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  Cumulus (software)

  Cumulus is a digital asset management software designed for client/server system which is developed by Canto Software. The product makes use of metadata for indexing, organizing, and searching. == History == Cumulus was first released as a Macintosh application in 1992, and was named by Apple Computer as the "Most Innovative Product of 1992". Cumulus introduced search capabilities beyond those available in the Macintosh at the time, particularly relating to thumbnails. Cumulus 1.0 was a single-user product with no network capabilities. Among the main features of Cumulus 1.0, the search function automatically generated previews and contained support for the included AppleTalk – Peer-to-Peer – network. Cumulus 2.5 was available in five different languages and received the 1993 MacUser magazine Eddy award for "Best Publishing & Graphics Utility". In 1995, Canto introduced the scanner software "Cirrus" to focus on the development of Cumulus. Cumulus 3, released in 1996, introduced a server version for the first time and contained the possibility to spread files over the Internet via the "Web Publisher". Since Apple offered Cumulus 3 with its "Workgroup Server" as a bundle, Cumulus became one of the leading digital asset management systems. Cumulus 4 was the first version that was network-ready, and was available for Macintosh, Windows and UNIX operating systems allowing for cross-platform file sharing. Released in 1998, the support of Solaris was discounted later. Cumulus 5 modified the software core to use an open architecture providing an API to external systems and databases. The open architecture of Cumulus 5 also enabled a more functional bridge between Cumulus and the Internet. Cumulus 6 introduced Embedded Java Plugin (EJP) which allowed system integrators to build custom Java plug-ins in order to extend the functionality of the Cumulus client. Cumulus 6.5 marked the end of the Cumulus Single User Edition product, which was licensed to MediaDex for further development and distribution. Cumulus 7 was introduced summer of 2006. Cumulus 8 was released in June 2009, with new indexing capabilities taking advantage of multicore/multiprocessor systems, and ability to manage a wider variety of file formats. Cumulus 8.5 was released in May 2011. Support was added for multilingual metadata, sometimes referred to as "World Metadata." Cumulus Sites was updated to support metadata editing and file uploads. Cumulus 8.6 was released in July 2012, and contains an updated user interface for the administration of Cumulus Sites and additional features for web-based administration of Cumulus. Other additions include features for collaboration links, multi-language support and automated version control. Cumulus 9 was released in September 2013 and introduced a new Web Client User Interface and the Cumulus Video Cloud. The Cumulus Web Client UI was redesigned to provide users with a modern, easy-to-use interface to support and guide the user while addressing modern business needs. The Cumulus Video Cloud extends the Cumulus video handling capabilities to add conversion and global streaming. Cumulus 9 also saw the addition of upload collection links which allow external collaborators to drag and drop files directly into Cumulus without needing a Cumulus account. Cumulus 9.1 was released in May 2014 and introduced the Adobe Drive Adapter for Cumulus which allows users to browse and search digital assets in Cumulus directly from Adobe work environments such as Photoshop, InDesign, Illustrator, Premier and other Adobe applications. Cumulus 10 (Cumulus X) was released July 2015 and introduced two mobile-friendly products: the Cumulus app and Portals. The Cumulus app on iOS was designed to allow users to collaborate either on an iPhone or iPad. Portals is the read-only version of the Cumulus Web Client where users can work with assets that admins allow. Cumulus 10.1 was introduced in January 2016 and included the InDesign Client integration where users can work with Adobe InDesign while accessing their assets from Cumulus. Cumulus 10.2 was introduced in September 2016 and brought the Media Delivery Cloud using Amazon Web Services (AWS). It allows users to manage their media rendition in a single source and distribute media files globally across different channels and devices. Cumulus 10.2.3 was released in February 2017 and came with a "crop and customize photos" feature for Portals and the Web Client. == Product overview == The cataloging of the file via upload into the archive is where Cumulus transfers maximum information about the file from the metadata. For image or photo files, this is typically Exif and IPTC data. The metadata is mainly used to search the archive. The use of embargo data supports license management for copyrighted material. The managed files can be cataloged and their usage can be set. The indexing is based on a predefined taxonomy, which is governed by the internal rules of the organization or by industry standards. You can specify whether files can only be used for specific purposes or only by certain groups of people. The production management system includes version management for files. Via the publication function, the files can be distributed directly via links or e-mails. It's also possible to access from the outside via the Cumulus Portals web interface, which allows a read access to released content from the catalog. There are different variants, starting with the "Workgroup archive server" up to the "Enterprise Business Server" for large companies. Both server and client are extensible through a Java-based plug-in architecture. Since version 7.0, there is a web application based on Ajax with a separate user interface. For access to the Cumulus catalog on mobile, there has been an application for Apple devices based on iOS since 2010. == Miscellaneous == In 2015, Cumulus developer Canto established the first Canto digital asset management (DAM) event. The event is held annually in Berlin. The Henry Stewart team has been hosting DAM conferences since 2006.

