AI App Apple Watch

AI App Apple Watch — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Data augmentation

    Data augmentation

    Data augmentation is a statistical technique which allows maximum likelihood estimation from incomplete data. Data augmentation has important applications in Bayesian analysis, and the technique is widely used in machine learning to reduce overfitting when training machine learning models, achieved by training models on several slightly-modified copies of existing data. == Synthetic oversampling techniques for traditional machine learning == Synthetic Minority Over-sampling Technique (SMOTE) is a method used to address imbalanced datasets in machine learning. In such datasets, the number of samples in different classes varies significantly, leading to biased model performance. For example, in a medical diagnosis dataset with 90 samples representing healthy individuals and only 10 samples representing individuals with a particular disease, traditional algorithms may struggle to accurately classify the minority class. SMOTE rebalances the dataset by generating synthetic samples for the minority class. For instance, if there are 100 samples in the majority class and 10 in the minority class, SMOTE can create synthetic samples by randomly selecting a minority class sample and its nearest neighbors, then generating new samples along the line segments joining these neighbors. This process helps increase the representation of the minority class, improving model performance. == Data augmentation for image classification == When convolutional neural networks grew larger in mid-1990s, there was a lack of data to use, especially considering that some part of the overall dataset should be spared for later testing. It was proposed to perturb existing data with affine transformations to create new examples with the same labels, which were complemented by so-called elastic distortions in 2003, and the technique was widely used as of 2010s. Data augmentation can enhance CNN performance and acts as a countermeasure against CNN profiling attacks. Data augmentation has become fundamental in image classification, enriching training dataset diversity to improve model generalization and performance. The evolution of this practice has introduced a broad spectrum of techniques, including geometric transformations, color space adjustments, and noise injection. === Geometric Transformations === Geometric transformations alter the spatial properties of images to simulate different perspectives, orientations, and scales. Common techniques include: Affine Transformation Rotation: Rotating images by a specified degree to help models recognize objects at various angles. Reflection: Reflecting images horizontally or vertically to introduce variability in orientation. Translation: Shifting images in different directions to teach models positional invariance. Scaling Shear Mapping Cropping: Removing sections of the image to focus on particular features or simulate closer views. Elastic Distortion Morphing within the same class: Generating new samples by applying morphing techniques between two images belonging to the same class, thereby increasing intra-class diversity. === Color Space Transformations === Color space transformations modify the color properties of images, addressing variations in lighting, color saturation, and contrast. Techniques include: Brightness Adjustment: Varying the image's brightness to simulate different lighting conditions. Contrast Adjustment: Changing the contrast to help models recognize objects under various clarity levels. Saturation Adjustment: Altering saturation to prepare models for images with diverse color intensities. Color Jittering: Randomly adjusting brightness, contrast, saturation, and hue to introduce color variability. === Noise Injection === Injecting noise into images simulates real-world imperfections, teaching models to ignore irrelevant variations. Techniques involve: Gaussian Noise: Adding Gaussian noise mimics sensor noise or graininess. Salt and Pepper Noise: Introducing black or white pixels at random simulates sensor dust or dead pixels. == Data augmentation for signal processing == Residual or block bootstrap can be used for time series augmentation. === Biological signals === Synthetic data augmentation is of paramount importance for machine learning classification, particularly for biological data, which tend to be high dimensional and scarce. The applications of robotic control and augmentation in disabled and able-bodied subjects still rely mainly on subject-specific analyses. Data scarcity is notable in signal processing problems such as for Parkinson's Disease Electromyography signals, which are difficult to source - Zanini, et al. noted that it is possible to use a generative adversarial network (in particular, a DCGAN) to perform style transfer in order to generate synthetic electromyographic signals that corresponded to those exhibited by sufferers of Parkinson's Disease. The approaches are also important in electroencephalography (brainwaves). Wang, et al. explored the idea of using deep convolutional neural networks for EEG-Based Emotion Recognition, results show that emotion recognition was improved when data augmentation was used. A common approach is to generate synthetic signals by re-arranging components of real data. Lotte proposed a method of "Artificial Trial Generation Based on Analogy" where three data examples x 1 , x 2 , x 3 {\displaystyle x_{1},x_{2},x_{3}} provide examples and an artificial x s y n t h e t i c {\displaystyle x_{synthetic}} is formed which is to x 3 {\displaystyle x_{3}} what x 2 {\displaystyle x_{2}} is to x 1 {\displaystyle x_{1}} . A transformation is applied to x 1 {\displaystyle x_{1}} to make it more similar to x 2 {\displaystyle x_{2}} , the same transformation is then applied to x 3 {\displaystyle x_{3}} which generates x s y n t h e t i c {\displaystyle x_{synthetic}} . This approach was shown to improve performance of a Linear Discriminant Analysis classifier on three different datasets. Current research shows great impact can be derived from relatively simple techniques. For example, Freer observed that introducing noise into gathered data to form additional data points improved the learning ability of several models which otherwise performed relatively poorly. Tsinganos et al. studied the approaches of magnitude warping, wavelet decomposition, and synthetic surface EMG models (generative approaches) for hand gesture recognition, finding classification performance increases of up to +16% when augmented data was introduced during training. More recently, data augmentation studies have begun to focus on the field of deep learning, more specifically on the ability of generative models to create artificial data which is then introduced during the classification model training process. In 2018, Luo et al. observed that useful EEG signal data could be generated by Conditional Wasserstein Generative Adversarial Networks (GANs) which was then introduced to the training set in a classical train-test learning framework. The authors found classification performance was improved when such techniques were introduced. === Mechanical signals === The prediction of mechanical signals based on data augmentation brings a new generation of technological innovations, such as new energy dispatch, 5G communication field, and robotics control engineering. In 2022, Yang et al. integrate constraints, optimization and control into a deep network framework based on data augmentation and data pruning with spatio-temporal data correlation, and improve the interpretability, safety and controllability of deep learning in real industrial projects through explicit mathematical programming equations and analytical solutions.

