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Dabbler is natural media drawing software for beginners. It was initially developed by Fractal Design Corporation. It is a simplified version of Fractal Design Painter, and included multimedia tutorials and a fullscreen interface. Dabbler was released as "Art Dabbler" after the MetaCreations merger, and rights were eventually transferred to Corel. Dabbler operating systems are Mac OS and Microsoft Windows.
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Lion algorithm (LA) is one among the bio-inspired (or) nature-inspired optimization algorithms (or) that are mainly based on meta-heuristic principles. It was first introduced by B. R. Rajakumar in 2012 in the name, Lion’s Algorithm. It was further extended in 2014 to solve the system identification problem. This version was referred as LA, which has been applied by many researchers for their optimization problems. == Inspiration from lion’s social behaviour == Lions form a social system called a "pride", which consists of 1–3 pair of lions. A pride of lions shares a common area known as territory in which a dominant lion is called as territorial lion. The territorial lion safeguards its territory from outside attackers, especially nomadic lions. This process is called territorial defense. It protects the cubs till they become sexually matured. The maturity period is about 2–4 years. The pride undergoes survival fights to protect its territory and the cubs from nomadic lions. Upon getting defeated by the nomadic lions, the dominating nomadic lion takes the role of territorial lion by killing or driving out the cubs of the pride. The lioness of the pride give birth to cubs though the new territorial lion. When the cubs of the pride mature and considered to be stronger than the territorial lion, they take over the pride. This process is called territorial take-over. If territorial take-over happens, either the old territorial lion, which is considered to be laggard, is driven out or it leaves the pride. The stronger lions and lioness form the new pride and give birth to their own cubs == Terminology == In the LA, the terms that are associated with lion’s social system are mapped to the terminology of optimization problems. Few of such notable terms are related here. Lion: A potential solution to be generated or determined as optimal (or) near-optimal solution of the problem. The lion can be a territorial lion and lioness, cubs and nomadic lions that represent the solution based on the processing steps of the LA. Territorial lion: The strongest solution of the pride that tends to meet the objective function. Nomadic lion: A random solution, sometimes termed as nomad, to facilitate the exploration principle Laggard lion: Poor solutions that are failed in the survival fight. Pride: A pool of potential solutions i.e. a lion, lioness and their cubs, that are potential solutions of the search problem. Fertility evaluation: A process of evaluating whether the territorial lion and lioness are able to provide potential solutions in the future generations i.e. It ensures that the lion or lioness converge at every generation. Survival fight: It is a greedy selection process, which is often carried out between the pride and nomadic lion. == Algorithm == The steps involved in LA are given below: Pride Generation: Generate X m a l e {\displaystyle X^{male}} , X f e m a l e {\displaystyle X^{female}} and X 1 n o m a d {\displaystyle X_{1}^{nomad}} Determine f ( X m a l e ) {\displaystyle f(X^{male})} , f ( X f e m a l e ) {\displaystyle f(X^{female})} , f ( X 1 n o m a d ) {\displaystyle f(X_{1}^{nomad})} Initialize f r e f {\displaystyle f^{ref}} as f ( X m a l e ) {\displaystyle f(X^{male})} and N g {\displaystyle N_{g}} as 0 Memorize X m a l e {\displaystyle X^{male}} and X f e m a l e {\displaystyle X^{female}} Apply Fertility evaluation Process Generation of cubpool by mating Gender clustering: Define X c u b m a l e {\displaystyle X_{cub}^{male}} and X c u b f e m a l e {\displaystyle X_{cub}^{female}} Initialize a g e c u b {\displaystyle age_{cub}} as zero Apply Cub growth function Territorial defense: If X m a l e {\displaystyle X^{male}} (or pride) fails in the survival fight i.e. X 1 n o m a d {\displaystyle X_{1}^{nomad}} defeats the pride, go to step 4, else continue Increase a g e c u b {\displaystyle age_{cub}} by 1 and check whether cub attains maturity i.e., if a g e c u b > a g e m a x {\displaystyle age_{cub}>age_{max}} , go to Step 9, else continue Territorial takeover: If X c u b m a l e {\displaystyle X_{cub}^{male}} and X c u b f e m a l e {\displaystyle X_{cub}^{female}} are found to be closer to optimal solution, update X m a l e {\displaystyle X^{male}} and X f e m a l e {\displaystyle X^{female}} Increment N g {\displaystyle N_{g}} by 1 Repeat from Step 5, if termination criterion is not violated, else return X m a l e {\displaystyle X^{male}} as the near-optimal solution == Variants == The LA has been further taken forward to adopt in different problem areas. According to the characteristics of the problem area, significant amendment has been done in the processes and the models used in the LA. Accordingly, diverse variants have been developed by the researchers. They can be broadly grouped as hybrid LAs and non-hybrid LAs. Hybrid LAs are the LAs that are amended by the principle of other meta-heuristics, whereas the Non-hybrid LAs take any scientific amendment inside its operation that are felt to be essential to attend the respective problem area. == Applications == LA is applied in diverse engineering applications that range from network security, text mining, image processing, electrical systems, data mining and many more. Few of the notable applications are discussed here. Networking applications: In WSN, LA is used to solve the cluster head selection problem by determining optimal cluster head. Route discovery problem in both the VANET and MANET are also addressed by the LA in the literature. It is also used to detect attacks in advanced networking scenarios such as Software-Defined Networks (SDN) Power Systems: LA has attended generation rescheduling problem in a deregulated environment, optimal localization and sizing of FACTS devices for power quality enhancement and load-frequency controlling problem Cloud computing: LA is used in optimal container-resource allocation problem in cloud environment and cloud security
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Broadcast is a collective communication primitive in parallel programming to distribute programming instructions or data to nodes in a cluster. It is the reverse operation of reduction. The broadcast operation is widely used in parallel algorithms, such as matrix-vector multiplication, Gaussian elimination and shortest paths. The Message Passing Interface implements broadcast in MPI_Bcast. == Definition == A message M [ 1.. m ] {\displaystyle M[1..m]} of length m {\displaystyle m} should be distributed from one node to all other p − 1 {\displaystyle p-1} nodes. T byte {\displaystyle T_{\text{byte}}} is the time it takes to send one byte. T start {\displaystyle T_{\text{start}}} is the time it takes for a message to travel to another node, independent of its length. Therefore, the time to send a package from one node to another is t = s i z e × T byte + T start {\displaystyle t=\mathrm {size} \times T_{\text{byte}}+T_{\text{start}}} . p {\displaystyle p} is the number of nodes and the number of processors. == Binomial Tree Broadcast == With Binomial Tree Broadcast the whole message is sent at once. Each node that has already received the message sends it on further. This grows exponentially as each time step the amount of sending nodes is doubled. The algorithm is ideal for short messages but falls short with longer ones as during the time when the first transfer happens only one node is busy. Sending a message to all nodes takes log 2 ( p ) t {\displaystyle \log _{2}(p)t} time which results in a runtime of log 2 ( p ) ( m T byte + T start ) {\displaystyle \log _{2}(p)(mT_{\text{byte}}+T_{\text{start}})} == Linear Pipeline Broadcast == The message is split up into k {\displaystyle k} packages and sent piecewise from node n {\displaystyle n} to node n + 1 {\displaystyle n+1} . The time needed to distribute the first message piece is p t = m k T byte + T start {\textstyle pt={\frac {m}{k}}T_{\text{byte}}+T_{\text{start}}} whereby t {\displaystyle t} is the time needed to send a package from one processor to another. Sending a whole message takes ( p + k ) ( m T byte k + T start ) = ( p + k ) t = p t + k t {\displaystyle (p+k)\left({\frac {mT_{\text{byte}}}{k}}+T_{\text{start}}\right)=(p+k)t=pt+kt} . Optimal is to choose k = m ( p − 2 ) T byte T start {\displaystyle k={\sqrt {\frac {m(p-2)T_{\text{byte}}}{T_{\text{start}}}}}} resulting in a runtime of approximately m T byte + p T start + m p T start T byte {\displaystyle mT_{\text{byte}}+pT_{\text{start}}+{\sqrt {mpT_{\text{start}}T_{\text{byte}}}}} The run time is dependent on not only message length but also the number of processors that play