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  Holographic algorithm

  In computer science, a holographic algorithm is an algorithm that uses a holographic reduction. A holographic reduction is a constant-time reduction that maps solution fragments many-to-many such that the sum of the solution fragments remains unchanged. These concepts were introduced by Leslie Valiant, who called them holographic because "their effect can be viewed as that of producing interference patterns among the solution fragments". The algorithms are unrelated to laser holography, except metaphorically. Their power comes from the mutual cancellation of many contributions to a sum, analogous to the interference patterns in a hologram. Holographic algorithms have been used to find polynomial-time solutions to problems without such previously known solutions for special cases of satisfiability, vertex cover, and other graph problems. They have received notable coverage due to speculation that they are relevant to the P versus NP problem and their impact on computational complexity theory. Although some of the general problems are #P-hard problems, the special cases solved are not themselves #P-hard, and thus do not prove FP = #P. Holographic algorithms have some similarities with quantum computation, but are completely classical. == Holant problems == Holographic algorithms exist in the context of Holant problems, which generalize counting constraint satisfaction problems (#CSP). A #CSP instance is a hypergraph G=(V,E) called the constraint graph. Each hyperedge represents a variable and each vertex v {\displaystyle v} is assigned a constraint f v . {\displaystyle f_{v}.} A vertex is connected to an hyperedge if the constraint on the vertex involves the variable on the hyperedge. The counting problem is to compute ∑ σ : E → { 0 , 1 } ∏ v ∈ V f v ( σ | E ( v ) ) , ( 1 ) {\displaystyle \sum _{\sigma :E\to \{0,1\}}\prod _{v\in V}f_{v}(\sigma |_{E(v)}),~~~~~~~~~~(1)} which is a sum over all variable assignments, the product of every constraint, where the inputs to the constraint f v {\displaystyle f_{v}} are the variables on the incident hyperedges of v {\displaystyle v} . A Holant problem is like a #CSP except the input must be a graph, not a hypergraph. Restricting the class of input graphs in this way is indeed a generalization. Given a #CSP instance, replace each hyperedge e of size s with a vertex v of degree s with edges incident to the vertices contained in e. The constraint on v is the equality function of arity s. This identifies all of the variables on the edges incident to v, which is the same effect as the single variable on the hyperedge e. In the context of Holant problems, the expression in (1) is called the Holant after a related exponential sum introduced by Valiant. == Holographic reduction == A standard technique in complexity theory is a many-one reduction, where an instance of one problem is reduced to an instance of another (hopefully simpler) problem. However, holographic reductions between two computational problems preserve the sum of solutions without necessarily preserving correspondences between solutions. For instance, the total number of solutions in both sets can be preserved, even though individual problems do not have matching solutions. The sum can also be weighted, rather than simply counting the number of solutions, using linear basis vectors. === General example === It is convenient to consider holographic reductions on bipartite graphs. A general graph can always be transformed it into a bipartite graph while preserving the Holant value. This is done by replacing each edge in the graph by a path of length 2, which is also known as the 2-stretch of the graph. To keep the same Holant value, each new vertex is assigned the binary equality constraint. Consider a bipartite graph G=(U,V,E) where the constraint assigned to every vertex u ∈ U {\displaystyle u\in U} is f u {\displaystyle f_{u}} and the constraint assigned to every vertex v ∈ V {\displaystyle v\in V} is f v {\displaystyle f_{v}} . Denote this counting problem by Holant ( G , f u , f v ) . {\displaystyle {\text{Holant}}(G,f_{u},f_{v}).} If the vertices in U are viewed as one large vertex of degree |E|, then the constraint of this vertex is the tensor product of f u {\displaystyle f_{u}} with itself |U| times, which is denoted by f u ⊗ | U | . {\displaystyle f_{u}^{\otimes |U|}.} Likewise, if the vertices in V are viewed as one large vertex of degree |E|, then the constraint of this vertex is f v ⊗ | V | . {\displaystyle f_{v}^{\otimes |V|}.} Let the constraint f u {\displaystyle f_{u}} be represented by its weighted truth table as a row vector and the constraint f v {\displaystyle f_{v}} be represented by its weighted truth table as a column vector. Then the Holant of this constraint graph is simply f u ⊗ | U | f v ⊗ | V | . {\displaystyle f_{u}^{\otimes |U|}f_{v}^{\otimes |V|}.} Now for any complex 2-by-2 invertible matrix T (the columns of which are the linear basis vectors mentioned above), there is a holographic reduction between Holant ( G , f u , f v ) {\displaystyle {\text{Holant}}(G,f_{u},f_{v})} and Holant ( G , f u T ⊗ ( deg ⁡ u ) , ( T − 1 ) ⊗ ( deg ⁡ v ) f v ) . {\displaystyle {\text{Holant}}(G,f_{u}T^{\otimes (\deg u)},(T^{-1})^{\otimes (\deg v)}f_{v}).} To see this, insert the identity matrix T ⊗ | E | ( T − 1 ) ⊗ | E | {\displaystyle T^{\otimes |E|}(T^{-1})^{\otimes |E|}} in between f u ⊗ | U | f v ⊗ | V | {\displaystyle f_{u}^{\otimes |U|}f_{v}^{\otimes |V|}} to get f u ⊗ | U | f v ⊗ | V | {\displaystyle f_{u}^{\otimes |U|}f_{v}^{\otimes |V|}} = f u ⊗ | U | T ⊗ | E | ( T − 1 ) ⊗ | E | f v ⊗ | V | {\displaystyle =f_{u}^{\otimes |U|}T^{\otimes |E|}(T^{-1})^{\otimes |E|}f_{v}^{\otimes |V|}} = ( f u T ⊗ ( deg ⁡ u ) ) ⊗ | U | ( f v ( T − 1 ) ⊗ ( deg ⁡ v ) ) ⊗ | V | . {\displaystyle =\left(f_{u}T^{\otimes (\deg u)}\right)^{\otimes |U|}\left(f_{v}(T^{-1})^{\otimes (\deg v)}\right)^{\otimes |V|}.} Thus, Holant ( G , f u , f v ) {\displaystyle {\text{Holant}}(G,f_{u},f_{v})} and Holant ( G , f u T ⊗ ( deg ⁡ u ) , ( T − 1 ) ⊗ ( deg ⁡ v ) f v ) {\displaystyle {\text{Holant}}(G,f_{u}T^{\otimes (\deg u)},(T^{-1})^{\otimes (\deg v)}f_{v})} have exactly the same Holant value for every constraint graph. They essentially define the same counting problem. === Specific examples === ==== Vertex covers and independent sets ==== Let G be a graph. There is a 1-to-1 correspondence between the vertex covers of G and the independent sets of G. For any set S of vertices of G, S is a vertex cover in G if and only if the complement of S is an independent set in G. Thus, the number of vertex covers in G is exactly the same as the number of independent sets in G. The equivalence of these two counting problems can also be proved using a holographic reduction. For simplicity, let G be a 3-regular graph. The 2-stretch of G gives a bipartite graph H=(U,V,E), where U corresponds to the edges in G and V corresponds to the vertices in G. The Holant problem that naturally corresponds to counting the number of vertex covers in G is Holant ( H , OR 2 , EQUAL 3 ) . {\displaystyle {\text{Holant}}(H,{\text{OR}}_{2},{\text{EQUAL}}_{3}).} The truth table of OR2 as a row vector is (0,1,1,1). The truth table of EQUAL3 as a column vector is ( 1 , 0 , 0 , 0 , 0 , 0 , 0 , 1 ) T = [ 1 0 ] ⊗ 3 + [ 0 1 ] ⊗ 3 {\displaystyle (1,0,0,0,0,0,0,1)^{T}={\begin{bmatrix}1\\0\end{bmatrix}}^{\otimes 3}+{\begin{bmatrix}0\\1\end{bmatrix}}^{\otimes 3}} . Then under a holographic transformation by [ 0 1 1 0 ] , {\displaystyle {\begin{bmatrix}0&1\\1&0\end{bmatrix}},} OR 2 ⊗ | U | EQUAL 3 ⊗ | V | {\displaystyle {\text{OR}}_{2}^{\otimes |U|}{\text{EQUAL}}_{3}^{\otimes |V|}} = ( 0 , 1 , 1 , 1 ) ⊗ | U | ( [ 1 0 ] ⊗ 3 + [ 0 1 ] ⊗ 3 ) ⊗ | V | {\displaystyle =(0,1,1,1)^{\otimes |U|}\left({\begin{bmatrix}1\\0\end{bmatrix}}^{\otimes 3}+{\begin{bmatrix}0\\1\end{bmatrix}}^{\otimes 3}\right)^{\otimes |V|}} = ( 0 , 1 , 1 , 1 ) ⊗ | U | [ 0 1 1 0 ] ⊗ | E | [ 0 1 1 0 ] ⊗ | E | ( [ 1 0 ] ⊗ 3 + [ 0 1 ] ⊗ 3 ) ⊗ | V | {\displaystyle =(0,1,1,1)^{\otimes |U|}{\begin{bmatrix}0&1\\1&0\end{bmatrix}}^{\otimes |E|}{\begin{bmatrix}0&1\\1&0\end{bmatrix}}^{\otimes |E|}\left({\begin{bmatrix}1\\0\end{bmatrix}}^{\otimes 3}+{\begin{bmatrix}0\\1\end{bmatrix}}^{\otimes 3}\right)^{\otimes |V|}} = ( ( 0 , 1 , 1 , 1 ) [ 0 1 1 0 ] ⊗ 2 ) ⊗ | U | ( ( [ 0 1 1 0 ] [ 1 0 ] ) ⊗ 3 + ( [ 0 1 1 0 ] [ 0 1 ] ) ⊗ 3 ) ⊗ | V | {\displaystyle =\left((0,1,1,1){\begin{bmatrix}0&1\\1&0\end{bmatrix}}^{\otimes 2}\right)^{\otimes |U|}\left(\left({\begin{bmatrix}0&1\\1&0\end{bmatrix}}{\begin{bmatrix}1\\0\end{bmatrix}}\right)^{\otimes 3}+\left({\begin{bmatrix}0&1\\1&0\end{bmatrix}}{\begin{bmatrix}0\\1\end{bmatrix}}\right)^{\otimes 3}\right)^{\otimes |V|}} = ( 1 , 1 , 1 , 0 ) ⊗ | U | ( [ 0 1 ] ⊗ 3 + [ 1 0 ] ⊗ 3 ) ⊗ | V | {\displaystyle =(1,1,1,0)^{\otimes |U|}\left({\begin{bmatrix}0\\1\end{bmatrix}}^{\otimes 3}+{\begin{bmatrix}1\\0\end{bmatrix}}^{\otimes 3}\right)^{\otimes |V|}} = NAND 2 ⊗ | U | EQUAL 3 ⊗ | V | , {\displaystyle ={\text{NAND}}_{2}^{\otim

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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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  Encyclopaedistics

