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Java Caps Future of Java CAPS Java_Caps > Future of Java CAPS After the Sun acquisition, Oracle incorporated features and functions of Sun SOA products to Oracle SOA products. Oracle offers tools that help in the migration of Java CAPS projects to Oracle SOA Suite. The premier support of Java CAPS 6.3 was extended until April 2016. Oracle does not promote the product anymore, and pushes users to migrate to Oracle SOA Suite. OpenESB, the open-source version of Java CAPS, is backed by a community and can be an alternative for companies that want to protect their investments.
Tietze syndrome Diagnosis Tietze_syndrome > Diagnosis Diagnosis for Tietze syndrome is primarily a clinical one, though some studies suggest the use of radiologic imaging. Musculoskeletal conditions are estimated to account for 20-50% of non-cardiac related chest pain in the emergency department. Ruling out other conditions, especially potentially life-threatening ones such as myocardial infarction (heart attack) and angina pectoris, is extremely important as they can present similarly to Tietze syndrome. These can usually be ruled out with diagnostic tools such as an electrocardiogram and a physical examination showing reproducible chest wall tenderness, .
Sensory neurons Connection with the central nervous system Sensory_receptor > Connection with the central nervous system Information coming from the sensory neurons in the head enters the central nervous system (CNS) through cranial nerves. Information from the sensory neurons below the head enters the spinal cord and passes towards the brain through the 31 spinal nerves. The sensory information traveling through the spinal cord follows well-defined pathways. The nervous system codes the differences among the sensations in terms of which cells are active.
Zeeman slower Outgoing atoms Zeeman_slower > Outgoing atoms It is linked to the fluctuations of the speed along the three axis around its mean values, since the final speed was said to be an average over a large number of processes. These fluctuations are linked to the atom having a Brownian motion due to the random reemission of the absorbed photon. They may cause difficulties when loading the atoms in the next trap. == References ==
Controlled thermonuclear fusion Accident potential Fusion_energy > Safety and the environment > Accident potential By comparison, a fission reactor is typically loaded with enough fuel for months or years, and no additional fuel is necessary to continue the reaction. This large fuel supply is what offers the possibility of a meltdown.In magnetic containment, strong fields develop in coils that are mechanically held in place by the reactor structure. Failure of this structure could release this tension and allow the magnet to "explode" outward.
Univariate time series Summary Time-series_regression In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data.
Crystallography, x-ray Summary X-ray_crystallographer X-ray crystal structures can also account for unusual electronic or elastic properties of a material, shed light on chemical interactions and processes, or serve as the basis for designing pharmaceuticals against diseases. In a single-crystal X-ray diffraction measurement, a crystal is mounted on a goniometer. The goniometer is used to position the crystal at selected orientations.
Stateless protocol Stacking of stateless and stateful protocol layers Stateless_protocol > Stacking of stateless and stateful protocol layers There can be complex interactions between stateful and stateless protocols among different protocol layers. For example, HTTP, a stateless protocol, is layered on top of TCP, a stateful protocol, which is layered on top of IP, another stateless protocol, which is routed on a network that employs BGP, another stateful protocol, to direct the IP packets riding on the network. This stacking of layers continues even above HTTP. As a workaround for the lack of a retained session state, HTTP servers implement various session management methods, typically utilizing a session identifier in an HTTP cookie referencing a session state stored on the server, effectively creating a stateful protocol on top of HTTP. HTTP cookies violate the REST architectural style because even without referencing a session state stored on the server, they are independent of session state (they affect previous pages of the same website in the browser history) and they have no defined semantics.
Pulmonary contusion Ventilation/perfusion mismatch Blast_lung > Pathophysiology > Ventilation/perfusion mismatch Pulmonary hypoxic vasoconstriction, in which blood vessels near the hypoxic alveoli constrict (narrow their diameter) in response to the lowered oxygen levels, can occur in pulmonary contusion. The vascular resistance increases in the contused part of the lung, leading to a decrease in the amount of blood that flows into it, directing blood to better-ventilated areas. Although reducing blood flow to the unventilated alveoli is a way to compensate for the fact that blood passing unventilated alveoli is not oxygenated, the oxygenation of the blood remains lower than normal. If it is severe enough, the hypoxemia resulting from fluid in the alveoli cannot be corrected just by giving supplemental oxygen; this problem is the cause of a large portion of the fatalities that result from trauma.
Queueing models Routing algorithms Queuing_theory > Queueing networks > Routing algorithms In discrete-time networks where there is a constraint on which service nodes can be active at any time, the max-weight scheduling algorithm chooses a service policy to give optimal throughput in the case that each job visits only a single-person service node. In the more general case where jobs can visit more than one node, backpressure routing gives optimal throughput. A network scheduler must choose a queueing algorithm, which affects the characteristics of the larger network.
Affinity label Quiescent affinity labels Affinity_label > Classifications > Quiescent affinity labels Quiescent affinity labels represent a promising approach for inhibiting enzymes using ‘masked’ reactive functionalities that are only uncovered within the active site. This approach differs from mechanism-based inactivators in that the catalysis must be "off-pathway". One of the best examples to explain this form of catalysis is in the inactivation dimethylargine dimethylaminohydrolase (DDAH) by 4-halopyridines. At physiological pH, the 4-halo group has near negligible reactivity with thiolates but upon protonation of the nitrogen, the reactivity increases ~4500-fold.
End of transmission character Meaning in Unix End_of_Transmission > Meaning in Unix If the input buffer is empty (because no characters have been typed since the last end-of-line or end-of-file), a program reading from the terminal reads a count of zero bytes. In Unix, such a condition is understood as having reached the end of the file. This can be demonstrated with the cat program on Unix-like operating systems such as Linux: Run the cat command with no arguments, so it accepts its input from the keyboard and prints output to the screen.
Custom-fit Rapid Manufacturing Systems, Tools and Materials Custom-fit > Technical Tools > Rapid Manufacturing Systems, Tools and Materials The attracted layer is transferred to a punch and transported to the consolidation unit where each layer of part material is sintered onto the previous by pressure and heat. The procedure is repeated layer-by-layer until the three-dimensional object is fully formed and consolidated. MPP has the ability to print different powders within the same layer and progressively change from one material to another, i.e., producing a functionally graded material.