    Read more →
  • Communication-avoiding algorithm

    Communication-avoiding algorithm

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

    Read more →
  • Sieve of Eratosthenes

    Sieve of Eratosthenes

    In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime number, 2. The multiples of a given prime are generated as a sequence of numbers starting from that prime, with constant difference between them that is equal to that prime. This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime. Once all the multiples of each discovered prime have been marked as composites, the remaining unmarked numbers are primes. The earliest known reference to the sieve (Ancient Greek: κόσκινον Ἐρατοσθένους, kóskinon Eratosthénous) is in Nicomachus of Gerasa's Introduction to Arithmetic, an early 2nd-century CE book which attributes it to Eratosthenes of Cyrene, a 3rd-century BCE Greek mathematician, though describing the sieving by odd numbers instead of by primes. One of a number of prime number sieves, it is one of the most efficient ways to find all of the smaller primes. It may be used to find primes in arithmetic progressions. == Overview == A prime number is a natural number that has exactly two distinct natural number divisors: the number 1 and itself. To find all the prime numbers less than or equal to a given integer n by Eratosthenes's method: Create a list of consecutive integers from 2 through n: (2, 3, 4, ..., n). Initially, let p equal 2, the smallest prime number. Enumerate the multiples of p by counting in increments of p from 2p to n, and mark them in the list (these will be 2p, 3p, 4p, ...; the p itself should not be marked). Find the smallest number in the list greater than p that is not marked. If there was no such number, stop. Otherwise, let p now equal this new number (which is the next prime), and repeat from step 3. When the algorithm terminates, the numbers remaining not marked in the list are all the primes below n. The main idea here is that every value given to p will be prime, because if it were composite it would be marked as a multiple of some other, smaller prime. Note that some of the numbers may be marked more than once (e.g., 15 will be marked both for 3 and 5). The key property of the sieve is that only additions are needed, no multiplications or divisions are used. As a refinement, it is sufficient to mark the numbers in step 3 starting from p2, as all the smaller multiples of p will have already been marked at that point. This means that the algorithm is allowed to terminate in step 4 when p2 is greater than n. Another refinement is to initially list odd numbers only, (3, 5, ..., n), and count in increments of 2p in step 3, thus marking only odd multiples of p. This actually appears in the original algorithm. This can be generalized with wheel factorization, forming the initial list only from numbers coprime with the first few primes and not just from odds (i.e., numbers coprime with 2), and counting in the correspondingly adjusted increments so that only such multiples of p are generated that are coprime with those small primes, in the first place. === Example === To find all the prime numbers less than or equal to 30, proceed as follows. First, generate a list of natural numbers from 2 to 30: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 The first number in the list is 2; cross out every 2nd number in the list after 2 by counting up from 2 in increments of 2 (these will be all the multiples of 2 in the list): 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 The next number in the list after 2 is 3; cross out every 3rd number in the list after 3 by counting up from 3 in increments of 3 (these will be all the multiples of 3 in the list): 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 The next number not yet crossed out in the list after 3 is 5; cross out every 5th number in the list after 5 by counting up from 5 in increments of 5 (i.e. all the multiples of 5): 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 The next number not yet crossed out in the list after 5 is 7; the next step would be to cross out every 7th number in the list after 7, but they are all already crossed out at this point, as these numbers (14, 21, 28) are also multiples of smaller primes because 7 × 7 is greater than 30. The numbers not crossed out at this point in the list are all the prime numbers below 30: 2 3 5 7 11 13 17 19 23 29 == Algorithm and variants == === Pseudocode === The sieve of Eratosthenes can be expressed in pseudocode, as follows: algorithm Sieve of Eratosthenes is input: an integer n > 1. output: all prime numbers from 2 through n. let A be an array of Boolean values, indexed by integers 2 to n, initially all set to true. for i = 2, 3, 4, ..., not exceeding √n do if A[i] is true for j = i2, i2+i, i2+2i, i2+3i, ..., not exceeding n do set A[j] := false return all i such that A[i] is true. This algorithm produces all primes not greater than n. It includes a common optimization, which is to start enumerating the multiples of each prime i from i2. The time complexity of this algorithm is O(n log log n), provided the array update is an O(1) operation, as is usually the case. === Segmented sieve === As Sorenson notes, the problem with the sieve of Eratosthenes is not the number of operations it performs but rather its memory requirements. For large n, the range of primes may not fit in memory; worse, even for moderate n, its cache use is highly suboptimal. The algorithm walks through the entire array A, exhibiting almost no locality of reference. A solution to these problems is offered by segmented sieves, where only portions of the range are sieved at a time. These have been known since the 1970s, and work as follows: Divide the range 2 through n into segments of some size Δ ≥ √n. Find the primes in the first (i.e. the lowest) segment, using the regular sieve. For each of the following segments, in increasing order, with m being the segment's topmost value, find the primes in it as follows: Set up a Boolean array of size Δ. Mark as non-prime the positions in the array corresponding to the multiples of each prime p ≤ √m found so far, by enumerating its multiples in steps of p starting from the lowest multiple of p between m - Δ and m. The remaining non-marked positions in the array correspond to the primes in the segment. It is not necessary to mark any multiples of these primes, because all of these primes are larger than √m, as for k ≥ 1, one has ( k Δ + 1 ) 2 > ( k + 1 ) Δ {\displaystyle (k\Delta +1)^{2}>(k+1)\Delta } . If Δ is chosen to be √n, the space complexity of the algorithm is O(√n), while the time complexity is the same as that of the regular sieve. For ranges with upper limit n so large that the sieving primes below √n as required by the page segmented sieve of Eratosthenes cannot fit in memory, a slower but much more space-efficient sieve like the pseudosquares prime sieve, developed by Jonathan P. Sorenson, can be used instead. === Incremental sieve === An incremental formulation of the sieve generates primes indefinitely (i.e., without an upper bound) by interleaving the generation of primes with the generation of their multiples (so that primes can be found in gaps between the multiples), where the multiples of each prime p are generated directly by counting up from the square of the prime in increments of p (or 2p for odd primes). The generation must be initiated only when the prime's square is reached, to avoid adverse effects on efficiency. It can be expressed symbolically under the dataflow paradigm as primes = [2, 3, ...] \ [[p², p²+p, ...] for p in primes], using list comprehension notation with \ denoting set subtraction of arithmetic progressions of numbers. Primes can also be produced by iteratively sieving out the composites through divisibility testing by sequential primes, one prime at a time. It is not the sieve of Eratosthenes but is often confused with it, even though the sieve of Eratosthenes directly generates the composites instead of testing for them. Trial division has worse theoretical complexity than that of the sieve of Eratosthenes in generating ranges of primes. When testing each prime, the optimal trial division algorithm uses all prime numbers not exceeding its square root, whereas the sieve of Eratosthenes produces each composite from its prime factors only, and gets the primes "for free", between the composites. The widely known 1975 functional sieve code by David Turner is often presented as an example of the sieve of Eratosthenes but is actually a sub-optimal trial division sieve. == Algorithmic complexity == The sieve of Eratosthenes is a popular way to benchmark computer performance. The time complexity of calculating all primes below n in the random access machine model is O(n log log n) ope

