AI Coding For Game Development

AI Coding For Game Development — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Incremental heuristic search

  Incremental heuristic search algorithms combine both incremental and heuristic search to speed up searches of sequences of similar search problems, which is important in domains that are only incompletely known or change dynamically. Incremental search has been studied at least since the late 1960s. Incremental search algorithms reuse information from previous searches to speed up the current search and solve search problems potentially much faster than solving them repeatedly from scratch. Similarly, heuristic search has also been studied at least since the late 1960s. Heuristic search algorithms, often based on A, use heuristic knowledge in the form of approximations of the goal distances to focus the search and solve search problems potentially much faster than uninformed search algorithms. The resulting search problems, sometimes called dynamic path planning problems, are graph search problems where paths have to be found repeatedly because the topology of the graph, its edge costs, the start vertex or the goal vertices change over time. So far, three main classes of incremental heuristic search algorithms have been developed: The first class restarts A at the point where its current search deviates from the previous one (example: Fringe Saving A). The second class updates the h-values (heuristic, i.e. approximate distance to goal) from the previous search during the current search to make them more informed (example: Generalized Adaptive A). The third class updates the g-values (distance from start) from the previous search during the current search to correct them when necessary, which can be interpreted as transforming the A search tree from the previous search into the A search tree for the current search (examples: Lifelong Planning A, D, D Lite). All three classes of incremental heuristic search algorithms are different from other replanning algorithms, such as planning by analogy, in that their plan quality does not deteriorate with the number of replanning episodes. == Applications == Incremental heuristic search has been extensively used in robotics, where a larger number of path planning systems are based on either D (typically earlier systems) or D Lite (current systems), two different incremental heuristic search algorithms.