Audio feedback Contemporary uses Acoustic_feedback > Deliberate uses > Contemporary uses Audio feedback became a signature feature of many underground rock bands during the 1980s. American noise-rockers Sonic Youth melded the rock-feedback tradition with a compositional/classical approach (notably covering Reich's "Pendulum Music"), and guitarist/producer Steve Albini's group Big Black also worked controlled feedback into the makeup of their songs. With the alternative rock movement of the 1990s, feedback again saw a surge in popular usage by suddenly mainstream acts like Nirvana, the Red Hot Chili Peppers, Rage Against the Machine and the Smashing Pumpkins. The use of the "no-input-mixer" method for sound generation by feeding a mixing console back into itself has been adopted in experimental electronic and noise music by practitioners such as Toshimaru Nakamura.
Digital signal processors Summary Digital_signal_processors A digital signal processor (DSP) is a specialized microprocessor chip, with its architecture optimized for the operational needs of digital signal processing. : 104–107 DSPs are fabricated on MOS integrated circuit chips. They are widely used in audio signal processing, telecommunications, digital image processing, radar, sonar and speech recognition systems, and in common consumer electronic devices such as mobile phones, disk drives and high-definition television (HDTV) products.The goal of a DSP is usually to measure, filter or compress continuous real-world analog signals.
Superparamagnetic relaxometry Magnetizing field and magnetic sensors Superparamagnetic_relaxometry > Magnetizing field and magnetic sensors Following this, the sensors are turned on and measure the decaying field for a sufficient time to obtain an accurate value of the decay time constant; 1–3 s. Magnetizing fields of ~5 mT for a Helmholtz coil of 1 m in diameter are used. The magnetic sensors that measure the decaying magnetic fields require high magnetic field sensitivity in order to determine magnetic moments of NP with adequate sensitivity. SQUID sensors, similar to those used in magnetoencephalography are appropriate for this task.
Quick Sort Relation to other algorithms Quicksort > Relation to other algorithms The more complex, or disk-bound, data structures tend to increase time cost, in general making increasing use of virtual memory or disk. The most direct competitor of quicksort is heapsort. Heapsort's running time is O(n log n), but heapsort's average running time is usually considered slower than in-place quicksort.
Path integral formalism Quantum field theory Path_integral_formulation_of_quantum_mechanics > Quantum field theory Both the Schrödinger and Heisenberg approaches to quantum mechanics single out time and are not in the spirit of relativity. For example, the Heisenberg approach requires that scalar field operators obey the commutation relation = i δ 3 ( x − y ) {\displaystyle =i\delta ^{3}(x-y)} for two simultaneous spatial positions x and y, and this is not a relativistically invariant concept. The results of a calculation are covariant, but the symmetry is not apparent in intermediate stages. If naive field-theory calculations did not produce infinite answers in the continuum limit, this would not have been such a big problem – it would just have been a bad choice of coordinates.
Continuous and progressive aspects French Continuous_and_progressive_aspects > Continuous and progressive in various languages > French The preposition en may be omitted if the gerund has an implied subject and takes an object which is not a pronoun; in that case the object may be prefixed before the gerund verb (and its possessive may be omitted when it refers to that implied subject), e.g. Chemin faisant, il ne pense à rien (lit. "Path making," i.e. "While making his path", "he doesn't think about anything").
Great circle Summary Great_circles Any other circle of the sphere is called a small circle, and is the intersection of the sphere with a plane not passing through its center. Small circles are the spherical-geometry analog of circles in Euclidean space. Every circle in Euclidean 3-space is a great circle of exactly one sphere. The disk bounded by a great circle is called a great disk: it is the intersection of a ball and a plane passing through its center. In higher dimensions, the great circles on the n-sphere are the intersection of the n-sphere with 2-planes that pass through the origin in the Euclidean space Rn + 1.
Symmetry of diatomic molecules Symmetry operations, point groups and permutation-inversion groups Symmetry_of_diatomic_molecules > Geometrical symmetries > Symmetry operations, point groups and permutation-inversion groups The elements of permutation-inversion groups commute with the full molecular Hamiltonian. In addition to point groups, there exists another kind of group important in crystallography, where translation in 3-D also needs to be taken care of. They are known as space groups.
Search for the Higgs boson The Higgs boson Search_for_the_Higgs_boson > Background > The Higgs boson The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. In the Standard Model, the Higgs particle is a massive scalar boson with zero spin, even (positive) parity, no electric charge, and no colour charge, that couples to (interacts with) mass. It is also very unstable, decaying into other particles almost immediately.
Dijkstra’s Algorithm Algorithm Dijkstra_algorithm > Algorithm Assign to every node a tentative distance value: set it to zero for our initial node and to infinity for all other nodes. During the run of the algorithm, the tentative distance of a node v is the length of the shortest path discovered so far between the node v and the starting node. Since initially no path is known to any other vertex than the source itself (which is a path of length zero), all other tentative distances are initially set to infinity.
SVG filter effect Summary SVG_filter_effects The filter property is set on a container element or on a graphics element to apply a filter effect to it. Each filter element contains a set of filter primitives as its children. Each filter primitive performs a single fundamental graphical operation (e.g., a Gaussian blur or a lighting effect) on one or more inputs, producing a graphical result.
Closed architecture Summary Closed_architecture Open architecture is a type of computer architecture or software architecture intended to make adding, upgrading, and swapping components with other computers easy. For example, the IBM PC, Amiga 500 and Apple IIe have an open architecture supporting plug-in cards, whereas the Apple IIc computer has a closed architecture. Open architecture systems may use a standardized system bus such as S-100, PCI or ISA or they may incorporate a proprietary bus standard such as that used on the Apple II, with up to a dozen slots that allow multiple hardware manufacturers to produce add-ons, and for the user to freely install them. By contrast, closed architectures, if they are expandable at all, have one or two "expansion ports" using a proprietary connector design that may require a license fee from the manufacturer, or enhancements may only be installable by technicians with specialized tools or training.
Pandemic prevention CRISPR-based immune subsystems Pandemic_prevention > Measures > Technology-centric measures > CRISPR-based immune subsystems In an editorial published in February 2020 another group of scientists claimed that they have implemented a flexible and efficient approach for targeting RNA with CRISPR-Cas13d which they have put under review and propose that the system can be used to also target SARS-CoV-2 in specific. There have also been earlier successful efforts in fighting viruses with CRISPR-based technology in human cells. In March 2020 researchers reported that they have developed a new kind of CRISPR-Cas13d screening platform for effective guide RNA design to target RNA.
Denial of service attack Distributed DoS attack DNS_amplification_attack > Attack techniques > Distributed DoS attack It uses a layered structure where the attacker uses a client program to connect to handlers, which are compromised systems that issue commands to the zombie agents, which in turn facilitate the DDoS attack. Agents are compromised via the handlers by the attacker. Each handler can control up to a thousand agents.