    Read more →
  • Energy informatics

    Energy informatics

    Energy informatics is a research field covering the use of information and communication technology to address energy utilization and management challenges. Methods used for "smart" implementations often combine IoT sensors with artificial intelligence and machine learning. Energy Informatics is founded on flow networks that are the major suppliers and consumers of energy. Their efficiency can be improved by collecting and analyzing information. == Application areas == The field among other consider application areas within: Smart Buildings by developing ICT-centred solutions for improving the energy-efficiency of buildings. Smart Cities by investigating the synergies between demand patterns and supply availability of energy flows in cities and communities to improve energy efficiency, increase integration of renewable sources, and provide resilience towards system faults caused by extreme situations, like hurricanes and flooding. Smart Industries including the development of ICT-centred solutions for improving the energy efficiency and predictability of energy intensive industrial processes, without compromising process and product quality. Smart Energy Networks by developing ICT-centred solutions for coordinating the supply and demand in environmentally sustainable energy networks.

    Read more →
  • Global serializability

    Global serializability

    In concurrency control of databases, transaction processing (transaction management), and other transactional distributed applications, global serializability (or modular serializability) is a property of a global schedule of transactions. A global schedule is the unified schedule of all the individual database (and other transactional object) schedules in a multidatabase environment (e.g., federated database). Complying with global serializability means that the global schedule is serializable, has the serializability property, while each component database (module) has a serializable schedule as well. In other words, a collection of serializable components provides overall system serializability, which is usually incorrect. A need in correctness across databases in multidatabase systems makes global serializability a major goal for global concurrency control (or modular concurrency control). With the proliferation of the Internet, Cloud computing, Grid computing, and small, portable, powerful computing devices (e.g., smartphones), as well as increase in systems management sophistication, the need for atomic distributed transactions and thus effective global serializability techniques, to ensure correctness in and among distributed transactional applications, seems to increase. In a federated database system or any other more loosely defined multidatabase system, which are typically distributed in a communication network, transactions span multiple (and possibly distributed) databases. Enforcing global serializability in such system, where different databases may use different types of concurrency control, is problematic. Even if every local schedule of a single database is serializable, the global schedule of a whole system is not necessarily serializable. The massive communication exchanges of conflict information needed between databases to reach conflict serializability globally would lead to unacceptable performance, primarily due to computer and communication latency. Achieving global serializability effectively over different types of concurrency control has been open for several years. == The global serializability problem == === Problem statement === The difficulties described above translate into the following problem: Find an efficient (high-performance and fault tolerant) method to enforce Global serializability (global conflict serializability) in a heterogeneous distributed environment of multiple autonomous database systems. The database systems may employ different concurrency control methods. No limitation should be imposed on the operations of either local transactions (confined to a single database system) or global transactions (span two or more database systems). === Quotations === Lack of an appropriate solution for the global serializability problem has driven researchers to look for alternatives to serializability as a correctness criterion in a multidatabase environment (e.g., see Relaxing global serializability below), and the problem has been characterized as difficult and open. The following two quotations demonstrate the mindset about it by the end of the year 1991, with similar quotations in numerous other articles: "Without knowledge about local as well as global transactions, it is highly unlikely that efficient global concurrency control can be provided... Additional complications occur when different component DBMSs [Database Management Systems] and the FDBMSs [Federated Database Management Systems] support different concurrency mechanisms... It is unlikely that a theoretically elegant solution that provides conflict serializability without sacrificing performance (i.e., concurrency and/or response time) and availability exists." === Proposed solutions === Several solutions, some partial, have been proposed for the global serializability problem. Among them: Global conflict graph (serializability graph, precedence graph) checking Distributed Two-phase locking (Distributed 2PL) Distributed Timestamp ordering Tickets (local logical timestamps which define local total orders, and are propagated to determine global partial order of transactions) == Relaxing global serializability == Some techniques have been developed for relaxed global serializability (i.e., they do not guarantee global serializability; see also Relaxing serializability). Among them (with several publications each): Quasi serializability Two-level serializability Another common reason nowadays for Global serializability relaxation is the requirement of availability of internet products and services. This requirement is typically answered by large scale data replication. The straightforward solution for synchronizing replicas' updates of a same database object is including all these updates in a single atomic distributed transaction. However, with many replicas such a transaction is very large, and may span several computers and networks that some of them are likely to be unavailable. Thus such a transaction is likely to end with abort and miss its purpose. Consequently, Optimistic replication (Lazy replication) is often utilized (e.g., in many products and services by Google, Amazon, Yahoo, and alike), while global serializability is relaxed and compromised for eventual consistency. In this case relaxation is done only for applications that are not expected to be harmed by it. Classes of schedules defined by relaxed global serializability properties either contain the global serializability class, or are incomparable with it. What differentiates techniques for relaxed global conflict serializability (RGCSR) properties from those of relaxed conflict serializability (RCSR) properties that are not RGCSR is typically the different way global cycles (span two or more databases) in the global conflict graph are handled. No distinction between global and local cycles exists for RCSR properties that are not RGCSR. RCSR contains RGCSR. Typically RGCSR techniques eliminate local cycles, i.e., provide local serializability (which can be achieved effectively by regular, known concurrency control methods); however, obviously they do not eliminate all global cycles (which would achieve global serializability).