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  Timeline of algorithms

  The following timeline of algorithms outlines the development of algorithms (mainly "mathematical recipes") since their inception. == Antiquity == Before – writing about "recipes" (on cooking, rituals, agriculture and other themes) c. 1700–2000 BC – Egyptians develop earliest known algorithms for multiplying two numbers c. 1600 BC – Babylonians develop earliest known algorithms for factorization and finding square roots c. 300 BC – Euclid's algorithm c. 200 BC – the Sieve of Eratosthenes 263 AD – Gaussian elimination described by Liu Hui == Medieval Period == 628 – Chakravala method described by Brahmagupta c. 820 – Al-Khawarizmi described algorithms for solving linear equations and quadratic equations in his Algebra; the word algorithm comes from his name 825 – Al-Khawarizmi described the algorism, algorithms for using the Hindu–Arabic numeral system, in his treatise On the Calculation with Hindu Numerals, which was translated into Latin as Algoritmi de numero Indorum, where "Algoritmi", the translator's rendition of the author's name gave rise to the word algorithm (Latin algorithmus) with a meaning "calculation method" c. 850 – cryptanalysis and frequency analysis algorithms developed by Al-Kindi (Alkindus) in A Manuscript on Deciphering Cryptographic Messages, which contains algorithms on breaking encryptions and ciphers c. 1025 – Ibn al-Haytham (Alhazen), was the first mathematician to derive the formula for the sum of the fourth powers, and in turn, he develops an algorithm for determining the general formula for the sum of any integral powers c. 1400 – Ahmad al-Qalqashandi gives a list of ciphers in his Subh al-a'sha which include both substitution and transposition, and for the first time, a cipher with multiple substitutions for each plaintext letter; he also gives an exposition on and worked example of cryptanalysis, including the use of tables of letter frequencies and sets of letters which can not occur together in one word == Before 1940 == 1540 – Lodovico Ferrari discovered a method to find the roots of a quartic polynomial 1545 – Gerolamo Cardano published Cardano's method for finding the roots of a cubic polynomial 1614 – John Napier develops method for performing calculations using logarithms 1671 – Newton–Raphson method developed by Isaac Newton 1690 – Newton–Raphson method independently developed by Joseph Raphson 1706 – John Machin develops a quickly converging inverse-tangent series for π and computes π to 100 decimal places 1768 – Leonhard Euler publishes his method for numerical integration of ordinary differential equations in problem 85 of Institutiones calculi integralis 1789 – Jurij Vega improves Machin's formula and computes π to 140 decimal places, 1805 – FFT-like algorithm known by Carl Friedrich Gauss 1842 – Ada Lovelace writes the first algorithm for a computing engine 1903 – A fast Fourier transform algorithm presented by Carle David Tolmé Runge 1918 - Soundex 1926 – Borůvka's algorithm 1926 – Primary decomposition algorithm presented by Grete Hermann 1927 – Hartree–Fock method developed for simulating a quantum many-body system in a stationary state. 1934 – Delaunay triangulation developed by Boris Delaunay 1936 – Turing machine, an abstract machine developed by Alan Turing, with others developed the modern notion of algorithm. == 1940s == 1942 – A fast Fourier transform algorithm developed by G.C. Danielson and Cornelius Lanczos 1945 – Merge sort developed by John von Neumann 1947 – Simplex algorithm developed by George Dantzig == 1950s == 1950 – Hamming codes developed by Richard Hamming 1952 – Huffman coding developed by David A. Huffman 1953 – Simulated annealing introduced by Nicholas Metropolis 1954 – Radix sort computer algorithm developed by Harold H. Seward 1964 – Box–Muller transform for fast generation of normally distributed numbers published by George Edward Pelham Box and Mervin Edgar Muller. Independently pre-discovered by Raymond E. A. C. Paley and Norbert Wiener in 1934. 1956 – Kruskal's algorithm developed by Joseph Kruskal 1956 – Ford–Fulkerson algorithm developed and published by R. Ford Jr. and D. R. Fulkerson 1957 – Prim's algorithm developed by Robert Prim 1957 – Bellman–Ford algorithm developed by Richard E. Bellman and L. R. Ford, Jr. 1959 – Dijkstra's algorithm developed by Edsger Dijkstra 1959 – Shell sort developed by Donald L. Shell 1959 – De Casteljau's algorithm developed by Paul de Casteljau 1959 – QR factorization algorithm developed independently by John G.F. Francis and Vera Kublanovskaya 1959 – Rabin–Scott powerset construction for converting NFA into DFA published by Michael O. Rabin and Dana Scott == 1960s == 1960 – Karatsuba multiplication 1961 – CRC (Cyclic redundancy check) invented by W. Wesley Peterson 1962 – AVL trees 1962 – Quicksort developed by C. A. R. Hoare 1962 – Bresenham's line algorithm developed by Jack E. Bresenham 1962 – Gale–Shapley 'stable-marriage' algorithm developed by David Gale and Lloyd Shapley 1964 – Heapsort developed by J. W. J. Williams 1964 – multigrid methods first proposed by R. P. Fedorenko 1965 – Cooley–Tukey algorithm rediscovered by James Cooley and John Tukey 1965 – Levenshtein distance developed by Vladimir Levenshtein 1965 – Cocke–Younger–Kasami (CYK) algorithm independently developed by Tadao Kasami 1965 – Buchberger's algorithm for computing Gröbner bases developed by Bruno Buchberger 1965 – LR parsers invented by Donald Knuth 1966 – Dantzig algorithm for shortest path in a graph with negative edges 1967 – Viterbi algorithm proposed by Andrew Viterbi 1967 – Cocke–Younger–Kasami (CYK) algorithm independently developed by Daniel H. Younger 1968 – A graph search algorithm described by Peter Hart, Nils Nilsson, and Bertram Raphael 1968 – Risch algorithm for indefinite integration developed by Robert Henry Risch 1969 – Strassen algorithm for matrix multiplication developed by Volker Strassen == 1970s == 1970 – Dinic's algorithm for computing maximum flow in a flow network by Yefim (Chaim) A. Dinitz 1970 – Knuth–Bendix completion algorithm developed by Donald Knuth and Peter B. Bendix 1970 – BFGS method of the quasi-Newton class 1970 – Needleman–Wunsch algorithm published by Saul B. Needleman and Christian D. Wunsch 1972 – Edmonds–Karp algorithm published by Jack Edmonds and Richard Karp, essentially identical to Dinic's algorithm from 1970 1972 – Graham scan developed by Ronald Graham 1972 – Red–black trees and B-trees discovered 1973 – RSA encryption algorithm discovered by Clifford Cocks 1973 – Jarvis march algorithm developed by R. A. Jarvis 1973 – Hopcroft–Karp algorithm developed by John Hopcroft and Richard Karp 1974 – Pollard's p − 1 algorithm developed by John Pollard 1974 – Quadtree developed by Raphael Finkel and J.L. Bentley 1975 – Genetic algorithms popularized by John Holland 1975 – Pollard's rho algorithm developed by John Pollard 1975 – Aho–Corasick string matching algorithm developed by Alfred V. Aho and Margaret J. Corasick 1975 – Cylindrical algebraic decomposition developed by George E. Collins 1976 – Salamin–Brent algorithm independently discovered by Eugene Salamin and Richard Brent 1976 – Knuth–Morris–Pratt algorithm developed by Donald Knuth and Vaughan Pratt and independently by J. H. Morris 1977 – Boyer–Moore string-search algorithm for searching the occurrence of a string into another string. 1977 – RSA encryption algorithm rediscovered by Ron Rivest, Adi Shamir, and Len Adleman 1977 – LZ77 algorithm developed by Abraham Lempel and Jacob Ziv 1977 – multigrid methods developed independently by Achi Brandt and Wolfgang Hackbusch 1978 – LZ78 algorithm developed from LZ77 by Abraham Lempel and Jacob Ziv 1978 – Bruun's algorithm proposed for powers of two by Georg Bruun 1979 – Khachiyan's ellipsoid method developed by Leonid Khachiyan 1979 – ID3 decision tree algorithm developed by Ross Quinlan == 1980s == 1980 – Brent's Algorithm for cycle detection Richard P. Brendt 1981 – Quadratic sieve developed by Carl Pomerance 1981 – Smith–Waterman algorithm developed by Temple F. Smith and Michael S. Waterman 1983 – Simulated annealing developed by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi 1983 – Classification and regression tree (CART) algorithm developed by Leo Breiman, et al. 1984 – LZW algorithm developed from LZ78 by Terry Welch 1984 – Karmarkar's interior-point algorithm developed by Narendra Karmarkar 1984 – ACORN PRNG discovered by Roy Wikramaratna and used privately 1985 – Simulated annealing independently developed by V. Cerny 1985 – Car–Parrinello molecular dynamics developed by Roberto Car and Michele Parrinello 1985 – Splay trees discovered by Sleator and Tarjan 1986 – Blum Blum Shub proposed by L. Blum, M. Blum, and M. Shub 1986 – Push relabel maximum flow algorithm by Andrew Goldberg and Robert Tarjan 1986 – Barnes–Hut tree method developed by Josh Barnes and Piet Hut for fast approximate simulation of n-body problems 1987 – Fast multipole method developed by Leslie Greengard and Vladimir

