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Biorobotics

Biorobotics is an interdisciplinary science that combines the fields of biomedical engineering, cybernetics, and robotics to develop new technologies that integrate biology with mechanical systems to develop more efficient communication, alter genetic information, and create machines that imitate biological systems. == Cybernetics == Cybernetics focuses on the communication and system of living organisms and machines that can be applied and combined with multiple fields of study such as biology, mathematics, computer science, engineering, and much more. This discipline falls under the branch of biorobotics because of its combined field of study between biological bodies and mechanical systems. Studying these two systems allows for advanced analysis on the functions and processes of each system as well as the interactions between them. === History === Cybernetic theory is a concept that has existed for centuries, dating back to the era of Plato where he applied the term to refer to the "governance of people". The term cybernetique is seen in the mid-1800s used by physicist André-Marie Ampère. The term cybernetics was popularized in the late 1940s to refer to a discipline that touched on, but was separate, from established disciplines, such as electrical engineering, mathematics, and biology. === Science === Cybernetics is often misunderstood because of the breadth of disciplines it covers. In the early 20th century, it was coined as an interdisciplinary field of study that combines biology, science, network theory, and engineering. Today, it covers all scientific fields with system related processes. The goal of cybernetics is to analyze systems and processes of any system or systems in an attempt to make them more efficient and effective. === Applications === Cybernetics is used as an umbrella term so applications extend to all systems related scientific fields such as biology, mathematics, computer science, engineering, management, psychology, sociology, art, and more. Cybernetics is used amongst several fields to discover principles of systems, adaptation of organisms, information analysis and much more. == Genetic engineering == Genetic engineering is a field that uses advances in technology to modify biological organisms. Through different methods, scientists are able to alter the genetic material of microorganisms, plants and animals to provide them with desirable traits. For example, making plants grow bigger, better, and faster. Genetic engineering is included in biorobotics because it uses new technologies to alter biology and change an organism's DNA for their and society's benefit. === History === Although humans have modified genetic material of animals and plants through artificial selection for millennia (such as the genetic mutations that developed teosinte into corn and wolves into dogs), genetic engineering refers to the deliberate alteration or insertion of specific genes to an organism's DNA. The first successful case of genetic engineering occurred in 1973 when Herbert Boyer and Stanley Cohen were able to transfer a gene with antibiotic resistance to a bacterium. === Science === There are three main techniques used in genetic engineering: The plasmid method, the vector method and the biolistic method. ==== Plasmid method ==== This technique is used mainly for microorganisms such as bacteria. Through this method, DNA molecules called plasmids are extracted from bacteria and placed in a lab where restriction enzymes break them down. As the enzymes do this, some develop a rough edge that resembles that of a staircase which is considered 'sticky' and capable of reconnecting. These 'sticky' molecules are inserted into another bacteria where they will connect to the DNA rings with the altered genetic material. ==== Vector method ==== The vector method is considered a more precise technique than the plasmid method as it involves the transfer of a specific gene instead of a whole sequence. In the vector method, a specific gene from a DNA strand is isolated through restriction enzymes in a laboratory and is inserted into a vector. Once the vector accepts the genetic code, it is inserted into the host cell where the DNA will be transferred. ==== Biolistic method ==== The biolistic method is typically used to alter the genetic material of plants. This method embeds the desired DNA with a metallic particle such as gold or tungsten in a high speed gun. The particle is then bombarded into the plant. Due to the high velocities and the vacuum generated during bombardment, the particle is able to penetrate the cell wall and inserts the new DNA into the cell. === Applications === Genetic engineering has many uses in the fields of medicine, research and agriculture. In the medical field, genetically modified bacteria are used to produce drugs such as insulin, human growth hormones and vaccines. In research, scientists genetically modify organisms to observe physical and behavioral changes to understand the function of specific genes. In agriculture, genetic engineering is extremely important as it is used by farmers to grow crops that are resistant to herbicides and to insects such as BTCorn. == Bionics == Bionics is a medical engineering field and a branch of biorobotics consisting of electrical and mechanical systems that imitate biological systems, such as prosthetics and hearing aids. It's a portmanteau that combines biology and electronics. === History === The history of bionics goes as far back in time as ancient Egypt. A prosthetic toe made out of wood and leather was found on the foot of a mummy. The time period of the mummy corpse was estimated to be from around the fifteenth century B.C. Bionics can also be witnessed in ancient Greece and Rome. Prosthetic legs and arms were made for amputee soldiers. In the early 16th century, a French military surgeon by the name of Ambroise Pare became a pioneer in the field of bionics. He was known for making various types of upper and lower prosthetics. One of his most famous prosthetics, Le Petit Lorrain, was a mechanical hand operated by catches and springs. During the early 19th century, Alessandro Volta further progressed bionics. He set the foundation for the creation of hearing aids with his experiments. He found that electrical stimulation could restore hearing by inserting an electrical implant to the saccular nerve of a patient's ear. In 1945, the National Academy of Sciences created the Artificial Limb Program, which focused on improving prosthetics since there were a large number of World War II amputee soldiers. Since this creation, prosthetic materials, computer design methods, and surgical procedures have improved, creating modern-day bionics. === Science === ==== Prosthetics ==== The important components that make up modern-day prosthetics are the pylon, the socket, and the suspension system. The pylon is the internal frame of the prosthetic that is made up of metal rods or carbon-fiber composites. The socket is the part of the prosthetic that connects the prosthetic to the person's missing limb. The socket consists of a soft liner that makes the fit comfortable, but also snug enough to stay on the limb. The suspension system is important in keeping the prosthetic on the limb. The suspension system is usually a harness system made up of straps, belts or sleeves that are used to keep the limb attached. The operation of a prosthetic could be designed in various ways. The prosthetic could be body-powered, externally-powered, or myoelectrically powered. Body-powered prosthetics consist of cables attached to a strap or harness, which is placed on the person's functional shoulder, allowing the person to manipulate and control the prosthetic as he or she deems fit. Externally-powered prosthetics consist of motors to power the prosthetic and buttons and switches to control the prosthetic. Myoelectrically powered prosthetics are new, advanced forms of prosthetics where electrodes are placed on the muscles above the limb. The electrodes will detect the muscle contractions and send electrical signals to the prosthetic to move the prosthetic. The downside to this type of prosthetic is that if the sensors are not placed correctly on the limb then the electrical impulses will fail to move the prosthetic. TrueLimb is a specific brand of prosthetics that uses myoelectrical sensors which enable a person to have control of their bionic limb. ==== Hearing aids ==== Four major components make up the hearing aid: the microphone, the amplifier, the receiver, and the battery. The microphone takes in outside sound, turns that sound to electrical signals, and sends those signals to the amplifier. The amplifier increases the sound and sends that sound to the receiver. The receiver changes the electrical signal back into sound and sends the sound into the ear. Hair cells in the ear will sense the vibrations from the sound, convert the vibrations into nerve signals, and send it to the brain so
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Novell File Reporter