roles. This approach shines when the length of the message is much larger than the amount of processors. == Pipelined Binary Tree Broadcast == This algorithm combines Binomial Tree Broadcast and Linear Pipeline Broadcast, which makes the algorithm work well for both short and long messages. The aim is to have as many nodes work as possible while maintaining the ability to send short messages quickly. A good approach is to use Fibonacci trees for splitting up the tree, which are a good choice as a message cannot be sent to both children at the same time. This results in a binary tree structure. We will assume in the following that communication is full-duplex. The Fibonacci tree structure has a depth of about d ≈ log Φ ( p ) {\displaystyle d\approx \log _{\Phi }(p)} whereby Φ = 1 + 5 2 {\displaystyle \Phi ={\frac {1+{\sqrt {5}}}{2}}} the golden ratio. The resulting runtime is ( m k T byte + T start ) ( d + 2 k − 2 ) {\textstyle ({\frac {m}{k}}T_{\text{byte}}+T_{\text{start}})(d+2k-2)} . Optimal is k = n ( d − 2 ) T byte 3 T start {\displaystyle k={\sqrt {\frac {n(d-2)T_{\text{byte}}}{3T_{\text{start}}}}}} . This results in a runtime of 2 m T byte + T start log Φ ( p ) + 2 m log Φ ( p ) T start T byte {\displaystyle 2mT_{\text{byte}}+T_{\text{start}}\log _{\Phi }(p)+{\sqrt {2m\log _{\Phi }(p)T_{\text{start}}T_{\text{byte}}}}} . == Two Tree Broadcast (23-Broadcast) == === Definition === This algorithm aims to improve on some disadvantages of tree structure models with pipelines. Normally in tree structure models with pipelines (see above methods), leaves receive just their data and cannot contribute to send and spread data. The algorithm concurrently uses two binary trees to communicate over. Those trees will be called tree A and B. Structurally in binary trees there are relatively more leave nodes than inner nodes. Basic Idea of this algorithm is to make a leaf node of tree A be an inner node of tree B. It has also the same technical function in opposite side from B to A tree. This means, two packets are sent and received by inner nodes and leaves in different steps. === Tree construction === The number of steps needed to construct two parallel-working binary trees is dependent on the amount of processors. Like with other structures one processor can is the root node who sends messages to two trees. It is not necessary to set a root node, because it is not hard to recognize that the direction of sending messages in binary tree is normally top to bottom. There is no limitation on the number of processors to build two binary trees. Let the height of the combined tree be h = ⌈log(p + 2)⌉. Tree A and B can have a height of h − 1 {\displaystyle h-1} . Especially, if the number of processors correspond to p = 2 h − 1 {\displaystyle p=2^{h}-1} , we can make both sides trees and a root node. To construct this model efficiently and easily with a fully built tree, we can use two methods called "Shifting" and "Mirroring" to get second tree. Let assume tree A is already modeled and tree B is supposed to be constructed based on tree A. We assume that we have p {\displaystyle p} processors ordered from 0 to p − 1 {\displaystyle p-1} . ==== Shifting ==== The "Shifting" method, first copies tree A and moves every node one position to the left to get tree B. The node, which will be located on -1, becomes a child of processor p − 2 {\displaystyle p-2} . ==== Mirroring ==== "Mirroring" is ideal for an even number of processors. With this method tree B can be more easily constructed by tree A, because there are no structural transformations in order to create the new tree. In addition, a symmetric process makes this approach simple. This method can also handle an odd number of processors, in this case, we can set processor p − 1 {\displaystyle p-1} as root node for both trees. For the remaining processors "Mirroring" can be used. === Coloring === We need to find a schedule in order to make sure that no processor has to send or receive two messages from two trees in a step. The edge, is a communication connection to connect two nodes, and can be labelled as either 0 or 1 to make sure that every processor can alternate between 0 and 1-labelled edges. The edges of A and B can be colored with two colors (0 and 1) such that no processor is connected to its parent nodes in A and B using edges of the same color- no processor is connected to its children nodes in A or B using edges of the same color. In every even step the edges with 0 are activated and edges with 1 are activated in every odd step. === Time complexity === In this case the number of packet k is divided in half for each tree. Both trees are working together the total number of packets k = k / 2 + k / 2 {\displaystyle k=k/2+k/2} (upper tree + bottom tree) In each binary tree sending a message to another nodes takes 2 i {\displaystyle 2i} steps until a processor has at least a packet in step i {\displaystyle i} . Therefore, we can calculate all steps as d := log 2 ( p + 1 ) ⇒ log 2 ( p + 1 ) ≈ log 2 ( p ) {\displaystyle d:=\log _{2}(p+1)\Rightarrow \log _{2}(p+1)\approx \log _{2}(p)} . The resulting run time is T ( m , p , k ) ≈ ( m k T byte + T start ) ( 2 d + k − 1 ) {\textstyle T(m,p,k)\approx ({\frac {m}{k}}T_{\text{byte}}+T_{\text{start}})(2d+k-1)} . (Optimal k = m ( 2 d − 1 ) T byte / T start {\textstyle k={\sqrt {{m(2d-1)T_{\text{byte}}}/{T_{\text{start}}}}}} ) This results in a run time of T ( m , p ) ≈ m T byte + T start ⋅ 2 log 2 ( p ) + m ⋅ 2 log 2 ( p ) T start T byte {\displaystyle T(m,p)\approx mT_{\text{byte}}+T_{\text{start}}\cdot 2\log _{2}(p)+{\sqrt {m\cdot 2\log _{2}(p)T_{\text{start}}T_{\text{byte}}}}} . == ESBT-Broadcasting (Edge-disjoint Spanning Binomial Trees) == In this section, another broadcasting algorithm with an underlying telephone communication model will be introduced. A Hypercube creates network system with p = 2 d ( d = 0 , 1 , 2 , 3 , . . . ) {\displaystyle p=2^{d}(d=0,1,2,3,...)} . Every node is represented by binary 0 , 1 {\displaystyle {0,1}} depending on the number of dimensions. Fundamentally ESBT(Edge-disjoint Spanning Binomial Trees) is based on hypercube graphs, pipelining( m {\displaystyle m} messages are divided by k {\displaystyle k} packets) and binomial trees. The Processor 0 d {\displaystyle 0^{d}} cyclically spreads packets to roots of ESB
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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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DAVE, or Digital Application Virtual Engineer, is a software development and code generation tool for microcontroller applications created in C/C++. == Versions == === Version 4 (beta) === The successor of the Eclipse-based development environment for C/C++ and/or graphical user interface (GUI) based development using application software (apps). It generates code for the latest XMC1xxx and XMC4xxx microcontrollers using ARM Cortex-M processors. DAVE software development kit (SDK) is a free integrated development environment to set up its own apps for DAVE. === Version 3 === Automatic code generation is based on the use of case-oriented, configurable, and tested software (SW) components, called DAVE Apps. They are comparable to executable and configurable application notes that can be downloaded from the web. The environment is based on Eclipse. Ordinary program development using C/C++ is also available. The targets for this development are XMC1xxx and XMC4xxx microcontrollers that use Cortex-M processors. === Previous versions === This version targets 32-bit microcontroller units (MCUs) (Infineon TriCore AUDO family), 16-bit MCUs (C166, XC166, XE166, and XC2000 family), and 8-bit MCUs (XC800 family) from Infineon. After the initial setup, the configuration wizard appears and gives an overview of the hardware peripherals, control units, and modules. The microcontroller application can be created by selecting the desired functions. At this step, module-specific functions must be selected for module initializing and control. Finally, the application source files will be generated by DAVE and embedded in a project in the selected development environment, where the code can still be modified or added to an extant project. == DAVE-related software == Infineon also developed additional software that can be used in conjunction with DAVE for specific microcontroller families or additional hardware: DAVE Bench for XC800 is a platform providing free development tools for Infineon's 8-bit microcontroller family, based on the Open Source Eclipse architecture. DAVE Drive is a GUI-based software tool that allows application developers to create embedded software for the control of brushless synchronous three-phase motors. == Alternative software == The Infineon MCUs are directly supported by several commercial products, depending on the selected MCU target. An embedded programming library for MATLAB exists. As a free alternative to DAVE, the developer can use the Keil Microcontroller Development Kit (MDK) Version 5. Code for the XMX1000 series up to 128 kB can be developed this way without purchasing a license from Keil.