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  VMDS

  VMDS abbreviates the relational database technology called Version Managed Data Store provided by GE Energy as part of its Smallworld technology platform and was designed from the outset to store and analyse the highly complex spatial and topological networks typically used by enterprise utilities such as power distribution and telecommunications. VMDS was originally introduced in 1990 as has been improved and updated over the years. Its current version is 6.0. VMDS has been designed as a spatial database. This gives VMDS a number of distinctive characteristics when compared to conventional attribute only relational databases. == Distributed server processing == VMDS is composed of two parts: a simple, highly scalable data block server called SWMFS (Smallworld Master File Server) and an intelligent client API written in C and Magik. Spatial and attribute data are stored in data blocks that reside in special files called data store files on the server. When the client application requests data it has sufficient intelligence to work out the optimum set of data blocks that are required. This request is then made to SWMFS which returns the data to the client via the network for processing. This approach is particularly efficient and scalable when dealing with spatial and topological data which tends to flow in larger volumes and require more processing then plain attribute data (for example during a map redraw operation). This approach makes VMDS well suited to enterprise deployment that might involve hundreds or even thousands of concurrent clients. == Support for long transactions == Relational databases support short transactions in which changes to data are relatively small and are brief in terms in duration (the maximum period between the start and the end of a transaction is typically a few seconds or less). VMDS supports long transactions in which the volume of data involved in the transaction can be substantial and the duration of the transaction can be significant (days, weeks or even months). These types of transaction are common in advanced network applications used by, for example, power distribution utilities. Due to the time span of a long transaction in this context the amount of change can be significant (not only within the scope of the transaction, but also within the context of the database as a whole). Accordingly, it is likely that the same record might be changed more than once. To cope with this scenario VMDS has inbuilt support for automatically managing such conflicts and allows applications to review changes and accept only those edits that are correct. == Spatial and topological capabilities == As well as conventional relational database features such as attribute querying, join fields, triggers and calculated fields, VMDS has numerous spatial and topological capabilities. This allows spatial data such as points, texts, polylines, polygons and raster data to be stored and analysed. Spatial functions include: find all features within a polygon, calculate the Voronoi polygons of a set of sites and perform a cluster analysis on a set of points. Vector spatial data such as points, polylines and polygons can be given topological attributes that allow complex networks to be modelled. Network analysis engines are provided to answer questions such as find the shortest path between two nodes or how to optimize a delivery route (the travelling salesman problem). A topology engine can be configured with a set of rules that define how topological entities interact with each other when new data is added or existing data edited. == Data abstraction == In VMDS all data is presented to the application as objects. This is different from many relational databases that present the data as rows from a table or query result using say JDBC. VMDS provides a data modelling tool and underlying infrastructure as part of the Smallworld technology platform that allows administrators to associate a table in the database with a Magik exemplar (or class). Magik get and set methods for the Magik exemplar can be automatically generated that expose a table's field (or column). Each VMDS row manifests itself to the application as an instance of a Magik object and is known as an RWO (or real world object). Tables are known as collections in Smallworld parlance. # all_rwos hold all the rwos in the database and is heterogeneous all_rwos << my_application.rwo_set() # valve_collection holds the valve collection valves << all_rwos.select(:collection, {:valve}) number_of_valves << valves.size Queries are built up using predicate objects: # find 'open' valves. open_valves << valves.select(predicate.eq(:operating_status, "open")) number_of_open_valves << open_valves.size _for valve _over open_valves.elements() _loop write(valve.id) _endloop Joins are implemented as methods on the parent RWO. For example, a manager might have several employees who report to him: # get the employee collection. employees << my_application.database.collection(:gis, :employees) # find a manager called 'Steve' and get the first matching element steve << employees.select(predicate.eq(:name, "Steve").and(predicate.eq(:role, "manager")).an_element() # display the names of his direct reports. name is a field (or column) # on the employee collection (or table) _for employee _over steve.direct_reports.elements() _loop write(employee.name) _endloop Performing a transaction: # each key in the hash table corresponds to the name of the field (or column) in # the collection (or table) valve_data << hash_table.new_with( :asset_id, 57648576, :material, "Iron") # get the valve collection directly valve_collection << my_application.database.collection(:gis, :valve) # create an insert transaction to insert a new valve record into the collection a # comment can be provide that describes the transaction transaction << record_transaction.new_insert(valve_collection, valve_data, "Inserted a new valve") transaction.run()

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  Seismological Facility for the Advancement of Geoscience

  The U.S. National Science Foundation's Seismological Facility for the Advancement of Geoscience (NSF SAGE) is a distributed, multi-user national facility that provides support for state of-the-art seismic research. It is operated by EarthScope Consortium. Its previous operator was the Incorporated Research Institutions for Seismology (IRIS), until its merger with UNAVCO to become EarthScope Consortium. NSF SAGE is one of the two premier geophysical facilities in support of geoscience and geoscience education of the National Science Foundation. The other premiere geophysical facility is NSF GAGE, the Geodetic Facility for the Advancement of Geoscience. The services of the facility include support for the Global Seismographic Network (GSN), Data Services, and instrument support via the EarthScope Primary Instrument Center (EPIC), including magnetotelluric (MT) geophysical research. == Global Seismographic Network (GSN) == NSF SAGE manages 40 stations of the 152-station Global Seismographic Network (GSN) for basic global seismicity and Earth structure research. The GSN also enables earthquake hazard mission-related data operations such as: Earthquake location and characterization Tsunami warning Nuclear explosion monitoring == Data Services == SAGE Data Services (DS) is the largest facility for the archiving, curation, and distribution of seismological and other geophysical data in the world. == EarthScope Primary Instrument Center (EPIC) == The EPIC facility maintains the largest open access, shared-use pool of portable seismic sensors in the world. It is located on the campus of New Mexico Tech. == MT == NSF SAGE provides instruments for magnetotelluric (MT) or electromagnetic geophysical research for the recording of our planet's ambient electric and magnetic fields, which allow for the characterization of the conductivity of the area consisting of the shallow crust to upper mantle. This helps with analysis of results obtained from seismic imaging methodologies. The NSF SAGE facility is: Developing open source MT data formatting and processing software. Providing access to proprietary software products.

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  Decorrelation

  Decorrelation is a general term for any process that is used to reduce autocorrelation within a signal, or cross-correlation within a set of signals, while preserving other aspects of the signal. A frequently used method of decorrelation is the use of a matched linear filter to reduce the autocorrelation of a signal as far as possible. Since the minimum possible autocorrelation for a given signal energy is achieved by equalising the power spectrum of the signal to be similar to that of a white noise signal, this is often referred to as signal whitening. == Process == === Signal processing === Most decorrelation algorithms are linear, but there are also non-linear decorrelation algorithms. Many data compression algorithms incorporate a decorrelation stage. For example, many transform coders first apply a fixed linear transformation that would, on average, have the effect of decorrelating a typical signal of the class to be coded, prior to any later processing. This is typically a Karhunen–Loève transform, or a simplified approximation such as the discrete cosine transform. By comparison, sub-band coders do not generally have an explicit decorrelation step, but instead exploit the already-existing reduced correlation within each of the sub-bands of the signal, due to the relative flatness of each sub-band of the power spectrum in many classes of signals. Linear predictive coders can be modelled as an attempt to decorrelate signals by subtracting the best possible linear prediction from the input signal, leaving a whitened residual signal. Decorrelation techniques can also be used for many other purposes, such as reducing crosstalk in a multi-channel signal, or in the design of echo cancellers. In image processing decorrelation techniques can be used to enhance or stretch, colour differences found in each pixel of an image. This is generally termed as 'decorrelation stretching'. === Neuroscience === In neuroscience, decorrelation is used in the analysis of the neural networks in the human visual system. The raw inputs from cone cells and rod cells under go many steps of processing before it is handled by the visual cortex. These steps generally perform decorrelation, both spatial (surround suppression in the retina) and temporal (handling of movement in the lateral geniculate nucleus). === Cryptography === In cryptography, decorrelation is used in cipher design (see Decorrelation theory) and in the design of hardware random number generators.