Novell File Reporter (NFR) is software that allows network administrators to identify files stored on the network and generates reports regarding the size of individual files, file type, when files were last accessed, and where duplicates exist. Additionally, the File Reporter tracks storage volume capacity and usage. It is a component of the Novell File Management Suite. == How it works == Novell File Reporter examines and reports on terabytes of data via a central reporting engine (NFR Engine) and distributed agents (NFR Agents). The NFR Engine schedules the scans of file instances conducted by NFR Agents, processes and compiles the scans for reporting purposes, and provides report information to the user interface. In addition to the standard reports it can generate, the NFR Engine can also produce "trigger reports" in response to specific events (a server volume crossing a capacity threshold, for example). Accordingly, the NFR Engine monitors the data gathered by the NFR Agents in order to identify these "triggers." The NFR Engine when working in either eDirectory or Active Directory connects to the directory via a Directory Services Interface (DSI) and thus can monitor and check file permissions.
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Car–Parrinello molecular dynamics

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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Algorithms and Combinatorics

Algorithms and Combinatorics (ISSN 0937-5511) is a book series in mathematics, and particularly in combinatorics and the design and analysis of algorithms. It is published by Springer Science+Business Media, and was founded in 1987. == Books == The books published in this series include: The Simplex Method: A Probabilistic Analysis (Karl Heinz Borgwardt, 1987, vol. 1) Geometric Algorithms and Combinatorial Optimization (Martin Grötschel, László Lovász, and Alexander Schrijver, 1988, vol. 2; 2nd ed., 1993) Systems Analysis by Graphs and Matroids (Kazuo Murota, 1987, vol. 3) Greedoids (Bernhard Korte, László Lovász, and Rainer Schrader, 1991, vol. 4) Mathematics of Ramsey Theory (Jaroslav Nešetřil and Vojtěch Rödl, eds., 1990, vol. 5) Matroid Theory and its Applications in Electric Network Theory and in Statics (Andras Recszki, 1989, vol. 6) Irregularities of Partitions: Papers from the meeting held in Fertőd, July 7–11, 1986 (Gábor Halász and Vera T. Sós, eds., 1989, vol. 8) Paths, Flows, and VLSI-Layout: Papers from the meeting held at the University of Bonn, Bonn, June 20–July 1, 1988 (Bernhard Korte, László Lovász, Hans Jürgen Prömel, and Alexander Schrijver, eds., 1990, vol. 9) New Trends in Discrete and Computational Geometry (János Pach, ed., 1993, vol. 10) Discrete Images, Objects, and Functions in Z n {\displaystyle \mathbb {Z} ^{n}} (Klaus Voss, 1993, vol. 11) Linear Optimization and Extensions (Manfred Padberg, 1999, vol. 12) The Mathematics of Paul Erdős I (Ronald Graham and Jaroslav Nešetřil, eds., 1997, vol. 13) The Mathematics of Paul Erdős II (Ronald Graham and Jaroslav Nešetřil, eds., 1997, vol. 14) Geometry of Cuts and Metrics (Michel Deza and Monique Laurent, 1997, vol. 15) Probabilistic Methods for Algorithmic Discrete Mathematics (M. Habib, C. McDiarmid, J. Ramirez-Alfonsin, and B. Reed, 1998, vol. 16) Modern Cryptography, Probabilistic Proofs and Pseudorandomness (Oded Goldreich, 1999, vol. 17) Geometric Discrepancy: An Illustrated Guide (Jiří Matoušek, 1999, vol. 18) Applied Finite Group Actions (Adalbert Kerber, 1999, vol. 19) Matrices and Matroids for Systems Analysis (Kazuo Murota, 2000, vol. 20; corrected ed., 2010) Combinatorial Optimization (Bernhard Korte and Jens Vygen, 2000, vol. 21; 5th ed., 2012) The Strange Logic of Random Graphs (Joel Spencer, 2001, vol. 22) Graph Colouring and the Probabilistic Method (Michael Molloy and Bruce Reed, 2002, Vol. 23) Combinatorial Optimization: Polyhedra and Efficiency (Alexander Schrijver, 2003, vol. 24. In three volumes: A. Paths, flows, matchings; B. Matroids, trees, stable sets; C. Disjoint paths, hypergraphs) Discrete and Computational Geometry: The Goodman-Pollack Festschrift (B. Aronov, S. Basu, J. Pach, and M. Sharir, eds., 2003, vol. 25) Topics in Discrete Mathematics: Dedicated to Jarik Nešetril on the Occasion of his 60th birthday (M. Klazar, J. Kratochvíl, M. Loebl, J. Matoušek, R. Thomas, and P. Valtr, eds., 2006, vol. 26) Boolean Function Complexity: Advances and Frontiers (Stasys Jukna, 2012, Vol. 27) Sparsity: Graphs, Structures, and Algorithms (Jaroslav Nešetřil and Patrice Ossona de Mendez, 2012, vol. 28) Optimal Interconnection Trees in the Plane (Marcus Brazil and Martin Zachariasen, 2015, vol. 29) Combinatorics and Complexity of Partition Functions (Alexander Barvinok, 2016, vol. 30)
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Coalition for App Fairness