    Read more →
  • Irish logarithm

    Irish logarithm

    The Irish logarithm was a system of number manipulation invented by Percy Ludgate for machine multiplication. The system used a combination of mechanical cams as lookup tables and mechanical addition to sum pseudo-logarithmic indices to produce partial products, which were then added to produce results. The technique is similar to Zech logarithms (also known as Jacobi logarithms), but uses a system of indices original to Ludgate. == Concept == Ludgate's algorithm compresses the multiplication of two single decimal numbers into two table lookups (to convert the digits into indices), the addition of the two indices to create a new index which is input to a second lookup table that generates the output product. Because both lookup tables are one-dimensional, and the addition of linear movements is simple to implement mechanically, this allows a less complex mechanism than would be needed to implement a two-dimensional 10×10 multiplication lookup table. Ludgate stated that he deliberately chose the values in his tables to be as small as he could make them; given this, Ludgate's tables can be simply constructed from first principles, either via pen-and-paper methods, or a systematic search using only a few tens of lines of program code. They do not correspond to either Zech logarithms, Remak indexes or Korn indexes. == Pseudocode == The following is an implementation of Ludgate's Irish logarithm algorithm in the Python programming language: Table 1 is taken from Ludgate's original paper; given the first table, the contents of Table 2 can be trivially derived from Table 1 and the definition of the algorithm. Note since that the last third of the second table is entirely zeros, this could be exploited to further simplify a mechanical implementation of the algorithm.

    Read more →
  • Algorism

    Algorism

    Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist. This positional notation system has largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude, such as Roman numerals, and in some cases required a device such as an abacus. == Etymology == The word algorism comes from the name Al-Khwārizmī (c. 780–850), a Persian mathematician, astronomer, geographer and scholar in the House of Wisdom in Baghdad, whose name means "the native of Khwarezm", which is now in modern-day Uzbekistan. He wrote a treatise in Arabic language in the 9th century, which was translated into Latin in the 12th century under the title Algoritmi de numero Indorum. This title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name. Al-Khwarizmi was the most widely read mathematician in Europe in the late Middle Ages, primarily through his other book, the Algebra. In late medieval Latin, algorismus, the corruption of his name, simply meant the "decimal number system" that is still the meaning of modern English algorism. During the 17th century, the French form for the word – but not its meaning – was changed to algorithm, following the model of the word logarithm, this form alluding to the ancient Greek arithmos = number. English adopted the French very soon afterwards, but it wasn't until the late 19th century that "algorithm" took on the meaning that it has in modern English. In English, it was first used about 1230 and then by Chaucer in 1391. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu. It begins thus: Haec algorismus ars praesens dicitur, in qua / Talibus Indorum fruimur bis quinque figuris. which translates as: This present art, in which we use those twice five Indian figures, is called algorismus. The word algorithm also derives from algorism, a generalization of the meaning to any set of rules specifying a computational procedure. Occasionally algorism is also used in this generalized meaning, especially in older texts. == History == Starting with the integer arithmetic developed in India using base 10 notation, Al-Khwārizmī along with other mathematicians in medieval Islam, documented new arithmetic methods and made many other contributions to decimal arithmetic (see the articles linked below). These included the concept of the decimal fractions as an extension of the notation, which in turn led to the notion of the decimal point. This system was popularized in Europe by Leonardo of Pisa, now known as Fibonacci.