  Encyclopaedistics or encyclopaedics as a discipline, is the academic scholarship of encyclopedias as sources of encyclopedic knowledge and cultural objects as well; in this sense, this discipline is also known as "encyclopaedia studies" and can be termed as "theoretical encyclopaediography" by analogy with theoretical lexicography. Encyclopaedistics as a practical activity (profession or business) also called "encyclopaedic practice" or "encyclopedism" is the process of assembling encyclopaedias available to the public for sale or for free (encyclopaedia publishing or practical encyclopediography). In this sense, it is the art or craft of writing, compiling, and editing the paper or online encyclopedias. As a practical activity, encyclopaedistics originated in the Middle Ages in connection with the development of compendiums based on alphabetical structuring (e.g. first edition of Polyanthea by Dominicus Nanus Mirabellius). Encyclopaedistics is often defined as "the art and science of selecting and disseminating the information most significant to mankind". == Field of study == Encyclopaedistics is a specialized aspect of information science and communication science. At the same time, encyclopaedistics is also considered as one of scholarly disciplines which are seen as auxiliary for historical research (auxiliary sciences of history) . Third, encyclopaedics is a domain of philosophy (Romanticism). This term associated with German philosophers of the 18th century, such as Novalis, Friedrich Schlegel, who sought to create a "Scientific Bible" - both real and ideal book as the quintessence of human education (enlightenment). In any case, the most popular topics in encyclopaedia studies refferd the history of organization of encyclopaedic knowledge, encyclopaedic knowledge determination and selection, glossary composition, current state of development of encyclopaedic activity, features of making encyclopaedias and encyclopaedic articles, usage, role and significance of encyclopaedias, typology of encyclopaedic literature, encyclopaedists and encyclopaedic schools, opposition of classical encyclopaedias and Wikipedia as well as paper encyclopaedias and online encyclopaedias, case experience in building encyclopedias etc. In general, scholarly studies contribute to appearance of successful well-crafted encyclopaedias with high-quality articles. == Contemporary encyclopaedic practice == Today, academic institutions, universities, and publishing companies worldwide are engaged in encyclopaedic activity building national, multinational (universal), regional and subject-specific encyclopaedias, or doing studies related encyclopaedias. The development of national encyclopaedias is one of the prerogatives of the European Parliament in the policy of protection of accurate and verified information and in the fight against mis- and disinformation as well as in the policy of protecting, promoting and projecting Europe's values and interests in the world.

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  A Logical Calculus of the Ideas Immanent in Nervous Activity

  "A Logical Calculus of the Ideas Immanent in Nervous Activity" is a 1943 paper written by Warren Sturgis McCulloch and Walter Pitts, published in the journal The Bulletin of Mathematical Biophysics. The paper proposed a mathematical model of the nervous system as a network of simple logical elements, later known as artificial neurons, or McCulloch–Pitts neurons. These neurons receive inputs, perform a weighted sum, and fire an output signal based on a threshold function. By connecting these units in various configurations, McCulloch and Pitts demonstrated that their model could perform all logical functions. It is a seminal work in cognitive science, computational neuroscience, computer science, and artificial intelligence. It was a foundational result in automata theory. John von Neumann cited it as a significant result. == Mathematics == The artificial neuron used in the original paper is slightly different from the modern version. They considered neural networks that operate in discrete steps of time t = 0 , 1 , … {\displaystyle t=0,1,\dots } . The neural network contains a number of neurons. Let the state of a neuron i {\displaystyle i} at time t {\displaystyle t} be N i ( t ) {\displaystyle N_{i}(t)} . The state of a neuron can either be 0 or 1, standing for "not firing" and "firing". Each neuron also has a firing threshold θ {\displaystyle \theta } , such that it fires if the total input exceeds the threshold. Each neuron can connect to any other neuron (including itself) with positive synapses (excitatory) or negative synapses (inhibitory). That is, each neuron can connect to another neuron with a weight w {\displaystyle w} taking an integer value. A peripheral afferent is a neuron with no incoming synapses. We can regard each neural network as a directed graph, with the nodes being the neurons, and the directed edges being the synapses. A neural network has a circle or a circuit if there exists a directed circle in the graph. Let w i j ( t ) {\displaystyle w_{ij}(t)} be the connection weight from neuron j {\displaystyle j} to neuron i {\displaystyle i} at time t {\displaystyle t} , then its next state is N i ( t + 1 ) = H ( ∑ j = 1 n w i j ( t ) N j ( t ) − θ i ( t ) ) , {\displaystyle N_{i}(t+1)=H\left(\sum _{j=1}^{n}w_{ij}(t)N_{j}(t)-\theta _{i}(t)\right),} where H {\displaystyle H} is the Heaviside step function (outputting 1 if the input is greater than or equal to 0, and 0 otherwise). === Symbolic logic === The paper used, as a logical language for describing neural networks, "Language II" from The Logical Syntax of Language by Rudolf Carnap with some notations taken from Principia Mathematica by Alfred North Whitehead and Bertrand Russell. Language II covers substantial parts of classical mathematics, including real analysis and portions of set theory. To describe a neural network with peripheral afferents N 1 , N 2 , … , N p {\displaystyle N_{1},N_{2},\dots ,N_{p}} and non-peripheral afferents N p + 1 , N p + 2 , … , N n {\displaystyle N_{p+1},N_{p+2},\dots ,N_{n}} they considered logical predicate of form P r ( N 1 , N 2 , … , N p , t ) {\displaystyle Pr(N_{1},N_{2},\dots ,N_{p},t)} where P r {\displaystyle Pr} is a first-order logic predicate function (a function that outputs a boolean), N 1 , … , N p {\displaystyle N_{1},\dots ,N_{p}} are predicates that take t {\displaystyle t} as an argument, and t {\displaystyle t} is the only free variable in the predicate. Intuitively speaking, N 1 , … , N p {\displaystyle N_{1},\dots ,N_{p}} specifies the binary input patterns going into the neural network over all time, and P r ( N 1 , N 2 , … , N n , t ) {\displaystyle Pr(N_{1},N_{2},\dots ,N_{n},t)} is a function that takes some binary input patterns, and constructs an output binary pattern P r ( N 1 , N 2 , … , N n , 0 ) , P r ( N 1 , N 2 , … , N n , 1 ) , … {\displaystyle Pr(N_{1},N_{2},\dots ,N_{n},0),Pr(N_{1},N_{2},\dots ,N_{n},1),\dots } . A logical sentence P r ( N 1 , N 2 , … , N n , t ) {\displaystyle Pr(N_{1},N_{2},\dots ,N_{n},t)} is realized by a neural network iff there exists a time-delay T ≥ 0 {\displaystyle T\geq 0} , a neuron i {\displaystyle i} in the network, and an initial state for the non-peripheral neurons N p + 1 ( 0 ) , … , N n ( 0 ) {\displaystyle N_{p+1}(0),\dots ,N_{n}(0)} , such that for any time t {\displaystyle t} , the truth-value of the logical sentence is equal to the state of the neuron i {\displaystyle i} at time t + T {\displaystyle t+T} . That is, ∀ t = 0 , 1 , 2 , … , P r ( N 1 , N 2 , … , N p , t ) = N i ( t + T ) {\displaystyle \forall t=0,1,2,\dots ,\quad Pr(N_{1},N_{2},\dots ,N_{p},t)=N_{i}(t+T)} === Equivalence === In the paper, they considered some alternative definitions of artificial neural networks, and have shown them to be equivalent, that is, neural networks under one definition realizes precisely the same logical sentences as neural networks under another definition. They considered three forms of inhibition: relative inhibition, absolute inhibition, and extinction. The definition above is relative inhibition. By "absolute inhibition" they meant that if any negative synapse fires, then the neuron will not fire. By "extinction" they meant that if at time t {\displaystyle t} , any inhibitory synapse fires on a neuron i {\displaystyle i} , then θ i ( t + j ) = θ i ( 0 ) + b j {\displaystyle \theta _{i}(t+j)=\theta _{i}(0)+b_{j}} for j = 1 , 2 , 3 , … {\displaystyle j=1,2,3,\dots } , until the next time an inhibitory synapse fires on i {\displaystyle i} . It is required that b j = 0 {\displaystyle b_{j}=0} for all large j {\displaystyle j} . Theorem 4 and 5 state that these are equivalent. They considered three forms of excitation: spatial summation, temporal summation, and facilitation. The definition above is spatial summation (which they pictured as having multiple synapses placed close together, so that the effect of their firing sums up). By "temporal summation" they meant that the total incoming signal is ∑ τ = 0 T ∑ j = 1 n w i j ( t ) N j ( t − τ ) {\displaystyle \sum _{\tau =0}^{T}\sum _{j=1}^{n}w_{ij}(t)N_{j}(t-\tau )} for some T ≥ 1 {\displaystyle T\geq 1} . By "facilitation" they meant the same as extinction, except that b j ≤ 0 {\displaystyle b_{j}\leq 0} . Theorem 6 states that these are equivalent. They considered neural networks that do not change, and those that change by Hebbian learning. That is, they assume that at t = 0 {\displaystyle t=0} , some excitatory synaptic connections are not active. If at any t {\displaystyle t} , both N i ( t ) = 1 , N j ( t ) = 1 {\displaystyle N_{i}(t)=1,N_{j}(t)=1} , then any latent excitatory synapse between i , j {\displaystyle i,j} becomes active. Theorem 7 states that these are equivalent. === Logical expressivity === They considered "temporal propositional expressions" (TPE), which are propositional formulas with one free variable t {\displaystyle t} . For example, N 1 ( t ) ∨ N 2 ( t ) ∧ ¬ N 3 ( t ) {\displaystyle N_{1}(t)\vee N_{2}(t)\wedge \neg N_{3}(t)} is such an expression. Theorem 1 and 2 together showed that neural nets without circles are equivalent to TPE. For neural nets with loops, they noted that "realizable P r {\displaystyle Pr} may involve reference to past events of an indefinite degree of remoteness". These then encodes for sentences like "There was some x such that x was a ψ" or ( ∃ x ) ( ψ x ) {\displaystyle (\exists x)(\psi x)} . Theorems 8 to 10 showed that neural nets with loops can encode all first-order logic with equality and conversely, any looped neural networks is equivalent to a sentence in first-order logic with equality, thus showing that they are equivalent in logical expressiveness. As a remark, they noted that a neural network, if furnished with a tape, scanners, and write-heads, is equivalent to a Turing machine, and conversely, every Turing machine is equivalent to some such neural network. Thus, these neural networks are equivalent to Turing computability and Church's lambda-definability. == Context == === Previous work === The paper built upon several previous strands of work. In the symbolic logic side, it built on the previous work by Carnap, Whitehead, and Russell. This was contributed by Walter Pitts, who had a strong proficiency with symbolic logic. Pitts provided mathematical and logical rigor to McCulloch’s vague ideas on psychons (atoms of psychological events) and circular causality. In the neuroscience side, it built on previous work by the mathematical biology research group centered around Nicolas Rashevsky, of which McCulloch was a member. The paper was published in the Bulletin of Mathematical Biophysics, which was founded by Rashevsky in 1939. During the late 1930s, Rashevsky's research group was producing papers that had difficulty publishing in other journals at the time, so Rashevsky decided to found a new journal exclusively devoted to mathematical biophysics. Also in the Rashevsky's group was Alston Scott Householder, who in 1941 published an abstract model

