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Interface Control Document Characteristics Interface_Control_Document > Characteristics An application programming interface is a form of interface for a software system, in that it describes how to access the functions and services provided by a system via an interface. If a system producer wants others to be able to use the system, an ICD and interface specs (or their equivalent) is a worthwhile investment. An ICD should only describe the detailed interface documentation itself, and not the characteristics of the systems which use it to connect. The function and logic of those systems should be described in their own requirements and design documents as needed.
Broken order reaction Integral method Rate_equation_(chemistry) > Power laws > Determination of reaction order > Integral method The tentative rate equation determined by the method of initial rates is therefore normally verified by comparing the concentrations measured over a longer time (several half-lives) with the integrated form of the rate equation; this assumes that the reaction goes to completion. For example, the integrated rate law for a first-order reaction is ln ⁡ = − k t + ln ⁡ 0 , {\displaystyle \ln {}=-kt+\ln {_{0}},} where {\displaystyle }}} is the concentration at time t {\displaystyle t} and 0 {\displaystyle _{0}}}} is the initial concentration at zero time. The first-order rate law is confirmed if ln ⁡ {\displaystyle \ln {}} is in fact a linear function of time. In this case the rate constant k {\displaystyle k} is equal to the slope with sign reversed.
Dimensionality reduction Summary Dimensionality_reduction Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable (hard to control or deal with). Dimensionality reduction is common in fields that deal with large numbers of observations and/or large numbers of variables, such as signal processing, speech recognition, neuroinformatics, and bioinformatics.Methods are commonly divided into linear and nonlinear approaches. Approaches can also be divided into feature selection and feature extraction. Dimensionality reduction can be used for noise reduction, data visualization, cluster analysis, or as an intermediate step to facilitate other analyses.
Binet equation Classical Binet_equation > Examples > Kepler problem > Classical The traditional Kepler problem of calculating the orbit of an inverse square law may be read off from the Binet equation as the solution to the differential equation If the angle θ {\displaystyle \theta } is measured from the periapsis, then the general solution for the orbit expressed in (reciprocal) polar coordinates is The above polar equation describes conic sections, with l {\displaystyle l} the semi-latus rectum (equal to h 2 / μ = h 2 m / k {\displaystyle h^{2}/\mu =h^{2}m/k} ) and ε {\displaystyle \varepsilon } the orbital eccentricity.
Luis Santaló Introduction to Integral Geometry (1953) Luis_Santaló > Works > Introduction to Integral Geometry (1953) Ch. III. General integral geometry: Lie groups on the plane: central-affine, unimodular affine, projective groups.
Screw compressor Variable speed Rotary_screw_compressor > Control schemes > Variable speed While an air compressor powered by a variable-speed drive can offer the lowest operating-energy cost without any appreciable reduction in service life over a properly maintained load/unload compressor, the variable-frequency power inverter of a variable-speed drive typically adds significant cost to the design of such a compressor, reducing its economic benefits over a properly sized load/unload compressor if air demand is constant. However, a variable-speed drive provides for a nearly linear relationship between compressor power consumption and free air delivery allowing the most efficient operation over a very wide range of air demand. The compressor will still have to enter start/stop mode for very low demand as efficiency still drops off rapidly at low production rates due to rotor leakage. In harsh environments (hot, humid or dusty) the electronics of variable-speed drives may have to be protected to retain expected service life.
Structural Biology Applications Structural_biologist > Applications For example, researchers have used structural biology to better understand Met, a protein encoded by a protooncogene that is an important drug target in cancer. Similar research has been conducted for HIV targets to treat people with AIDS. Researchers are also developing new antimicrobials for mycobacterial infections using structure-driven drug discovery.
Diagonalizable matrices Quantum mechanical application Matrix_diagonalisation > Quantum mechanical application In quantum mechanical and quantum chemical computations matrix diagonalization is one of the most frequently applied numerical processes. The basic reason is that the time-independent Schrödinger equation is an eigenvalue equation, albeit in most of the physical situations on an infinite dimensional space (a Hilbert space). A very common approximation is to truncate Hilbert space to finite dimension, after which the Schrödinger equation can be formulated as an eigenvalue problem of a real symmetric, or complex Hermitian matrix. Formally this approximation is founded on the variational principle, valid for Hamiltonians that are bounded from below. First-order perturbation theory also leads to matrix eigenvalue problem for degenerate states.