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  Certifying algorithm

  In theoretical computer science, a certifying algorithm is an algorithm that outputs, together with a solution to the problem it solves, a proof that the solution is correct. A certifying algorithm is said to be efficient if the combined runtime of the algorithm and a proof checker is slower by at most a constant factor than the best known non-certifying algorithm for the same problem. The proof produced by a certifying algorithm should be in some sense simpler than the algorithm itself, for otherwise any algorithm could be considered certifying (with its output verified by running the same algorithm again). Sometimes this is formalized by requiring that a verification of the proof take less time than the original algorithm, while for other problems (in particular those for which the solution can be found in linear time) simplicity of the output proof is considered in a less formal sense. For instance, the validity of the output proof may be more apparent to human users than the correctness of the algorithm, or a checker for the proof may be more amenable to formal verification. Implementations of certifying algorithms that also include a checker for the proof generated by the algorithm may be considered to be more reliable than non-certifying algorithms. For, whenever the algorithm is run, one of three things happens: it produces a correct output (the desired case), it detects a bug in the algorithm or its implication (undesired, but generally preferable to continuing without detecting the bug), or both the algorithm and the checker are faulty in a way that masks the bug and prevents it from being detected (undesired, but unlikely as it depends on the existence of two independent bugs). == Examples == Many examples of problems with checkable algorithms come from graph theory. For instance, a classical algorithm for testing whether a graph is bipartite would simply output a Boolean value: true if the graph is bipartite, false otherwise. In contrast, a certifying algorithm might output a 2-coloring of the graph in the case that it is bipartite, or a cycle of odd length if it is not. Any graph is bipartite if and only if it can be 2-colored, and non-bipartite if and only if it contains an odd cycle. Both checking whether a 2-coloring is valid and checking whether a given odd-length sequence of vertices is a cycle may be performed more simply than testing bipartiteness. Analogously, it is possible to test whether a given directed graph is acyclic by a certifying algorithm that outputs either a topological order or a directed cycle. It is possible to test whether an undirected graph is a chordal graph by a certifying algorithm that outputs either an elimination ordering (an ordering of all vertices such that, for every vertex, the neighbors that are later in the ordering form a clique) or a chordless cycle. And it is possible to test whether a graph is planar by a certifying algorithm that outputs either a planar embedding or a Kuratowski subgraph. The extended Euclidean algorithm for the greatest common divisor of two integers x and y is certifying: it outputs three integers g (the divisor), a, and b, such that ax + by = g. This equation can only be true of multiples of the greatest common divisor, so testing that g is the greatest common divisor may be performed by checking that g divides both x and y and that this equation is correct.

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  Bartels–Stewart algorithm

  In numerical linear algebra, the Bartels–Stewart algorithm is used to numerically solve the Sylvester matrix equation A X − X B = C {\displaystyle AX-XB=C} . Developed by R.H. Bartels and G.W. Stewart in 1971, it was the first numerically stable method that could be systematically applied to solve such equations. The algorithm works by using the real Schur decompositions of A {\displaystyle A} and B {\displaystyle B} to transform A X − X B = C {\displaystyle AX-XB=C} into a triangular system that can then be solved using forward or backward substitution. In 1979, G. Golub, C. Van Loan and S. Nash introduced an improved version of the algorithm, known as the Hessenberg–Schur algorithm. It remains a standard approach for solving Sylvester equations when X {\displaystyle X} is of small to moderate size. == The algorithm == Let X , C ∈ R m × n {\displaystyle X,C\in \mathbb {R} ^{m\times n}} , and assume that the eigenvalues of A {\displaystyle A} are distinct from the eigenvalues of B {\displaystyle B} . Then, the matrix equation A X − X B = C {\displaystyle AX-XB=C} has a unique solution. The Bartels–Stewart algorithm computes X {\displaystyle X} by applying the following steps: 1.Compute the real Schur decompositions R = U T A U , {\displaystyle R=U^{T}AU,} S = V T B T V . {\displaystyle S=V^{T}B^{T}V.} The matrices R {\displaystyle R} and S {\displaystyle S} are block-upper triangular matrices, with diagonal blocks of size 1 × 1 {\displaystyle 1\times 1} or 2 × 2 {\displaystyle 2\times 2} . 2. Set F = U T C V . {\displaystyle F=U^{T}CV.} 3. Solve the simplified system R Y − Y S T = F {\displaystyle RY-YS^{T}=F} , where Y = U T X V {\displaystyle Y=U^{T}XV} . This can be done using forward substitution on the blocks. Specifically, if s k − 1 , k = 0 {\displaystyle s_{k-1,k}=0} , then ( R − s k k I ) y k = f k + ∑ j = k + 1 n s k j y j , {\displaystyle (R-s_{kk}I)y_{k}=f_{k}+\sum _{j=k+1}^{n}s_{kj}y_{j},} where y k {\displaystyle y_{k}} is the k {\displaystyle k} th column of Y {\displaystyle Y} . When s k − 1 , k ≠ 0 {\displaystyle s_{k-1,k}\neq 0} , columns [ y k − 1 ∣ y k ] {\displaystyle [y_{k-1}\mid y_{k}]} should be concatenated and solved for simultaneously. 4. Set X = U Y V T . {\displaystyle X=UYV^{T}.} === Computational cost === Using the QR algorithm, the real Schur decompositions in step 1 require approximately 10 ( m 3 + n 3 ) {\displaystyle 10(m^{3}+n^{3})} flops, so that the overall computational cost is 10 ( m 3 + n 3 ) + 2.5 ( m n 2 + n m 2 ) {\displaystyle 10(m^{3}+n^{3})+2.5(mn^{2}+nm^{2})} . === Simplifications and special cases === In the special case where B = − A T {\displaystyle B=-A^{T}} and C {\displaystyle C} is symmetric, the solution X {\displaystyle X} will also be symmetric. This symmetry can be exploited so that Y {\displaystyle Y} is found more efficiently in step 3 of the algorithm. == The Hessenberg–Schur algorithm == The Hessenberg–Schur algorithm replaces the decomposition R = U T A U {\displaystyle R=U^{T}AU} in step 1 with the decomposition H = Q T A Q {\displaystyle H=Q^{T}AQ} , where H {\displaystyle H} is an upper-Hessenberg matrix. This leads to a system of the form H Y − Y S T = F {\displaystyle HY-YS^{T}=F} that can be solved using forward substitution. The advantage of this approach is that H = Q T A Q {\displaystyle H=Q^{T}AQ} can be found using Householder reflections at a cost of ( 5 / 3 ) m 3 {\displaystyle (5/3)m^{3}} flops, compared to the 10 m 3 {\displaystyle 10m^{3}} flops required to compute the real Schur decomposition of A {\displaystyle A} . == Software and implementation == The subroutines required for the Hessenberg-Schur variant of the Bartels–Stewart algorithm are implemented in the SLICOT library. These are used in the MATLAB control system toolbox. == Alternative approaches == For large systems, the O ( m 3 + n 3 ) {\displaystyle {\mathcal {O}}(m^{3}+n^{3})} cost of the Bartels–Stewart algorithm can be prohibitive. When A {\displaystyle A} and B {\displaystyle B} are sparse or structured, so that linear solves and matrix vector multiplies involving them are efficient, iterative algorithms can potentially perform better. These include projection-based methods, which use Krylov subspace iterations, methods based on the alternating direction implicit (ADI) iteration, and hybridizations that involve both projection and ADI. Iterative methods can also be used to directly construct low rank approximations to X {\displaystyle X} when solving A X − X B = C {\displaystyle AX-XB=C} .