Complex societies The Collapse of Complex Societies Complex_society > The Collapse of Complex Societies Joseph Tainter (the author of The Collapse of Complex Societies) argued that as complex societies try to deal with the problems that they face, they tend to become more and more complex. This complexity exists under the purview of mechanisms that coordinate numerous differentiated and specialized social and economic roles by which complex societies are recognized. To deal with the problems that it faces, a society resorts to creating bureaucratic layers, infrastructure, and changes of social class that are relevant in addressing the problems. Tainter gives the Western Roman Empire, the Maya civilization, and the Chaco culture as examples of collapsed complex societies.
Polymer capacitor Polymer tantalum chip capacitors Polymer_electrolytic > Types and styles > Rectangular chip style > Polymer tantalum chip capacitors This layers achieves the cathode connection of the capacitor. The capacitive cell then is generally molded by a synthetic resin. Basic construction of a polymer tantalum capacitor Polymer tantalum electrolytic capacitors have ESR values that are approximately only 1/10 of the value of tantalum electrolytic capacitors with manganese dioxide electrolyte of the same size.
Conditioned stimulus The SOP model Conditioned_stimulus > Theories > Theoretical issues and alternatives to the Rescorla–Wagner model > Element-based models > The SOP model The rise and decay of element activation enables the model to explain time-dependent effects such as the fact that conditioning is strongest when the CS comes just before the US, and that when the CS comes after the US ("backward conditioning") the result is often an inhibitory CS. Many other more subtle phenomena are explained as well.A number of other powerful models have appeared in recent years which incorporate element representations. These often include the assumption that associations involve a network of connections between "nodes" that represent stimuli, responses, and perhaps one or more "hidden" layers of intermediate interconnections. Such models make contact with a current explosion of research on neural networks, artificial intelligence and machine learning.
Probability metric Divergences Statistically_close > Examples > Divergences Kullback–Leibler divergence Rényi divergence Jensen–Shannon divergence Bhattacharyya distance (despite its name it is not a distance, as it violates the triangle inequality) f-divergence: generalizes several distances and divergences Discriminability index, specifically the Bayes discriminability index, is a positive-definite symmetric measure of the overlap of two distributions.
Glossary of computer science S Glossary_of_computer_science > S In different programming languages, a subroutine may be called a routine, subprogram, function, method, or procedure. Technically, these terms all have different definitions.
Zigzag transformer Applications Zigzag_transformer > Applications Zigzag transformers are often required by utilities when connecting three-phase inverters (usually for renewable energy) to the grid to provide a stable neutral voltage and prevent excessive phase-to-ground voltages. This also protects the switching devices inside the inverters, which are usually insulated-gate bipolar transistors (IGBTs). == References ==
Cryptolect Anti-language Cryptolect > Anti-language All who employ this same form of communication are reality-maintaining others. The anti-language is a vehicle of resocialisation. There is continuity between language and anti-language.Examples of anti-languages include Cockney rhyming slang, CB slang, verlan, the grypsera of Polish prisons, thieves' cant, Polari, and possibly Bangime.
Zero point energy Chaotic and emergent phenomena Quantum_vacuum_zero_point_energy > Chaotic and emergent phenomena The mathematical models used in classical electromagnetism, quantum electrodynamics (QED) and the Standard Model all view the electromagnetic vacuum as a linear system with no overall observable consequence. For example, in the case of the Casimir effect, Lamb shift, and so on these phenomena can be explained by alternative mechanisms other than action of the vacuum by arbitrary changes to the normal ordering of field operators. See the alternative theories section. This is a consequence of viewing electromagnetism as a U(1) gauge theory, which topologically does not allow the complex interaction of a field with and on itself.
Java collections framework SortedMap interface Collections_Framework > Map interfaces > Map subinterfaces > SortedMap interface The java.util.SortedMap interface extends the java.util.Map interface. This interface defines a Map that's sorted by the keys provided. Using, once again, the compareTo() method or a method provided in the constructor to the SortedMap, the key-element pairs are sorted by the keys.
Octave-repeating scale Western music Non-octave-repeating_scale > Western music In the 19th century (to a certain extent), but more in the 20th century, additional types of scales were explored: The chromatic scale (twelve notes) The whole-tone scale (six notes) The pentatonic scale (five notes) The octatonic or diminished scales (eight notes)A large variety of other scales exists, some of the more common being: The Phrygian dominant scale (a mode of the harmonic minor scale) The Arabic scales The Hungarian minor scale The Byzantine music scales (called echoi) The Persian scaleScales such as the pentatonic scale may be considered gapped relative to the diatonic scale. An auxiliary scale is a scale other than the primary or original scale. See: modulation (music) and Auxiliary diminished scale.
HTTP protocol HTTP application session HTTP_protocol > HTTP application session HTTP is a stateless protocol. A stateless protocol does not require the web server to retain information or status about each user for the duration of multiple requests. Some web applications need to manage user sessions, so they implement states, or server side sessions, using for instance HTTP cookies or hidden variables within web forms. To start an application user session, an interactive authentication via web application login must be performed. To stop a user session a logout operation must be requested by user. These kind of operations do not use HTTP authentication but a custom managed web application authentication.
Mind wandering Executive functions Mind_wandering > Executive functions Shifting controls the ability to go between multiple tasks. All three EFs have a relationship to mind-wandering.Executive functions have roles in attention problems, attention control, thought control, and working memory capacity. Attention problems relate to behavioral problems such as inattention, impulsivity and hyperactivity.
Double-layer capacitance Capacitance Double-layer_capacitance > Capacitance Helmholtz laid the theoretical foundations for understanding the double layer phenomenon. The formation of double layers is exploited in every electrochemical capacitor to store electrical energy. Every capacitor has two electrodes, mechanically separated by a separator.
Linearization Linearization of a function Linearization > Linearization of a function The point-slope form of an equation forms an equation of a line, given a point ( H , K ) {\displaystyle (H,K)} and slope M {\displaystyle M} . The general form of this equation is: y − K = M ( x − H ) {\displaystyle y-K=M(x-H)} . Using the point ( a , f ( a ) ) {\displaystyle (a,f(a))} , L a ( x ) {\displaystyle L_{a}(x)} becomes y = f ( a ) + M ( x − a ) {\displaystyle y=f(a)+M(x-a)} .
Temporal dynamics of music and language Neuroanotomy of language and music Temporal_dynamics_of_music_and_language > Neuroanotomy of language and music These regions are believed to act as transmission routes that conduct information. These neural impulses allow the above regions to communicate and process information correctly. These structures include the thalamus and the basal ganglia.Some of the above-mentioned areas have been shown to be active in both music and language processing through PET and fMRI studies. These areas include the primary motor cortex, the Brocas area, the cerebellum, and the primary auditory cortices.