Satellite system (astronomy) Orbital configurations Proto-satellite_disk > Features and interactions > Gravitational interactions > Orbital configurations The Saturnian moons Janus and Epimetheus share their orbits, the difference in semi-major axes being less than either's mean diameter. Libration is a perceived oscillating motion of orbiting bodies relative to each other. The Earth-moon satellite system is known to produce this effect.
Models of communication Newcomb Models_of_communication > History > Newcomb It is relevant, for example, whether A and B like each other and whether they have the same attitude towards X.Newcomb understands communication as a "learned response to strain" caused by discrepancies between orientations. The social function of communication is to maintain equilibrium in the social system by keeping the different orientations in balance. In Newcomb's words, communication enables "two or more individuals to maintain simultaneous orientation to each other and towards objects of the external environment".
Medical equipment management Data Quality Management Medical_equipment_management > Data Quality Management Accurate, comprehensive data are needed in any automated medical equipment management system. Data quality initiatives can help to insure the accuracy of clinical/biomedical engineering data. The data needed to establish basic, accurate, maintainable automated records for medical equipment management includes: nomenclature, manufacturer, nameplate model, serial number, acquisition cost, condition code, and maintenance assessment. Other useful data could include: warranty, location, other contractor agencies, scheduled maintenance due dates, and intervals.
Patient empowerment Transatlantic rise of health advocacy Patient_empowerment > Transatlantic rise of health advocacy She is cited in a more recent open-access survey laying out researchers' various views, especially on the ethical dimensions of engaging patients as partners within research teams.In Norway, Nilsen et al. were critical of patients' role in health policy and clinical guideline development in their Cochrane Intervention Review. Two other Norwegian researchers, though, in unison with the workshop findings above, expand the list of areas where patients' views matter: "The central arena for patient participation is the meeting between patient and health professional, but other important areas of involvement include decisions at the system and policy levels".In the United States there are several trends emerging with potential international implications: Health 2.0, artificial intelligence in healthcare (AI), the role of entrepreneurs, the value of patient participation in precision medicine and mobile health or MHealth, which will be dealt with in greater detail below. In Israel, a multicenter study at eight fertility units located in hospitals across the country found that unit directors are familiar with the patient-centered care approach and in general support it.
Cache coherency protocols (examples) MOESI protocol Cache_coherency_protocols_(examples) > Coherency protocols > MOESI protocol States MEOSI = D-R-SD-V-I = T-MESI IBM – Use of bus "shared line" to detect "shared" copy on the other cachesProcessor operationsRead Miss– If there is a M or O or E (*) copy in another cache the data is supplied by this cache (intervention). The requesting cache is set S , M is changed to O and E to S – else the data is read from MM. – If "shared line" is "on" the requesting cache is set S else EWrite Hit– If the cache is M or E (exclusiveness), the write can take place locally without any other action – else O or S (sharing) an "Invalidation" transaction is sent on the bus to invalidate all the other caches. – The cache is set (or remains) MWrite Miss– A RWITM operation is sent to the bus – Data is supplied from the "owner" or from MM as with Read Miss, then cache is written (updated) – The cache is set M and all the other caches are set IBus transactionsBus Read– If the cache is M or O or E (*) the data is sent to requesting cache (intervention). If the cache is E the state is changed in S, else is set (or remains) O – else the state is changed or remains in SBus Read – (RWITM)– If the cache is M or O or E (*) the data is sent to the bus (Intervention) – The cache is set "Invalid" (I)Bus Invalidate Transaction– The cache is set "Invalid" (I)OperationsWrite Allocate Intervention: from M-O-E (*) Write Invalidate Copy-Back: M-O replacement– (*) implementation depending for E————————————————————————————————————————
Multiprocessor system architecture Examples of interconnection Multiprocessor_system_architecture > Tightly-coupled (shared memory) multiprocessor system > cc-NUMA system > Examples of interconnection To overcome this limit, a large remote cache (see Remote cache) is normally used. With this solution, the cc-NUMA system becomes very close to a large SMP system.