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  Algorithmic logic

  Algorithmic logic is a calculus of programs that allows the expression of semantic properties of programs by appropriate logical formulas. It provides a framework that enables proving the formulas from the axioms of program constructs such as assignment, iteration and composition instructions and from the axioms of the data structures in question see Mirkowska & Salwicki (1987), Banachowski et al. (1977). The following diagram helps to locate algorithmic logic among other logics. [ P r o p o s i t i o n a l l o g i c o r S e n t e n t i a l c a l c u l u s ] ⊂ [ P r e d i c a t e c a l c u l u s o r F i r s t o r d e r l o g i c ] ⊂ [ C a l c u l u s o f p r o g r a m s o r Algorithmic logic ] {\displaystyle \qquad \left[{\begin{array}{l}\mathrm {Propositional\ logic} \\or\\\mathrm {Sentential\ calculus} \end{array}}\right]\subset \left[{\begin{array}{l}\mathrm {Predicate\ calculus} \\or\\\mathrm {First\ order\ logic} \end{array}}\right]\subset \left[{\begin{array}{l}\mathrm {Calculus\ of\ programs} \\or\\{\mbox{Algorithmic logic}}\end{array}}\right]} The formalized language of algorithmic logic (and of algorithmic theories of various data structures) contains three types of well formed expressions: Terms - i.e. expressions denoting operations on elements of data structures, formulas - i.e. expressions denoting the relations among elements of data structures, programs - i.e. algorithms - these expressions describe the computations. For semantics of terms and formulas consult pages on first-order logic and Tarski's semantics. The meaning of a program K {\displaystyle K} is the set of possible computations of the program. Algorithmic logic is one of many logics of programs. Another logic of programs is dynamic logic, see dynamic logic, Harel, Kozen & Tiuryn (2000).

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  Semantic space

  Semantic spaces in the natural language domain aim to create representations of natural language that are capable of capturing meaning. The original motivation for semantic spaces stems from two core challenges of natural language: Vocabulary mismatch (the fact that the same meaning can be expressed in many ways) and ambiguity of natural language (the fact that the same term can have several meanings). The application of semantic spaces in natural language processing (NLP) aims at overcoming limitations of rule-based or model-based approaches operating on the keyword level. The main drawback with these approaches is their brittleness, and the large manual effort required to create either rule-based NLP systems or training corpora for model learning. Rule-based and machine learning based models are fixed on the keyword level and break down if the vocabulary differs from that defined in the rules or from the training material used for the statistical models. Research in semantic spaces dates back more than 20 years. In 1996, two papers were published that raised a lot of attention around the general idea of creating semantic spaces: latent semantic analysis and Hyperspace Analogue to Language. However, their adoption was limited by the large computational effort required to construct and use those semantic spaces. A breakthrough with regard to the accuracy of modelling associative relations between words (e.g. "spider-web", "lighter-cigarette", as opposed to synonymous relations such as "whale-dolphin", "astronaut-driver") was achieved by explicit semantic analysis (ESA) in 2007. ESA was a novel (non-machine learning) based approach that represented words in the form of vectors with 100,000 dimensions (where each dimension represents an Article in Wikipedia). However practical applications of the approach are limited due to the large number of required dimensions in the vectors. More recently, advances in neural network techniques in combination with other new approaches (tensors) led to a host of new recent developments: Word2vec from Google, GloVe from Stanford University, and fastText from Facebook AI Research (FAIR) labs.