The Coalition for App Fairness (CAF) is a coalition comprised by companies, who aim to reach a fairer deal for the inclusion of their apps into the Apple App Store or the Google Play Store. The organization's executive director is Meghan DiMuzio and its headquarters are located in Washington, D.C. == Background == In July 2015, Spotify launched an email campaign to urge its App Store subscribers to cancel their subscriptions and start new ones through its website, bypassing the 30% transaction fee for in-app purchases required for iOS applications by technology company Apple Inc. A later update to the Spotify app on iOS was rejected by Apple, prompting Spotify's general counsel Horacio Gutierrez to write a letter to Apple's then-general counsel Bruce Sewell, stating: "This latest episode raises serious concerns under both U.S. and EU competition law. It continues a troubling pattern of behavior by Apple to exclude and diminish the competitiveness of Spotify on iOS and as a rival to Apple Music, particularly when seen against the backdrop of Apple's previous anticompetitive conduct aimed at Spotify … we cannot stand by as Apple uses the App Store approval process as a weapon to harm competitors." In August 2020, Epic Games updated their Fortnite Battle Royale game app on both Apple's App Store and Google's Google Play to include its own storefront that offered a 20% discount on V-Bucks, the in-game currency, if players bought through there rather than through the app stores' storefront, both which take a 30% revenue cut of the sale. Both Apple and Google removed the Fortnite app within hours, as this alternate storefront violated their terms of use that required all in-app purchases to be made through their storefronts. Epic immediately filed lawsuits against both companies challenging their storefront policies on antitrust principles, arguing that their non-negotiable 30% revenue cut is too high and the restrictions against alternate storefronts anticompetitive. Apple countersued Epic over its behavior, leading to a highly publicized 2021 bench trial. Ultimately, Epic largely lost its lawsuit against Apple, though the court did order Apple to allow developers to point users to alternative payment methods. Conversely, Epic won its antitrust lawsuit against Google in late 2023. == Foundation == On 24 September 2020, Epic Games joined forces with thirteen other prominent companies—including the music streaming platform Spotify, Tinder owner Match Group, the encrypted mail service Proton Mail, and the crypto currency website Blockchain.com—to establish the Coalition for App Fairness. It also includes Basecamp. The coalition criticizes the fact that for now the app stores of both Apple and Google charge their clients a 30% fee on any purchases made over their stores. Apple and Google defended themselves by arguing that the 30% transaction fee is a standard in the industry while the Coalition for App Fairness states that there is no other transaction fee which is even close to the 30%. In October 2020, it was reported that the coalition grew from 13 to 40 members since its foundation and received more than 400 applications for membership. In October 2025, X (formerly Twitter) joined CAF. This was seen as a larger pushback in the industry against Apple and Google, and a step towards hopefully passing the Bipartisan Open App Markets Act. == Aims == The group has broadened their demands for the app stores and now also aim for a better treatment for the apps available in the App Store. They claim that Apple favors its own services before other services available on the market and unjustifiably excludes other apps from their App Store. The group has also been viewing other transaction fees like the 5% fee which is charged by credit card companies, and states that Apple charges up to 600% more and would like the 30% fee, which was only included in 2011 by Apple, adapted to a comparable percentage that charge other providers of payment solutions. Its demands are mainly directed at Apple's strict control over its App Store, but to a lesser extent are also directed towards Google. Google allows apps to be downloaded over an independent web link or also another App Store, such as the Epic Game App Store. The organization emphasizes that no app developer should come into the position in which they are discriminated and are not granted the same rights as to the developers of the owner of the app store. == Reactions == In October 2020, Microsoft presented a new framework concerning the access to its Windows 10 operating system by app stores other than the one offered by Microsoft. The new framework is based on the demands of the Coalition for App Fairness. Microsoft emphasized though, that these principles would not apply to the Xbox. In December 2020, Apple announced that they would be lowering the revenue cut Apple takes for app developers making $1M or less from 30% to 15% if app developers fill out an application for the lowered revenue cut. In March 2021, Google followed suit by also lowering the revenue cut from the Play Store from 30% to 15% for the first million in revenue earned by a developer each year. == Notable members == Members listed are notable companies listed as members the groups website: Blockchain.com Deezer Epic Games European Digital SME Alliance Fanfix Life360 Masimo Nium Proton Mail Spotify TapTap Threema Vipps
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Vinberg's algorithm

In mathematics, Vinberg's algorithm is an algorithm, introduced by Ernest Borisovich Vinberg, for finding a fundamental domain of a hyperbolic reflection group. Conway (1983) used Vinberg's algorithm to describe the automorphism group of the 26-dimensional even unimodular Lorentzian lattice II25,1 in terms of the Leech lattice. == Description of the algorithm == Let Γ < I s o m ( H n ) {\displaystyle \Gamma <\mathrm {Isom} (\mathbb {H} ^{n})} be a hyperbolic reflection group. Choose any point v 0 ∈ H n {\displaystyle v_{0}\in \mathbb {H} ^{n}} ; we shall call it the basic (or initial) point. The fundamental domain P 0 {\displaystyle P_{0}} of its stabilizer Γ v 0 {\displaystyle \Gamma _{v_{0}}} is a polyhedral cone in H n {\displaystyle \mathbb {H} ^{n}} . Let H 1 , . . . , H m {\displaystyle H_{1},...,H_{m}} be the faces of this cone, and let a 1 , . . . , a m {\displaystyle a_{1},...,a_{m}} be outer normal vectors to it. Consider the half-spaces H k − = { x ∈ R n , 1 | ( x , a k ) ≤ 0 } . {\displaystyle H_{k}^{-}=\{x\in \mathbb {R} ^{n,1}|(x,a_{k})\leq 0\}.} There exists a unique fundamental polyhedron P {\displaystyle P} of Γ {\displaystyle \Gamma } contained in P 0 {\displaystyle P_{0}} and containing the point v 0 {\displaystyle v_{0}} . Its faces containing v 0 {\displaystyle v_{0}} are formed by faces H 1 , . . . , H m {\displaystyle H_{1},...,H_{m}} of the cone P 0 {\displaystyle P_{0}} . The other faces H m + 1 , . . . {\displaystyle H_{m+1},...} and the corresponding outward normals a m + 1 , . . . {\displaystyle a_{m+1},...} are constructed by induction. Namely, for H j {\displaystyle H_{j}} we take a mirror such that the root a j {\displaystyle a_{j}} orthogonal to it satisfies the conditions (1) ( v 0 , a j ) < 0 {\displaystyle (v_{0},a_{j})<0} ; (2) ( a i , a j ) ≤ 0 {\displaystyle (a_{i},a_{j})\leq 0} for all i < j {\displaystyle i Read more →
Knowledge organization system