Reaction Progress Kinetic Analysis Changes in catalyst resting state Reaction_Progress_Kinetic_Analysis > Catalytic kinetics and catalyst resting state > Changes in catalyst resting state While a reaction may exhibit one set of kinetic behavior at early conversion, that behavior may change due to: changes in catalyst resting state influenced by changing substrate concentrations multiple or changing mechanisms influenced by substrate or product concentrations catalyst activation (an initiation period) product inhibition irreversible (or reversible) catalyst deathIn the case of saturation kinetics described above, provided that is not present in a large excess relative to , saturation conditions will only apply at the beginning of the reaction. As the substrate is consumed, the concentration decreases and eventually is no longer sufficient to completely overwhelm . This is manifested by a gradual change in rate from 0-order to some higher (i.e. 1st, 2nd, etc.) order in . This can also be described as a change in catalyst resting state from the bound form to the unbound form over the course of the reaction.
Opinion polls Margin of error due to sampling Opinion_polling > Potential for inaccuracy > Margin of error due to sampling For example, if you assume that the breakdown of the US population by party identification has not changed since the previous presidential election, you may underestimate a victory or a defeat of a particular party candidate that saw a surge or decline in its party registration relative to the previous presidential election cycle. A caution is that an estimate of a trend is subject to a larger error than an estimate of a level. This is because if one estimates the change, the difference between two numbers X and Y, then one has to contend with errors in both X and Y. A rough guide is that if the change in measurement falls outside the margin of error it is worth attention.
Jean-Robert Argand Life Jean-Robert_Argand > Life Argand moved to Paris in 1806 with his family and, when managing a bookshop there, privately published his Essai sur une manière de représenter les quantités imaginaires dans les constructions géométriques (Essay on a method of representing imaginary quantities). In 1813, it was republished in the French journal Annales de Mathématiques. The Essay discussed a method of graphing complex numbers via analytical geometry.
Bovine tuberculosis Summary Mycobacterium_bovis Mycobacterium bovis is a slow-growing (16- to 20-hour generation time) aerobic bacterium and the causative agent of tuberculosis in cattle (known as bovine TB). It is related to Mycobacterium tuberculosis, the bacterium which causes tuberculosis in humans. M. bovis can jump the species barrier and cause tuberculosis-like infection in humans and other mammals.
GOMS Disadvantages GOMS > Qualification > Disadvantages Another big disadvantage is the lack of account for errors, even skilled users make errors but GOMS does not account for errors. Mental workload is not addressed in the model, making this an unpredictable variable. The same applies to fatigue.
Paranoid schizophrenic Comorbidities Negative_symptoms_of_schizophrenia > Diagnosis > Comorbidities Many people with schizophrenia may have one or more other mental disorders, such as panic disorder, obsessive–compulsive disorder, or substance use disorder. These are separate disorders that require treatment. When comorbid with schizophrenia, substance use disorder and antisocial personality disorder both increase the risk for violence. Comorbid substance use disorder also increases the risk of suicide.Sleep disorders often co-occur with schizophrenia, and may be an early sign of relapse.
Chest pain Chest wall Chest_pain > Differential diagnosis > Chest wall Breast conditions Herpes zoster (shingles): It is usually described as a burning sensation over the chest in a unilateral dermatome distribution. However, diagnosis can be difficult because the pain usually appears before the characteristic rash is visible. Tuberculosis Osteoarthritis Bornholm disease Rib fracture
IRT Powerhouse Structural features IRT_Powerhouse > Architecture > Structural features The building is supported by a skeletal steel superstructure that weighs about 12,000 short tons (11,000 long tons; 11,000 t). The floors and coal bunkers generally consist of I-beams, as well as plate girders similar to those used on plate girder bridges. The strength of the steelwork necessitated that the building use girders that would normally be used on bridges. The American Bridge Company manufactured the steel used in the superstructure.
Feature matching Definition Point_feature_matching > Definition Feature detection is a low-level image processing operation. That is, it is usually performed as the first operation on an image, and examines every pixel to see if there is a feature present at that pixel. If this is part of a larger algorithm, then the algorithm will typically only examine the image in the region of the features.
Ronald C. Arkin Students Ronald_C._Arkin > Students Robin Murphy (Summer, 1992). Thesis: An Architecture for Intelligent Sensor Fusion. Founder of rescue robot and currently a professor at the Texas A&M University, College Station, TX. Erika Rogers (Fall, 1992).
Real Analysis Integration Real_Analysis > Scope > Integration Integration is a formalization of the problem of finding the area bound by a curve and the related problems of determining the length of a curve or volume enclosed by a surface. The basic strategy to solving problems of this type was known to the ancient Greeks and Chinese, and was known as the method of exhaustion. Generally speaking, the desired area is bounded from above and below, respectively, by increasingly accurate circumscribing and inscribing polygonal approximations whose exact areas can be computed.