Small-group communication Group decisions Group_communication > Social influence in groups > Group decisions During a small group decision the process can be more open, vulnerable and can rely on several decision techniques. A common process that small groups incorporate in decision making situations starts by a orientation where each member starts to familiarize or socialize with other members. Secondly, small group members face conflict, where each person shares ideas or possible solutions to a problem.
Lexicographic max-min optimization Saturation Algorithm for convex problems Lexicographic_max-min_optimization > Algorithms for continuous variables > Saturation Algorithm for convex problems In some cases, the dual variables are given as a byproduct of solving (P1), for example, when the objectives and constraints are linear and the solver is the simplex algorithm. In this case, (P2) is not needed at all, and the run-time of the algorithm is at most n {\displaystyle n} times the run-time of the solver of (P1). : Alg.4 All these variants work only for convex problems. For non-convex problems, there might be no saturated objective, so the algorithm might not stop.
Embodied philosophy Memory Embodied_psychology > Scope > Memory The relationships between memory and embodied cognition have been demonstrated in studies in different fields and through various tasks. In general, studies on embodied cognition and memory investigate how manipulations on the body cause changes in memory performance, or vice versa, manipulations through memory tasks subsequently lead to bodily changes. Researchers has drawn attention to the relationship between memory and action from an embodied cognition approach where memory is defined as integrated patterns of actions limited by the body.
Individualized cancer immunotherapy Background Individualized_cancer_immunotherapy > Background These molecules may be recognized by CD8+ cytotoxic T lymphocytes as foreign neoepitopes and, with the help of CD4+ T lymphocytes, trigger an immune response leading to tumor-specific killing. CD8+ T cells are specialized for direct tumor cell killing. CD4+ T cells can interact with antigen-presenting cells such as dendritic cells to recruit other immune cells or stimulate effector cells.Most cancer neoantigens in humans arise from unique mutations.
Positive feedback In electronics Positive_feedback > Examples and applications > In electronics If there is a frequency (usually a high frequency) where the phase shift reaches 180°, then the designer must ensure that the amplifier gain at that frequency is very low (usually by low-pass filtering). If the loop gain (the product of the amplifier gain and the extent of the positive feedback) at any frequency is greater than one, then the amplifier will oscillate at that frequency (Barkhausen stability criterion). Such oscillations are sometimes called parasitic oscillations.
Sulfoglycolysis Summary Sulfoglycolysis Sulfoglycolysis is a catabolic process in primary metabolism in which sulfoquinovose (6-deoxy-6-sulfonato-glucose) is metabolized to produce energy and carbon-building blocks. Sulfoglycolysis pathways occur in a wide variety of organisms, and enable key steps in the degradation of sulfoquinovosyl diacylglycerol (SQDG), a sulfolipid found in plants and cyanobacteria into sulfite and sulfate. Sulfoglycolysis converts sulfoquinovose (C6H12O8S−) into various smaller metabolizable carbon fragments such as pyruvate and dihydroxyacetone phosphate that enter central metabolism. The free energy is used to form the high-energy molecules ATP (adenosine triphosphate) and NADH (reduced nicotinamide adenine dinucleotide).
Solution of a differential equation Higher order with variable coefficients System_of_linear_differential_equations > Higher order with variable coefficients This analogy extends to the proof methods and motivates the denomination of differential Galois theory. Similarly to the algebraic case, the theory allows deciding which equations may be solved by quadrature, and if possible solving them. However, for both theories, the necessary computations are extremely difficult, even with the most powerful computers. Nevertheless, the case of order two with rational coefficients has been completely solved by Kovacic's algorithm.
Mollifier Notes on Friedrichs' definition Cutoff_function > Definition > Notes on Friedrichs' definition Note 1. When the theory of distributions was still not widely known nor used, property (3) above was formulated by saying that the convolution of the function φ ϵ {\displaystyle \scriptstyle \varphi _{\epsilon }} with a given function belonging to a proper Hilbert or Banach space converges as ε → 0 to that function: this is exactly what Friedrichs did. This also clarifies why mollifiers are related to approximate identities.Note 2. As briefly pointed out in the "Historical notes" section of this entry, originally, the term "mollifier" identified the following convolution operator: Φ ϵ ( f ) ( x ) = ∫ R n φ ϵ ( x − y ) f ( y ) d y {\displaystyle \Phi _{\epsilon }(f)(x)=\int _{\mathbb {R} ^{n}}\varphi _{\epsilon }(x-y)f(y)\mathrm {d} y} where φ ϵ ( x ) = ϵ − n φ ( x / ϵ ) {\displaystyle \varphi _{\epsilon }(x)=\epsilon ^{-n}\varphi (x/\epsilon )} and φ {\displaystyle \varphi } is a smooth function satisfying the first three conditions stated above and one or more supplementary conditions as positivity and symmetry.
Internet area network History Internet_area_network > History After the dot-com bubble, Amazon played a key role in the development of cloud computing by modernizing their data centers, which, like most computer networks, were using as little as 10% of their capacity at any one time, just to leave room for occasional spikes. Having found that the new cloud architecture resulted in significant internal efficiency improvements whereby small, fast-moving "two-pizza teams" (teams small enough to be fed with two pizzas) could add new features faster and more easily, Amazon initiated a new product development effort to provide cloud computing to external customers, and launched Amazon Web Services (AWS) on a utility computing basis in 2006.In early 2008, Eucalyptus became the first open-source, AWS API-compatible platform for deploying private clouds. In early 2008, OpenNebula, enhanced in the RESERVOIR European Commission-funded project, became the first open-source software for deploying private and hybrid clouds, and for the federation of clouds.
Coumarin Summary Coumarin Coumarin () or 2H-chromen-2-one is an aromatic organic chemical compound with formula C9H6O2. Its molecule can be described as a benzene molecule with two adjacent hydrogen atoms replaced by an unsaturated lactone ring −(CH)=(CH)−(C=O)−O−, forming a second six-membered heterocycle that shares two carbons with the benzene ring. It belongs to the benzopyrone chemical class and considered as a lactone.Coumarin is a colorless crystalline solid with a sweet odor resembling the scent of vanilla and a bitter taste. It is found in many plants, where it may serve as a chemical defense against predators. By inhibiting synthesis of vitamin K, a related compound is used as the prescription drug warfarin – an anticoagulant – to inhibit formation of blood clots, deep vein thrombosis, and pulmonary embolism.