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Proof of authority (PoA) is a category of consensus protocols used with blockchains based on reputation and identity as a stake that delivers comparatively fast and efficient transactions (compared to proof-of-work and proof-of-stake). The most notable platforms using PoA are VeChain, Bitgert, Palm Network and Xodex. == Description == Proof-of-authority is a category of consensus protocols for networks and blockchains where transactions and blocks are built and validated by approved entities known as validators. Their permissions are often granted through a centralized authority, but they can also be granted through a council or decentralized organization. The term "proof-of-authority" was coined by Gavin Wood, co-founder of Ethereum and Parity Technologies. With PoA, validators are incentivized to maintain good behavior and honesty when validating blocks to avoid developing a negative reputation. PoA can have higher security than PoW and even PoS due to validators wanting to avoid damaging their reputation. Because PoA is permissioned, it is not fully trustless. Validators without good reputation may risk having their validator permissions removed. PoA is generally more efficient than PoW and PoS because it operates with fewer nodes and validators, thus requiring fewer duplicated resources.
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An algorithm is a fundamental set of rules or defined procedures that are typically designed and used to be a simpler way to solve a specific problem or a broad set of problems. Simply speaking, algorithms define different processes, sets of rules and regulations, or methodologies that are to be followed through in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations. With the increasing automation of services, more and more decisions are being made by algorithms. Some general examples are risk assessments, anticipatory policing, and pattern recognition technology. The following is a list of well-known algorithms. == Automated planning == == Combinatorial algorithms == === General combinatorial algorithms === Brent's algorithm: finds a cycle in function value iterations using only two iterators Floyd's cycle-finding algorithm: finds a cycle in function value iterations Gale–Shapley algorithm: solves the stable matching problem Pseudorandom number generators (uniformly distributed—see also List of pseudorandom number generators for other PRNGs with varying degrees of convergence and varying statistical quality): ACORN generator Blum Blum Shub Lagged Fibonacci generator Linear congruential generator Mersenne Twister === Graph algorithms === Blossom algorithm: algorithm for constructing maximum-cardinality matching on graphs. Coloring algorithm: algorithms for graph (vertex or edge) coloring (subject to constraints, e.g. proper coloring or list coloring) Hopcroft–Karp algorithm: convert a bipartite graph to a maximum-cardinality matching Hungarian algorithm: algorithm for finding a perfect matching Prüfer coding: conversion between a labeled tree and its Prüfer sequence Tarjan's off-line lowest common ancestors algorithm: computes lowest common ancestors for pairs of nodes in a tree Topological sort: finds linear order of nodes (e.g. jobs) based on their dependencies. ==== Graph drawing ==== Coin graph drawing algorithms for finite connected planar graphs (approximately computing the theoretical circle-packing given by the Koebe-Andreev-Thurston theorem). See also Fáry's theorem on straight-line drawings of planar graphs. Force-based algorithms (also known as force-directed algorithms or spring-based algorithms) Spectral layout ==== Network theory ==== Network analysis Link analysis Girvan–Newman algorithm: detect communities in complex systems Web link analysis Hyperlink-Induced Topic Search (HITS) (also known as Hubs and authorities) PageRank TrustRank Flow networks Dinic's algorithm: is a strongly polynomial algorithm for computing the maximum flow in a flow network. Edmonds–Karp algorithm: implementation of Ford–Fulkerson Ford–Fulkerson algorithm: computes the maximum flow in a graph Karger's algorithm: a Monte Carlo method to compute the minimum cut of a connected graph Push–relabel algorithm: computes a maximum flow in a graph ==== Routing for graphs ==== Edmonds' algorithm (also known as Chu–Liu/Edmonds' algorithm): find maximum or minimum branchings Euclidean minimum spanning tree: algorithms for computing the minimum spanning tree of a set of points in the plane Longest path problem: find a simple path of maximum length in a given graph Minimum spanning tree Borůvka's algorithm Kruskal's algorithm Prim's algorithm Reverse-delete algorithm Nonblocking minimal spanning switch say, for a telephone exchange Shortest path problem Bellman–Ford algorithm: computes shortest paths in a weighted graph (where some of the edge weights may be negative) Dijkstra's algorithm: computes shortest paths in a graph with non-negative edge weights Floyd–Warshall algorithm: solves the all pairs shortest path problem in a weighted, directed graph Johnson's algorithm: all pairs shortest path algorithm in sparse weighted directed graph Transitive closure problem: find the transitive closure of a given binary relation Traveling salesman problem Christofides algorithm Nearest neighbour algorithm Vehicle routing problem Clarke and Wright Saving algorithm Warnsdorff's rule: a heuristic method for solving the Knight's tour problem ==== Graph search ==== A: special case of best-first search that uses heuristics to improve speed B: a best-first graph search algorithm that finds the least-cost path from a given initial node to any goal node (out of one or more possible goals) Backtracking: abandons partial solutions when they are found not to satisfy a complete solution Beam search: is a heuristic search algorithm that is an optimization of best-first search that reduces its memory requirement Beam stack search: integrates backtracking with beam search Best-first search: traverses a graph in the order of likely importance using a priority queue Bidirectional search: find the shortest path from an initial vertex to a goal vertex in a directed graph Breadth-first search: traverses a graph level by level Brute-force search: an exhaustive and reliable search method, but computationally inefficient in many applications D: an incremental heuristic search algorithm Depth-first search: traverses a graph branch by branch Dijkstra's algorithm: a special case of A for which no heuristic function is used General Problem Solver: a seminal theorem-proving algorithm intended to work as a universal problem solver machine. Iterative deepening depth-first search (IDDFS): a state space search strategy Jump point search: an optimization to A which may reduce computation time by an order of magnitude using further heuristics Lexicographic breadth-first search (also known as Lex-BFS): a linear time algorithm for ordering the vertices of a graph SSS: state space search traversing a game tree in a best-first fashion similar to that of the A search algorithm Uniform-cost search: a tree search that finds the lowest-cost route where costs vary ==== Subgraphs ==== Cliques Bron–Kerbosch algorithm: a technique for finding maximal cliques in an undirected graph MaxCliqueDyn maximum clique algorithm: find a maximum clique in an undirected graph Strongly connected components Kosaraju's algorithm Path-based strong component algorithm Tarjan's strongly connected components algorithm Subgraph isomorphism problem === Sequence algorithms === ==== Approximate sequence matching ==== Bitap algorithm: fuzzy algorithm that determines if strings are approximately equal. Phonetic algorithms Daitch–Mokotoff Soundex: a Soundex refinement which allows matching of Slavic and Germanic surnames Double Metaphone: an improvement on Metaphone Match rating approach: a phonetic algorithm developed by Western Airlines Metaphone: an algorithm for indexing words by their sound, when pronounced in English NYSIIS: phonetic algorithm, improves on Soundex Soundex: a phonetic algorithm for indexing names by sound, as pronounced in English String metrics: computes a similarity or dissimilarity (distance) score between two pairs of text strings Damerau–Levenshtein distance: computes a distance measure between two strings, improves on Levenshtein distance Dice's coefficient (also known as the Dice coefficient): a similarity measure related to the Jaccard index Hamming distance: sum number of positions which are different Jaro–Winkler distance: is a measure of similarity between two strings Levenshtein edit distance: computes a metric for the amount of difference between two sequences Trigram search: search for text when the exact syntax or spelling of the target object is not precisely known ==== Selection algorithms ==== Introselect Quickselect ==== Sequence search ==== Linear search: locates an item in an unsorted sequence Selection algorithm: finds the kth largest item in a sequence Sorted lists Binary search algorithm: locates an item in a sorted sequence Eytzinger binary search: cache friendly binary search algorithm Fibonacci search technique: search a sorted sequence using a divide and conquer algorithm that narrows down possible locations with the aid of Fibonacci numbers Jump search (or block search): linear search on a smaller subset of the sequence Predictive search: binary-like search which factors in magnitude of search term versus the high and low values in the search. Sometimes called dictionary search or interpolated search. Uniform binary search: an optimization of the classic binary search algorithm Ternary search: a technique for finding the minimum or maximum of a function that is either strictly increasing and then strictly decreasing or vice versa ==== Sequence merging ==== k-way merge algorithm Simple merge algorithm Union (merge, with elements on the output not repeated) ==== Sequence permutations ==== Fisher–Yates shuffle (also known as the Knuth shuffle): randomly shuffle a finite set Heap's permutation generation algorithm: interchange elements to generate next permutation Schensted algorithm: constructs a pair of Young tableaux from a permutation Steinhaus–Johnson–Trotter algorithm (also known as the Johnson–Trotter algorithm):