    Read more →
  • Hybrid algorithm

    Hybrid algorithm

    A hybrid algorithm is an algorithm that combines two or more other algorithms that solve the same problem, either choosing one based on some characteristic of the data, or switching between them over the course of the algorithm. This is generally done to combine desired features of each, so that the overall algorithm is better than the individual components. "Hybrid algorithm" does not refer to simply combining multiple algorithms to solve a different problem – many algorithms can be considered as combinations of simpler pieces – but only to combining algorithms that solve the same problem, but differ in other characteristics, notably performance. == Examples == In computer science, hybrid algorithms are very common in optimized real-world implementations of recursive algorithms, particularly implementations of divide-and-conquer or decrease-and-conquer algorithms, where the size of the data decreases as one moves deeper in the recursion. In this case, one algorithm is used for the overall approach (on large data), but deep in the recursion, it switches to a different algorithm, which is more efficient on small data. A common example is in sorting algorithms, where the insertion sort, which is inefficient on large data, but very efficient on small data (say, five to ten elements), is used as the final step, after primarily applying another algorithm, such as merge sort or quicksort. Merge sort and quicksort are asymptotically optimal on large data, but the overhead becomes significant if applying them to small data, hence the use of a different algorithm at the end of the recursion. A highly optimized hybrid sorting algorithm is Timsort, which combines merge sort, insertion sort, together with additional logic (including binary search) in the merging logic. A general procedure for a simple hybrid recursive algorithm is short-circuiting the base case, also known as arm's-length recursion. In this case whether the next step will result in the base case is checked before the function call, avoiding an unnecessary function call. For example, in a tree, rather than recursing to a child node and then checking if it is null, checking null before recursing. This is useful for efficiency when the algorithm usually encounters the base case many times, as in many tree algorithms, but is otherwise considered poor style, particularly in academia, due to the added complexity. Another example of hybrid algorithms for performance reasons are introsort and introselect, which combine one algorithm for fast average performance, falling back on another algorithm to ensure (asymptotically) optimal worst-case performance. Introsort begins with a quicksort, but switches to a heap sort if quicksort is not progressing well; analogously introselect begins with quickselect, but switches to median of medians if quickselect is not progressing well. Centralized distributed algorithms can often be considered as hybrid algorithms, consisting of an individual algorithm (run on each distributed processor), and a combining algorithm (run on a centralized distributor) – these correspond respectively to running the entire algorithm on one processor, or running the entire computation on the distributor, combining trivial results (a one-element data set from each processor). A basic example of these algorithms are distribution sorts, particularly used for external sorting, which divide the data into separate subsets, sort the subsets, and then combine the subsets into totally sorted data; examples include bucket sort and flashsort. However, in general distributed algorithms need not be hybrid algorithms, as individual algorithms or combining or communication algorithms may be solving different problems. For example, in models such as MapReduce, the Map and Reduce step solve different problems, and are combined to solve a different, third problem.

    Read more →
  • Machine learning

    Machine learning

    Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of statistical algorithms that can learn from data and generalize to unseen data, and thus perform tasks without being explicitly programmed. Advances in the field of deep learning have allowed neural networks, a class of statistical algorithms, to surpass many previous machine learning approaches in performance. Statistics and mathematical optimisation methods compose the foundations of machine learning. Data mining is a related field of study, focusing on exploratory data analysis (EDA) through unsupervised learning. From a theoretical viewpoint, probably approximately correct learning provides a mathematical and statistical framework for describing machine learning. Most traditional machine learning and deep learning algorithms can be described as empirical risk minimisation under this framework. == History == The term machine learning was coined in 1959 by Arthur Samuel, an IBM employee and pioneer in the field of computer gaming and artificial intelligence. The synonym self-teaching computers was also used during this time period. The earliest machine learning program was introduced in the 1950s, when Samuel invented a computer program that calculated the chance of winning in checkers for each side, but the history of machine learning is rooted in decades of efforts to study human cognitive processes. In 1949, Canadian psychologist Donald Hebb published the book The Organization of Behavior, in which he introduced a theoretical neural structure formed by certain interactions among nerve cells. The Hebbian theory of neuron interaction set the groundwork for how many machine learning algorithms work, with connected artificial neurons changing the strength of their connections based on data. Other researchers who have studied human cognitive systems contributed to the modern machine learning technologies as well, including Walter Pitts and Warren McCulloch, who proposed the first mathematical model of neural networks including algorithms that mirror human thought processes. By the early 1960s, an experimental "learning machine" with punched tape memory, called Cybertron, had been developed by Raytheon Company to analyse sonar signals, electrocardiograms, and speech patterns using rudimentary reinforcement learning. It was repetitively "trained" by a human operator/teacher to recognise patterns and equipped with a "goof" button to cause it to reevaluate incorrect decisions. A representative book on research into machine learning during the 1960s was Nils Nilsson's book "Learning Machines", dealing mostly with machine learning for pattern classification. Interest related to pattern recognition continued into the 1970s, as described by Duda and Hart in 1973. In 1981, a report was given on using teaching strategies so that an artificial neural network learns to recognise 40 characters (26 letters, 10 digits, and 4 special symbols) from a computer terminal. Tom M. Mitchell provided a widely quoted, more formal definition of the algorithms studied in the machine learning field: "A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P if its performance at tasks in T, as measured by P, improves with experience E." This definition of the tasks in which machine learning is concerned is fundamentally operational rather than defining the field in cognitive terms. This follows Alan Turing's proposal in his paper "Computing Machinery and Intelligence", in which the question, "Can machines think?", is replaced by asking whether machines can convincingly imitate a human in its responses to human-posed questions. In 2014 Ian Goodfellow and others introduced generative adversarial networks (GANs) which could produce realistic synthetic data. By 2016 AlphaGo had won against top human players in Go using reinforcement learning techniques. == Relationships to other fields == === Artificial intelligence === As a scientific endeavour, machine learning grew out of the quest for artificial intelligence (AI). In the early days of AI as an academic discipline, some researchers were interested in having machines learn from data. They attempted to approach the problem with various symbolic methods, as well as what were then termed "neural networks"; these were mostly perceptrons and other models that were later found to be reinventions of the generalised linear models of statistics. Probabilistic reasoning was also employed, especially in automated medical diagnosis. However, an increasing emphasis on the logical, knowledge-based approach caused a rift between AI and machine learning. Probabilistic systems were plagued by theoretical and practical problems of data acquisition and representation. By 1980, expert systems had come to dominate AI, and statistics was out of favour. Work on symbolic/knowledge-based learning continued within AI, leading to inductive logic programming (ILP), but the more statistical line of research was now outside the field of AI proper, in pattern recognition and information retrieval. Neural network research was abandoned by AI and computer science around the same time. This subfield, termed "connectionism", was continued by researchers from other disciplines, including John Hopfield, David Rumelhart, and Geoffrey Hinton. Their main success came in the mid-1980s with the reinvention of backpropagation. Machine learning (ML), reorganised and recognised as its own field, started to flourish in the 1990s. The field changed its goal from achieving artificial intelligence to tackling solvable problems of a practical nature. It shifted focus away from the symbolic approaches it had inherited from AI, and toward methods and models borrowed from statistics, fuzzy logic, and probability theory. === Data compression === === Data mining === Machine learning and data mining often employ the same methods and overlap significantly, but while machine learning focuses on prediction based on known properties learned from the training data, data mining focuses on the discovery of previously unknown properties in the data (this is the analysis step of knowledge discovery in databases). Data mining uses many machine learning methods, but with different goals; on the other hand, machine learning also employs data mining methods as "unsupervised learning" or as a preprocessing step to improve learner accuracy. Much of the confusion between these two research communities comes from the basic assumptions they work with: in machine learning, performance is usually evaluated with respect to the ability to reproduce known knowledge, while in knowledge discovery and data mining (KDD) the key task is the discovery of previously unknown knowledge. Evaluated with respect to known knowledge, an uninformed (unsupervised) method will easily be outperformed by other supervised methods, while in a typical KDD task, supervised methods cannot be used due to the unavailability of training data. Machine learning also has intimate ties to optimization: Many learning problems are formulated as minimisation of some loss function on a training set of examples. Loss functions express the discrepancy between the predictions of the model being trained and the actual problem instances (for example, in classification, one wants to assign a label to instances, and models are trained to correctly predict the preassigned labels of a set of examples). === Generalization === Characterizing the generalisation of various learning algorithms is an active topic of current research, especially for deep learning algorithms. === Statistics === Machine learning and statistics are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population inferences from a sample, while machine learning finds generalisable predictive patterns. Conventional statistical analyses require the a priori selection of a model most suitable for the study data set. In addition, only significant or theoretically relevant variables based on previous experience are included for analysis. In contrast, machine learning is not built on a pre-structured model; rather, the data shape the model by detecting underlying patterns. The more variables (input) used to train the model, the more accurate the ultimate model will be. Leo Breiman distinguished two statistical modelling paradigms: the data model and the algorithmic model, wherein "algorithmic model" means more or less the machine learning algorithms like Random forest. Some statisticians have adopted methods from machine learning, producing the field of statistical learning. === Statistical physics === Analytical and computational techniques derived from deep-rooted physics of disordered systems can be extended to large-scale problems, including machine learning, e.g., to analyse the weight space of deep neural networks. Statistical physics is thus