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  Ordered key–value store

  An ordered key–value store (OKVS) is a type of data storage paradigm that can support multi-model databases. An OKVS is an ordered mapping of bytes to bytes. An OKVS will keep the key–value pairs sorted by the key lexicographic order. OKVS systems provides different set of features and performance trade-offs. Most of them are shipped as a library without network interfaces, in order to be embedded in another process. Most OKVS support ACID guarantees. Some OKVS are distributed databases. Ordered key–value stores found their way into many modern database systems including NewSQL database systems. == History == The origin of ordered key–value store stems from the work of Ken Thompson on dbm in 1979. Later in 1991, Berkeley DB was released that featured a B-Tree backend that allowed the keys to stay sorted. Berkeley DB was said to be very fast and made its way into various commercial product. It was included in Python standard library until 2.7. In 2009, Tokyo Cabinet was released that was superseded by Kyoto Cabinet that support both transaction and ordered keys. In 2011, LMDB was created to replace Berkeley DB in OpenLDAP. There is also Google's LevelDB that was forked by Facebook in 2012 as RocksDB. In 2014, WiredTiger, successor of Berkeley DB was acquired by MongoDB and is since 2019 the primary backend of MongoDB database. Other notable implementation of the OKVS paradigm are Sophia and SQLite3 LSM extension. Another notable use of OKVS paradigm is the multi-model database system called ArangoDB based on RocksDB. Some NewSQL databases are supported by ordered key–value stores. JanusGraph, a property graph database, has both a Berkeley DB backend and FoundationDB backend. == Key concepts == === Lexicographic encoding === There are algorithms that encode basic data types (boolean, string, number) and composition of those data types inside sorted containers (tuple, list, vector) that preserve their natural ordering. It is possible to work with an ordered key–value store without having to work directly with bytes. In FoundationDB, it is called the tuple layer. === Range query === Inside an OKVS, keys are ordered, and because of that it is possible to do range queries. A range query retrieves all keys between two specified keys, ensuring that the fetched keys are returned in a sorted order. === Subspaces === === Key composition === One can construct key spaces to build higher level abstractions. The idea is to construct keys, that takes advantage of the ordered nature of the top level key space. When taking advantage of the ordered nature of the key space, one can query ranges of keys that have particular pattern. === Denormalization === Denormalization, as in, repeating the same piece of data in multiple subspace is common practice. It allows to create secondary representation, also called indices, that will allow to speed up queries. == Higher level abstractions == The following abstraction or databases were built on top ordered key–value stores: Timeseries database, Record Database, also known as Row store databases, they behave similarly to what is dubbed RDBMS, Tuple Stores, also known as Triple Store or Quad Store but also Generic Tuple Store, Document database, that mimics MongoDB API, Full-text search Geographic Information Systems Property Graph Versioned Data Vector space database for Approximate Nearest Neighbor All those abstraction can co-exist with the same OKVS database and when ACID is supported, the operations happens with the guarantees offered by the transaction system. == Feature matrix == == Use-cases == OKVS are useful to implement two strategies: optimize a small feature e.g. to make a 10% improvement in read or write latency; the second strategy is to take advantage of the distributed nature of FoundationDB, and TiKV, for which there is no equivalent at very large scale in resilience. Both users need to re-implement the needed high level abstractions, because there are no portable ready-to-use libraries of high-level abstraction. There is still a complex balance, of complexity, maintainability, fine-tuning, and readily available features that makes it still a choice of experts. Sometime more specialized data-structures can be faster than a high-level abstraction on top of an OKVS. Another interest of OKVS paradigm stems from it simple, and versatile interface, that makes it an interesting target for experimental storage algorithms, and data structures.

