaming business. The project later evolved into a standalone AI photography application. The current version of the Artisse app was developed following the company's relocation to Hong Kong in 2022. In January 2024, Artisse secured $6.7 million in seed funding, led by The London Fund. The investment was aimed at supporting product development, marketing, and user acquisition. Artisse uses an AI algorithm to create hyperrealistic images from uploaded photos. The app generates personalized images by combining generative AI technology, a global pool of licensed talent, and finished art services. The app works with individual users and businesses, offering professional-grade photos and advertisement images. According to the British newspaper Evening Standard the company has developed the world's first and most advanced AI photographer. It captures 15-30 photos of the user and generates 2D images, placing them in various outfits and locations worldwide. === Catheron Gaming === Artisse AI originated from Catheon Gaming, a blockchain gaming and entertainment company founded in 2021 by William Wu. Catheon Gaming published more than 30 Web3 titles in its first year, developed a blockchain game distribution platform, and offered advisory services to external developers. In 2022, HSBC and KPMG listed Catheon Gaming among the "Top 10 Emerging Giants" in the Asia–Pacific region, selected from a pool of more than 6,000 startups. In June 2023, Catheon Gaming was rebranded as Artisse Interactive, creating two divisions: Artisse Gaming, which continued blockchain and Web3 game development, and Artisse AI, which focused on generative photography technology. == Technology == Artisse uses a proprietary generative AI model combined with open-source imaging frameworks and diffusion models. Users are prompted to upload between 15 and 30 personal images, allowing the AI to train a personalized model in 30 to 40 minutes. After training, the app generates new images based on either textual or visual prompts, with options to adjust elements such as clothing, hairstyles, lighting, and backgrounds. To enhance realism, the app integrates augmented reality features and image refinement tools. The company has introduced features to address representation issues related to body shape and skin tone, although concerns persist about the ethical implications of altering personal traits. == Products == === Artisse mobile app === Available on iOS and Android platforms in 35 languages. Users initially receive 25 free images, after which the app adopts a subscription pricing model ranging from approximately $6 to $30 per month. By early 2024, the app reported around 4,000 paying subscribers out of more than 200,000 downloads. === Business and enterprise services === Artisse provides B2B solutions for creating marketing imagery and partners with agencies like Iconic Management to enable cost-effective virtual photoshoots. Additional features in development include virtual try-on capabilities and augmented reality integration for fashion retail. == Reception == Media coverage has noted the app's photorealistic image outputs with some sources highlighting its ease of use. However, concerns have been raised regarding image authenticity, algorithmic biases, and the potential impact on professional photography and modeling. Artisse has been widely covered by media outlets including TechCrunch, PetaPixel, Forbes Australia, and The Evening Standard. These publications discussed the app's integration of generative AI technology within the consumer photography space, its growing market influence, and its rapid adoption by users worldwide.

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  Recommender system

  A recommender system, also called a recommendation algorithm, recommendation engine, or recommendation platform, is a type of information filtering system that suggests items most relevant to a particular user. The value of these systems becomes particularly evident in scenarios where users must select from a large number of options, such as products, media, or content. Major social media platforms and streaming services rely on recommender systems that employ machine learning to analyze user behavior and preferences, thereby enabling personalized content feeds. Typically, the suggestions refer to a variety decision-making processes, including the selection of a product, musical selection, or online news source to read. The implementation of recommender systems is pervasive, with commonly recognised examples including the generation of playlist for video and music services, the provision of product recommendations for e-commerce platforms, and the recommendation of content on social media platforms and the open web. These systems can operate using a single type of input, such as music, or multiple inputs from diverse platforms, including news, books and search queries. Additionally, popular recommender systems have been developed for specific topics, such as restaurants