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  Information pollution

  Information pollution (also referred to as info pollution) is the contamination of an information supply with irrelevant, redundant, unsolicited, hampering, and low-value information. Examples include misinformation, disinformation, junk e-mail, and media violence. The spread of useless and undesirable information can have a detrimental effect on human activities. It is considered to be an adverse effect of the information revolution. == Overview == Information pollution generally applies to digital communication, such as e-mail, instant messaging (IM), and social media. The term acquired particular relevance in 2003 when web usability expert Jakob Nielsen published articles discussing the topic. As early as 1971 researchers were expressing doubts about the negative effects of having to recover "valuable nodules from a slurry of garbage in which it is a randomly dispersed minor component." People use information in order to make decisions and adapt to circumstances. Cognitive studies demonstrated human beings can process only limited information before the quality of their decisions begins to deteriorate. Information overload is a related concept that can also harm decision-making. It refers to an abundance of available information, without respect to its quality. Although technology is thought to have exacerbated the problem, it is not the only cause of information pollution. Anything that distracts attention from the essential facts required to perform a task or make a decision could be considered an information pollutant. Information pollution is seen as the digital equivalent of the environmental pollution generated by industrial processes. Some authors claim that information overload is a crisis of global proportions, on the same scale as threats faced by environmental destruction. Others have expressed the need for the development of an information management paradigm that parallels environmental management practices. == Manifestations == The manifestations of information pollution can be classified into two groups: those that provoke disruption, and those that damage information quality. Typical examples of disrupting information pollutants include unsolicited electronic messages (spam) and instant messages, particularly in the workplace. Mobile phones (ring tones and content) are disruptive in many contexts. Disrupting information pollution is not always technology based. A common example are newspapers, where subscribers read less than half or even none of the articles provided. Superfluous messages, such as unnecessary labels on a map, also distract. Alternatively, information may be polluted when its quality is reduced. This may be due to inaccurate or outdated information, but it also happens when information is badly presented. For example, when content is unfocused or unclear or when they appear in cluttered, wordy, or poorly organised documents it is difficult for the reader to understand. Laws and regulations undergo changes and revisions. Handbooks and other sources used for interpreting these laws can fall years behind the changes, which can cause the public to be misinformed. == Causes == === Cultural factors === Traditionally, information has been seen positively. People are accustomed to statements like "you cannot have too much information", "the more information the better", and "knowledge is power". The publishing and marketing industries have become used to printing many copies of books, magazines, and brochures regardless of customer demand, just in case they are needed. Democratised information sharing is an example of a new technology that has made it easier for information to reach everyone. Such technologies are perceived as a sign of progress and individual empowerment, as well as a positive step to bridge the digital divide. However, they also increase the volume of distracting information, making it more difficult to distinguish valuable information from noise. The continuous use of advertising in websites, technologies, newspapers, and everyday life is known as "cultural pollution". === Information technology === Technological advances of the 20th century and, in particular, the internet play a key role in the increase of information pollution. Blogs, social networks, personal websites, and mobile technology all contribute to increased "noise". The level of pollution may depend on the context. For example, e-mail is likely to cause more information pollution in a corporate setting, whereas mobile phones are likely to be particularly disruptive in a confined space shared by multiple people, such as a train carriage. == Effects == The effects of information pollution can be seen at multiple levels. === Individual === At a personal level, information pollution affects individuals' capacity to evaluate options and find adequate solutions. This can lead to information overload, anxiety, decision paralysis, and stress. It can disrupt the learning process. === Society === Some authors argue that information pollution and information overload can cause loss of perspective and moral values. This argument may explain the indifferent attitude that society shows toward topics such as scientific discoveries, health warnings, or politics. Pollution makes people less sensitive to headlines and more cynical toward new messages. === Business === Information pollution contributes to information overload and stress, which can disrupt the kinds information processing and decision-making needed to complete tasks at work. This leads to delayed or flawed decisions, which can translate into loss of productivity and revenue as well as an increased risk of critical errors. == Solutions == Proposed solutions include management techniques and refined technology. Technology-based alternatives include decision support systems and dashboards that enable prioritisation of information. Technologies that create frequent interruptions can be replaced with less-"polluting" options. Further, technology can improve the presentation quality, aiding understanding. E-mail usage policies and information integrity assurance strategies can help. Time management and stress management can be applied; these solutions would involve setting priorities and minimising interruptions. Improved writing and presentation practices can minimise information pollution effects on others. == Related terms == The term infollution or informatization pollution was coined by Dr. Paek-Jae Cho, former president & CEO of KTC (Korean Telecommunication Corp.), in a 2002 speech at the International Telecommunications Society (ITS) 14th biennial conference to describe any undesirable side effect brought about by information technology and its applications.

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  Hall circles

  Hall circles (also known as M-circles and N-circles) are a graphical tool in control theory used to obtain values of a closed-loop transfer function from the Nyquist plot (or the Nichols plot) of the associated open-loop transfer function. Hall circles have been introduced in control theory by Albert C. Hall in his thesis. == Construction == Consider a closed-loop linear control system with open-loop transfer function given by transfer function G ( s ) {\displaystyle G(s)} and with a unit gain in the feedback loop. The closed-loop transfer function is given by T ( s ) = G ( s ) 1 + G ( s ) {\textstyle T(s)={\frac {G(s)}{1+G(s)}}} . To check the stability of T(s), it is possible to use the Nyquist stability criterion with the Nyquist plot of the open-loop transfer function G(s). Note, however, that the Nyquist plot of G(s) does not give the actual values of T(s). To get this information from the G(s)-plane, Hall proposed to construct the locus of points in the G(s)-plane such that T(s) has constant magnitude and also the locus of points in the G(s)-plane such that T(s) has constant phase angle. Given a positive real value M representing a fixed magnitude, and denoting G(s) by z, the points satisfying M = | T ( s ) | = | G ( s ) | | 1 + G ( s ) | = | z | | 1 + z | {\displaystyle M=|T(s)|={\frac {|G(s)|}{|1+G(s)|}}={\frac {|z|}{|1+z|}}} are given by the points z in the G(s)-plane such that the ratio of the distance between z and 0 and the distance between z and -1 is equal to M. The points z satisfying this locus condition are circles of Apollonius, and this locus is known in the context of control systems as M-circles. Given a positive real value N representing a phase angle, the points satisfying N = arg ⁡ [ G ( s ) 1 + G ( s ) ] = arg ⁡ [ G ( s ) ] − arg ⁡ [ 1 + G ( s ) ] = arg ⁡ [ z ] − arg ⁡ [ 1 + z ] {\displaystyle N=\arg \left[{\frac {G(s)}{1+G(s)}}\right]=\arg[G(s)]-\arg[1+G(s)]=\arg[z]-\arg[1+z]} are given by the points z in the G(s)-plane such that the angle between -1 and z and the angle between 0 and z is constant. In other words, the angle opposed to the line segment between -1 and 0 must be constant. This implies that the points z satisfying this locus condition are arcs of circles, and this locus is known in the context of control systems as N-circles. == Usage == To use the Hall circles, a plot of M and N circles is done over the Nyquist plot of the open-loop transfer function. The points of the intersection between these graphics give the corresponding value of the closed-loop transfer function. Hall circles are also used with the Nichols plot and in this setting, are also known as Nichols chart. Rather than overlaying directly the Hall circles over the Nichols plot, the points of the circles are transferred to a new coordinate system where the ordinate is given by 20 log 10 ⁡ ( | G ( s ) | ) {\displaystyle 20\log _{10}(|G(s)|)} and the abscissa is given by arg ⁡ ( G ( s ) ) {\displaystyle \arg(G(s))} . The advantage of using Nichols chart is that adjusting the gain of the open loop transfer function directly reflects in up and down translation of the Nichols plot in the chart.