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  Storage area network

  A storage area network (SAN) or storage network is a computer network which provides access to consolidated, block-level data storage. SANs are primarily used to access data storage devices, such as disk arrays and tape libraries from servers so that the devices appear to the operating system as direct-attached storage. A SAN typically is a dedicated network of storage devices not accessible through the local area network (LAN). Although a SAN provides only block-level access, file systems built on top of SANs do provide file-level access and are known as shared-disk file systems. Newer SAN configurations enable hybrid SAN and allow traditional block storage that appears as local storage but also object storage for web services through APIs. == Storage architectures == Storage area networks (SANs) are sometimes referred to as network behind the servers and historically developed out of a centralized data storage model, but with its own data network. A SAN is, at its simplest, a dedicated network for data storage. In addition to storing data, SANs allow for the automatic backup of data, and the monitoring of the storage as well as the backup process. A SAN is a combination of hardware and software. It grew out of data-centric mainframe architectures, where clients in a network can connect to several servers that store different types of data. To scale storage capacities as the volumes of data grew, direct-attached storage (DAS) was developed, where disk arrays or just a bunch of disks (JBODs) were attached to servers. In this architecture, storage devices can be added to increase storage capacity. However, the server through which the storage devices are accessed is a single point of failure, and a large part of the LAN network bandwidth is used for accessing, storing and backing up data. To solve the single point of failure issue, a direct-attached shared storage architecture was implemented, where several servers could access the same storage device. DAS was the first network storage system and is still widely used where data storage requirements are not very high. Out of it developed the network-attached storage (NAS) architecture, where one or more dedicated file server or storage devices are made available in a LAN. Therefore, the transfer of data, particularly for backup, still takes place over the existing LAN. If more than a terabyte of data was stored at any one time, LAN bandwidth became a bottleneck. Therefore, SANs were developed, where a dedicated storage network was attached to the LAN, and terabytes of data are transferred over a dedicated high speed and bandwidth network. Within the SAN, storage devices are interconnected. Transfer of data between storage devices, such as for backup, happens behind the servers and is meant to be transparent. In a NAS architecture data is transferred using the TCP and IP protocols over Ethernet. Distinct protocols were developed for SANs, such as Fibre Channel, iSCSI, Infiniband. Therefore, SANs often have their own network and storage devices, which have to be bought, installed, and configured. This makes SANs inherently more expensive than NAS architectures. == Components == SANs have their own networking devices, such as SAN switches. To access the SAN, so-called SAN servers are used, which in turn connect to SAN host adapters. Within the SAN, a range of data storage devices may be interconnected, such as SAN-capable disk arrays, JBODs and tape libraries. === Host layer === Servers that allow access to the SAN and its storage devices are said to form the host layer of the SAN. Such servers have host adapters, which are cards that attach to slots on the server motherboard (usually PCI slots) and run with a corresponding firmware and device driver. Through the host adapters the operating system of the server can communicate with the storage devices in the SAN. In Fibre channel deployments, a cable connects to the host adapter through the gigabit interface converter (GBIC). GBICs are also used on switches and storage devices within the SAN, and they convert digital bits into light impulses that can then be transmitted over the Fibre Channel cables. Conversely, the GBIC converts incoming light impulses back into digital bits. The predecessor of the GBIC was called gigabit link module (GLM). === Fabric layer === The fabric layer consists of SAN networking devices that include SAN switches, routers, protocol bridges, gateway devices, and cables. SAN network devices move data within the SAN, or between an initiator, such as an HBA port of a server, and a target, such as the port of a storage device. When SANs were first built, hubs were the only devices that were Fibre Channel capable, but Fibre Channel switches were developed and hubs are now rarely found in SANs. Switches have the advantage over hubs that they allow all attached devices to communicate simultaneously, as a switch provides a dedicated link to connect all its ports with one another. When SANs were first built, Fibre Channel had to be implemented over copper cables, these days multimode optical fibre cables are used in SANs. SANs are usually built with redundancy, so SAN switches are connected with redundant links. SAN switches connect the servers with the storage devices and are typically non-blocking allowing transmission of data across all attached wires at the same time. SAN switches are for redundancy purposes set up in a meshed topology. A single SAN switch can have as few as 8 ports and up to 32 ports with modular extensions. So-called director-class switches can have as many as 128 ports. In switched SANs, the Fibre Channel switched fabric protocol FC-SW-6 is used under which every device in the SAN has a hardcoded World Wide Name (WWN) address in the host bus adapter (HBA). If a device is connected to the SAN its WWN is registered in the SAN switch name server. In place of a WWN, or worldwide port name (WWPN), SAN Fibre Channel storage device vendors may also hardcode a worldwide node name (WWNN). The ports of storage devices often have a WWN starting with 5, while the bus adapters of servers start with 10 or 21. === Storage layer === The serialized Small Computer Systems Interface (SCSI) protocol is often used on top of the Fibre Channel switched fabric protocol in servers and SAN storage devices. The Internet Small Computer Systems Interface (iSCSI) over Ethernet and the Infiniband protocols may also be found implemented in SANs, but are often bridged into the Fibre Channel SAN. However, Infiniband and iSCSI storage devices, in particular, disk arrays, are available. The various storage devices in a SAN are said to form the storage layer. It can include a variety of hard disk and magnetic tape devices that store data. In SANs, disk arrays are joined through a RAID which makes a lot of hard disks look and perform like one big storage device. Every storage device, or even partition on that storage device, has a logical unit number (LUN) assigned to it. This is a unique number within the SAN. Every node in the SAN, be it a server or another storage device, can access the storage by referencing the LUN. The LUNs allow for the storage capacity of a SAN to be segmented and for the implementation of access controls. A particular server, or a group of servers, may, for example, be only given access to a particular part of the SAN storage layer, in the form of LUNs. When a storage device receives a request to read or write data, it will check its access list to establish whether the node, identified by its LUN, is allowed to access the storage area, also identified by a LUN. LUN masking is a technique whereby the host bus adapter and the SAN software of a server restrict the LUNs for which commands are accepted. In doing so LUNs that should never be accessed by the server are masked. Another method to restrict server access to particular SAN storage devices is fabric-based access control, or zoning, which is enforced by the SAN networking devices and servers. Under zoning, server access is restricted to storage devices that are in a particular SAN zone. == Network protocols == A mapping layer to other protocols is used to form a network: ATA over Ethernet (AoE), mapping of AT Attachment (ATA) over Ethernet Fibre Channel Protocol (FCP), a mapping of SCSI over Fibre Channel Fibre Channel over Ethernet (FCoE) ESCON over Fibre Channel (FICON), used by mainframe computers HyperSCSI, mapping of SCSI over Ethernet iFCP or SANoIP mapping of FCP over IP iSCSI, mapping of SCSI over TCP/IP iSCSI Extensions for RDMA (iSER), mapping of iSCSI over InfiniBand Network block device, mapping device node requests on UNIX-like systems over stream sockets like TCP/IP SCSI RDMA Protocol (SRP), another SCSI implementation for remote direct memory access (RDMA) transports Storage networks may also be built using Serial Attached SCSI (SAS) and Serial ATA (SATA) technologies. SAS evolved from SCSI direct-attached storage. SATA evolved from Para

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  Magic state distillation

  Magic state distillation is a method for creating more accurate quantum states from multiple noisy ones, which is important for building fault tolerant quantum computers. It has also been linked to quantum contextuality, a concept thought to contribute to quantum computers' power. The technique was first proposed by Emanuel Knill in 2004, and further analyzed by Sergey Bravyi and Alexei Kitaev the same year. Thanks to the Gottesman–Knill theorem, it is known that some quantum operations (operations in the Clifford group) can be perfectly simulated in polynomial time on a classical computer. In order to achieve universal quantum computation, a quantum computer must be able to perform operations outside this set. Magic state distillation achieves this, in principle, by concentrating the usefulness of imperfect resources, represented by mixed states, into states that are conducive for performing operations that are difficult to simulate classically. A variety of qubit magic state distillation routines and distillation routines for qubits with various advantages have been proposed. == Stabilizer formalism == The Clifford group consists of a set of n {\displaystyle n} -qubit operations generated by the gates {H, S, CNOT} (where H is Hadamard and S is [ 1 0 0 i ] {\displaystyle {\begin{bmatrix}1&0\\0&i\end{bmatrix}}} ) called Clifford gates. The Clifford group generates stabilizer states which can be efficiently simulated classically, as shown by the Gottesman–Knill theorem. This set of gates with a non-Clifford operation is universal for quantum computation. == Magic states == Magic states are purified from n {\displaystyle n} copies of a mixed state ρ {\displaystyle \rho } . These states are typically provided via an ancilla to the circuit. A magic state for the π / 6 {\displaystyle \pi /6} rotation operator is | M ⟩ = cos ⁡ ( β / 2 ) | 0 ⟩ + e i π 4 sin ⁡ ( β / 2 ) | 1 ⟩ {\displaystyle |M\rangle =\cos(\beta /2)|0\rangle +e^{i{\frac {\pi }{4}}}\sin(\beta /2)|1\rangle } where β = arccos ⁡ ( 1 3 ) {\displaystyle \beta =\arccos \left({\frac {1}{\sqrt {3}}}\right)} . A non-Clifford gate can be generated by combining (copies of) magic states with Clifford gates. Since a set of Clifford gates combined with a non-Clifford gate is universal for quantum computation, magic states combined with Clifford gates are also universal. == Purification algorithm for distilling |M〉 == The first magic state distillation algorithm, invented by Sergey Bravyi and Alexei Kitaev, is as follows. Input: Prepare 5 imperfect states. Output: An almost pure state having a small error probability. repeat Apply the decoding operation of the five-qubit error correcting code and measure the syndrome. If the measured syndrome is | 0000 ⟩ {\displaystyle |0000\rangle } , the distillation attempt is successful. else Get rid of the resulting state and restart the algorithm. until The states have been distilled to the desired purity.