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TurboQuant is an online vector quantization algorithm for compressing high-dimensional Euclidean vectors while preserving their geometric structure. It was proposed in 2025 by Amir Zandieh, Majid Daliri, Majid Hadian, and Vahab Mirrokni in the paper TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate. The paper lists Zandieh and Mirrokni as affiliated with Google Research, Daliri with New York University, and Hadian with Google DeepMind. The method was developed for applications including large language model (LLM) inference, key–value (KV) cache compression, vector databases, and nearest neighbor search. TurboQuant consists of two related algorithms: TurboQuantmse, which is optimized for mean squared error (MSE), and TurboQuantprod, which is optimized for unbiased inner product estimation. The algorithm uses a random rotation of input vectors, applies scalar quantizers to the rotated coordinates, and, for inner-product estimation, applies a one-bit Quantized Johnson–Lindenstrauss (QJL) transform to the residual error. == Background == Vector quantization is a compression method that maps high-dimensional vectors to a finite set of codewords. The problem has roots in Shannon's source coding theory and rate–distortion theory. In machine learning and information retrieval, vector quantization is used to reduce the memory required to store embeddings, activation vectors, and other numerical representations. In Transformer-based large language models, the KV cache stores key and value vectors from previous tokens during autoregressive decoding. The size of this cache grows with context length, the number of attention heads, and the number of concurrent requests, making it a major memory bottleneck in LLM serving. Similar compression problems appear in vector search, where large collections of embedding vectors must be stored and searched efficiently. Earlier approaches to vector quantization include product quantization, scalar quantization, and data-dependent k-means codebook construction. The TurboQuant paper argues that many existing methods either require offline preprocessing and calibration or suffer from suboptimal distortion guarantees in online settings. == Algorithm == === TurboQuantmse === TurboQuantmse is the version of the algorithm optimized for mean-squared error. For a unit vector x ∈ S d − 1 {\displaystyle x\in S^{d-1}} , the algorithm first applies a random rotation matrix Π ∈ R d × d {\displaystyle \Pi \in \mathbb {R} ^{d\times d}} and sets z = Π x {\displaystyle z=\Pi x} . Each coordinate of the rotated vector follows a shifted and scaled beta distribution, which converges to a normal distribution in high dimensions. In high dimensions, distinct coordinates also become nearly independent, allowing the algorithm to apply scalar quantizers independently to each coordinate. The scalar quantizer is constructed by solving a one-dimensional continuous k-means or Lloyd–Max quantization problem. If the centroids are c 1 , c 2 , … , c 2 b {\displaystyle c_{1},c_{2},\ldots ,c_{2^{b}}} , the quantization step stores, for each coordinate, i d x j = a r g m i n k ∈ [ 2 b ] | z j − c k | . {\displaystyle \mathrm {idx} _{j}=\operatorname {} {arg\,min}_{k\in [2^{b}]}|z_{j}-c_{k}|.} During dequantization, the stored index for each coordinate is replaced by the corresponding centroid, giving a reconstructed rotated vector z ~ {\displaystyle {\tilde {z}}} . The algorithm then rotates back: x ~ = Π ⊤ z ~ . {\displaystyle {\tilde {x}}=\Pi ^{\top }{\tilde {z}}.} The paper gives the following bound for TurboQuantmse: D m s e ≤ 3 π 2 ⋅ 1 4 b . {\displaystyle D_{\mathrm {mse} }\leq {\frac {\sqrt {3\pi }}{2}}\cdot {\frac {1}{4^{b}}}.} It also reports finer-grained MSE values of approximately 0.36, 0.117, 0.03, and 0.009 for bit-widths b = 1 , 2 , 3 , 4 {\displaystyle b=1,2,3,4} , respectively. === TurboQuantprod === TurboQuantprod is optimized for unbiased inner-product estimation. The authors note that an MSE-optimized quantizer may introduce bias when used to estimate inner products. To address this, TurboQuantprod first applies TurboQuantmse with bit-width b − 1 {\displaystyle b-1} , then applies a one-bit Quantized Johnson–Lindenstrauss transform to the remaining residual vector. Let r = x − Q m s e − 1 ( Q m s e ( x ) ) {\displaystyle r=x-Q_{\mathrm {mse} }^{-1}(Q_{\mathrm {mse} }(x))} be the residual after MSE quantization, and let γ = ‖ r ‖ 2 {\displaystyle \gamma =\|r\|_{2}} . The QJL step stores a sign vector for the residual. For γ ≠ 0 {\displaystyle \gamma \neq 0} , this can be written using the normalized residual u = r / γ {\displaystyle u=r/\gamma } : q j l = sign ( S u ) , {\displaystyle qjl=\operatorname {sign} (Su),} where S ∈ R d × d {\displaystyle S\in \mathbb {R} ^{d\times d}} is a random projection matrix. Since the sign function is invariant under positive rescaling, this is equivalent to sign ( S r ) {\displaystyle \operatorname {sign} (Sr)} when r ≠ 0 {\displaystyle r\neq 0} . If γ = 0 {\displaystyle \gamma =0} , the residual correction is zero. TurboQuantprod stores the MSE quantization, the QJL sign vector, and the residual norm: Q p r o d ( x ) = [ Q m s e ( x ) , q j l , γ ] . {\displaystyle Q_{\mathrm {prod} }(x)=\left[Q_{\mathrm {mse} }(x),qjl,\gamma \right].} The dequantized vector is reconstructed as x ~ = x ~ m s e + π / 2 d γ S ⊤ q j l . {\displaystyle {\tilde {x}}={\tilde {x}}_{\mathrm {mse} }+{\frac {\sqrt {\pi /2}}{d}}\,\gamma S^{\top }qjl.} The paper proves that TurboQuantprod is unbiased for inner-product estimation: E x ~ [ ⟨ y , x ~ ⟩ ] = ⟨ y , x ⟩ . {\displaystyle \mathbb {E} _{\tilde {x}}\left[\langle y,{\tilde {x}}\rangle \right]=\langle y,x\rangle .} It also gives the distortion bound D p r o d ≤ 3 π 2 ⋅ ‖ y ‖ 2 2 d ⋅ 1 4 b . {\displaystyle D_{\mathrm {prod} }\leq {\frac {\sqrt {3\pi }}{2}}\cdot {\frac {\|y\|_{2}^{2}}{d}}\cdot {\frac {1}{4^{b}}}.} == Performance and applications == The TurboQuant paper reports that the algorithm achieves near-optimal distortion rates within a small constant factor of information-theoretic lower bounds. The authors report that, for KV cache quantization, TurboQuant achieved quality neutrality at 3.5 bits per channel and marginal degradation at 2.5 bits per channel. In long-context LLM experiments using Llama 3.1 8B Instruct, the paper evaluated the method on a "needle-in-a-haystack" retrieval task with document lengths from 4,000 to 104,000 tokens. It reported that TurboQuant matched the uncompressed full-precision baseline while using more than 4× compression, and compared the method against PolarQuant, SnapKV, PyramidKV, and KIVI. Google Research stated that TurboQuant was evaluated on long-context benchmarks including LongBench, Needle in a Haystack, ZeroSCROLLS, RULER, and L-Eval using open-source models including Gemma and Mistral. According to a report in Tom's Hardware, Google described the method as reducing KV-cache memory by at least six times and achieving up to an eightfold improvement in attention-logit computation on Nvidia H100 GPUs compared with unquantized 32-bit keys. TurboQuant has also been applied to nearest-neighbor vector search. The original paper reports experiments on DBpedia entity embeddings and GloVe embeddings, comparing TurboQuant with product quantization and other vector-search quantization baselines. == Relationship to other methods == TurboQuant is related to several methods for efficient large language model inference and high-dimensional search: Product quantization – a vector quantization technique widely used for approximate nearest-neighbor search Quantization (machine learning) – reducing the numerical precision of weights, activations, or cached tensors in machine learning models PagedAttention – a memory-management algorithm for LLM serving that reduces fragmentation in the KV cache Johnson–Lindenstrauss lemma – a result in high-dimensional geometry used in random projection methods Lloyd's algorithm – an algorithm for scalar and vector quantization, including k-means-style codebook construction Unlike PagedAttention, which focuses on memory allocation and cache layout, TurboQuant reduces the numerical storage cost of the vectors themselves. Unlike many product-quantization methods, TurboQuant is designed to be data-oblivious and online, avoiding dataset-specific codebook training. == Limitations == The strongest performance claims for TurboQuant come from the original paper and Google Research's own publication. Coverage in technology media has noted that the broader impact of the method will depend on real-world implementation details, workloads, and hardware architectures.