    Read more →
  • Information architecture

    Information architecture

    Information architecture is the structural design of shared information environments, in particular the organisation of websites and software to support usability and findability. The term information architecture was coined by Richard Saul Wurman. Since its inception, information architecture has become an emerging community of practice focused on applying principles of design, architecture and information science in digital spaces. Typically, a model or concept of information is used and applied to activities which require explicit details of complex information systems. These activities include library systems and database development. == Definition == The term information architecture has different meanings in different branches of information systems or information technology. === User experience === In user experience design, information architecture has been described as the structural design of shared information environments, comprising the study and practice of organising and labelling web sites, intranets, online communities, and software to support user experience, in particular, the findability and usability of information. It has also been described as an emerging community of practice focused on bringing principles of design and architecture to the digital landscape. === Information systems === Technically speaking, information architecture comprises the combination of organization, labeling, search and navigation systems within websites and intranets, serving as a navigational aid to the content of information-rich systems. === Data architecture === Information architecture can be described as a subset of data architecture where usable data is constructed, designed, and arranged in a fashion most useful to the users of data. === Systems design === In the field of systems design, for example, information architecture is a component of enterprise architecture that deals with the information component when describing the structure of an enterprise. Some system design practitioners regard information architecture as strictly the application of information science to web design, which considers such issues as classification and information retrieval, and not factors like user experience and information design. == Principles == Principles of information architecture include the following: The principle of objects The principle of choices The principle of disclosure The principle of exemplars The principle of front doors The principle of multiple classification The principle of focused navigation The principle of growth == History == Richard Saul Wurman is credited with coining the term information architecture in relation to the design of information. From 1998 to 2015, Peter Morville and Louis Rosenfeld were co-authors of Information Architecture for the World Wide Web. Other authors include Jesse James Garrett and Christina Wodtke.