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  Run-to-completion scheduling

  Run-to-completion scheduling or nonpreemptive scheduling is a scheduling model in which each task runs until it either finishes, or explicitly yields control back to the scheduler. Run-to-completion systems typically have an event queue which is serviced either in strict order of admission by an event loop, or by an admission scheduler which is capable of scheduling events out of order, based on other constraints such as deadlines. Some preemptive multitasking scheduling systems behave as run-to-completion schedulers in regard to scheduling tasks at one particular process priority level, at the same time as those processes still preempt other lower priority tasks and are themselves preempted by higher priority tasks.

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  Coolgorilla

  Coolgorilla was one of the earliest software developers that created 3rd party native applications for Apple iPod devices. Coolgorilla was an early adopter of using a sponsorship business model to enable mobile applications to be given away freely. Coolgorilla developed a series of Talking Phrasebooks for iPods in 2006. They partnered with online travel company lastminute.com who sponsored the applications enabling them to be made available to download completely free of charge. As mobile devices became more sophisticated, Coolgorilla developed the Talking Phrasebooks for Sony Ericsson and Nokia Mobile Devices which at the time were considerably noteworthy since the applications used real voice audio translations. With Apple's introduction of the iPhone in 2007, Coolgorilla developed a Web App before having four of the iPhone Talking Phrasebooks available to download from Apple's App Store on the day it opened in 2008. == Almanac in Chronological Order == On 23 December 2005, CoolGorilla, a new start-up, launched a trivia game for the iPod. It was titled "Rock and Pop Quiz". It was a quiz game that tested users' knowledge on bands such as U2, Metallica, Beyonce, and the Beatles. The quiz contained twenty megabytes of audible trivia questions. The free game was compatible with 3rd, 4th and 5th generation iPods, iPod mini and nano. In March 2006, Coolgorilla released "Movie Quiz for iPods" with a price of $5. It was an audio game narrated by New York's DJ Thomas, a radio and television host, voice over artist and event Master of Ceremonies. There were questions on Star Wars, Spiderman, The Godfather, Pulp Fiction, The Matrix, James Bond, and others. The user could keep track of their score. The game included a secret code for players who answered all questions correctly which enabled users to enter their name on the Coolgorilla Hall of Fame. In May 2006, Coolgorilla launched a World Cup Encyclopedia which was released prior to the 2006 FIFA World Cup. It had information on the World Cup schedule, details of every player from every team, every score from every world cup game ever played, stadium details, and manager profiles. It was a free download. In June 2006, Coolgorilla released a series of iPod Phrasebooks in German, Greek, French and Spanish. They were sponsored by lastminute.com and were free. The phrasebooks included common words and phrases for tourists with 750 sound files. They were accessed through the iPod's Notes feature. In April 2007, Coolgorilla released a downloadable version of the Talking Phrasebooks for Nokia and Sony Ericsson mobile devices. French, Spanish, German, Greek, Italian, and Portuguese were produced. The application provided real voice translations. They initially sold for £3 but 3 months later were offered for free. The branding was lastminute.com branding. Apple's iPhone was released at the end of June 2007. Soon after, Coolgorilla released an online all-in-one version of their Talking Phrasebooks for iPhone (Web App). The Phrasebooks were made available online in the form of a web app as iPhone did not yet allow for the download of additional apps. The app provided both text and audio translations in French, Spanish, Portuguese, Italian, German, and Greek. The iPhone translated the phrases using the recordings of real, native voice-over artists. A text translation on screen was also displayed. Apple's App Store opened in July 2008 with approximately 500 native apps available. Four of these Apps were Coolgorilla's Talking Phrasebooks for iPhone (Native Apps). There was French, German, Italian, and Spanish. These Apps carried lastminute.com branding and were available for free download. In the first three weeks following their release, the phrasebooks had over 350,000 downloads. Subsequently, Dutch, Arabic, Mandarin and Cantonese were also released. In October 2008, Coolgorilla released an iPhone London Travel Guide. Coolgorilla featured on NBC News in August 2009. In 2010, FIAT used the Italian Phrasebook to help promote the release of their FIAT 500 in the US. There has been no further activity since.