and online dating services. Recommender systems have also been developed to explore research articles and experts, collaborators, and financial services. A content discovery platform is a software recommendation platform that employs recommender system tools. It utilizes user metadata in order to identify and suggest relevant content, whilst reducing ongoing maintenance and development costs. A content discovery platform delivers personalized content to websites, mobile devices, and set-top boxes. A large range of content discovery platforms currently exist for various forms of content ranging from news articles and academic journal articles to television. As operators compete to serve as the gateway to home entertainment, personalized television emerges as a key service differentiator. Academic content discovery has recently become another area of interest, the emergence of numerous companies dedicated to assisting academic researchers in keeping up to date with relevant academic content and facilitating serendipitous discovery of new content. == Overview == Recommender systems usually make use of either or both collaborative filtering and content-based filtering, as well as other systems such as knowledge-based systems. Collaborative filtering approaches build a model from a user's past behavior (e.g., items previously purchased or selected and/or numerical ratings given to those items) as well as similar decisions made by other users. This model is then used to predict items (or ratings for items) that the user may have an interest in. Content-based filtering approaches utilize a series of discrete, pre-tagged characteristics of an item in order to recommend additional items with similar properties. === Example === The differences between collaborative and content-based filtering can be demonstrated by comparing two early music recommender systems, Last.fm and Pandora Radio. We can also look at how these methods are applied in e-commerce, for example, on platforms like Amazon. Last.fm creates a "station" of recommended songs by observing what bands and individual tracks the user has listened to on a regular basis and comparing those against the listening behavior of other users. Last.fm will play tracks that do not appear in the user's library, but are often played by other users with similar interests. As this approach leverages the behavior of users, it is an example of a collaborative filtering technique. Pandora uses the properties of a song or artist (a subset of the 450 attributes provided by the Music Genome Project) to seed a "station" that plays music with similar properties. User feedback is used to refine the station's results, deemphasizing certain attributes when a user "dislikes" a particular song and emphasizing other attributes when a user "likes" a song. This is an example of a content-based approach. In e-commerce, Amazon's well-known "customers who bought X also bought Y" feature is a prime example of collaborative filtering. It also uses content-based filtering when it recommends a book by the same author you've previously read or a pair of shoes in a similar style to ones you've viewed. Each type of system has its strengths and weaknesses. In the above example, Last.fm requires a large amount of information about a user to make accurate recommendations. This is an example of the cold start problem, and is common in collaborative filtering systems. Whereas Pandora needs very little information to start, it is far more limited in scope (for example, it can only make recommendations that are similar to the original seed). === Alternative implementations === Recommender systems are a useful alternative to search algorithms since they help users discover items they might not have found otherwise. Of note, recommender systems are often implemented using search engines indexing non-traditional data. In some cases, like in the Gonzalez v. Google Supreme Court case, may argue that search and recommendation algorithms are different technologies. Recommender systems have been the focus of several granted patents, and there are more than 50 software libraries that support the development of recommender systems including LensKit, RecBole, ReChorus and RecPack. == History == Elaine Rich created the first recommender system in 1979, called Grundy. She looked for a way to recommend users books they might like. Her idea was to create a system that asks users specific questions and classifies them into classes of preferences, or "stereotypes", depending on their answers. Depending on users' stereotype membership, they would then get recommendations for books they might like. Another early recommender system, called a "digital bookshelf", was described in a 1990 technical report by Jussi Karlgren at Columbia University, and implemented at scale and worked through in technical reports and publications from 1994 onwards by Jussi Karlgren, then at SICS, and research groups led by Pattie Maes at MIT, Will Hill at Bellcore, and