Knowledge organization system (KOS), concept system, or concept scheme is the generic term used in knowledge organization (KO) for the selection of concepts with an indication of selected semantic relations. Despite their differences in type, coverage, and application, all KOS aim to support the organization of knowledge and information to facilitate their management and retrieval. KOS vary in complexity from simple sorted lists to complex relational networks. They represent both structural and functional features, and serve to eliminate ambiguity, control synonyms, establish relationships, and present properties. From their origins in library and information science (LIS), KOS have been applied to other domains and disciplines within science and industry, although scholarly research and debate remain primarily within the KO field. Challenges of KOS include ambiguity of terminology, repercussions of biased systems, and potential obsolescence. KOS can be expressed in RDF and RDFS as per the Simple Knowledge Organization System (SKOS) recommendation by W3C, which aims to enable the sharing and linking of KOS via the Web. One of the largest collections of KOS is the BARTOC registry. == Types == While different schema of KOS have been proposed, most are generally arranged in terms of the complexity of their construction and maintenance. Some scholars argue that organizing KOS on a spectrum oversimplifies the shared characteristics among them, and may even result in a non-ideal structure being chosen. The following types are not exhaustive, and are often not mutually-exclusive in practice. === Term lists === Term lists are the least structured form of KOS. They include lists, glossaries, dictionaries, and synonym rings. Authority files and gazetteers may also be considered term lists, however other scholars categorize them and directories as "metadata-like models". Examples include the Union List of Artist Names name authority file and the GeoNames gazetteer. === Categorization and classification === KOS that emphasize specific (and often hierarchical) structures include subject headings, taxonomies, categorization schema, and classification schema & systems. Despite inconsistent use of the terms "categorization" and "classification" in some literature, categorization is generally loosely-assembled grouping schema and may include attributes that are not mutually exclusive (or having fuzzy boundaries), while classification is related to the arrangement of non-overlapping and mutually-exclusive classes. Classification schema may be universal (such as Dewey Decimal Classification and Information Coding Classification) or domain-specific (such as the National Library of Medicine Classification). === Relationship models === The types of KOS with greatest complexity and which utilize connections between concepts include thesauri, semantic networks, and ontologies. One of the most prominent examples of a semantic network is WordNet. === Others === Certain structures proposed to be considered types of KOS—but are not consistently included in schema—include folksonomies, topic maps, web directory structures, publication organization systems, and bibliometric maps. Some KOS organize other KOS themselves—for instance, PeriodO is a gazetteer of periodization categories. == Applications == Some early KOS were developed as a support system for abstracting and indexing services to be used by specially-trained searchers. With the growth of information digitization, usability became increasingly accessible, and more complex structures were developed. Prominent examples of KOS outside of LIS include organism taxonomy in biology, the periodic table of elements in chemistry, SIC and NAICS classification systems for industry & business, and AGROVOC agricultural controlled vocabulary. == Challenges == The study and design of KOS is an ongoing topic of discussion among KO scholars. === Terminology === [There is] a serious lack of vocabulary control in the literature on controlled vocabulary. Inconsistency of terminology within the study of KOS is a common issue. For instance, "ontology" is used for both a specific type of KOS as well as a generic term for any KOS. The terms "taxonomy", "classification", and "categorization" are also sometimes used interchangeably. === Bias === As knowledge can be historically and culturally biased, scholars have also discussed how KOS themselves can perpetuate harmful practices or stereotypes. For example, a number of concerns and criticisms about the classification of mental disorders in the Diagnostic and Statistical Manual of Mental Disorders have been raised, contributing to ongoing revisions. Ethical and intentional design approaches have been proposed for multi-perspective KOS in efforts to mitigate bias and other harmful practices. === Obsolescence === The possible obsolescence of the thesaurus and other simpler KOS has been the topic of debate, especially in the face of increasingly complex ontologies, the growing usage of "Google-like retrieval systems", and the move of KO theory and research away from LIS and toward computer science. Supporters of thesauri argue its continued usefulness for metadata enrichment, vocabulary mapping, and web services, as well as its usage in specific domains such as corporate intranets and digital image libraries.
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MarkLogic Server

MarkLogic Server is a document-oriented database developed by MarkLogic. It is a NoSQL multi-model database that evolved from an XML database to natively store JSON documents and RDF triples, the data model for semantics. MarkLogic is designed to be a data hub for operational and analytical data. == History == MarkLogic Server was built to address shortcomings with existing search and data products. The product first focused on using XML as the document markup standard and XQuery as the query standard for accessing collections of documents up to hundreds of terabytes in size. Currently the MarkLogic platform is widely used in publishing, government, finance and other sectors. MarkLogic's customers are mostly Global 2000 companies. == Technology == MarkLogic uses documents without upfront schemas to maintain a flexible data model. In addition to having a flexible data model, MarkLogic uses a distributed, scale-out architecture that can handle hundreds of billions of documents and hundreds of terabytes of data. It has received Common Criteria certification, and has high availability and disaster recovery. MarkLogic is designed to run on-premises and within public or private cloud environments like Amazon Web Services. == Features == Indexing MarkLogic indexes the content and structure of documents including words, phrases, relationships, and values in over 200 languages with tokenization, collation, and stemming for core languages. Functionality includes the ability to toggle range indexes, geospatial indexes, the RDF triple index, and reverse indexes on or off based on your data, the kinds of queries that you will run, and your desired performance. Full-text search MarkLogic supports search across its data and metadata using a word or phrase and incorporates Boolean logic, stemming, wildcards, case sensitivity, punctuation sensitivity, diacritic sensitivity, and search term weighting. Data can be searched using JavaScript, XQuery, SPARQL, and SQL. Semantics MarkLogic uses RDF triples to provide semantics for ease of storing metadata and querying. ACID Unlike other NoSQL databases, MarkLogic maintains ACID consistency for transactions. Replication MarkLogic provides high availability with replica sets. Scalability MarkLogic scales horizontally using sharding. MarkLogic can run over multiple servers, balancing the load or replicating data to keep the system up and running in the event of hardware failure. Security MarkLogic has built in security features such as element-level permissions and data redaction. Optic API for Relational Operations An API that lets developers view their data as documents, graphs or rows. Security MarkLogic provides redaction, encryption, and element-level security (allowing for control on read and write rights on parts of a document). == Applications == Banking Big Data Fraud prevention Insurance Claims Management and Underwriting Master data management Recommendation engines == Licensing == MarkLogic is available under various licensing and delivery models, namely a free Developer or an Essential Enterprise license.[3] Licenses are available from MarkLogic or directly from cloud marketplaces such as Amazon Web Services and Microsoft Azure. == Releases == 2001 – Cerisent XQE 1: ACID transactions, Full-text search, XML Storage, XQuery, Role-based security 2004 – Cerisent XQE 2: Scale-out architecture, Enhanced search (stemming, thesaurus, wildcard), Backup and restore 2005 – MarkLogic Server 3: Continuing search improvements, Content Processing Framework (including PDF, Word, Excel, PPT), Failover 2008 – MarkLogic Server 4: Geospatial search, entity extraction, advanced XQuery, performance, scalability enhancements, auditing 2011 – MarkLogic Server 5: Flexible replication / DDIL, real-time indexing, advanced search, improved analytics, concurrency enhancements 2012 – MarkLogic Server 6: REST and Java APIs, App Builder, enhanced UI, improved search 2013 – MarkLogic Server 7: Semantic graph, bitemporal data, tiered storage, improved search, better management 2015 – MarkLogic Server 8: A Native JSON storage, Server-side JavaScript, Bitemporal, Node.js client API, Incremental backup, Flexible replication[16] 2017 – MarkLogic Server 9: Data integration across Relational and Non-Relational data, Advanced Encryption, Element Level Security, Redaction 2019 – MarkLogic Server 10: Enhanced Data Hub, improved SQL, security, analytics performance, cloud support 2022 – MarkLogic Server 11: MarkLogic Ops Director (Monitoring and Administration Improvements), expanded PKI 2025 – MarkLogic Server 12: Generative AI and Native Vector Search, Graph Algorithm Support, Virtual TDEs (relational views on the fly)
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Powerset (company)