Organizing principle Examples Organizing_principle > Examples The central organising principle of the Welsh Government is sustainability. Legitimation code theory is an explanatory framework in the sociology of knowledge and education that seeks to understand different social fields of practices in terms of their organizing principles, which determines the basis of success and failure. The organizing principle of the aphorism "as above, so below" is based on man's primordial sense of up and down and that this sense is a result of the symmetries in nature. Theism holds that there is a cause for things that are evidently effects or passive to a force or action and that this involves a vital force that produces effects that demonstrate design and concordance.
Standard Model of Particle Physics Higgs boson Standard_Model_of_Particle_Physics > Particle content > Higgs boson Experiments to confirm and determine the nature of the Higgs boson using the Large Hadron Collider (LHC) at CERN began in early 2010 and were performed at Fermilab's Tevatron until its closure in late 2011. Mathematical consistency of the Standard Model requires that any mechanism capable of generating the masses of elementary particles must become visible at energies above 1.4 TeV; therefore, the LHC (designed to collide two 7 TeV proton beams) was built to answer the question of whether the Higgs boson actually exists.On 4 July 2012, two of the experiments at the LHC (ATLAS and CMS) both reported independently that they had found a new particle with a mass of about 125 GeV/c2 (about 133 proton masses, on the order of 10−25 kg), which is "consistent with the Higgs boson". On 13 March 2013, it was confirmed to be the searched-for Higgs boson.
Variational Bayes Algorithm for computing the parameters Variational_Bayes > A basic example > Algorithm for computing the parameters Note also that the posterior distributions have the same form as the corresponding prior distributions. We did not assume this; the only assumption we made was that the distributions factorize, and the form of the distributions followed naturally. It turns out (see below) that the fact that the posterior distributions have the same form as the prior distributions is not a coincidence, but a general result whenever the prior distributions are members of the exponential family, which is the case for most of the standard distributions.
Filter bag Cartridge collectors Filter_bag > Fabric filters > Types of bag cleaning > Cartridge collectors Cartridge collectors use perforated metal cartridges that contain a pleated, nonwoven filtering media, as opposed to woven or felt bags used in baghouses. The pleated design allows for a greater total filtering surface area than in a conventional bag of the same diameter, The greater filtering area results in a reduced air to media ratio, pressure drop, and overall collector size. Cartridge collectors are available in single use or continuous duty designs. In single-use collectors, the dirty cartridges are changed and collected dirt is removed while the collector is off. In the continuous duty design, the cartridges are cleaned by the conventional pulse-jet cleaning system.
Emotional conflict Physical symptoms Emotional_conflict > Physical symptoms Inner emotional conflicts can result in physical discomfort or pain, often in the form of tension headaches, which can be episodic or chronic, and may last from a few minutes or hours, to days - associated pain being mild, moderate, or severe. "The physiology of nervous headaches still presents many unsolved problems", as in general do all such "physical alterations...rooted in unconscious instinctual conflicts". However physical discomfort or pain without apparent cause may be the way our body is telling us of an underlying emotional turmoil and anxiety, triggered by some recent event.
Air conditioner Operating principles Air_Conditioning > Operation > Operating principles Cooling in traditional air conditioner systems is accomplished using the vapor-compression cycle, which uses the forced circulation and phase change of a refrigerant between gas and liquid to transfer heat. The vapor-compression cycle can occur within a unitary, or packaged piece of equipment; or within a chiller that is connected to terminal cooling equipment (such as a fan coil unit in an air handler) on its evaporator side and heat rejection equipment such as a cooling tower on its condenser side. An air source heat pump shares many components with an air conditioning system, but includes a reversing valve which allows the unit to be used to heat as well as cool a space.Air conditioning equipment will reduce the absolute humidity of the air processed by the system if the surface of the evaporator coil is significantly cooler than the dew point of the surrounding air.
Ferredoxin reductase Summary Ferredoxin_reductase Ferredoxin reductase may refer to: Ferredoxin—NADP(+) reductase (FNR) Ferredoxin—NAD(+) reductase Ferredoxin—nitrite reductase Ferredoxin-thioredoxin reductase
Combustion analysis History CHN_analyzer > History The method was invented by Joseph Louis Gay-Lussac. Justus von Liebig studied the method while working with Gay-Lussac between 1822 and 1824 and improved the method in the following years to a level that it could be used as standard procedure for organic analysis.