    Read more →
  • Concordance (publishing)

    Concordance (publishing)

    A concordance is an alphabetical list of the principal words used in a book or body of work, listing every instance of each word with its immediate context. Historically, concordances have been compiled only for works of special importance, such as the Vedas, Bible, Qur'an or the works of Shakespeare, James Joyce or classical Latin and Greek authors, because of the time, difficulty, and expense involved in creating a concordance in the pre-computer era. A concordance is more than an index, with additional material such as commentary, definitions and topical cross-indexing which makes producing one a labor-intensive process even when assisted by computers. In the precomputing era, search technology was unavailable, and a concordance offered readers of long works such as the Bible something comparable to search results for every word that they would have been likely to search for. Today, the ability to combine the result of queries concerning multiple terms (such as searching for words near other words) has reduced interest in concordance publishing. In addition, mathematical techniques such as latent semantic indexing have been proposed as a means of automatically identifying linguistic information based on word context. A bilingual concordance is a concordance based on aligned parallel text. A topical concordance is a list of subjects that a book covers (usually The Bible), with the immediate context of the coverage of those subjects. Unlike a traditional concordance, the indexed word does not have to appear in the verse. The best-known topical concordance is Nave's Topical Bible. The first Bible concordance was compiled for the Vulgate Bible by Hugh of St Cher (d.1262), who employed 500 friars to assist him. In 1448, Rabbi Mordecai Nathan completed a concordance to the Hebrew Bible. It took him ten years. A concordance to the Greek New Testament was published in 1546 by Sixt Birck, and the Septuagint was done a by Conrad Kircher in 1602. The first concordance to the English Bible was published in 1550 by John Merbecke. According to Cruden, it did not employ the verse numbers devised by Robert Stephens in 1545, but "the pretty large concordance" of Mr Cotton did. Then followed Cruden's Concordance and Strong's Concordance. == Use in linguistics == Concordances are frequently used in linguistics, when studying a text. For example: comparing different usages of the same word analysing keywords analysing word frequencies finding and analysing phrases and idioms finding translations of subsentential elements, e.g. terminology, in bitexts and translation memories creating indexes and word lists (also useful for publishing) Concordancing techniques are widely used in national text corpora such as American National Corpus (ANC), British National Corpus (BNC), and Corpus of Contemporary American English (COCA) available on-line. Stand-alone applications that employ concordancing techniques are known as concordancers or more advanced corpus managers. Some of them have integrated part-of-speech taggers (POS taggers) and enable the user to create their own POS-annotated corpora to conduct various types of searches adopted in corpus linguistics. == Inversion == The reconstruction of the text of some of the Dead Sea Scrolls involved a concordance. Access to some of the scrolls was governed by a "secrecy rule" that allowed only the original International Team or their designates to view the original materials. After the death of Roland de Vaux in 1971, his successors repeatedly refused to even allow the publication of photographs to other scholars. This restriction was circumvented by Martin Abegg in 1991, who used a computer to "invert" a concordance of the missing documents made in the 1950s which had come into the hands of scholars outside of the International Team, to obtain an approximate reconstruction of the original text of 17 of the documents. This was soon followed by the release of the original text of the scrolls.

    Read more →
  • Predictor–corrector method

    Predictor–corrector method

    In numerical analysis, predictor–corrector methods belong to a class of algorithms designed to integrate ordinary differential equations – to find an unknown function that satisfies a given differential equation. All such algorithms proceed in two steps: The initial, "prediction" step, starts from a function fitted to the function-values and derivative-values at a preceding set of points to extrapolate ("anticipate") this function's value at a subsequent, new point. The next, "corrector" step refines the initial approximation by using the predicted value of the function and another method to interpolate that unknown function's value at the same subsequent point. == Predictor–corrector methods for solving ODEs == When considering the numerical solution of ordinary differential equations (ODEs), a predictor–corrector method typically uses an explicit method for the predictor step and an implicit method for the corrector step. === Example: Euler method with the trapezoidal rule === A simple predictor–corrector method (known as Heun's method) can be constructed from the Euler method (an explicit method) and the trapezoidal rule (an implicit method). Consider the differential equation y ′ = f ( t , y ) , y ( t 0 ) = y 0 , {\displaystyle y'=f(t,y),\quad y(t_{0})=y_{0},} and denote the step size by h {\displaystyle h} . First, the predictor step: starting from the current value y i {\displaystyle y_{i}} , calculate an initial guess value y ~ i + 1 {\displaystyle {\tilde {y}}_{i+1}} via the Euler method, y ~ i + 1 = y i + h f ( t i , y i ) . {\displaystyle {\tilde {y}}_{i+1}=y_{i}+hf(t_{i},y_{i}).} Next, the corrector step: improve the initial guess using trapezoidal rule, y i + 1 = y i + 1 2 h ( f ( t i , y i ) + f ( t i + 1 , y ~ i + 1 ) ) . {\displaystyle y_{i+1}=y_{i}+{\tfrac {1}{2}}h{\bigl (}f(t_{i},y_{i})+f(t_{i+1},{\tilde {y}}_{i+1}){\bigr )}.} That value is used as the next step. === PEC mode and PECE mode === There are different variants of a predictor–corrector method, depending on how often the corrector method is applied. The Predict–Evaluate–Correct–Evaluate (PECE) mode refers to the variant in the above example: y ~ i + 1 = y i + h f ( t i , y i ) , y i + 1 = y i + 1 2 h ( f ( t i , y i ) + f ( t i + 1 , y ~ i + 1 ) ) . {\displaystyle {\begin{aligned}{\tilde {y}}_{i+1}&=y_{i}+hf(t_{i},y_{i}),\\y_{i+1}&=y_{i}+{\tfrac {1}{2}}h{\bigl (}f(t_{i},y_{i})+f(t_{i+1},{\tilde {y}}_{i+1}){\bigr )}.\end{aligned}}} It is also possible to evaluate the function f only once per step by using the method in Predict–Evaluate–Correct (PEC) mode: y ~ i + 1 = y i + h f ( t i , y ~ i ) , y i + 1 = y i + 1 2 h ( f ( t i , y ~ i ) + f ( t i + 1 , y ~ i + 1 ) ) . {\displaystyle {\begin{aligned}{\tilde {y}}_{i+1}&=y_{i}+hf(t_{i},{\tilde {y}}_{i}),\\y_{i+1}&=y_{i}+{\tfrac {1}{2}}h{\bigl (}f(t_{i},{\tilde {y}}_{i})+f(t_{i+1},{\tilde {y}}_{i+1}){\bigr )}.\end{aligned}}} Additionally, the corrector step can be repeated in the hope that this achieves an even better approximation to the true solution. If the corrector method is run twice, this yields the PECECE mode: y ~ i + 1 = y i + h f ( t i , y i ) , y ^ i + 1 = y i + 1 2 h ( f ( t i , y i ) + f ( t i + 1 , y ~ i + 1 ) ) , y i + 1 = y i + 1 2 h ( f ( t i , y i ) + f ( t i + 1 , y ^ i + 1 ) ) . {\displaystyle {\begin{aligned}{\tilde {y}}_{i+1}&=y_{i}+hf(t_{i},y_{i}),\\{\hat {y}}_{i+1}&=y_{i}+{\tfrac {1}{2}}h{\bigl (}f(t_{i},y_{i})+f(t_{i+1},{\tilde {y}}_{i+1}){\bigr )},\\y_{i+1}&=y_{i}+{\tfrac {1}{2}}h{\bigl (}f(t_{i},y_{i})+f(t_{i+1},{\hat {y}}_{i+1}){\bigr )}.\end{aligned}}} The PECEC mode has one fewer function evaluation than PECECE mode. More generally, if the corrector is run k times, the method is in P(EC)k or P(EC)kE mode. If the corrector method is iterated until it converges, this could be called PE(CE)∞.