Isotopic signatures Carbon isotopes Isotope_signature > Stable isotopes > Carbon isotopes Many recent studies combine leaf level isotopic fractionation with annual patterns of wood formation (i.e. tree ring δ13C) to quantify the impacts of climatic variations and atmospheric composition on physiological processes of individual trees and forest stands. The next phase of understanding, in terrestrial ecosystems at least, seems to be the combination of multiple isotopic proxies to decipher interactions between plants, soils and the atmosphere, and predict how changes in land use will affect climate change. Similarly, marine fish contain more 13C than freshwater fish, with values approximating the C4 and C3 plants respectively.
Tesla Coil Resonant transformer Tesla_Coil > Operation > Resonant transformer Since the ground (Earth) serves as the return path for the high voltage, streamer arcs from the terminal tend to jump to any nearby grounded object. Bipolar: Neither end of the secondary winding is grounded, and both are brought out to high-voltage terminals. The primary winding is located at the center of the secondary coil, equidistant between the two high potential terminals, to discourage arcing.
Granular layer (cerebellum) Deep nuclei Cerebellar_cortex > Structure > Microanatomy > Deep nuclei The flocculus of the flocculonodular lobe is the only part of the cerebellar cortex that does not project to the deep nuclei—its output goes to the vestibular nuclei instead.The majority of neurons in the deep nuclei have large cell bodies and spherical dendritic trees with a radius of about 400 μm, and use glutamate as their neurotransmitter. These cells project to a variety of targets outside the cerebellum. Intermixed with them are a lesser number of small cells, which use GABA as a neurotransmitter and project exclusively to the inferior olivary nucleus, the source of climbing fibers.
Field homomorphism Galois theory Glossary_of_field_theory > Galois theory Kummer theory The Galois theory of taking n-th roots, given enough roots of unity. It includes the general theory of quadratic extensions. Artin–Schreier theory Covers an exceptional case of Kummer theory, in characteristic p. Normal basis A basis in the vector space sense of L over K, on which the Galois group of L over K acts transitively. Tensor product of fields A different foundational piece of algebra, including the compositum operation (join of fields).
Particle diffusion Character of the solutions Solving_the_heat_equation_using_Fourier_series > Interpretation > Character of the solutions For example, if two isolated bodies, initially at uniform but different temperatures u 0 {\displaystyle u_{0}} and u 1 {\displaystyle u_{1}} , are made to touch each other, the temperature at the point of contact will immediately assume some intermediate value, and a zone will develop around that point where u {\displaystyle u} will gradually vary between u 0 {\displaystyle u_{0}} and u 1 {\displaystyle u_{1}} . If a certain amount of heat is suddenly applied to a point in the medium, it will spread out in all directions in the form of a diffusion wave. Unlike the elastic and electromagnetic waves, the speed of a diffusion wave drops with time: as it spreads over a larger region, the temperature gradient decreases, and therefore the heat flow decreases too.
Coordination complexes History Coordination_complex > History Werner discovered the spatial arrangements of the ligands that were involved in the formation of the complex hexacoordinate cobalt. His theory allows one to understand the difference between a coordinated ligand and a charge balancing ion in a compound, for example the chloride ion in the cobaltammine chlorides and to explain many of the previously inexplicable isomers. In 1911, Werner first resolved the coordination complex hexol into optical isomers, overthrowing the theory that only carbon compounds could possess chirality.
Naked DNA DNA-binding proteins Deoxyribonucleic_acids > Interactions with proteins > DNA-binding proteins This changes the accessibility of the DNA template to the polymerase.As these DNA targets can occur throughout an organism's genome, changes in the activity of one type of transcription factor can affect thousands of genes. Consequently, these proteins are often the targets of the signal transduction processes that control responses to environmental changes or cellular differentiation and development. The specificity of these transcription factors' interactions with DNA come from the proteins making multiple contacts to the edges of the DNA bases, allowing them to "read" the DNA sequence. Most of these base-interactions are made in the major groove, where the bases are most accessible.
2-Norbornyl cation Spectroscopic evidence 2-Norbornyl_cation > Geometry > Spectroscopic evidence One probe for testing whether or not the 2-norbornyl cation is non-classical is investigating the inherent symmetry of the cation. Many spectroscopic tools, such as nuclear magnetic resonance spectroscopy (NMR spectroscopy) and Raman spectroscopy, give hints about the reflectional and rotational symmetry present in a molecule or ion. Each of the three proposed structures of the 2-norbornyl cation illustrates a different molecular symmetry. The non-classical form contains a reflection plane through carbons 4, 5, 6, and the midpoint of carbons 1 and 2.
Infinite group theory Chemistry and materials science Group_Theory > Applications of group theory > Chemistry and materials science In molecules with more than one rotation axis, the Cn axis having the largest value of n is the highest order rotation axis or principal axis. For example in boron trifluoride (BF3), the highest order of rotation axis is C3, so the principal axis of rotation is C3. In the reflection operation (σ) many molecules have mirror planes, although they may not be obvious.
Queap Summary Queap The data structure consists of a doubly linked list and a 2–4 tree data structure, each modified to keep track of its minimum-priority element. The basic operation of the structure is to keep newly inserted elements in the doubly linked list, until a deletion would remove one of the list items, at which point they are all moved into the 2–4 tree. The 2–4 tree stores its elements in insertion order, rather than the more conventional priority-sorted order. Both the data structure and its name were devised by John Iacono and Stefan Langerman.
Three sigma Cumulative distribution function Three-sigma_rule > Cumulative distribution function These numerical values "68%, 95%, 99.7%" come from the cumulative distribution function of the normal distribution. The prediction interval for any standard score z corresponds numerically to (1 − (1 − Φμ,σ2(z)) · 2). For example, Φ(2) ≈ 0.9772, or Pr(X ≤ μ + 2σ) ≈ 0.9772, corresponding to a prediction interval of (1 − (1 − 0.97725)·2) = 0.9545 = 95.45%. This is not a symmetrical interval – this is merely the probability that an observation is less than μ + 2σ. To compute the probability that an observation is within two standard deviations of the mean (small differences due to rounding): This is related to confidence interval as used in statistics: X ¯ ± 2 σ n {\displaystyle {\bar {X}}\pm 2{\frac {\sigma }{\sqrt {n}}}} is approximately a 95% confidence interval when X ¯ {\displaystyle {\bar {X}}} is the average of a sample of size n {\displaystyle n} .