Tree crown measurement Google Earth measurements. Tree_crown_measurement > Crown spread methodologies > Google Earth measurements. One option, the Polygonal Method, measures each side of a triangle to compute its area. The second and third methods uses azimuths and one distance to the trunk calculate the area. The fourth method, the Azimuth Method, requires only azimuths and distance measurements from point to point around the crown perimeter.
Jacobi elliptic functions Schellbach Schwarz integer sequence Jacobian_elliptic_functions > The elliptic nome and its series > Schellbach Schwarz integer sequence The mathematician Karl Heinrich Schellbach discovered the integer number sequence that appears in the MacLaurin series of the Elliptic Nome function. This scientist constructed this sequence A002103 in his work Die Lehre von den elliptischen Integralen und den Thetafunktionen in detail. Especially on page 60 of this work a synthesis route of this sequence is written down in his work. Also the Silesian German mathematician Hermann Amandus Schwarz wrote in his work Formeln und Lehrsätze zum Gebrauche der elliptischen Funktionen in the chapter Berechnung der Grösse k on pages 54 to 56 that integer number sequence down.
Range of a matrix Basis Row_and_column_spaces > Row space > Basis The row space is not affected by elementary row operations. This makes it possible to use row reduction to find a basis for the row space. For example, consider the matrix A = . {\displaystyle A={\begin{bmatrix}1&3&2\\2&7&4\\1&5&2\end{bmatrix}}.}
Usability Engineering Bibliography for Usability Engineering Usability_Engineering > Bibliography for Usability Engineering Usability Engineering: Process, Products & Examples. Prentice Hall. ISBN 978-0-13-157008-5.
Prices of production Level of abstraction Prices_of_production > Evaluation > Level of abstraction A more serious criticism of Marx is that the theory of prices of production is still pitched at a far too abstract theoretical level to be able to explain anything like specific real price movements. That is, Marx only illustrated with examples the general results towards which the competitive process would tend to move in capitalism as a social system. He tried to establish what regulates product prices in the "simplest and purest case".
Lebesgue measurable Examples Lebesgue_measure > Examples If the axiom of determinacy holds then all sets of reals are Lebesgue-measurable. Determinacy is however not compatible with the axiom of choice. Vitali sets are examples of sets that are not measurable with respect to the Lebesgue measure.
History of astronomy Copernican Revolution History_of_astronomy > Renaissance and Early Modern Europe > Copernican Revolution In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma. (It is assumed here that the mass m is constant) When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.Thus while Kepler explained how the planets moved, Newton accurately managed to explain why the planets moved the way they do. Newton's theoretical developments laid many of the foundations of modern physics.
Fluorescence spectroscopy Analysis of data Fluorescence_spectroscopy > Analysis of data Firstly, the distortion arising from the instrument is discussed. As a start, the light source intensity and wavelength characteristics varies over time during each experiment and between each experiment.
Geon (physics) Summary Geon_(physics) In theoretical general relativity, a geon is a nonsingular electromagnetic or gravitational wave which is held together in a confined region by the gravitational attraction of its own field energy. They were first investigated theoretically in 1955 by J. A. Wheeler, who coined the term as a contraction of "gravitational electromagnetic entity".
Fundamental theorem of the calculus Generalizations Fundamental_theorem_of_the_calculus > Generalizations Conversely, if f is any integrable function, then F as given in the first formula will be absolutely continuous with F′ = f almost everywhere. The conditions of this theorem may again be relaxed by considering the integrals involved as Henstock–Kurzweil integrals. Specifically, if a continuous function F(x) admits a derivative f(x) at all but countably many points, then f(x) is Henstock–Kurzweil integrable and F(b) − F(a) is equal to the integral of f on .
Unit of energy Food industry Unit_of_energy > Food industry The calorie is defined as the amount of thermal energy necessary to raise the temperature of one gram of water by 1 Celsius degree, from a temperature of 14.5 °C, at a pressure of 1 atm. For thermochemistry a calorie of 4.184 J is used, but other calories have also been defined, such as the International Steam Table calorie of 4.1868 J. In many regions, food energy is measured in large calories or kilocalories equalling 1000 calories, sometimes written capitalized as Calories. In the European Union, food energy labeling in joules is mandatory, often with calories as supplementary information.