    Read more →
  • Misskey

    Misskey

    Misskey (Japanese: ミスキー, romanized: Misukī) is an open source, federated, social networking service created in 2014 by Japanese software engineer Eiji "syuilo" Shinoda. Misskey uses the ActivityPub protocol for federation, allowing users to interact between independent Misskey instances, and other ActivityPub compatible platforms. Misskey is generally considered to be part of the Fediverse. Despite being a decentralized service, Misskey is not philosophically opposed to centralization. The name Misskey comes from the lyrics of Brain Diver, a song by the Japanese singer May'n. == History == Misskey was initially developed as a BBS-style internet forum by high school student Eiji Shinoda in 2014. After introducing a timeline feature, Misskey gained popularity as the microblogging platform it is today. In 2018, Misskey added support for ActivityPub, becoming a federated social media platform. The flagship Misskey server, Misskey.io, was started on April 15, 2019. Misskey, alongside Mastodon and Bluesky, has received attention as a potential replacement for Twitter following Twitter's acquisition by Elon Musk in 2022. On April 8, 2023, Misskey.io incorporated as MisskeyHQ K.K. As of February 2024, over 450,000 users were registered, making it the largest instance of Misskey. Misskey.io is crowdfunded. The administrator of Misskey.io is Japanese system administrator Yoshiki Eto, who operates under the alias Murakami-san. Eiji Shinoda serves as director. In July 2023, Twitter introduced extreme restrictions on their API in order to combat scraping from bots. Some users were critical of the changes, and as a result migrated to other social networks. The number of users registering on Misskey.io, Misskey's official instance and the largest one, increased rapidly, with other Misskey instances also receiving a spike in signups. In response to this trend, Skeb, a platform for sharing art, announced on July 14, 2023 that it would sponsor the Misskey development team. In early 2024, Misskey was targeted by a spam attack from Japan. The cause of the attack is believed to be a dispute between rival groups on a Japanese hacker forum and a DDoS attack on a Discord bot. Mastodon instances with open registration were used in the attack. In November 2025, Eto announced intentions to replace ActivityPub with Misskey's own low-overhead federation system in "a few years". Shinoda later said that this was "fake news". == Development == Misskey is open source software and is licensed under the AGPLv3. The Misskey API is publicly available and is documented using the OpenAPI Specification, which allows users to build automated accounts and use it on any Misskey instance. The service is translated using Crowdin. Misskey is developed using Node.js. TypeScript is used on both the frontend and backend. PostgreSQL is used as its database. Vue.js is used for the frontend. == Functionality == Posts on Misskey are called "notes". Notes are limited to a maximum of 3,000 characters (a limit which can be customized by instances), and can be accompanied by any file, including polls, images, videos, and audio. Notes can be reposted, either by themselves or with another "quote" note. Misskey comes with multiple timelines to sort through the notes that an instance has available, and are displayed in reverse chronological order. The Home timeline shows notes from users that you follow, the Local timeline shows all notes from the instance in use, the Social timeline shows both the Home and Local timeline, and the Global timeline shows every public note that the instance knows about. Notes have customizable privacy settings to control what users can see a note, similar to Mastodon's post visibility ranges. Public notes show up on all timelines, while Home notes only show on a user's Home timeline. Notes can also be set to be available only for followers. Direct messages using notes can be sent to users.

    Read more →
  • Ordered key–value store

    Ordered key–value store

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

    Read more →
  • SciDB

    SciDB

    SciDB is a column-oriented database management system (DBMS) designed for multidimensional data management and analytics common to scientific, geospatial, financial, and industrial applications. It is developed by Paradigm4 and co-created by Michael Stonebraker. == History == Stonebraker claims that arrays are 100 times faster in SciDB than in a relational DBMS on a class of problems. It is swapping rows and columns for mathematical arrays that put fewer restrictions on the data and can work in any number of dimensions unlike the conventionally widely used relational database management system model, in which each relation supports only one dimension of records. A 2011 conference presentation on SciDB promoted it as "not Hadoop". Marilyn Matz became chief executive Paradigm4 in 2014.

    Read more →