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In statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena. In smoothing, the data points of a signal are modified so individual points higher than the adjacent points (presumably because of noise) are reduced, and points that are lower than the adjacent points are increased, leading to a smoother signal. Reducing noise by smoothing may aid in data analysis in two notable ways: Help uncover more meaningful information from the underlying data, such as trends. Provide analyses that are both flexible and robust. Many different algorithms are used in smoothing, most commonly binning, kernels, and local weighted regression. == Compared to curve fitting == Smoothing may be distinguished from the related and partially overlapping concept of curve fitting in the following ways: curve fitting often involves the use of an explicit function form for the result, whereas the immediate results from smoothing are the "smoothed" values with no later use made of a functional form if there is one; the aim of smoothing is to give a general idea of relatively slow changes of value with little attention paid to the close matching of data values, while curve fitting concentrates on achieving as close a match as possible. smoothing methods often have an associated tuning parameter which is used to control the extent of smoothing. Curve fitting will adjust any number of parameters of the function to obtain the 'best' fit. == Linear smoothers == In the case that the smoothed values can be written as a linear transformation of the observed values, the smoothing operation is known as a linear smoother; the matrix representing the transformation is known as a smoother matrix or hat matrix. The operation of applying such a matrix transformation is called convolution. Thus the matrix is also called convolution matrix or a convolution kernel. In the case of simple series of data points (rather than a multi-dimensional image), the convolution kernel is a one-dimensional vector. == Algorithms == One of the most common algorithms is the "moving average", often used to try to capture important trends in repeated statistical surveys. In image processing and computer vision, smoothing ideas are used in scale space representations. The simplest smoothing algorithm is the "rectangular" or "unweighted sliding-average smooth". This method replaces each point in the signal with the average of "m" adjacent points, where "m" is a positive integer called the "smooth width". Usually m is an odd number. The triangular smooth is like the rectangular smooth except that it implements a weighted smoothing function. Some specific smoothing and filter types, with their respective uses, pros and cons are:
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Metadata management involves managing metadata about other data, whereby this "other data" is generally referred to as content data. The term is used most often in relation to digital media, but older forms of metadata are catalogs, dictionaries, and taxonomies. For example, the Dewey Decimal Classification is a metadata management system developed in 1876 for libraries. == Metadata schema == Metadata management goes by the end-to-end process and governance framework for creating, controlling, enhancing, attributing, defining and managing a metadata schema, model or other structured aggregation system, either independently or within a repository and the associated supporting processes (often to enable the management of content). For web-based systems, URLs, images, video etc. may be referenced from a triples table of object, attribute and value. == Scope == With specific knowledge domains, the boundaries of the metadata for each must be managed, since a general ontology is not useful to experts in one field whose language is knowledge-domain specific. == Metadata Manager == In the process of developing a knowledge management solution, creating a metadata schema, and a system in which metadata is managed, a dedicated resource may be appointed to maintain adherence to metadata standards as defined by data owners as well as general best practice. This person is responsible for curation of the business and technical layers of the metadata schema, and commonly involved with strategy and implementation. A metadata manager is not required to master all aspects, or be involved with everything concerning the solution, but an understanding of as much of the process as possible to ensure a relevant schema is developed. == Metadata management over time == Managing the metadata in a knowledge management solution is an important step in a metadata strategy. It is part of the strategy to make sure that the metadata are complete, current and correct at any given time. Managing a metadata project is also about making sure that users of the system are aware of the possibilities allowed by a well-designed metadata system and how to maximize the benefits of metadata. Regularly monitoring the metadata to ensure that the schema remains relevant is advised. === Wikipedia metadata === Wikipedia is a project that actively manages metadata for its articles and files. For example, volunteer editors carefully curate new biographical articles based on the notability (claim to fame), name, birth, and/or death dates. Similarly, volunteer editors carefully curate new architectural articles based on name, municipality, or geo coordinates. When new articles with a valid alternate spelling are added to Wikipedia that match up to existing articles based on metadata, these are then manually checked and if needed, tagged for merging. When new articles are added that are considered out of scope or otherwise unfit for Wikipedia, these are nominated for deletion. To help keep track of metadata on Wikipedia, the new Wikimedia project Wikidata was established in 2012. Click on the pictures to view more metadata about these images:
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The information audit (IA) extends the concept of auditing from a traditional scope of accounting and finance to the organisational information management system. Information is representative of a resource which requires effective management and this led to the development of interest in the use of an IA. Prior the 1990s and the methodologies of Orna, Henczel, Wood, Buchanan and Gibb, IA approaches and methodologies focused mainly upon an identification of formal information resources (IR). Later approaches included an organisational analysis and the mapping of the information flow. This gave context to analysis within an organisation's information systems and a holistic view of their IR and as such could contribute to the development of the information systems architecture (ISA). In recent years the IA has been overlooked in favour of the systems development process which can be less expensive than the IA, yet more heavily technically focused, project specific (not holistic) and does not favour the top-down analysis of the IA. == Definition == A definition for the Information Audit cannot be universally agreed-upon amongst scholars, however the definition offered by ASLIB received positive support from a few notable scholars including Henczel, Orna and Wood; “(the IA is a) systematic examination of information use, resources and flows, with a verification by reference to both people and existing documents, in order to establish the extent to which they are contributing to an organisation’s objectives” In summary, the term audit itself implies a counting, the IA being much the same yet it counts IR and analyses how they are used and how critical they are to the success of a given task. == Role and scope of an IA == In much the same way as the IA is difficult to define, it can be utilised in a range of contexts by the information professional, from complying with freedom of information legislation to identifying any existing gaps, duplications, bottlenecks or other inefficiencies in information flows and to understand how existing channels can be used for knowledge transfer In 2007 Buchanan and Gibb developed upon their 1998 examination of the IA process by outlining a summary of its main objectives: To identify an organisation’s information resource To identify an organisation’s information needs Furthermore, Buchanan and Gibb went on to state that the IA also had to meet the following additional objectives: To identify the cost/benefits of information resources To identify the opportunities to use the information resources for strategic competitive advantage To integrate IT investment with strategic business initiatives To identify information flow and processes To develop an integrated information strategy and/or policy To create an awareness of the importance of Information Resource Management (IRM) To monitor/evaluate conformance to information related standards, legislations, policy and guidelines. == Methodology evolution == === Overview === In 1976 Riley first published a definition of IA as a way of analysing IR based on a cost-benefit model. Since Riley, scholars have outlined further developed methodologies. Henderson took a cost-benefit approach hoping to draw focus from manpower-costing to information storage and acquisition which he felt was being overlooked. In 1985 Gillman focused upon identifying the relationships which existed between various components in order to map them to one another. Neither Henderson nor Gillman’s methods offered alternative approaches beyond the existing organisational frameworks. Quinn took a hybrid-approach combining Gillman and Henderson’s methods to identify the purpose of existing IR and to position them within the organisation, as did Worlock. The differentiator between Quinn and Worlock lay in Worlock’s consideration of solutions outside of the current organisational structure. These approaches had thus far had paid little attention to the needs of the user or in making structured recommendations for the development of a corporate information strategy. Therefore, here follows a brief outline and overall comparison of four published strategic approaches in order that one might understand the development of the IA methodology. === Burk and Horton === In 1988 Burk and Horton developed InfoMap, the first IA methodology developed for widespread use. It aimed to discover, map and evaluate the IR within an organisation using a 4-stage process: Survey staff using questionnaires/interviews Measure the IR against cost/value Analyse resources Synthesise the findings and map the strengths and weaknesses of the IR against the objectives of the organisation. Although the method inventoried all IR (and therefore met standard ISO 1779) this bottom-up approach revealed limited analysis of the organisation holistically and the steps were not explicit enough. === Orna === Orna