Powerset was an American company based in San Francisco, California, that, in 2006, was developing a natural language search engine for the Internet. On July 1, 2008, Powerset was acquired by Microsoft for an estimated $100 million (~$143 million in 2024). Powerset was working on building a natural language search engine that could find targeted answers to user questions (as opposed to keyword based search). For example, when confronted with a question like "Which U.S. state has the highest income tax?", conventional search engines ignore the question phrasing and instead do a search on the keywords "state", "highest", "income", and "tax". Powerset on the other hand, attempts to use natural language processing to understand the nature of the question and return pages containing the answer. The company was in the process of "building a natural language search engine that reads and understands every sentence on the Web". The company has licensed natural language technology from PARC, the former Xerox Palo Alto Research Center. On May 11, 2008, the company unveiled a tool for searching a fixed subset of English Wikipedia using conversational phrases rather than keywords. Acquisition by Microsoft: One significant milestone in Powerset's history was its acquisition by Microsoft on July 1, 2008, for an estimated $100 million. This acquisition was part of Microsoft's broader strategy to enhance its search capabilities and compete more effectively with other search engine providers, particularly Google. Natural Language Search Engine: Powerset's primary focus was on developing a natural language search engine capable of understanding and interpreting user queries in a more human-like manner. Instead of simply matching keywords, Powerset aimed to comprehend the meaning behind the words, allowing for more accurate and contextually relevant search results. Technology and Partnerships: Powerset had licensed natural language technology from PARC, the Xerox Palo Alto Research Center. This technology likely played a crucial role in the development of Powerset's NLP capabilities. Wikipedia Search Tool: In May 2008, Powerset unveiled a search tool that allowed users to search a fixed subset of English Wikipedia using conversational phrases rather than traditional keywords. This demonstrated the potential of Powerset's NLP technology in providing more precise and relevant search results. == Powerlabs == In a form of beta testing, Powerset opened an online community called Powerlabs on September 17, 2007. Business Week said: "The company hopes the site will marshal thousands of people to help build and improve its search engine before it goes public next year." Said The New York Times: "[Powerset Labs] goes far beyond the 'alpha' or 'beta' testing involved in most software projects, when users put a new product through rigorous testing to find its flaws. Powerset doesn’t have a product yet, but rather a collection of promising natural language technologies, which are the fruit of years of research at Xerox PARC." Powerlabs' initial search results are taken from Wikipedia. == Notable people == Barney Pell (born March 18, 1968, in Hollywood, California) was co-founder and CEO of Powerset. Pell received his Bachelor of Science degree in symbolic systems from Stanford University in 1989, where he graduated Phi Beta Kappa and was a National Merit Scholar. Pell received a PhD in computer science from Cambridge University in 1993, where he was a Marshall Scholar. He has worked at NASA, as chief strategist and vice president of business development at StockMaster.com (acquired by Red Herring in March, 2000) and at Whizbang! Labs. Prior to joining Powerset, Pell was an Entrepreneur-in-Residence at Mayfield Fund, a venture capital firm in Silicon Valley. Pell is also a founder of Moon Express, Inc., a U.S. company awarded a $10M commercial lunar contract by NASA and a competitor in the Google Lunar X PRIZE. Steve Newcomb was the COO and co-founder of Powerset. Prior to joining Powerset, he was a co-founder of Loudfire, General Manager at Promptu, and was on the board of directors at Jaxtr. He left Powerset in October 2007 to form Virgance, a social startup incubator. Lorenzo Thione (born in Como, Italy) was the product architect and co-founder of Powerset. Prior to joining Powerset, he worked at FXPAL in natural language processing and related research fields. Thione earned his master's degree in software engineering from the University of Texas at Austin. Ronald Kaplan, former manager of research in Natural Language Theory and Technology at PARC, served as the company's CTO and CSO. Ryan Ferrier is a member of the founding team of Powerset. He managed personnel and internal operations. After 2008 he went on to co-found Serious Business, which made Facebook applications and was later bought by Zynga. Another Powerset alumnus, Alex Le, became CTO of Serious Business and went on to become an executive producer at Zynga when it bought the company. Siqi Chen founded a stealth startup in mobile computing after leaving Powerset. Tom Preston-Werner worked at Powerset and left after the acquisition to found GitHub. == Investors == Powerset attracted a wide range of investors, many of whom had considerable experience in the venture capital field. The company received $12.5 million (~$18.2 million in 2024) in Series A funding during November 2007, co-led by the venture capital firms Foundation Capital and The Founders Fund. Among the better-known investors: Esther Dyson, founding chairman of ICANN, founder of the newsletter Release 1.0 and editor at Cnet Peter Thiel, founder and former CEO of PayPal Luke Nosek, founder of PayPal Todd Parker. Managing Partner, Hidden River Ventures Reid Hoffman, executive vice president of PayPal and founder of LinkedIn First Round Capital, seed-stage venture firm
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Super column

A super column is a tuple (a pair) with a binary super column name and a value that maps it to many columns. They consist of a key–value pairs, where the values are columns. Theoretically speaking, super columns are (sorted) associative array of columns. Similar to a regular column family where a row is a sorted map of column names and column values, a row in a super column family is a sorted map of super column names that maps to column names and column values. A super column is part of a keyspace together with other super columns and column families, and columns. == Code example == Written in the JSON-like syntax, a super column definition can be like this: Where: "databases" are keyspace; "Cassandra" and "HBase" are rowKeys; "name" and "address" are super column names; "firstName", "city", "age", etc. are column names.
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Enumeration algorithm