Cache Hierarchy Multi-level cache Cache_Hierarchy > Multi-level cache Accessing main memory for each instruction execution may result in slow processing, with the clock speed depending on the time required to find and fetch the data. In order to hide this memory latency from the processor, data caching is used. Whenever the data is required by the processor, it is fetched from the main memory and stored in the smaller memory structure called a cache.
Pro-inflammatory cytokine Summary Proinflammatory_cytokines An inflammatory cytokine or proinflammatory cytokine is a type of signaling molecule (a cytokine) that is secreted from immune cells like helper T cells (Th) and macrophages, and certain other cell types that promote inflammation. They include interleukin-1 (IL-1), IL-6, IL-12, and IL-18, tumor necrosis factor alpha (TNF-α), interferon gamma (IFNγ), and granulocyte-macrophage colony stimulating factor (GM-CSF) and play an important role in mediating the innate immune response. Inflammatory cytokines are predominantly produced by and involved in the upregulation of inflammatory reactions. Excessive chronic production of inflammatory cytokines contribute to inflammatory diseases, that have been linked to different diseases, such as atherosclerosis and cancer.
Probability spaces General case Probability_space > General case If Ω is uncountable, still, it may happen that p(ω) ≠ 0 for some ω; such ω are called atoms. They are an at most countable (maybe empty) set, whose probability is the sum of probabilities of all atoms. If this sum is equal to 1 then all other points can safely be excluded from the sample space, returning us to the discrete case. Otherwise, if the sum of probabilities of all atoms is between 0 and 1, then the probability space decomposes into a discrete (atomic) part (maybe empty) and a non-atomic part.
George Hadley Life George_Hadley > Life However, since the air mass is at all times in a state of circumnavigating the Earth axis, it is in fact the angular momentum that is conserved, causing an effect known as the Coriolis effect. When using the correct angular momentum conservation in calculations the predicted effect is twice as large as when the erroneous conservation of linear momentum is used. The fact that Hadley's principle is deficient in this respect is not known to everyone who should know; it can still be found in popular books and popular websites.
Pythagoras's theorem Trigonometric proof using Einstein's construction Pythagoras's_theorem > Other proofs of the theorem > Trigonometric proof using Einstein's construction Both the proof using similar triangles and Einstein's proof rely on constructing the height to the hypotenuse of the right triangle △ A B C {\displaystyle \triangle ABC} . The same construction provides a trigonometric proof of the Pythagorean theorem using the definition of the sine as a ratio inside a right triangle: sin ⁡ α = a c , {\displaystyle \sin \alpha ={\frac {a}{c}},} sin ⁡ β = b c , {\displaystyle \sin \beta ={\frac {b}{c}},} c = b sin ⁡ β + a sin ⁡ α = b 2 c + a 2 c , {\displaystyle c=b\sin \beta +a\sin \alpha ={\frac {b^{2}}{c}}+{\frac {a^{2}}{c}},} and thus c 2 = a 2 + b 2 . {\displaystyle c^{2}=a^{2}+b^{2}.} This proof is essentially the same as the above proof using similar triangles, where some ratios of lengths are replaced by sines.
Language planning Language status Language_planning > Types > Status planning > Language status Their respective frameworks differ slightly, but they emphasize four common attributes: Language origin – whether a given language is indigenous or imported to the speech community Degree of standardization – the extent of development of a formal set of norms that define 'correct' usage Juridical status Sole official language (e.g. French in France and Turkish in Turkey) Joint official language (e.g. English and Afrikaans in South Africa; French, German, Italian and Romansh in Switzerland) Regional official language (e.g. Igbo in Nigeria; Marathi in Maharashtra, India) Promoted language – lacks official status on a national or regional level but is promoted and sometimes used by public authorities for specific functions (e.g. Spanish in New Mexico; West African Pidgin English in Cameroon) Tolerated language – neither promoted nor proscribed; acknowledged but ignored (e.g. Native American languages in the United States in the present day) Proscribed language – discouraged by official sanction or restriction (e.g. Welsh in the UK in the past, Breton, Alsatian and others in France, Galician, Basque and Catalan during Francisco Franco's regime in Spain; Macedonian in Greece; indigenous American languages during the boarding school era) Vitality – the ratio, or percent, of users of a language to another variable, such as the total population. Kloss and Stewart both distinguish six classes of statistical distribution. However, they draw the line between classes at different percentages.