produced a top-down methodology in contrast to Burk and Horton, placing emphasis upon the importance of organisational analysis and aimed to assist in the production of a corporate information policy. Initially the method had just 4-stages, this later revised to a 10-stage process which included pre and post-audit stages as below: Conduct a preliminary review to confirm operational/strategic direction Gain support/resource from management Gain commitment from the other stakeholders (staff) Planning including the project, team, tools and techniques Identify the IR, information flow and produce a cost/value assessment Interpret findings based upon current versus desired state Produce a report to present findings Implement recommendations Monitor effects of change Repeat the IA Orna’s method introduced the need for a cyclical IA to be put in place in order for the IR to be continually tracked and improvements made regularly. Again this method was criticised for lacking some practical application and in 2004 Orna revised the methodology once more to try to rectify this problem === Buchanan and Gibb === In 1998, similarly to Orna's earlier publication, Buchanan and Gibb took a top-down approach, drawing techniques from established management disciplines to provide a framework and a level of familiarity for information professionals. This set of techniques was a notable contribution to IA methodologies and understood the need to be flexible for each organisation. Theirs was a 5-stage process: Promote benefits of the IA through seminars/surveys/CEO letter for cooperation Identify the mission objectives of the organisation, define environment (PEST), map information flow and examine organisation culture. Analyse and formulate action plan for problem areas, flow diagrams and a report of findings and recommendations Account for cost of IR and related services using Activity Based Costing (ABC) and Output Based Specification (OBS). Synthesise the whole process in final audit report and provide an information strategy (strategic direction) in relation to the organisation’s mission statement. This was the introduction of a new approach to costing the IR and had an integrated strategic direction, yet the scholars admitted that this method may be impractical for smaller organisations. === Henczel === Henczel’s methodology drew upon the strengths of Orna and Buchanan and Gibb to produce a 7-stage process: Planning and submission of business case for approval to proceed Data collection and development of an IR database and population through survey techniques Structured data analysis Data evaluation, interpretation and formulation of recommendations Communication of recommendations through a report Implementing recommendations through a devised programme The IA as a continuum-establishment of a cyclical process Focus was made once more on the strategic direction of the organisation conducting the IA. Furthermore, Henczel made examination into the use of the IA as a first-step in the development of a knowledge audit or knowledge management strategy as discussed in the later section. == Case studies == Scholars and information professionals have since tested the above methodologies with varied results. An early case study produced by Soy and Bustelo in a Spanish financial institution in 1999 aimed to identify the use of information resources for qualitative and quantitative data analysis due to the rapid expansion of the organisation within a six-year period. Although the methodology was not explicitly credited to any of the above-mentioned scholars, it did follow a strategic (post 1990's) IA process including gaining support from management, the use of questionnaires for data collection, analysis and evaluation of the data, identification and mapping of the IR, cost-analysis and outlining recommendations to assist with the establishment of an Information policy. In addition the IA report suggested that the process would need to be continual (cyclical as Orna, Henczel and Buchanan and Gibb suggest). Conclusions of this case-study stated that th
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Car–Parrinello molecular dynamics (CPMD) refers to either a method used in molecular dynamics (also known as the Car–Parrinello method) or the computational chemistry software package used to implement this method. The CPMD method is one of the major methods for calculating ab initio molecular dynamics (ab initio MD or AIMD). Ab initio molecular dynamics (AIMD) is a computational method that uses first principles through quantum mechanics to simulate the motion of atoms in a system. It is a type of molecular dynamics (MD) simulation that does not rely on empirical potentials or force fields to describe the interactions between atoms, but rather calculates these interactions entirely from the electronic structure of the system using quantum mechanics. In an ab initio MD simulation, the total energy of the system is calculated at each time step using density functional theory (DFT), Hartree-Fock (HF), or other electronic structure calculation methods. The forces acting on each atom are then determined from the gradient of the energy with respect to the atomic coordinates, and the equations of motion are solved to predict the trajectory of the atoms. AIMD permits chemical bond breaking and forming events to occur and accounts for electronic polarization effect. Therefore, Ab initio MD simulations can be used to study a wide range of phenomena, including the structural, thermodynamic, and dynamic properties of materials and chemical reactions. They are particularly useful for systems that are not well described by empirical potentials or force fields, such as systems with strong electronic correlation or systems with many degrees of freedom. However, ab initio MD simulations are computationally demanding and require significant computational resources. The CPMD method is related to the more common Born–Oppenheimer molecular dynamics (BOMD) method in that the quantum mechanical effect of the electrons is included in the calculation of energy and forces for the classical motion of the nuclei. CPMD and BOMD are different types of AIMD. However, whereas BOMD treats the electronic structure problem within the time-independent Schrödinger equation, CPMD explicitly includes the electrons as active degrees of freedom, via (fictitious) dynamical variables. The software is a parallelized plane wave / pseudopotential implementation of density functional theory, particularly designed for ab initio molecular dynamics. == Car–Parrinello method == The Car–Parrinello method is a type of molecular dynamics, usually employing periodic boundary conditions, planewave basis sets, and density functional theory, proposed by Roberto Car and Michele Parrinello in 1985 while working at SISSA, who were subsequently awarded the Dirac Medal by ICTP in 2009. In contrast to Born–Oppenheimer molecular dynamics wherein the nuclear (ions) degree of freedom are propagated using ionic forces which are calculated at each iteration by approximately solving the electronic problem with conventional matrix diagonalization methods, the Car–Parrinello method explicitly introduces the electronic degrees of freedom as (fictitious) dynamical variables, writing an extended Lagrangian for the system which leads to a system of coupled equations of motion for both ions and electrons. In this way, an explicit electronic minimization at each time step, as done in Born–Oppenheimer MD, is not needed: after an initial standard electronic minimization, the fictitious dynamics of the electrons keeps them on the electronic ground state corresponding to each new ionic configuration visited along the dynamics, thus yielding accurate ionic forces. In order to maintain this adiabaticity condition, it is necessary that the fictitious mass of the electrons is chosen small enough to avoid a significant energy transfer from the ionic to the electronic degrees of freedom. This small fictitious mass in turn requires that the equations of motion are integrated using a smaller time step than the one (1–10 fs) commonly used in Born–Oppenheimer molecular dynamics. Currently, the CPMD method can be applied to systems that consist of a few tens or hundreds of atoms and access timescales on the order of tens of picoseconds. == General approach == In CPMD the core electrons are usually described by a pseudopotential and the wavefunction of the valence electrons are approximated by a plane wave basis set. The ground state electronic density (for fixed nuclei) is calculated self-consistently, usually using the density functional theory method. Kohn-Sham equations are often used to calculate the electronic structure, where electronic orbitals are expanded in a plane-wave basis set. Then, using that density, forces on the nuclei can be computed, to update the trajectories (using, e.g. the Verlet integration algorithm). In addition, however, the coefficients used to obtain the electronic orbital functions can be treated as a set of extra spatial dimensions, and trajectories for the orbitals can be calculated in this context. == Fictitious dynamics == CPMD is an approximation of the Born–Oppenheimer MD (BOMD) method. In BOMD, the electrons' wave function must be minimized via matrix diagonalization at every step in the trajectory. CPMD uses fictitious dynamics to keep the electrons close to the ground state, preventing the need for a costly self-consistent iterative minimization at each time step. The fictitious dynamics relies on the use of a fictitious electron mass (usually in the range of 400 – 800 a.u.) to ensure that there is very little energy transfer from nuclei to electrons, i.e. to ensure adiabaticity. Any increase in the fictitious electron mass resulting in energy transfer would cause the system to leave the ground-state BOMD surface. === Lagrangian === L = 1 2 ( ∑ I n u c l e i M I R ˙ I 2 + μ ∑ i o r b i t a l s ∫ d r | ψ ˙ i ( r , t ) | 2 ) − E [ { ψ i } , { R I } ] + ∑ i j Λ i j ( ∫ d r ψ i ψ j − δ i j ) , {\displaystyle {\mathcal {L}}={\frac {1}{2}}\left(\sum _{I}^{\mathrm {nuclei} }\ M_{I}{\dot {\mathbf {R} }}_{I}^{2}+\mu \sum _{i}^{\mathrm {orbitals} }\int d\mathbf {r} \ |{\dot {\psi }}_{i}(\mathbf {r} ,t)|^{2}\right)-E\left[\{\psi _{i}\},\{\mathbf {R} _{I}\}\right]+\sum _{ij}\Lambda _{ij}\left(\int d\mathbf {r} \ \psi _{i}\psi _{j}-\delta _{ij}\right),} where μ {\displaystyle \mu } is the fictitious mass parameter; E[{ψi},{RI}] is the Kohn–Sham energy density functional, which outputs energy values when given Kohn–Sham orbitals and nuclear positions. === Orthogonality constraint === ∫ d r ψ i ∗ ( r , t ) ψ j ( r , t ) = δ i j , {\displaystyle \int d\mathbf {r} \ \psi _{i}^{}(\mathbf {r} ,t)\psi _{j}(\mathbf {r} ,t)=\delta _{ij},} where δij is the Kronecker delta. === Equations of motion === The