In computer science, an enumeration algorithm is an algorithm that enumerates the answers to a computational problem. Formally, such an algorithm applies to problems that take an input and produce a list of solutions, similarly to function problems. For each input, the enumeration algorithm must produce the list of all solutions, without duplicates, and then halt. The performance of an enumeration algorithm is measured in terms of the time required to produce the solutions, either in terms of the total time required to produce all solutions, or in terms of the maximal delay between two consecutive solutions and in terms of a preprocessing time, counted as the time before outputting the first solution. This complexity can be expressed in terms of the size of the input, the size of each individual output, or the total size of the set of all outputs, similarly to what is done with output-sensitive algorithms. == Formal definitions == An enumeration problem P {\displaystyle P} is defined as a relation R {\displaystyle R} over strings of an arbitrary alphabet Σ {\displaystyle \Sigma } : R ⊆ Σ ∗ × Σ ∗ {\displaystyle R\subseteq \Sigma ^{}\times \Sigma ^{}} An algorithm solves P {\displaystyle P} if for every input x {\displaystyle x} the algorithm produces the (possibly infinite) sequence y {\displaystyle y} such that y {\displaystyle y} has no duplicate and z ∈ y {\displaystyle z\in y} if and only if ( x , z ) ∈ R {\displaystyle (x,z)\in R} . The algorithm should halt if the sequence y {\displaystyle y} is finite. == Common complexity classes == Enumeration problems have been studied in the context of computational complexity theory, and several complexity classes have been introduced for such problems. A very general such class is EnumP, the class of problems for which the correctness of a possible output can be checked in polynomial time in the input and output. Formally, for such a problem, there must exist an algorithm A which takes as input the problem input x, the candidate output y, and solves the decision problem of whether y is a correct output for the input x, in polynomial time in x and y. For instance, this class contains all problems that amount to enumerating the witnesses of a problem in the class NP. Other classes that have been defined include the following. In the case of problems that are also in EnumP, these problems are ordered from least to most specific: Output polynomial, the class of problems whose complete output can be computed in polynomial time. Incremental polynomial time, the class of problems where, for all i, the i-th output can be produced in polynomial time in the input size and in the number i. Polynomial delay, the class of problems where the delay between two consecutive outputs is polynomial in the input (and independent from the output). Strongly polynomial delay, the class of problems where the delay before each output is polynomial in the size of this specific output (and independent from the input or from the other outputs). The preprocessing is generally assumed to be polynomial. Constant delay, the class of problems where the delay before each output is constant, i.e., independent from the input and output. The preprocessing phase is generally assumed to be polynomial in the input. == Common techniques == Backtracking: The simplest way to enumerate all solutions is by systematically exploring the space of possible results (partitioning it at each successive step). However, performing this may not give good guarantees on the delay, i.e., a backtracking algorithm may spend a long time exploring parts of the space of possible results that do not give rise to a full solution. Flashlight search: This technique improves on backtracking by exploring the space of all possible solutions but solving at each step the problem of whether the current partial solution can be extended to a partial solution. If the answer is no, then the algorithm can immediately backtrack and avoid wasting time, which makes it easier to show guarantees on the delay between any two complete solutions. In particular, this technique applies well to self-reducible problems. Closure under set operations: If we wish to enumerate the disjoint union of two sets, then we can solve the problem by enumerating the first set and then the second set. If the union is non disjoint but the sets can be enumerated in sorted order, then the enumeration can be performed in parallel on both sets while eliminating duplicates on the fly. If the union is not disjoint and both sets are not sorted then duplicates can be eliminated at the expense of a higher memory usage, e.g., using a hash table. Likewise, the cartesian product of two sets can be enumerated efficiently by enumerating one set and joining each result with all results obtained when enumerating the second step. == Examples of enumeration problems == The vertex enumeration problem, where we are given a polytope described as a system of linear inequalities and we must enumerate the vertices of the polytope. Enumerating the minimal transversals of a hypergraph. This problem is related to monotone dualization and is connected to many applications in database theory and graph theory. Enumerating the answers to a database query, for instance a conjunctive query or a query expressed in monadic second-order. There have been characterizations in database theory of which conjunctive queries could be enumerated with linear preprocessing and constant delay. The problem of enumerating maximal cliques in an input graph, e.g., with the Bron–Kerbosch algorithm Listing all elements of structures such as matroids and greedoids Several problems on graphs, e.g., enumerating independent sets, paths, cuts, etc. Enumerating the satisfying assignments of representations of Boolean functions, e.g., a Boolean formula written in conjunctive normal form or disjunctive normal form, a binary decision diagram such as an OBDD, or a Boolean circuit in restricted classes studied in knowledge compilation, e.g., NNF. == Connection to computability theory == The notion of enumeration algorithms is also used in the field of computability theory to define some high complexity classes such as RE, the class of all recursively enumerable problems. This is the class of sets for which there exist an enumeration algorithm that will produce all elements of the set: the algorithm may run forever if the set is infinite, but each solution must be produced by the algorithm after a finite time.
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MaPS S.A.

MaPS S.A. is a software editor founded in 2011 by Thierry Muller. The company is headquartered in Luxembourg. Its platform, called MaPS System, provides Data Management software for Multichannel Marketing. == History and funding == The first version of MaPS System was released under the agency Prem1um S.A. in 2005 in the partnership with Pingroom agency. In combination with MaPS System, Prem1um also provided various consulting services in Marketing, Publishing and Sales. This is where MaPS System takes its names (M stands for Marketing, P for Publishing and S for Sales). In 2011, after being successful, Prem1um S.A. decided to enable the software MaPS System to operate independently under MaPS S.A., as a separate company and editor of the software. The first financial supports were provided by Malta ICI, a Venture Capital firm, and the local partner Chameleon Invest, a seed-capital fund led by Business Angels, who invested €900,000. In a second investment round in 2014 led by Newion Investments, a Venture Capital firm, €1.4 Million were raised, thus amounting to total assets of €2.2 Million. In 2016, the company was taken over by three private investors. In 2018, after two years of continuous growth and European expansion in Belgium, Germany and Switzerland, MaPS S.A acquired Awevo, an e-commerce web agency. == Products == The services included in MaPS System range from the data centralization, Data Governance to an optimized Multichannel Marketing. The software currently includes more than 35 modules for Master Data Management, Product Information Management, Digital Asset Management, Business Process Management including catalogue Publishing features. == Certifications == In 2019, MaPS System and Awevo received "Made in Luxembourg" label, given to the companies whose services are entirely designed in Luxembourg, without any production or development offshoring. MaPS System is a member of ICT Cluster by Luxinnovation.
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Artifact (app)

Artifact was a personalized social news aggregator app that uses recommender systems to suggest articles. Launched in January 2023 by Nokto, Inc., a company founded by co-founders of Instagram Kevin Systrom and Mike Krieger, the app is available for iOS and Android. The app's name is a portmanteau of the words "articles", "artificial intelligence", and "fact". The app shut down in January 2024 as a result of low interest. == History == Nokto, Inc. was established on March 3, 2022, as a foreign stock company in California, with its headquarters in San Francisco. The company's main product, Artifact, is the first new product launched by Krieger and Systrom since their 2018 resignation from Instagram after conflicts with parent company Meta, which acquired Instagram in 2012. Artifact launched on January 31, 2023, after the team had been working on it for over a year, offering the option to sign up for a waiting list for its private beta, which grew to about 160,000 people, and then launching in open beta on February 22, 2023. With a team of seven employees in San Francisco, the app was free throughout its lifetime, with the founders explaining at the time that different business models - such as advertising or subscription fees - could be explored in the future. In January 2024, cofounder Kevin Systrom announced that the app would be shutting down after concluding that "the market opportunity isn’t big enough to warrant continued investment in this way." In April 2024, it was announced Artifact had been acquired by Yahoo, who intended to use the service's technology in an upgraded Yahoo! News app. == Features == Frequently described as "TikTok for text" and a competitor to Twitter, Artifact was a news aggregator that used machine learning to make personalized recommendations based on topics, news sources, and authors that the reader is interested in. In addition to reading articles, the app offered the ability to like articles, leave comments, or listen to an audio version of an article read by AI-generated voices, including a simulation of the voices of Snoop Dogg or Gwyneth Paltrow. AI also would rewrite clickbait headlines that users flagged. Artifact later expanded to a social network where users could post links, images and text to their profile, which could be liked or commented on by other users. Similar to other social news websites like Reddit, reader accounts had profiles with reputation scores.
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Dependency network (graphical model)