Quad chart Summary Quad_chart A quad chart is a form of technical documentation used to briefly describe an invention or other innovation through writing, illustration and/or photographs. Such documents are described as "quad" charts because they are divided into four quadrants laid out on a landscape perspective. They are typically one-page only; their succinctness facilitates rapid decision-making. Though shorter, quad charts often serve in a similar capacity to white papers and the two documents are often requested alongside one another.
Roadable aircraft Lift Flying_car > Design > Lift Like other aircraft, lift in flight is provided by a fixed wing, spinning rotor or direct powered lift. The powered helicopter rotor and direct lift both offer VTOL capability, while the fixed wing and autogyro rotor take off conventionally from a runway. The simplest and earliest approach was to take a driveable car and attach removable flying surfaces and propeller. However when on the road, such a design must either tow its removable parts on a separate trailer or leave them behind and drive back to them before taking off again.
Co-location (satellite) How it works Co-location_(satellite) > How it works Co-located satellites cannot actually be positioned at the same point on the geostationary satellite arc. In fact, they are just close enough together to appear to be at the same position so far as the beamwidth of the receiving dish is concerned. SES maintains its co-located satellites within an imaginary 150 km cube in space, centred on the notional orbital position.All geostationary satellites are influenced by gravity of the Earth, the Moon and the Sun, and tend to drift from their initial orbital position. They are maintained on-station with on-board thrusters fired under the control of the operations centre on the ground. With a group of co-located satellites, the task is complex as each satellite must be maintained within the 150 km box but kept at a suitable distance (typically over 5 km) from the other satellites in the group to avoid collision or mutual interference, at the same time expending the least possible fuel to prolong the life of the satellite.
Cirrhosis of the liver Pathology Hepatic_fibrosis > Diagnosis > Pathology Its surface is irregular, the consistency is firm, and if associated with steatosis the color is yellow. Depending on the size of the nodules, there are three macroscopic types: micronodular, macronodular, and mixed cirrhosis. In the micronodular form (Laennec's cirrhosis or portal cirrhosis), regenerating nodules are under 3 mm. In macronodular cirrhosis (post-necrotic cirrhosis), the nodules are larger than 3 mm. Mixed cirrhosis consists of nodules of different sizes.
Psychrometric chart Locating parameters on chart Psychrometric_chart > Psychrometric charts > Locating parameters on chart The outer scale gives the ratio of enthalpy difference to humidity difference. This is used to establish the slope of a condition line between two processes. The horizontal component of the condition line is the change in sensible heat while the vertical component is the change in latent heat.
Reciprocity law Summary Reciprocity_law In mathematics, a reciprocity law is a generalization of the law of quadratic reciprocity to arbitrary monic irreducible polynomials f ( x ) {\displaystyle f(x)} with integer coefficients. Recall that first reciprocity law, quadratic reciprocity, determines when an irreducible polynomial f ( x ) = x 2 + a x + b {\displaystyle f(x)=x^{2}+ax+b} splits into linear terms when reduced mod p {\displaystyle p} . That is, it determines for which prime numbers the relation f ( x ) ≡ f p ( x ) = ( x − n p ) ( x − m p ) ( mod p ) {\displaystyle f(x)\equiv f_{p}(x)=(x-n_{p})(x-m_{p}){\text{ }}({\text{mod }}p)} holds. For a general reciprocity lawpg 3, it is defined as the rule determining which primes p {\displaystyle p} the polynomial f p {\displaystyle f_{p}} splits into linear factors, denoted Spl { f ( x ) } {\displaystyle {\text{Spl}}\{f(x)\}} .
Multiple Sclerosis Differential diagnosis Primary_progressive_multiple_sclerosis > Diagnosis > Differential diagnosis Several diseases present similarly to MS. Medical professionals use a patient's specific presentation, history, and exam findings to make an individualized differential. Red flags are findings that suggest an alternate diagnosis, although they do not rule out MS. Red flags include a patient younger than 15 or older than 60, less than 24 hours of symptoms, involvement of multiple cranial nerves, involvement of organs outside of the nervous system, and atypical lab and exam findings.In an emergency setting, it is important to rule out a stroke or bleeding in the brain.
Photovoltaic solar arrays Costs and economy Solar_PV_system > Costs and economy Panels are usually mounted at an angle based on latitude, and often they are adjusted seasonally to meet the changing solar declination. Solar tracking can also be utilized to access even more perpendicular sunlight, thereby raising the total energy output.
Genetic interaction network Biological implications Genetic_interaction_network > Biological implications While a variety of explanations have been proposed, genetic interactions could majorly decrease the amount of missing heritability by increasing the explanatory power of known genetic sources. Such genetic interactions would most likely go beyond the pairwise interactions considered in genetic interaction networks. == References ==
Mutational signatures Summary Mutational_signatures Mutational signatures are characteristic combinations of mutation types arising from specific mutagenesis processes such as DNA replication infidelity, exogenous and endogenous genotoxin exposures, defective DNA repair pathways, and DNA enzymatic editing.The term is used for two distinct concepts, often conflated: mutagen signatures and tumor signatures. Its original use, mutagen signature, referred to a pattern of mutations made in the laboratory by a known mutagen and not made by other mutagens – unique to the mutagen as a human signature is unique to the signer. Uniqueness allows the mutagen to be deduced from a cell's mutations Later, the phrase referred to a pattern of mutations characteristic of a tumor type, although usually not unique to the tumor type nor to a mutagen. If a tumor mutational signature matches a unique mutagen mutational signature, it is valid to deduce the carcinogen exposure or mutagenesis process that occurred in the patient's distant past.
Gametogenesis In animals Gametogenesis > In animals These diploid cells undergo meiotic division to create secondary spermatocytes. These secondary spermatocytes undergo a second meiotic division to produce immature sperms or spermatids. These spermatids undergo spermiogenesis in order to develop into sperm. LH, FSH, GnRH, and androgens are just a few of the hormones that help to promote spermatogenesis. oogenesis (female)
Four-square cipher Algorithm Four-square_cipher > Algorithm The encrypted digraph is simply the letters at the other two corners, with the upper-right letter coming first. Decryption works the same way, but in reverse.
Range of quantification Order of quantifiers (nesting) Logical_quantifier > Order of quantifiers (nesting) A function f from R to R is called Pointwise continuous if Uniformly continuous if In the former case, the particular value chosen for δ can be a function of both ε and x, the variables that precede it. In the latter case, δ can be a function only of ε (i.e., it has to be chosen independent of x). For example, f(x) = x2 satisfies pointwise, but not uniform continuity (its slope is unbound).