equations of motion are obtained by finding the stationary point of the Lagrangian under variations of ψi and RI, with the orthogonality constraint. M I R ¨ I = − ∇ I E [ { ψ i } , { R I } ] {\displaystyle M_{I}{\ddot {\mathbf {R} }}_{I}=-\nabla _{I}\,E\left[\{\psi _{i}\},\{\mathbf {R} _{I}\}\right]} μ ψ ¨ i ( r , t ) = − δ E δ ψ i ∗ ( r , t ) + ∑ j Λ i j ψ j ( r , t ) , {\displaystyle \mu {\ddot {\psi }}_{i}(\mathbf {r} ,t)=-{\frac {\delta E}{\delta \psi _{i}^{}(\mathbf {r} ,t)}}+\sum _{j}\Lambda _{ij}\psi _{j}(\mathbf {r} ,t),} where Λij is a Lagrangian multiplier matrix to comply with the orthonormality constraint. === Born–Oppenheimer limit === In the formal limit where μ → 0, the equations of motion approach Born–Oppenheimer molecular dynamics. == Software packages == There are a number of software packages available for performing AIMD simulations. Some of the most widely used packages include: CP2K: an open-source software package for AIMD. Quantum Espresso: an open-source package for performing DFT calculations. It includes a module for AIMD. VASP: a commercial software package for performing DFT calculations. It includes a module for AIMD. Gaussian: a commercial software package that can perform AIMD. NWChem: an open-source software package for AIMD. LAMMPS: an open-source software package for performing classical and ab initio MD simulations. SIESTA: an open-source software package for AIMD. ORCA: a general-purpose quantum chemistry package. == Applications == Studying the behavior of water across different environments, such as near a hydrophobic graphene sheet. Investigating the structure and dynamics of liquid water at ambient temperature. Solving the heat transfer problems (heat conduction and thermal radiation), such as in Si/Ge superlattices. Probing the proton transfer along hydrogen-bonds in different environments, such as in 1D water chains inside carbon nanotubes. Evaluating the critical point of crystals, composites, and solid-state materials, such as aluminum. Predicting and modelling different phases and phase transitions, such as in the amorphous phase of the phase-change memory material GeSbTe. Studying the combustion of combustibles, such as lignite-water systems. Measuring th
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In computer displays, filmmaking, television production, video games and other kinetic displays, scrolling is sliding text, images or video across a monitor or display, vertically or horizontally. "Scrolling," as such, does not change the layout of the text or pictures but moves (pans or tilts) the user's view across what is apparently a larger image that is not wholly seen. A common television and movie special effect is to scroll credits, while leaving the background stationary. Scrolling may take place completely without user intervention (as in film credits) or, on an interactive device, be triggered by touchscreen or a keypress and continue without further intervention until a further user action, or be entirely controlled by input devices. Scrolling may take place in discrete increments (perhaps one or a few lines of text at a time), or continuously (smooth scrolling). Frame rate is the speed at which an entire image is redisplayed. It is related to scrolling in that changes to text and image position can only happen as often as the image can be redisplayed. When frame rate is a limiting factor, one smooth scrolling technique is to blur images during movement that would otherwise appear to "jump". == Computing == === Implementation === Scrolling is often carried out on a computer by the CPU (software scrolling) or by a graphics processor. Some systems feature hardware scrolling, where an image may be offset as it is displayed, without any frame buffer manipulation (see also hardware windowing). This was especially common in 8 and 16bit video game consoles. === UI paradigms === In a WIMP-style graphical user interface (GUI), user-controlled scrolling is carried out by manipulating a scrollbar with a mouse, or using keyboard shortcuts, often the arrow keys. Scrolling is often supported by text user interfaces and command line interfaces. Older computer terminals changed the entire contents of the display one screenful ("page") at a time; this paging mode requires fewer resources than scrolling. Scrolling displays often also support page mode. Typically certain keys or key combinations page up or down; on PC-compatible keyboards the page up and page down keys or the space bar are used; earlier computers often used control key combinations. Some computer mice have a scroll wheel, which scrolls the display, often vertically, when rolled; others have scroll balls or tilt wheels which allow both vertical and horizontal scrolling. Some software supports other ways of scrolling. Adobe Reader has a mode identified by a small hand icon ("hand tool") on the document, which can then be dragged by clicking on it and moving the mouse as if sliding a large sheet of paper. When this feature is implemented on a touchscreen it is called kinetic scrolling. Touch-screens often use inertial scrolling, in which the scrolling motion of an object continues in a decaying fashion after release of the touch, simulating the appearance of an object with inertia. An early implementation of such behavior was in the "Star7" PDA of Sun Microsystems ca. 1991–1992. Scrolling can be controlled in other software-dependent ways by a PC mouse. Some scroll wheels can be pressed down, functioning like a button. Depending on the software, this allows both horizontal and vertical scrolling by dragging in the direction desired; when the mouse is moved to the original position, scrolling stops. A few scroll wheels can also be tilted, scrolling horizontally in one direction until released. On touchscreen devices, scrolling is a multi-touch gesture, done by swiping a finger on the screen vertically in the direction opposite to where the user wants to scroll to. If any content is too wide to fit on a display, horizontal scrolling is required to view all of it. In applications such as graphics and spreadsheets there is often more content than can fit either the width or the height of the screen at a comfortable scale, and scrolling in both directions is necessary. === Infinite scrolling === In contrast to material divided into discrete pages, the web design approach of infinite scrolling dynamically adds new material to the user display, leading to a continuous, apparently bottomless or endless scrolling experience. === Text === In languages written horizontally, such as most Western languages, text documents longer than will fit on the screen are often displayed wrapped and sized to fit the screen width, and scrolled vertically to bring desired content into view. It is possible to display lines too long to fit the display without wrapping, scrolling horizontally to view each entire line. However, this requires inconvenient constant line-by-line scrolling, while vertical scrolling is only needed after reading a full screenful. Software such as word processors and web browsers normally uses word-wrapping to display as many words in a single line as will fit the width of the screen or window or, for text organised in columns, each column. === Demos === Scrolling texts, also referred to as scrolltexts or scrollers, played an important part in the birth of the computer demo culture. The software crackers often used their deep knowledge of computer platforms to transform the information that accompanied their releases into crack intros. The sole role of these intros was to scroll the text on the screen in an impressive way. == Film and television == Scrolling is commonly used to display the credits at the end of films and television programs. Scrolling is often used in the form of a news ticker towards the bottom of the picture for content such as television news, scrolling sideways across the screen, delivering short-form content. In the dynamic layout of kinetic typography, scrolling typography can scroll across the flat screen, or can appear to recede or advance. An iconic example is the Star Wars opening crawl inspired by the Flash Gordon serials. == Video games == In computer and video games, scrolling of a playing field allows the player to control an object in a large contiguous area. Early examples of this method include Taito's 1974 vertical-scrolling racing video game Speed Race, Sega's 1976 forward-scrolling racing games Moto-Cross (Fonz) and Road Race, and Super Bug. Previously the flip-screen method was used to indicate moving backgrounds. The Namco Galaxian arcade system board introduced with Galaxian in 1979 pioneered a sprite system that animated pre-loaded sprites over a scrolling background, which became the basis for Nintendo's Radar Scope and Donkey Kong arcade hardware and home consoles such as the Nintendo Entertainment System. Parallax scrolling, which was first featured in Moon Patrol, involves several semi-transparent layers (called playfields), which scroll on top of each other at varying rates in order to give an early pseudo-3D illusion of depth. Belt scrolling is a method used in side-scrolling beat 'em up games with a downward camera angle where players can move up and down in addition to left and right. == Studies == A 1993 article by George Fitzmaurice studied spatially aware palmtop computers. These devices had a 3D sensor, and moving the device caused the contents to move as if the contents were fixed in place. This interaction could be referred to as “moving to scroll.” Also, if the user moved the device away from their body, they would zoom in; conversely, the device would zoom out if the user pulled the device closer to them. Smartphone cameras and “optical flow” image analysis utilize this technique nowadays. A 1996 research paper by Jun Rekimoto analyzed tilting operations as scrolling techniques on small screen interfaces. Users could not only tilt to scroll, but also tilt to select menu items. These techniques proved especially useful for field workers, since they only needed to hold and control the device with one hand. A study from 2013 by Selina Sharmin, Oleg Špakov, and Kari-Jouko Räihä explored the action of reading text on a screen while the text auto-scrolls based on the user's eye tracking patterns. The control group simply read text on a screen and manually scrolled. The study found that participants preferred to read primarily at the top of the screen, so the screen scrolled down whenever participants’ eyes began to look toward the bottom of the screen. This auto-scrolling caused no statistically significant difference in reading speed or performance. An undated study occurring during or after 2010 by Dede Frederick, James Mohler, Mihaela Vorvoreanu, and Ronald Glotzbach noted that parallax scrolling "may cause certain people to experience nausea."