Dependency networks (DNs) are graphical models, similar to Markov networks, wherein each vertex (node) corresponds to a random variable and each edge captures dependencies among variables. Unlike Bayesian networks, DNs may contain cycles. Each node is associated to a conditional probability table, which determines the realization of the random variable given its parents. == Markov blanket == In a Bayesian network, the Markov blanket of a node is the set of parents and children of that node, together with the children's parents. The values of the parents and children of a node evidently give information about that node. However, its children's parents also have to be included in the Markov blanket, because they can be used to explain away the node in question. In a Markov random field, the Markov blanket for a node is simply its adjacent (or neighboring) nodes. In a dependency network, the Markov blanket for a node is simply the set of its parents. == Dependency network versus Bayesian networks == Dependency networks have advantages and disadvantages with respect to Bayesian networks. In particular, they are easier to parameterize from data, as there are efficient algorithms for learning both the structure and probabilities of a dependency network from data. Such algorithms are not available for Bayesian networks, for which the problem of determining the optimal structure is NP-hard. Nonetheless, a dependency network may be more difficult to construct using a knowledge-based approach driven by expert-knowledge. == Dependency networks versus Markov networks == Consistent dependency networks and Markov networks have the same representational power. Nonetheless, it is possible to construct non-consistent dependency networks, i.e., dependency networks for which there is no compatible valid joint probability distribution. Markov networks, in contrast, are always consistent. == Definition == A consistent dependency network for a set of random variables X = ( X 1 , … , X n ) {\textstyle \mathbf {X} =(X_{1},\ldots ,X_{n})} with joint distribution p ( x ) {\displaystyle p(\mathbf {x} )} is a pair ( G , P ) {\displaystyle (G,P)} where G {\displaystyle G} is a cyclic directed graph, where each of its nodes corresponds to a variable in X {\displaystyle \mathbf {X} } , and P {\displaystyle P} is a set of conditional probability distributions. The parents of node X i {\displaystyle X_{i}} , denoted P a i {\displaystyle \mathbf {Pa_{i}} } , correspond to those variables P a i ⊆ ( X 1 , … , X i − 1 , X i + 1 , … , X n ) {\displaystyle \mathbf {Pa_{i}} \subseteq (X_{1},\ldots ,X_{i-1},X_{i+1},\ldots ,X_{n})} that satisfy the following independence relationships p ( x i ∣ p a i ) = p ( x i ∣ x 1 , … , x i − 1 , x i + 1 , … , x n ) = p ( x i ∣ x − x i ) . {\displaystyle p(x_{i}\mid \mathbf {pa_{i}} )=p(x_{i}\mid x_{1},\ldots ,x_{i-1},x_{i+1},\ldots ,x_{n})=p(x_{i}\mid \mathbf {x} -{x_{i}}).} The dependency network is consistent in the sense that each local distribution can be obtained from the joint distribution p ( x ) {\displaystyle p(\mathbf {x} )} . Dependency networks learned using large data sets with large sample sizes will almost always be consistent. A non-consistent network is a network for which there is no joint probability distribution compatible with the pair ( G , P ) {\displaystyle (G,P)} . In that case, there is no joint probability distribution that satisfies the independence relationships subsumed by that pair. == Structure and parameters learning == Two important tasks in a dependency network are to learn its structure and probabilities from data. Essentially, the learning algorithm consists of independently performing a probabilistic regression or classification for each variable in the domain. It comes from observation that the local distribution for variable X i {\displaystyle X_{i}} in a dependency network is the conditional distribution p ( x i | x − x i ) {\displaystyle p(x_{i}|\mathbf {x} -{x_{i}})} , which can be estimated by any number of classification or regression techniques, such as methods using a probabilistic decision tree, a neural network or a probabilistic support-vector machine. Hence, for each variable X i {\displaystyle X_{i}} in domain X {\displaystyle X} , we independently estimate its local distribution from data using a classification algorithm, even though it is a distinct method for each variable. Here, we will briefly show how probabilistic decision trees are used to estimate the local distributions. For each variable X i {\displaystyle X_{i}} in X {\displaystyle \mathbf {X} } , a probabilistic decision tree is learned where X i {\displaystyle X_{i}} is the target variable and X − X i {\displaystyle \mathbf {X} -X_{i}} are the input variables. To learn a decision tree structure for X i {\displaystyle X_{i}} , the search algorithm begins with a singleton root node without children. Then, each leaf node in the tree is replaced with a binary split on some variable X j {\displaystyle X_{j}} in X − X i {\displaystyle \mathbf {X} -X_{i}} , until no more replacements increase the score of the tree. == Probabilistic Inference == A probabilistic inference is the task in which we wish to answer probabilistic queries of the form p ( y ∣ z ) {\displaystyle p(\mathbf {y\mid z} )} , given a graphical model for X {\displaystyle \mathbf {X} } , where Y {\displaystyle \mathbf {Y} } (the 'target' variables) Z {\displaystyle \mathbf {Z} } (the 'input' variables) are disjoint subsets of X {\displaystyle \mathbf {X} } . One of the alternatives for performing probabilistic inference is using Gibbs sampling. A naive approach for this uses an ordered Gibbs sampler, an important difficulty of which is that if either p ( y ∣ z ) {\displaystyle p(\mathbf {y\mid z} )} or p ( z ) {\displaystyle p(\mathbf {z} )} is small, then many iterations are required for an accurate probability estimate. Another approach for estimating p ( y ∣ z ) {\displaystyle p(\mathbf {y\mid z} )} when p ( z ) {\displaystyle p(\mathbf {z} )} is small is to use modified ordered Gibbs sampler, where Z = z {\displaystyle \mathbf {Z=z} } is fixed during Gibbs sampling. It may also happen that y {\displaystyle \mathbf {y} } is rare, e.g. when Y {\displaystyle \mathbf {Y} } has many variables. So, the law of total probability along with the independencies encoded in a dependency network can be used to decompose the inference task into a set of inference tasks on single variables. This approach comes with the advantage that some terms may be obtained by direct lookup, thereby avoiding some Gibbs sampling. You can see below an algorithm that can be used for obtain p ( y | z ) {\displaystyle p(\mathbf {y|z} )} for a particular instance of y ∈ Y {\displaystyle \mathbf {y} \in \mathbf {Y} } and z ∈ Z {\displaystyle \mathbf {z} \in \mathbf {Z} } , where Y {\displaystyle \mathbf {Y} } and Z {\displaystyle \mathbf {Z} } are disjoint subsets. Algorithm 1: U := Y {\displaystyle \mathbf {U:=Y} } ( the unprocessed variables ) P := Z {\displaystyle \mathbf {P:=Z} } ( the processed and conditioning variables ) p := z {\displaystyle \mathbf {p:=z} } ( the values for P {\displaystyle \mathbf {P} } ) While U ≠ ∅ {\displaystyle \mathbf {U} \neq \emptyset } : Choose X i ∈ U {\displaystyle X_{i}\in \mathbf {U} } such that X i {\displaystyle X_{i}} has no more parents in U {\displaystyle U} than any variable in U {\displaystyle U} If all the parents of X {\displaystyle X} are in P {\displaystyle \mathbf {P} } p ( x i | p ) := p ( x i | p a i ) {\displaystyle p(x_{i}|\mathbf {p} ):=p(x_{i}|\mathbf {pa_{i}} )} Else Use a modified ordered Gibbs sampler to determine p ( x i | p ) {\displaystyle p(x_{i}|\mathbf {p} )} U := U − X i {\displaystyle \mathbf {U:=U} -X_{i}} P := P + X i {\displaystyle \mathbf {P:=P} +X_{i}} p := p + x i {\displaystyle \mathbf {p:=p} +x_{i}} Returns the product of the conditionals p ( x i | p ) {\displaystyle p(x_{i}|\mathbf {p} )} == Applications == In addition to the applications to probabilistic inference, the following applications are in the category of Collaborative Filtering (CF), which is the task of predicting preferences. Dependency networks are a natural model class on which to base CF predictions, once an algorithm for this task only needs estimation of p ( x i = 1 | x − x i = 0 ) {\displaystyle p(x_{i}=1|\mathbf {x} -{x_{i}}=0)} to produce recommendations. In particular, these estimates may be obtained by a direct lookup in a dependency network. Predicting what movies a person will like based on his or her ratings of movies seen; Predicting what web pages a person will access based on his or her history on the site; Predicting what news stories a person is interested in based on other stories he or she read; Predicting what product a person will buy based on products he or she has already purchased and/or dropped into his or her shopping basket. Another class of useful applications for dependency networks is related to data visualization, that is
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Artificial intelligence in industry