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  Video browsing

  Video browsing, also known as exploratory video search, is the interactive process of skimming through video content in order to satisfy some information need or to interactively check if the video content is relevant. While originally proposed to help users inspecting a single video through visual thumbnails, modern video browsing tools enable users to quickly find desired information in a video archive by iterative human–computer interaction through an exploratory search approach. Many of these tools presume a smart user that wants features to interactively inspect video content, as well as automatic content filtering features. For that purpose, several video interaction features are usually provided, such as sophisticated navigation in video or search by a content-based query. Video browsing tools often build on lower-level video content analysis, such as shot transition detection, keyframe extraction, semantic concept detection, and create a structured content overview of the video file or video archive. Furthermore, they usually provide sophisticated navigation features, such as advanced timelines, visual seeker bars or a list of selected thumbnails, as well as means for content querying. Examples of content queries are shot filtering through visual concepts (e.g., only shots showing cars), through some specific characteristics (e.g., color or motion filtering), through user-provided sketches (e.g., a visually drawn sketch), or through content-based similarity search. == History == Video browsing was originally proposed by Iranian engineer Farshid Arman, Taiwanese computer scientist Arding Hsu, and computer scientist Ming-Yee Chiu, while working at Siemens, and it was presented at the ACM International Conference in August 1993. They described a shot detection algorithm for compressed video that was originally encoded with discrete cosine transform (DCT) video coding standards such as JPEG, MPEG and H.26x. The basic idea was that, since the DCT coefficients are mathematically related to the spatial domain and represent the content of each frame, they can be used to detect the differences between video frames. In the algorithm, a subset of blocks in a frame and a subset of DCT coefficients for each block are used as motion vector representation for the frame. By operating on compressed DCT representations, the algorithm significantly reduces the computational requirements for decompression and enables effective video browsing. The algorithm represents separate shots of a video sequence by an r-frame, a thumbnail of the shot framed by a motion tracking region. A variation of this concept was later adopted for QBIC video content mosaics, where each r-frame is a salient still from the shot it represents. === Video Notebook === Modern video browsing solutions include Video Notebook, a Menlo Park startup founded in 2021 by Mike Lanza, which uses computer vision to extract slides and optical character recognition and speech recognition to facilitate video search. The software can be either used on the client side (using a browser extension), where the slides and text are extracted while the video is watched (e.g. on a video platform like YouTube or Udemy), or on the server side. Processed videos, which can be viewed in the Video Notebook web app, feature a video browsing user interface with extracted timestamped slides, a search bar for querying the video (or a collection of videos), and text chapters. Video Notebook customers include organisations like Ernst & Young. === Video Browser Showdown === The Video Browser Showdown (VBS) is an annual live evaluation competition for exploratory video search tools, where international researchers use video browsing tools to solve ad-hoc video search tasks on a moderately large data set as fast as possible. The main goal of the VBS, which started in 2012 at the International Conference on MultiMedia Modeling (MMM), is to advance the performance of video browsing tools. Since 2016, the VBS also collaborates with TRECVID. The aim of the VBS is to evaluate video browsing tools for efficiency at known-item search (KIS) tasks with a well-defined data set in direct comparison to other tools.

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  Sardinas–Patterson algorithm

  In coding theory, the Sardinas–Patterson algorithm is a classical algorithm for determining in polynomial time whether a given variable-length code is uniquely decodable, named after August Albert Sardinas and George W. Patterson, who published it in 1953. The algorithm carries out a systematic search for a string which admits two different decompositions into codewords. As Knuth reports, the algorithm was rediscovered about ten years later in 1963 by Floyd, despite the fact that it was at the time already well known in coding theory. == Idea of the algorithm == Consider the code { a ↦ 1 , b ↦ 011 , c ↦ 01110 , d ↦ 1110 , e ↦ 10011 } {\displaystyle \{\,{\texttt {a}}\mapsto {\texttt {1}},{\texttt {b}}\mapsto {\texttt {011}},{\texttt {c}}\mapsto {\texttt {01110}},{\texttt {d}}\mapsto {\texttt {1110}},{\texttt {e}}\mapsto {\texttt {10011}}\,\}} . This code, which is based on an example by Berstel, is an example of a code which is not uniquely decodable, since the string 011101110011 can be interpreted as the sequence of codewords 01110 – 1110 – 011, but also as the sequence of codewords 011 – 1 – 011 – 10011. Two possible decodings of this encoded string are thus given by cdb and babe. In general, a codeword can be found by the following idea: In the first round, we choose two codewords x 1 {\displaystyle x_{1}} and y 1 {\displaystyle y_{1}} such that x 1 {\displaystyle x_{1}} is a prefix of y 1 {\displaystyle y_{1}} , that is, x 1 w = y 1 {\displaystyle x_{1}w=y_{1}} for some "dangling suffix" w {\displaystyle w} . If one tries first x 1 = 011 {\displaystyle x_{1}={\texttt {011}}} and y 1 = 01110 {\displaystyle y_{1}={\texttt {01110}}} , the dangling suffix is w = 10 {\displaystyle {\texttt {w}}={\texttt {10}}} . If we manage to find two sequences x 2 , … , x p {\displaystyle x_{2},\ldots ,x_{p}} and y 2 , … , y q {\displaystyle y_{2},\ldots ,y_{q}} of codewords such that x 2 ⋯ x p = w y 2 ⋯ y q {\displaystyle x_{2}\cdots x_{p}=wy_{2}\cdots y_{q}} , then we are finished: For then the string x = x 1 x 2 ⋯ x p {\displaystyle x=x_{1}x_{2}\cdots x_{p}} can alternatively be decomposed as y 1 y 2 ⋯ y q {\displaystyle y_{1}y_{2}\cdots y_{q}} , and we have found the desired string having at least two different decompositions into codewords. In the second round, we try out two different approaches: the first trial is to look for a codeword that has w as prefix. Then we obtain a new dangling suffix w, with which we can continue our search. If we eventually encounter a dangling suffix that is itself a codeword (or the empty word), then the search will terminate, as we know there exists a string with two decompositions. The second trial is to seek for a codeword that is itself a prefix of w. In our example, we have w = 10 {\displaystyle w={\texttt {10}}} , and the sequence 1 is a codeword. We can thus also continue with w = 0 {\displaystyle w={\texttt {0}}} as the new dangling suffix. == Precise description of the algorithm == The algorithm is described most conveniently using quotients of formal languages. In general, for two sets of strings D and N, the (left) quotient N − 1 D {\displaystyle N^{-1}D} is defined as the residual words obtained from D by removing some prefix in N. Formally, N − 1 D = { y ∣ x y ∈ D and x ∈ N } {\displaystyle N^{-1}D=\{\,y\mid xy\in D~{\textrm {and}}~x\in N\,\}} . Now let C {\displaystyle C} denote the (finite) set of codewords in the given code. The algorithm proceeds in rounds, where we maintain in each round not only one dangling suffix as described above, but the (finite) set of all potential dangling suffixes. Starting with round i = 1 {\displaystyle i=1} , the set of potential dangling suffixes will be denoted by S i {\displaystyle S_{i}} . The sets S i {\displaystyle S_{i}} are defined inductively as follows: S 1 = C − 1 C ∖ { ε } {\displaystyle S_{1}=C^{-1}C\setminus \{\varepsilon \}} . Here, the symbol ε {\displaystyle \varepsilon } denotes the empty word. S i + 1 = C − 1 S i ∪ S i − 1 C {\displaystyle S_{i+1}=C^{-1}S_{i}\cup S_{i}^{-1}C} , for all i ≥ 1 {\displaystyle i\geq 1} . The algorithm computes the sets S i {\displaystyle S_{i}} in increasing order of i {\displaystyle i} . As soon as one of the S i {\displaystyle S_{i}} contains a word from C or the empty word, then the algorithm terminates and answers that the given code is not uniquely decodable. Otherwise, once a set S i {\displaystyle S_{i}} equals a previously encountered set S j {\displaystyle S_{j}} with j < i {\displaystyle j Read more →

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  Lancichinetti–Fortunato–Radicchi benchmark