277 (number) Mathematical properties 277_(number) > Mathematical properties 277 is the 59th prime number, and is a regular prime. It is the smallest prime p such that the sum of the inverses of the primes up to p is greater than two. Since 59 is itself prime, 277 is a super-prime. 59 is also a super-prime (it is the 17th prime), as is 17 (the 7th prime).
External memory graph traversal External memory depth-first search External_memory_graph_traversal > External memory depth-first search The depth-first search algorithm explores a graph along each branch as deep as possible, before backtracing. For directed graphs Buchsbaum, Goldwasser, Venkatasubramanian and Westbrook proposed an algorithm with O ( ( V + E / B ) log 2 ⁡ ( V / B ) + sort ⁡ ( E ) ) {\displaystyle O((V+E/B)\log _{2}(V/B)+\operatorname {sort} (E))} I/Os. This algorithm is based on a data structure called buffered repository tree (BRT).
Cytoskeletal protein Common features and differences between prokaryotes and eukaryotes Cytoskeletal_protein > Common features and differences between prokaryotes and eukaryotes By definition, the cytoskeleton is composed of proteins that can form longitudinal arrays (fibres) in all organisms. These filament forming proteins have been classified into 4 classes. Tubulin-like, actin-like, Walker A cytoskeletal ATPases (WACA-proteins), and intermediate filaments.Tubulin-like proteins are tubulin in eukaryotes and FtsZ, TubZ, RepX in prokaryotes. Actin-like proteins are actin in eukaryotes and MreB, FtsA in prokaryotes.
Homoplasy Etymology Homoplasy > Etymology The term homoplasy was first used by Ray Lankester in 1870. The corresponding adjective is either homoplasic or homoplastic. It is derived from the two Ancient Greek words ὁμός (homós), meaning "similar, alike, the same", and πλάσσω (plássō), meaning "to shape, to mold".
Neo-classical economic theory Evolution Neoclassical_economics > Evolution The second, which was arguably not immediately influential, presented a model of temporary equilibrium. Hicks was influenced directly by Hayek's notion of intertemporal coordination and paralleled by earlier work by Lindhal. This was part of an abandonment of disaggregated long-run models. This trend probably reached its culmination with the Arrow–Debreu model of intertemporal equilibrium. The Arrow–Debreu model has canonical presentations in Gérard Debreu's Theory of Value (1959) and in Arrow and Hahn's "General Competitive Analysis" (1971).
André-Marie Ampère Work in electromagnetism André-Marie_Ampère > Work in electromagnetism Ampère also provided a physical understanding of the electromagnetic relationship, theorizing the existence of an "electrodynamic molecule" (the forerunner of the idea of the electron) that served as the component element of both electricity and magnetism. Using this physical explanation of electromagnetic motion, Ampère developed a physical account of electromagnetic phenomena that was both empirically demonstrable and mathematically predictive. Almost 100 years later, in 1915, Albert Einstein together with Wander Johannes de Haas made the proof of the correctness of Ampère's hypothesis through the Einstein–de Haas effect.
Heat treat Summary Heat_treatment Heat treating (or heat treatment) is a group of industrial, thermal and metalworking processes used to alter the physical, and sometimes chemical, properties of a material. The most common application is metallurgical. Heat treatments are also used in the manufacture of many other materials, such as glass.
Cobb-Douglas production function Criticisms Cobb-Douglas_production_function > Criticisms The function has been criticised for its lack of foundation. Cobb and Douglas were influenced by statistical evidence that appeared to show that labor and capital shares of total output were constant over time in developed countries; they explained this by statistical fitting least-squares regression of their production function. It is now widely accepted that labor share is declining in industrialized economies. The production function contains a principal assumption that may not always provide the most accurate representation of a country's productive capabilities and supply-side efficiencies.
Spread frequency-shift keying Summary Spread_frequency-shift_keying To avoid other interference, receivers can improve their signal-to-noise ratio by adapting their decoder. The silence and the preamble allow the receiver's signal processing to measure the channel's noise ratios. Depending on the signal to noise ratios, the bits can be recovered from the difference between the power of the mark and space tones, the power of the mark tones only, or the space tones only.
Comparison of programming languages Failsafe I/O and system calls Comparison_of_programming_languages > Failsafe I/O and system calls Psychologically, different cognitive biases (e.g., optimism bias) may affect novices and experts alike and lead them to skip these checks. This can lead to erroneous behavior. Failsafe I/O is a feature of 1C:Enterprise, Ada (exceptions), ALGOL (exceptions or return value depending on function), Ballerina, C#, Common Lisp ("conditions and restarts" system), Curry, D (throwing on failure), Erlang, Fortran, Go (unless result explicitly ignored), Gosu, Harbour, Haskell, ISLISP, Java, Julia, Kotlin, LabVIEW, Mathematica, Objective-C (exceptions), OCaml (exceptions), OpenLisp, PHP, Python, Raku, Rebol, Rexx (with optional signal on... trap handling), Ring, Ruby, Rust (unless result explicitly ignored), Scala, Smalltalk, Standard ML, Swift ≥ 2.0 (exceptions), Tcl, Visual Basic, Visual Basic .NET, Visual Prolog, Wolfram Language, Xojo, XPath/XQuery (exceptions), and Zeek. No Failsafe I/O: AutoHotkey (global ErrorLevel must be explicitly checked), C, COBOL, Eiffel (it actually depends on the library and it is not defined by the language), GLBasic (will generally cause program to crash), RPG, Lua (some functions do not warn or throw exceptions), and Perl.Some I/O checking is built in C++ (STL iostreams throw on failure but C APIs like stdio or POSIX do not) and Object Pascal, in Bash it is optional.
Centered dot In mathematics and science Centered_dot > In mathematics and science Another usage of this symbol in mathematics is with functions, where the dot is used as a placeholder for a function argument, in order to distinguish between the (general form of the) function itself and the value or a specific form of a function evaluated at a given point or with given specifications. For example, f ( ⋅ ) {\textstyle f(\cdot )} denotes the function x ↦ f ( x ) {\textstyle x\mapsto f(x)} , and θ ( s , a , ⋅ ) {\displaystyle \theta (s,a,\cdot )} denotes a partial application, where the first two arguments are given and the third argument shall take any valid value on its domain. The bullet operator, ∙, U+2219, is sometimes used to denote the "AND" relationship in formal logic.
Subaqueous fans Subclass of subaqueous fans Subaqueous_fans > Subclass of subaqueous fans These fan-shaped deposits refer to those that are underwater, leaving a broad range of options to fall under this category. A subclass of subaqueous fans may include underwater fan formations that are found on the ocean floor which can be specifically referred to as submarine or abyssal fans. These fan formations can be quite massive and are often the result of turbidite deposits from underwater density currents such as turbidity currents. These currents are typically short-lived, but are able to distribute great amounts of sediment into the deep ocean (Figure 4) making them a massive contributor to submarine fan formation.