Industrial artificial intelligence, or industrial AI, refers to the application of artificial intelligence to industrial business processes. Unlike general artificial intelligence which is a frontier research discipline to build computerized systems that perform tasks requiring human intelligence, industrial AI is more concerned with the application of such technologies to address industrial pain-points for customer value creation, productivity improvement, cost reduction, site optimization, predictive analysis and insight discovery. Artificial intelligence and machine learning have become key enablers to leverage data in production in recent years due to a number of different factors: More affordable sensors and the automated process of data acquisition; More powerful computation capability of computers to perform more complex tasks at a faster speed with lower cost; Faster connectivity infrastructure and more accessible cloud services for data management and computing power outsourcing. == Categories == Possible applications of industrial AI and machine learning in the production domain can be divided into seven application areas: Market and trend analysis Machinery and equipment Intralogistics Production process Supply chain Building Product Each application area can be further divided into specific application scenarios that describe concrete AI/ML scenarios in production. While some application areas have a direct connection to production processes, others cover production adjacent fields like logistics or the factory building. An example from the application scenario Process Design & Innovation are collaborative robots. Collaborative robotic arms are able to learn the motion and path demonstrated by human operators and perform the same task. Predictive and preventive maintenance through data-driven machine learning are application scenarios from the Machinery & Equipment application area. == Challenges == In contrast to entirely virtual systems, in which ML applications are already widespread today, real-world production processes are characterized by the interaction between the virtual and the physical world. Data is recorded using sensors and processed on computational entities and, if desired, actions and decisions are translated back into the physical world via actuators or by human operators. This poses major challenges for the application of ML in production engineering systems. These challenges are attributable to the encounter of process, data and model characteristics: The production domain's high reliability requirements, high risk and loss potential, the multitude of heterogeneous data sources and the non-transparency of ML model functionality impede a faster adoption of ML in real-world production processes. In particular, production data comprises a variety of different modalities, semantics and quality. Furthermore, production systems are dynamic, uncertain and complex, and engineering and manufacturing problems are data-rich but information-sparse. Besides that, due to the variety of use cases and data characteristics, problem-specific data sets are required, which are difficult to acquire, hindering both practitioners and academic researchers in this domain. === Process and industry characteristics === The domain of production engineering can be considered as a rather conservative industry when it comes to the adoption of advanced technology and their integration into existing processes. This is due to high demands on reliability of the production systems resulting from the potentially high economic harm of reduced process effectiveness due to e.g., additional unplanned downtime or insufficient product qualities. In addition, the specifics of machining equipment and products prevent area-wide adoptions across a variety of processes. Besides the technical reasons, the reluctant adoption of ML is fueled by a lack of IT and data science expertise across the domain. === Data characteristics === The data collected in production processes mainly stem from frequently sampling sensors to estimate the state of a product, a process, or the environment in the real world. Sensor readings are susceptible to noise and represent only an estimate of the reality under uncertainty. Production data typically comprises multiple distributed data sources resulting in various data modalities (e.g., images from visual quality control systems, time-series sensor readings, or cross-sectional job and product information). The inconsistencies in data acquisition lead to low signal-to-noise ratios, low data quality and great effort in data integration, cleaning and management. In addition, as a result from mechanical and chemical wear of production equipment, process data is subject to various forms of data drifts. === Machine learning model characteristics === ML models are considered as black-box systems given their complexity and intransparency of input-output relation. This reduces the comprehensibility of the system behavior and thus also the acceptance by plant operators. Due to the lack of transparency and the stochasticity of these models, no deterministic proof of functional correctness can be achieved, complicating the certification of production equipment. Given their inherent unrestricted prediction behavior, ML models are vulnerable against erroneous or manipulated data, further risking the reliability of the production system because of lacking robustness and safety. In addition to high development and deployment costs, the data drifts cause high maintenance costs, which is disadvantageous compared to purely deterministic programs. == Standard processes for data science in production == The development of ML applications – starting with the identification and selection of the use case and ending with the deployment and maintenance of the application – follows dedicated phases that can be organized in standard process models. The process models assist in structuring the development process and defining requirements that must be met in each phase to enter the next phase. The standard processes can be classified into generic and domain-specific ones. Generic standard processes (e.g., CRISP-DM, ASUM-DM, or knowledge discovery in databases (KDD)) describe a generally valid methodology and are thus independent of individual domains. Domain-specific processes on the other hand consider specific peculiarities and challenges of special application areas. The Machine Learning Pipeline in Production is a domain-specific data science methodology that is inspired by the CRISP-DM model and was specifically designed to be applied in fields of engineering and production technology. To address the core challenges of ML in engineering – process, data, and model characteristics – the methodology especially focuses on use-case assessment, achieving a common data and process understanding data integration, data preprocessing of real-world production data and the deployment and certification of real-world ML applications. == Industrial data sources == The foundation of most artificial intelligence and machine learning applications in industrial settings are comprehensive datasets from the respective fields. Those datasets act as the basis for training the employed models. In other domains, like computer vision, speech recognition or language models, extensive reference datasets (e.g. ImageNet, Librispeech, The People's Speech) and data scraped from the open internet are frequently used for this purpose. Such datasets rarely exist in the industrial context because of high confidentiality requirements and high specificity of the data. Industrial applications of artificial intelligence are therefore often faced with the problem of data availability. For these reasons, existing open datasets applicable to industrial applications, often originate from public institutions like governmental agencies or universities and data analysis competitions hosted by companies. In addition to this, data sharing platforms exist. However, most of these platforms have no industrial focus and offer limited filtering abilities regarding industrial data sources.
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