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  Open Compute Project

  The Open Compute Project (OCP) is an organization that facilitates the sharing of data center product designs and industry best practices among companies. Founded in 2011, OCP has significantly influenced the design and operation of large-scale computing facilities worldwide. As of February 2025, over 400 companies across the world are members of OCP, including Arm, Meta, IBM, Wiwynn, Intel, Nokia, Google, Microsoft, Seagate Technology, Dell, Rackspace, Hewlett Packard Enterprise, NVIDIA, Cisco, Goldman Sachs, Fidelity, Lenovo, Accton Technology Corporation and Alibaba Group. == Structure == The Open Compute Project Foundation is a 501(c)(6) non-profit incorporated in the state of Delaware, United States. OCP has multiple committees, including the board of directors, advisory board and steering committee to govern its operations. As of July 2020, there are seven members who serve on the board of directors which is made up of one individual member and six organizational members. Mark Roenigk (Facebook) is the Foundation's president and chairman. Andy Bechtolsheim is the individual member. In addition to Mark Roenigk who represents Facebook, other organizations on the Open Compute board of directors include Intel (Rebecca Weekly), Microsoft (Kushagra Vaid), Google (Partha Ranganathan), and Rackspace (Jim Hawkins). A list of members can be found on the OCP website. == History == The Open Compute Project began at Facebook (now Meta) in 2009 as an internal project called "Project Freedom". The hardware designs and engineering teams were led by Amir Michael (Manager, Hardware Design) and sponsored by Jonathan Heiliger (VP, Technical Operations) and Frank Frankovsky (Director, Hardware Design and Infrastructure). The three would later open source the designs of Project Freedom and co-found the Open Compute Project. The project was announced at a press event at Facebook's headquarters in Palo Alto on April 7, 2011. == OCP projects == The Open Compute Project Foundation maintains a number of OCP projects, such as: === Server designs === In 2013, two years after the Open Compute Project had started, it was noted that the goal of a more modular server design was "still a long way from live data centers". However, by then some aspects published had been used in Facebook's Prineville data center to improve energy efficiency, as measured by the power usage effectiveness index defined by The Green Grid. Efforts to advance server compute node designs included one for Intel processors and one for AMD processors. Also in 2013, Calxeda contributed a design with ARM architecture processors. Since then, several generations of OCP server designs have been deployed: Wildcat (Intel), Spitfire (AMD), Windmill (Intel E5-2600), Watermark (AMD), Winterfell (Intel E5-2600 v2) and Leopard (Intel E5-2600 v3). === OCP Accelerator Module === OCP Accelerator Module (OAM) is a design specification for hardware architectures that implement artificial intelligence systems that require high module-to-module bandwidth. OAM is used in some of AMD's Instinct accelerator modules. === Rack and power designs === Designs for a mechanical mounting system to replace standard 19-inch racks have been published, with a cabinet the same outside width (600 mm) and depth as existing racks, but with an interior space allowing for wider equipment chassis with a 537 mm width (21 inches). This allows more equipment to fit in the same volume and improves air flow. Compute chassis sizes are defined in multiples of an OpenU or OU, which is 48 mm, slightly taller than the 44 mm rack unit defined for 19-inch racks. As of March 2026, the most current base mechanical definition is the Open Rack V3.1 Specification. At the time the base specification was released, Meta also defined in greater depth the specifications for the rectifiers and power shelf. Specifications for the power monitoring interface (PMI), a communications interface enabling upstream communications between the rectifiers and battery backup unit(BBU) were published by Meta that same year, with Delta Electronics as the main technical contributor to the BBU spec. However, since 2022 the AI boom in the data center has created higher power requirements in order to satisfy the demands of AI accelerators that have been released. As of September 2024, Meta is in the process of updating its Open Rack v3 rectifier, power shelf, battery backup and power management interface specifications to accommodate this increased energy demand. In May 2024, at an Open Compute regional summit, Meta and Rittal outlined their plans for development of their High Power Rack (HPR) ecosystem in conjunction with rack, power and cable partners, increasing power capacity in the rack to 92 kilowatts or more. At the same meeting, Delta Electronics and Advanced Energy reported on their progress in developing new Open Compute standard specifications for power shelf and rectifier designs for HPR applications. Rittal also outlined their collaboration with Meta in designing airflow containment, busbar designs and grounding schemes for the new HPR requirements. === Data storage === Open Vault storage building blocks (also called "Knox") offer high disk densities, with 30 drives in a 2 OU Open Rack chassis designed for easy disk drive replacement. The 3.5 inch disks are stored in two drawers, five across and three deep in each drawer, with connections via serial attached SCSI. There is a "cold storage" variant where idle disks power down to reduce energy consumption. Another design concept was contributed by Hyve Solutions, a division of Synnex, in 2012. At the OCP Summit 2016 Facebook, together with Taiwanese ODM Wistron's spin-off Wiwynn, introduced "Lightning", a flexible NVMe JBOF (just a bunch of flash), based on the existing Open Vault (Knox) design. === Energy efficient data centers === The OCP has published data center designs for energy efficiency. These include power distribution at three-phase 277/480 VAC, which eliminates one transformer stage in typical North American data centers, a single voltage (12.5 VDC) power supply designed to work with 277/480 VAC input, and 48 VDC battery backup. For European (and other 230V countries) datacenters, there is a specification for 230/400 VAC power distribution and its conversion to 12.5 VDC. === Open networking switches === On May 8, 2013, an effort to define an open network switch was announced. The plan was to allow Facebook to load its own operating system software onto its top-of-rack switches. Press reports predicted that more expensive and higher-performance switches would continue to be popular, while less expensive products treated more like a commodity. The first attempt at an open networking switch by Facebook was designed together with Taiwanese ODM Accton using Broadcom Trident II chip and is called "Wedge"; the Linux OS that it runs is called "FBOSS". Later switch contributions include "6-pack" and Wedge-100, based on Broadcom Tomahawk chips. Similar switch hardware designs have been contributed by: Accton Technology Corporation (and its Edgecore Networks subsidiary), Mellanox Technologies, Interface Masters Technologies, Agema Systems. Capable of running Open Network Install Environment (ONIE)-compatible network operating systems such as Cumulus Linux, Switch Light OS by Big Switch Networks, or PICOS by Pica8. A similar project for a custom switch for the Google platform had been rumored, and evolved to use the OpenFlow protocol. === Servers === A sub-project for Mezzanine (NIC) OCP NIC 3.0 specification 1v00 was released in late 2019 establishing three form factors: SFF, TSFF, and LFF. == Litigation == In March, 2015, BladeRoom Group Limited and Bripco (UK) Limited sued Facebook, Emerson Electric Co. and others alleging that Facebook has disclosed BladeRoom and Bripco's trade secrets for prefabricated data centers in the Open Compute Project. Facebook petitioned for the lawsuit to be dismissed, but this was rejected in 2017. A confidential mid-trial settlement was agreed in April 2018.

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  HAKMEM

  HAKMEM, alternatively known as AI Memo 239, is a February 1972 "memo" (technical report) of the MIT AI Lab containing a wide variety of hacks, including useful and clever algorithms for mathematical computation, some number theory and schematic diagrams for hardware – in Guy L. Steele's words, "a bizarre and eclectic potpourri of technical trivia". Contributors included about two dozen members and associates of the AI Lab. The title of the report is short for "hacks memo", abbreviated to six upper case characters that would fit in a single PDP-10 machine word (using a six-bit character set). == History == HAKMEM is notable as an early compendium of algorithmic technique, particularly for its practical bent, and as an illustration of the wide-ranging interests of AI Lab people of the time, which included almost anything other than AI research. HAKMEM contains original work in some fields, notably continued fractions. == Introduction == Compiled with the hope that a record of the random things people do around here can save some duplication of effort -- except for fun. Here is some little known data which may be of interest to computer hackers. The items and examples are so sketchy that to decipher them may require more sincerity and curiosity than a non-hacker can muster. Doubtless, little of this is new, but nowadays it's hard to tell. So we must be content to give you an insight, or save you some cycles, and to welcome further contributions of items, new or used.

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