Paul Resnick, also at MIT, whose work with GroupLens was awarded the 2010 ACM Software Systems Award. Montaner provided the first overview of recommender systems from an intelligent agent perspective. Adomavicius provided a new, alternate overview of recommender systems. Herlocker provides an additional overview of evaluation techniques for recommender systems, and Beel et al. discussed the problems of offline evaluations. Beel et al. have also provided literature surveys on available research paper recommender systems and existing challenges. == Approaches == === Collaborative filtering === One approach to the design of recommender systems that has wide use is collaborative filtering. Collaborative filtering is based on the assumption that people who agreed in the past will agree in the future, and that they will like similar kinds of items as they liked in the past. The system generates recommendations using only information about rating profiles for different users or items. By locating peer users/items with a rating history similar to the current user or item, they generate recommendations using this neighborhood. This approach is a cornerstone for e-commerce sites that analyze the purchasing patterns of thousands of users to suggest what you might like. Collaborative filtering methods are classified as memory-based and model-based. A well-known example of memory-based approaches is the user-based algorithm, while that of model-based approaches is matrix factorization (recommender systems). A key advantage of the collaborative filtering approach is that it does not rely on machine analyzable content and therefore it is capable of accurately recommending complex items such as movies without requiring an "understanding" of the item itself. Many algorithms have been used in measuring user similarity or item similarity in recommender systems. For example, the k-nearest neighbor (k-NN) approach and the Pearson Correlation as first implemented by Allen. When building a model from a user's behavior, a distinction is often made between explicit and implicit forms of data collection. Examples of explicit data collection include the following: Asking a user to rate an item on a sliding scale. Asking a user to search. Asking a user to rank a collection of items from favorite to least favorite. Presenting two items to a user and asking him/her to choose the better one of them. Asking a user to create a list of items that he/she likes (see Rocchio classification or other similar techniques). Examples of implicit data collection include the following: Observing the items that a user views in an online store, media library, or other repository of med

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  Kullback–Leibler Upper Confidence Bound

  In multi-armed bandit problems, KL-UCB (for Kullback–Leibler Upper Confidence Bound) is a UCB-type algorithm that is asymptotically optimal, in the sense that its regret matches the problem-dependent Lai-Robbins lower bound. == Multi-armed bandit problem == The Multi-armed bandit problem is a sequential game where one player has to choose at each turn between K {\displaystyle K} actions (arms). Behind every arm a {\displaystyle a} there is an unknown distribution ν a {\displaystyle \nu _{a}} that lies in a set D {\displaystyle {\mathcal {D}}} known by the player (for example, D {\displaystyle {\mathcal {D}}} can be the set of Gaussian distributions or Bernoulli distributions). At each turn t {\displaystyle t} the player chooses (pulls) an arm a t {\displaystyle a_{t}} , he then gets an observation X t {\displaystyle X_{t}} of the distribution ν a t {\displaystyle \nu _{a_{t}}} . === Regret minimization === The goal is to minimize the regret at time T {\displaystyle T} that is defined as R T := ∑ a = 1 K Δ a E [ N a ( T ) ] {\displaystyle R_{T}:=\sum _{a=1}^{K}\Delta _{a}\mathbb {E} [N_{a}(T)]} where μ a := E [ ν a ] {\displaystyle \mu _{a}:=\mathbb {E} [\nu _{a}]} is the mean of arm a {\displaystyle a} μ ∗ := max a μ a {\displaystyle \mu ^{}:=\max _{a}\mu _{a}} is the highest mean Δ a := μ ∗ − μ a {\displaystyle \Delta _{a}:=\mu ^{}-\mu _{a}} N a ( t ) {\displaystyle N_{a}(t)} is the number of pulls of arm a {\displaystyle a} up to turn t {\displaystyle t} The player has to find an algorithm that chooses at each turn t {\displaystyle t} which arm to pull based on the previous actions and observations ( a s , X s ) s < t {\displaystyle (a_{s},X_{s})_{s μ } {\displaystyle {\mathcal {K}}_{inf}(\nu ,\mu ,{\mathcal {D}}):=\inf \left\{\mathrm {KL} (\nu ,{\tilde {\nu }})\ |\ {\tilde {\nu }}\in {\mathcal {D}},\ \mathbb {E} [{\tilde {\nu }}]>\mu \right\}} K L {\displaystyle \mathrm {KL} } is the Kullback–Leibler divergence ν ^ a ( t ) {\displaystyle {\hat {\nu }}_{a}(t)} is the empirical distribution of arm a {\displaystyle a} at turn t {\displaystyle t} δ t {\displaystyle \delta _{t}} is a well-chosen sequence of positive numbers, often equal to ln ⁡ t + c ln ⁡ ln ⁡ t {\displaystyle \ln t+c\ln \ln