Transfinite set theory Formalized set theory Transfinite_set_theory > Formalized set theory Sets and proper classes. These include Von Neumann–Bernays–Gödel set theory, which has the same strength as ZFC for theorems about sets alone, and Morse–Kelley set theory and Tarski–Grothendieck set theory, both of which are stronger than ZFC.The above systems can be modified to allow urelements, objects that can be members of sets but that are not themselves sets and do not have any members. The New Foundations systems of NFU (allowing urelements) and NF (lacking them), associate with Willard Van Orman Quine, are not based on a cumulative hierarchy.
Mutation rates Background Mutation_rates > Background Although measurements of this distribution have been inconsistent in the past, it is now generally thought that the majority of mutations are mildly deleterious, that many have little effect on an organism's fitness, and that a few can be favorable. Because of natural selection, unfavorable mutations will typically be eliminated from a population while favorable changes are generally kept for the next generation, and neutral changes accumulate at the rate they are created by mutations. This process happens by reproduction. In a particular generation the 'best fit' survive with higher probability, passing their genes to their offspring. The sign of the change in this probability defines mutations to be beneficial, neutral or harmful to organisms.
Watt governor Operation Centrifugal_governor > Operation This allows the two masses on lever arms to move outwards and upwards against gravity. If the motion goes far enough, this motion causes the lever arms to pull down on a thrust bearing, which moves a beam linkage, which reduces the aperture of a throttle valve. The rate of working-fluid entering the cylinder is thus reduced and the speed of the prime mover is controlled, preventing over-speeding. Mechanical stops may be used to limit the range of throttle motion, as seen near the masses in the image at right.
List of home computers by video hardware Explanation of the terms used in the tables List_of_home_computers_by_video_hardware > Explanation of the terms used in the tables HW accel Short for "hardware acceleration", can take several forms, the most obvious form is "bit blitting", that is the moving of groups of pixels from one place in video memory to another without the CPU doing any of the moving, another often-used technique is hardware scrolling which in fact emulates moving the whole screen in the video RAM, the third form of hardware acceleration is the use of sprites implemented in hardware. Some systems also supported drawing lines (and sometimes rectangles) using special line drawing hardware. The entry in the column reveals which methods the hardware supported with two letters for each method.
EIDR Handle System (EIDR Aspects) EIDR > Architecture > Handle System (EIDR Aspects) The distributed nature of the Handle System allows each local namespace to be hosted on multiple geographically distributed service sites. This is a federated model where each local name space has complete control over the placement and operation of its service sites. Furthermore, each service site may contain multiple resolution servers: requests directed to a particular service site will be dispatched evenly across its constituent servers.
Striation (fatigue) Tyre tracks Striation_(fatigue) > Striation-like features > Tyre tracks Tyre tracks are the marks on the fracture surface produced by something making an impression onto the surface from the repeated opening and closing of the crack faces. This can be produced by either a particle that becomes trapped between the crack faces or the faces themselves shifting and directly contacting the opposite surface.
Vigabatrin Central nervous system Vigabatrin > Adverse effects > Central nervous system Sleepiness (12.5%), headache (3.8%), dizziness (3.8%), nervousness (2.7%), depression (2.5%), memory disturbances (2.3%), diplopia (2.2%), aggression (2.0%), ataxia (1.9%), vertigo (1.9%), hyperactivity (1.8%), vision loss (1.6%) (See below), confusion (1.4%), insomnia (1.3%), impaired concentration (1.2%), personality issues (1.1%). Out of 299 children, 33 (11%) became hyperactive.Some patients develop psychosis during the course of vigabatrin therapy, which is more common in adults than in children. This can happen even in patients with no prior history of psychosis. Other rare CNS side effects include anxiety, emotional lability, irritability, tremor, abnormal gait, and speech disorder.
Glossary of genetics (0–L) I Glossary_of_gene_expression_terms > I insertion sequence (IS) Also insertion element or simply insert. Any nucleotide sequence that is inserted naturally or artificially into another sequence. The term is used in particular to refer to the part of a transposable element that codes for those proteins directly involved in the transposition process, e.g. the transposase enzyme.
Schamel equation Logarithmic Schamel equation Schamel_equation > Generalizations > Logarithmic Schamel equation Another generalization of the S-equation is obtained in the case of ion acoustic waves by admitting a second trapping channel. By considering an additional, non-perturbative trapping scenario, Schamel received: ϕ t + ( 1 + b ϕ − D ln ⁡ ϕ ) ϕ x + ϕ x x x = 0 {\displaystyle \qquad \qquad \phi _{t}+(1+b{\sqrt {\phi }}-D\ln \phi )\phi _{x}+\phi _{xxx}=0} , a generalization called logarithmic S-equation. In the absence of the square root nonlinearity, b = 0 {\displaystyle b=0} , it is solved by a Gaussian shaped hole solution: ϕ ( x ) = ψ e D x 2 / 4 {\displaystyle \phi (x)=\psi e^{Dx^{2}/4}} with D < 0 {\displaystyle D<0} and has a supersonic phase velocity v 0 = 1 + D ( ln ⁡ ψ − 3 / 2 ) > 1 {\displaystyle v_{0}=1+D(\ln \psi -3/2)>1} . The corresponding pseudo-potential is given by − V ( ϕ ) = D ϕ 2 2 ln ⁡ ϕ ψ {\displaystyle -{\mathcal {V}}(\phi )=D{\frac {\phi ^{2}}{2}}\ln {\frac {\phi }{\psi }}} .
Polyhedral groups Summary Polyhedral_group In geometry, the polyhedral group is any of the symmetry groups of the Platonic solids.
Bidiagonal matrix Bidiagonalization Bidiagonal_matrix > Usage > Bidiagonalization Bidiagonalization allows guaranteed accuracy when using floating-point arithmetic to compute singular values.
Feature hashing Mathematical motivation Feature_hashing > Motivation > Mathematical motivation , t m } {\displaystyle T=\{t_{1},t_{2},..,t_{m}\}} , then define ϕ ( t i ) = e i {\displaystyle \phi (t_{i})=e_{i}} . In other words, we assign a unique index i {\displaystyle i} to each token, then map the token with index i {\displaystyle i} to the unit basis vector e i {\displaystyle e_{i}} . One-hot encoding is easy to interpret, but it requires one to maintain the arbitrary enumeration of T {\displaystyle T} .

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