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An algorithmic paradigm or algorithm design paradigm is a generic model or framework which underlies the design of a class of algorithms. An algorithmic paradigm is an abstraction higher than the notion of an algorithm, just as an algorithm is an abstraction higher than a computer program. == List of well-known paradigms == === General === Backtracking Branch and bound Brute-force search Divide and conquer Dynamic programming Greedy algorithm Recursion Prune and search === Parameterized complexity === Kernelization Iterative compression === Computational geometry === Sweep line algorithms Rotating calipers Randomized incremental construction
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ISO 15926 is a standard for data integration, sharing, exchange, and hand-over between computer systems. The title, "Industrial automation systems and integration—Integration of life-cycle data for process plants including oil and gas production facilities", is regarded too narrow by the present ISO 15926 developers. Having developed a generic data model and reference data library for process plants, it turned out that this subject is already so wide, that actually any state information may be modelled with it. == History == In 1991 a European Union ESPRIT-, named ProcessBase, started. The focus of this research project was to develop a data model for lifecycle information of a facility that would suit the requirements of the process industries. At the time that the project duration had elapsed, a consortium of companies involved in the process industries had been established: EPISTLE (European Process Industries STEP Technical Liaison Executive). Initially individual companies were members, but later this changed into a situation where three national consortia were the only members: PISTEP (UK), POSC/Caesar (Norway), and USPI-NL (Netherlands). (later PISTEP merged into POSC/Caesar, and USPI-NL was renamed to USPI). EPISTLE took over the work of the ProcessBase project. Initially this work involved a standard called ISO 10303-221 (referred to as "STEP AP221"). In that AP221 we saw, for the first time, an Annex M with a list of standard instances of the AP221 data model, including types of objects. These standard instances would be for reference and would act as a knowledge base with knowledge about the types of objects. In the early nineties EPISTLE started an activity to extend Annex M to become a library of such object classes and their relationships: STEPlib. In the STEPlib activities a group of approx. 100 domain experts from all three member consortia, spread over the various expertises (e.g. Electrical, Piping, Rotating equipment, etc.), worked together to define the "core classes". The development of STEPlib was extended with many additional classes and relationships between classes and published as Open source data. Furthermore, the concepts and relation types from the AP221 and ISO 15926-2 data models were also added to the STEPlib dictionary. This resulted in the development of Gellish English, whereas STEPlib became the Gellish English dictionary. Gellish English is a structured subset of natural English and is a modeling language suitable for knowledge modeling, product modeling and data exchange. It differs from conventional modeling languages (meta languages) as used in information technology as it not only defines generic concepts, but also includes an English dictionary. The semantic expression capability of Gellish English was significantly increased by extending the number of relation types that can be used to express knowledge and information. For modelling-technical reasons POSC/Caesar proposed another standard than ISO 10303, called ISO 15926. EPISTLE (and ISO) supported that proposal, and continued the modelling work, thereby writing Part 2 of ISO 15926. This Part 2 has official ISO IS (International Standard) status since 2003. POSC/Caesar started to put together their own RDL (Reference Data Library). They added many specialized classes, for example for ANSI (American National Standards Institute) pipe and pipe fittings. Meanwhile, STEPlib continued its existence, mainly driven by some members of USPI. Since it was clear that it was not in the interest of the industry to have two libraries for, in essence, the same set of classes, the Management Board of EPISTLE decided that the core classes of the two libraries shall be merged into Part 4 of ISO 15926. This merging process has been finished. Part 4 should act as reference data for part 2 of ISO 15926 as well as for ISO 10303-221 and replaced its Annex M. On June 5, 2007 ISO 15926-4 was signed off as a TS (Technical Specification). In 1999 the work on an earlier version of Part 7 started. Initially this was based on XML Schema (the only useful W3C Recommendation available then), but when Web Ontology Language (OWL) became available it was clear that provided a far more suitable environment for Part 7. Part 7 passed the first ISO ballot by the end of 2005, and an implementation project started. A formal ballot for TS (Technical Specification) was planned for December 2007. However, it was decided then to split Part 7 into more than one part, because the scope was too wide. == Need for ISO15926 == In 2004, the National Institute of Standards and Technology (NIST) released a report on the impact of the lack of digital interoperability in the capital projects industry. The report estimated the cost of inadequate interoperability in the U.S. capital facilities industry to be $15.8 billion per year. This was considered likely to be a conservative figure. == The standard == ISO 15926 has thirteen parts (as of February 2022): Part 1 - Overview and fundamental principles Part 2 - Data model Part 3 - Reference data for geometry and topology Part 4 - Reference Data, the terms used within facilities for the process industry Part 6 - Methodology for the development and validation of reference data (under development) Part 7 - Template methodology Part 8 - OWL/RDF implementation Part 9 - Implementation standards, with the focus on standard web servers, web services, and security (under development) Part 10 - Conformance testing Part 11 - Methodology for simplified industrial usage of reference data (under development) Part 12 - Life cycle integration ontology in Web Ontology Language (OWL2) Part 13 - Integrated lifecycle asset planning === Description === The model and the library are suitable for representing lifecycle information about technical installations and their components. They can also be used for defining the terms used in product catalogs in e-commerce. Another, more limited, use of the standard is as a reference classification for harmonization purposes between shared databases and product catalogues that are not based on ISO 15926. The purpose of ISO 15926 is to provide a Lingua Franca for computer systems, thereby integrating the information produced by them. Although set up for the process industries with large projects involving many parties, and involving plant operations and maintenance lasting decades, the technology can be used by anyone willing to set up a proper vocabulary of reference data in line with Part 4. In Part 7 the concept of Templates is introduced. These are semantic constructs, using Part 2 entities, that represent a small piece of information. These constructs then are mapped to more efficient classes of n-ary relations that interlink the Nodes that are involved in the represented information. In Part 8 the Part 7 Templates are defined in OWL and instantiated in RDF. For validation and reasoning purposes all are represented in First-Order Logic as well. In Part 9 these Node and Template instances are stored in an RDF triple store, set up to a standard schema and an API. Each participating computer system maps its data from its internal format to such ISO-standard Node and Template instances. Data can be "handed over" from one triple store to another in cases where data custodianship is handed over (e.g. from a contractor to a plant owner, or from a manufacturer to the owners of the manufactured goods). Hand-over can be for a part of all data, whilst maintaining full referential integrity. Documents are user-definable. They are defined in XML Schema and they are, in essence, only a structure containing cells that make reference to instances of Templates. This represents a view on all lifecycle data: since the data model is a 4D (space-time) model, it is possible to present the data that was valid at any given point in time, thus providing a true historical record. It is expected that this will be used for Knowledge Mining. Data can be queried by means of SPARQL. In any implementation a restricted number of triple stores can be involved, with different access rights. This is done by means of creating a CPF Server (= Confederation of Participating Façades). An Ontology Browser allows for access to one or more triple stores in a given CPF, depending on the access rights. == Projects and applications == There are a number of projects working on the extension of the ISO 15926 standard in different application areas. === Capital-intensive projects === Within the application of Capital Intensive projects, some cooperating implementation projects are running: The DEXPI project: The objective of DEXPI is to develop and promote a general standard for the process industry covering all phases of the lifecycle of a (petro-)chemical plant, ranging from specification of functional requirements to assets in operation. Finalised projects include: The EDRC Project of FIATECH Capturing Equipment Data Requirements Using ISO 15926 and Assessing Conforma
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