t} with c > 0 {\displaystyle c>0} . Then we choose the arm a t {\displaystyle a_{t}} with the highest index: a t := arg ⁡ max a U a ( t ) {\displaystyle a_{t}:=\arg \max _{a}U_{a}(t)} We note that the algorithm does not require knowledge of T {\displaystyle T} . === Example === In the special case of Gaussian distribution with fixed variance σ 2 {\displaystyle \sigma ^{2}} , we have: U a ( t ) = μ ^ a ( t ) + 2 σ 2 δ t N a ( t ) {\displaystyle U_{a}(t)={\hat {\mu }}_{a}(t)+{\sqrt {\frac {2\sigma ^{2}\delta _{t}}{N_{a}(t)}}}} with μ ^ a ( t ) {\displaystyle {\hat {\mu }}_{a}(t)} being the empirical mean of arm a {\displaystyle a} at turn t {\displaystyle t} . === Pseudocode === The player gets the set D for each arm i do: n[i] ← 1; nu[i] ← None; d ← ln(K) for t from 1 to K do: select arm t observe reward r n[t] ← n[t] + 1 nu[t] ← update empirical distribution for t from K+1 to T do: for each arm i do: index[i] ← compute_index(n[i], nu[i], D, d) select arm a with highest index[a] observe reward r n[a] ← n[a] + 1 nu[a] ← update empirical distribution d ← ln(t+1) == Theoretical results == In the multi-armed bandit problem we have the Lai–Robbins asymptotic lower bound on regret. The algorithm KL-UCB matches this lower bound for one-dimensional exponential families with δ t := ln ⁡ t + 3 ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+3\ln \ln t} and for distributions bounded in [ 0 , 1 ] {\displaystyle [0,1]} with δ t := ln ⁡ t + ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+\ln \ln t} . === Lai–Robbins lower bound === In 1985 Lai and Robbins proved an asymptotic, problem-dependent lower bound on regret. It states that for every consistent algorithm on the set D {\displaystyle {\mathcal {D}}} — that is, an algorithm for which, for every ( ν 1 , … , ν K ) ∈ D K {\displaystyle (\nu _{1},\dots ,\nu _{K})\in {\mathcal {D}}^{K}} , the regret R T {\displaystyle R_{T}} is subpolynomial (i.e. R T = o T → + ∞ ( T α ) {\displaystyle R_{T}=o_{T\to +\infty }(T^{\alpha })} for all α > 0 {\displaystyle \alpha >0} ) — we have: R T ≥ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ , D ) ) ln ⁡ T + o T → + ∞ ( ln ⁡ T ) . {\displaystyle R_{T}\geq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{},{\mathcal {D}})}}\right)\ln T+o_{T\to +\infty }(\ln T).} This bound is asymptotic (as T → + ∞ {\displaystyle T\to +\infty } ) and gives a first-order lower bound of order ln ⁡ T {\displaystyle \ln T} with the optimal constant in front of it. === Regret bound for KL-UCB === The algorithm matches the Lai–Robbins lower bound for one-dimensional exponential-family distributions and for distributions bounded in [ 0 , 1 ] {\displaystyle [0,1]} . ==== One-dimensional exponential family ==== For D {\displaystyle {\mathcal {D}}} being the set of one-dimensional exponential families, with δ t := ln ⁡ t + 3 ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+3\ln \ln t} we have the following upper bound on the regret of KL-UCB: R T ≤ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ , D ) ) ln ⁡ T + O T ( ln ⁡ T ) . {\displaystyle R_{T}\leq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{},{\mathcal {D}})}}\right)\ln T+O_{T}({\sqrt {\ln T}}).} ==== Bounded distributions in [0,1] ==== For D = P ( [ 0 , 1 ] ) {\displaystyle {\mathcal {D}}={\mathcal {P}}([0,1])} (the set of distributions supported on [ 0 , 1 ] {\displaystyle [0,1]} ), and for δ t := ln ⁡ t + ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+\ln \ln t} , we have the following upper bound on the regret of KL-UCB: R T ≤ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ , D ) ) ln ⁡ T + O T ( ( ln ⁡ T ) 4 / 5 ln ⁡ ln ⁡ T ) . {\displaystyle R_{T}\leq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{},{\mathcal {D}})}}\right)\ln T+O_{T}{\big (}(\ln T)^{4/5}\ln \ln T{\big )}.} === Runtime === For D = P ( [ 0 , 1 ] ) {\displaystyle {\mathcal {D}}={\mathcal {P}}([0,1])} , the runtime needed per step and for an arm k {\displaystyle k} with n {\displaystyle n} observations is O ( n ( ln ⁡ n ) 2 ) {\displaystyle {\mathcal {O}}{\big (}n(\ln n)^{2}{\big )}} . This is higher than that of other optimal algorithms, such as NPTS with O ( n ) {\displaystyle {\mathcal {O}}(n)} . MED with O ( n ln ⁡ n ) {\displaystyle {\mathcal {O}}(n\ln n)} . and IMED with O ( n ln ⁡ n ) {\displaystyle {\mathcal {O}}(n\ln n)} . The high runtime of KL-UCB is due to a two-level optimisation: for each arm and candidate mean μ {\displaystyle \mu } , the algorithm evaluates K inf ( ν ^ a ( t ) , μ , D ) {\displaystyle {\mathcal {K}}_{\inf }({\hat {\nu }}_{a}(t),\mu ,{\mathcal {D}})} and then maximises μ {\displaystyle \mu } subject to N a ( t ) K inf ( ν ^ a ( t ) , μ , D ) ≤ δ t {\displaystyle N_{a}(t)\,{\mathcal {K}}_{\inf }({\hat {\nu }}_{a}(t),\mu ,{\mathcal {D}})\leq \delta _{t}} . For distributions bounded in [ 0 , 1 ] {\displaystyle [0,1]} the inner problem has no closed form and must be solved numerically, which increases the per-step cost.

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