  Lancichinetti–Fortunato–Radicchi benchmark is an algorithm that generates benchmark networks (artificial networks that resemble real-world networks). They have a priori known communities and are used to compare different community detection methods. The advantage of the benchmark over other methods is that it accounts for the heterogeneity in the distributions of node degrees and of community sizes. == The algorithm == The node degrees and the community sizes are distributed according to a power law, with different exponents. The benchmark assumes that both the degree and the community size have power law distributions with different exponents, γ {\displaystyle \gamma } and β {\displaystyle \beta } , respectively. N {\displaystyle N} is the number of nodes and the average degree is ⟨ k ⟩ {\displaystyle \langle k\rangle } . There is a mixing parameter μ {\displaystyle \mu } , which is the average fraction of neighboring nodes of a node that do not belong to any community that the benchmark node belongs to. This parameter controls the fraction of edges that are between communities. Thus, it reflects the amount of noise in the network. At the extremes, when μ = 0 {\displaystyle \mu =0} all links are within community links, if μ = 1 {\displaystyle \mu =1} all links are between nodes belonging to different communities. One can generate the benchmark network using the following steps. Step 1: Generate a network with nodes following a power law distribution with exponent γ {\displaystyle \gamma } and choose extremes of the distribution k min {\displaystyle k_{\min }} and k max {\displaystyle k_{\max }} to get desired average degree is ⟨ k ⟩ {\displaystyle \langle k\rangle } . Step 2: ( 1 − μ ) {\displaystyle (1-\mu )} fraction of links of every node is with nodes of the same community, while fraction μ {\displaystyle \mu } is with the other nodes. Step 3: Generate community sizes from a power law distribution with exponent β {\displaystyle \beta } . The sum of all sizes must be equal to N {\displaystyle N} . The minimal and maximal community sizes s min {\displaystyle s_{\min }} and s max {\displaystyle s_{\max }} must satisfy the definition of community so that every non-isolated node is in at least in one community: s min > k min {\displaystyle s_{\min }>k_{\min }} s max > k max {\displaystyle s_{\max }>k_{\max }} Step 4: Initially, no nodes are assigned to communities. Then, each node is randomly assigned to a community. As long as the number of neighboring nodes within the community does not exceed the community size a new node is added to the community, otherwise stays out. In the following iterations the “homeless” node is randomly assigned to some community. If that community is complete, i.e. the size is exhausted, a randomly selected node of that community must be unlinked. Stop the iteration when all the communities are complete and all the nodes belong to at least one community. Step 5: Implement rewiring of nodes keeping the same node degrees but only affecting the fraction of internal and external links such that the number of links outside the community for each node is approximately equal to the mixing parameter μ {\displaystyle \mu } . == Testing == Consider a partition into communities that do not overlap. The communities of randomly chosen nodes in each iteration follow a p ( C ) {\displaystyle p(C)} distribution that represents the probability that a randomly picked node is from the community C {\displaystyle C} . Consider a partition of the same network that was predicted by some community finding algorithm and has p ( C 2 ) {\displaystyle p(C_{2})} distribution. The benchmark partition has p ( C 1 ) {\displaystyle p(C_{1})} distribution. The joint distribution is p ( C 1 , C 2 ) {\displaystyle p(C_{1},C_{2})} . The similarity of these two partitions is captured by the normalized mutual information. I n = ∑ C 1 , C 2 p ( C 1 , C 2 ) log 2 ⁡ p ( C 1 , C 2 ) p ( C 1 ) p ( C 2 ) 1 2 H ( { p ( C 1 ) } ) + 1 2 H ( { p ( C 2 ) } ) {\displaystyle I_{n}={\frac {\sum _{C_{1},C_{2}}p(C_{1},C_{2})\log _{2}{\frac {p(C_{1},C_{2})}{p(C_{1})p(C_{2})}}}{{\frac {1}{2}}H(\{p(C_{1})\})+{\frac {1}{2}}H(\{p(C_{2})\})}}} If I n = 1 {\displaystyle I_{n}=1} the benchmark and the detected partitions are identical, and if I n = 0 {\displaystyle I_{n}=0} then they are independent of each other.

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  Information

  Information is an abstract concept that refers to something which has the power to inform. At the most fundamental level, it pertains to the interpretation (perhaps formally) of that which may be sensed, or their abstractions. Any natural process that is not completely random and any observable pattern in any medium can be said to convey some amount of information. Whereas digital signals and other data use discrete signs to convey information, other phenomena and artifacts such as analogue signals, poems, pictures, music or other sounds, and currents convey information in a more continuous form. Information is not knowledge itself, but the meaning that may be derived from a representation through interpretation. The concept of information is relevant to and connected with various concepts, including constraint, communication, control, data, form, education, knowledge, meaning, understanding, mental stimuli, pattern, perception, proposition, representation, and entropy. Information is often processed iteratively: Data available at one step are processed into information to be interpreted and processed at the next step. For example, in written text each symbol or letter conveys information relevant to the word it is part of, each word conveys information relevant to the phrase it is part of, each phrase conveys information relevant to the sentence it is part of, and so on until at the final step information is interpreted and becomes knowledge in a given domain. In a digital signal, bits may be interpreted into the symbols, letters, numbers, or structures that convey the information available at the next level up. The key characteristic of information is that it is subject to interpretation and processing. The derivation of information from a signal or message may be thought of as the resolution of ambiguity or uncertainty that arises during the interpretation of patterns within the signal or message. Information may be structured as data. Redundant data can be compressed up to an optimal size, which is the theoretical limit of compression. The information available through a collection of data may be derived by analysis. For example, a restaurant collects data from every customer order. That information may be analyzed to produce knowledge that is put to use when the business subsequently wants to identify the most popular or least popular dish. Information can be transmitted in time, via data storage, and space, via communication and telecommunication. Information is expressed either as the content of a message or through direct or indirect observation. That which is perceived can be construed as a message in its own right, and in that sense, all information is always conveyed as the content of a message. Information can be encoded into various forms for transmission and interpretation (for example, information may be encoded into a sequence of signs, or transmitted via a signal). It can also be encrypted for safe storage and communication. The uncertainty of an event is measured by its probability of occurrence. Uncertainty is proportional to the negative logarithm of the probability of occurrence. Information theory takes advantage of this by concluding that more uncertain events require more information to resolve their uncertainty. The bit is the standard unit of information. It is 'that which reduces uncertainty by half'. Other units such as the nat may be used. For example, the information encoded in one "fair" coin flip is log2(2/1) = 1 bit, and in two fair coin flips is log2(4/1) = 2 bits. A 2011 Science article estimates that 97% of technologically stored information was already in digital bits in 2007 and that the year 2002 was the beginning of the digital age for information storage (with digital storage capacity bypassing analogue for the first time). == Etymology and history of the concept == The English word "information" comes from Middle French enformacion/informacion/information 'a criminal investigation' and its etymon, Latin informatiō(n) 'conception, teaching, creation'. In English, "information" is an uncountable mass noun. References on "formation or molding of the mind or character, training, instruction, teaching" date from the 14th century in both English (according to Oxford English Dictionary) and other European languages. In the transition from Middle Ages to Modernity the use of the concept of information reflected a fundamental turn in epistemological basis – from "giving a (substantial) form to matter" to "communicating something to someone". Peters (1988, pp. 12–13) concludes: Information was readily deployed in empiricist psychology (though it played a less important role than other words such as impression or idea) because it seemed to describe the mechanics of sensation: objects in the world inform the senses. But sensation is entirely different from "form" – the one is sensual, the other intellectual; the one is subjective, the other objective. My sensation of things is fleeting, elusive, and idiosyncratic. For Hume, especially, sensory experience is a swirl of impressions cut off from any sure link to the real world... In any case, the empiricist problematic was how the mind is informed by sensations of the world. At first informed meant shaped by; later it came to mean received reports from. As its site of action drifted from cosmos to consciousness, the term's sense shifted from unities (Aristotle's forms) to units (of sensation). Information came less and less to refer to internal ordering or formation, since empiricism allowed for no preexisting intellectual forms outside of sensation itself. Instead, information came to refer to the fragmentary, fluctuating, haphazard stuff of sense. Information, like the early modern worldview in general, shifted from a divinely ordered cosmos to a system governed by the motion of corpuscles. Under the tutelage of empiricism, information gradually moved from structure to stuff, from form to substance, from intellectual order to sensory impulses. In the modern era, the most important influence on the concept of information is derived from the Information theory developed by Claude Shannon and others. This theory, however, reflects a fundamental contradiction. Northrup (1993) wrote: Thus, actually two conflicting metaphors are being used: The well-known metaphor of information as a quantity, like water in the water-pipe, is at work, but so is a second metaphor, that of information as a choice, a choice made by :an information provider, and a forced choice made by an :information receiver. Actually, the second metaphor implies that the information sent isn't necessarily equal to the information received, because any choice implies a comparison with a list of possibilities, i.e., a list of possible meanings. Here, meaning is involved, thus spoiling the idea of information as a pure "Ding an sich." Thus, much of the confusion regarding the concept of information seems to be related to the basic confusion of metaphors in Shannon's theory: is information an autonomous quantity, or is information always per SE information to an observer? Actually, I don't think that Shannon himself chose one of the two definitions. Logically speaking, his theory implied information as a subjective phenomenon. But this had so wide-ranging epistemological impacts that Shannon didn't seem to fully realize this logical fact. Consequently, he continued to use metaphors about information as if it were an objective substance. This is the basic, inherent contradiction in Shannon's information theory." (Northrup, 1993, p. 5). In their seminal book The Study of Information: Interdisciplinary Messages, Almach and Mansfield (1983) collected key views on the interdisciplinary controversy in computer science, artificial intelligence, library and information science, linguistics, psychology, and physics, as well as in the social sciences. Almach (1983, p. 660) himself disagrees with the use of the concept of information in the context of signal transmission, the basic senses of information in his view all referring "to telling something or to the something that is being told. Information is addressed to human minds and is received by human minds." All other senses, including its use with regard to nonhuman organisms as well to society as a whole, are, according to Machlup, metaphoric and, as in the case of cybernetics, anthropomorphic. Hjørland (2007) describes the fundamental difference between objective and subjective views of information and argues that the subjective view has been supported by, among others, Bateson, Yovits, Span-Hansen, Brier, Buckland, Goguen, and Hjørland. Hjørland provided the following example: A stone on a field could contain different information for different people (or from one situation to another). It is not possible for information systems to map all the stone's possible information for every individual. Nor is any one mapping the one "true" mapping. But peop

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  Double descent

  Double descent in statistics and machine learning is the phenomenon where a model's error rate on the test set initially decreases with the number of parameters, then peaks, then decreases again. This phenomenon has been considered surprising, as it contradicts assumptions about overfitting in classical machine learning. The increase usually occurs near the interpolation threshold, where the number of parameters is the same as the number of training data points (the model is just large enough to fit the training data). Or, more precisely, it is the maximum number of samples on which the model/training procedure achieves approximately on average 0 training error. == History == Early observations of what would later be called double descent in specific models date back to 1989. The term "double descent" was coined by Belkin et. al. in 2019, when the phenomenon gained popularity as a broader concept exhibited by many models. The latter development was prompted by a perceived contradiction between the conventional wisdom that too many parameters in the model result in a significant overfitting error (an extrapolation of the bias–variance tradeoff), and the empirical observations in the 2010s that some modern machine learning techniques tend to perform better with larger models. == Theoretical models == Double descent occurs in linear regression with isotropic Gaussian covariates and isotropic Gaussian noise. A model of double descent at the thermodynamic limit has been analyzed using the replica trick, and the result has been confirmed numerically. A number of works have suggested that double descent can be explained using the concept of effective dimension: While a network may have a large number of parameters, in practice only a subset of those parameters are relevant for generalization performance, as measured by the local Hessian curvature. This explanation is formalized through PAC-Bayes compression-based generalization bounds, which show that less complex models are expected to generalize better under a Solomonoff prior.

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  Chandy–Misra–Haas algorithm resource model

  The Chandy–Misra–Haas algorithm resource model checks for deadlock in a distributed system. It was developed by K. Mani Chandy, Jayadev Misra and Laura M. Haas. == Locally dependent == Consider the n processes P1, P2, P3, P4, P5,, ... ,Pn which are performed in a single system (controller). P1 is locally dependent on Pn, if P1 depends on P2, P2 on P3, so on and Pn−1 on Pn. That is, if P 1 → P 2 → P 3 → … → P n {\displaystyle P_{1}\rightarrow P_{2}\rightarrow P_{3}\rightarrow \ldots \rightarrow P_{n}} , then P 1 {\displaystyle P_{1}} is locally dependent on P n {\displaystyle P_{n}} . If P1 is said to be locally dependent to itself if it is locally dependent on Pn and Pn depends on P1: i.e. if P 1 → P 2 → P 3 → … → P n → P 1 {\displaystyle P_{1}\rightarrow P_{2}\rightarrow P_{3}\rightarrow \ldots \rightarrow P_{n}\rightarrow P_{1}} , then P 1 {\displaystyle P_{1}} is locally dependent on itself. == Description == The algorithm uses a message called probe(i,j,k) to transfer a message from controller of process Pj to controller of process Pk. It specifies a message started by process Pi to find whether a deadlock has occurred or not. Every process Pj maintains a boolean array dependent which contains the information about the processes that depend on it. Initially the values of each array are all "false". === Controller sending a probe === Before sending, the probe checks whether Pj is locally dependent on itself. If so, a deadlock occurs. Otherwise it checks whether Pj, and Pk are in different controllers, are locally dependent and Pj is waiting for the resource that is locked by Pk. Once all the conditions are satisfied it sends the probe. === Controller receiving a probe === On the receiving side, the controller checks whether Pk is performing a task. If so, it neglects the probe. Otherwise, it checks the responses given Pk to Pj and dependentk(i) is false. Once it is verified, it assigns true to dependentk(i). Then it checks whether k is equal to i. If both are equal, a deadlock occurs, otherwise it sends the probe to next dependent process. == Algorithm == In pseudocode, the algorithm works as follows: === Controller sending a probe === if Pj is locally dependent on itself then declare deadlock else for all Pj,Pk such that (i) Pi is locally dependent on Pj, (ii) Pj is waiting for 'Pk and (iii) Pj, Pk are on different controllers. send probe(i, j, k). to home site of Pk === Controller receiving a probe === if (i)Pk is idle / blocked (ii) dependentk(i) = false, and (iii) Pk has not replied to all requests of to Pj then begin "dependents""k"(i) = true; if k == i then declare that Pi is deadlocked else for all Pa,Pb such that (i) Pk is locally dependent on Pa, (ii) Pa is waiting for 'Pb and (iii) Pa, Pb are on different controllers. send probe(i, a, b). to home site of Pb end == Example == P1 initiates deadlock detection. C1 sends the probe saying P2 depends on P3. Once the message is received by C2, it checks whether P3 is idle. P3 is idle because it is locally dependent on P4 and updates dependent3(2) to True. As above, C2 sends probe to C3 and C3 sends probe to C1. At C1, P1 is idle so it update dependent1(1) to True. Therefore, deadlock can be declared. == Complexity == Suppose there are n {\displaystyle n} controllers and m {\displaystyle m} processes, at most m ( n − 1 ) / 2 {\displaystyle m(n-1)/2} messages need to be exchanged to detect a deadlock, with a delay of O ( n ) {\displaystyle O(n)} messages.

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  Collaborative diffusion

  Collaborative Diffusion is a type of pathfinding algorithm which uses the concept of antiobjects, objects within a computer program that function opposite to what would be conventionally expected. Collaborative Diffusion is typically used in video games, when multiple agents must path towards a single target agent. For example, the ghosts in Pac-Man. In this case, the background tiles serve as antiobjects, carrying out the necessary calculations for creating a path and having the foreground objects react accordingly, whereas having foreground objects be responsible for their own pathing would be conventionally expected. Collaborative Diffusion is favored for its efficiency over other pathfinding algorithms, such as A, when handling multiple agents. Also, this method allows elements of competition and teamwork to easily be incorporated between tracking agents. Notably, the time taken to calculate paths remains constant as the number of agents increases.

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