Protofection Possible therapeutic uses Protofection > Possible therapeutic uses One hypothesis for mitochondrial diseases is that mitochondrial damage and dysfunction play an important role in aging. Protofection is being researched as a possibly viable laboratory technique for constructing gene therapies for inherited mitochondrial diseases, such as Leber's hereditary optic neuropathy. Studies have shown that protofection can lead to improved mitochondrial function in targeted cells.Protofection could be applied to modified or artificial mitochondria. Mitochondria could be modified to produce few or no free radicals without compromising energy production. Recent studies have demonstrated that mitochondrial transplants may be useful to rejuvenate dead or dying tissue, such as in heart attacks, for which the mitochondria is the first part of the cell that dies.
Čech cohomology Relation to other cohomology theories Cech_cohomology > Relation to other cohomology theories {\displaystyle H^{1}(X;\mathbb {Z} )=0.} If X is a differentiable manifold and the cover U {\displaystyle {\mathcal {U}}} of X is a "good cover" (i.e. all the sets Uα are contractible to a point, and all finite intersections of sets in U {\displaystyle {\mathcal {U}}} are either empty or contractible to a point), then H ˇ ∗ ( U ; R ) {\displaystyle {\check {H}}^{*}({\mathcal {U}};\mathbb {R} )} is isomorphic to the de Rham cohomology. If X is compact Hausdorff, then Čech cohomology (with coefficients in a discrete group) is isomorphic to Alexander-Spanier cohomology.
Configuration model Diameter Configuration_model > Properties > Diameter Configuration model can assume any degree distribution and shows the small-world effect, since to leading order the diameter of the configuration model is just d = ln ⁡ ( N ) ln ⁡ ( c 2 / c 1 ) {\displaystyle d={\frac {\ln(N)}{\ln(c_{2}/c_{1})}}} .
Determinant Block matrices Determinant_(mathematics) > Properties of the determinant > Block matrices A similar result holds when D {\displaystyle D} is invertible, namely det ( A B C D ) = det ( D ) det ( A B C D ) det ( I m 0 − D − 1 C D − 1 ) ⏟ = det ( D − 1 ) = ( det D ) − 1 = det ( D ) det ( A − B D − 1 C B D − 1 0 I n ) = det ( D ) det ( A − B D − 1 C ) . {\displaystyle {\begin{aligned}\det {\begin{pmatrix}A&B\\C&D\end{pmatrix}}&=\det(D)\det {\begin{pmatrix}A&B\\C&D\end{pmatrix}}\underbrace {\det {\begin{pmatrix}I_{m}&0\\-D^{-1}C&D^{-1}\end{pmatrix}}} _{=\,\det(D^{-1})\,=\,(\det D)^{-1}}\\&=\det(D)\det {\begin{pmatrix}A-BD^{-1}C&BD^{-1}\\0&I_{n}\end{pmatrix}}\\&=\det(D)\det(A-BD^{-1}C).\end{aligned}}} Both results can be combined to derive Sylvester's determinant theorem, which is also stated below. If the blocks are square matrices of the same size further formulas hold.
Constructive neutral evolution Microbial communities Constructive_neutral_evolution > Examples of CNE > Microbial communities J. Jeffrey Morris and coauthors explained this through the "Black Queen Hypothesis". As a counterpart, W. Ford Doolittle and T. D. P. Brunet proposed the "Gray Queen Hypothesis" to explain the emergence of these communities with CNE. Initially, loss of genes required for synthesizing important nutrients would be detrimental to the organism and so eliminated.
Direct-drive sim racing wheel Torque Direct_drive_wheel > Construction > Torque The torque says something about how "powerful" the engine is, and can be specified in two ways: Continuous torque, the greatest load of which the motor still can perform continuous movement at a continuous speed, and thus performing continuous work Stall torque, the load which will cause the motor to stop so that it can no longer move, and thus produces a holding torque, but not performing any workThe latter always gives a higher number in newton-meters, and is therefore the number that usually is communicated the most by manufacturers to consumers, but is actually a less useful specification since the steering wheel in theory does not perform any work when rotation has stopped. One must therefore be aware of the type of torque specification given when comparing two motors. The relationship between the continuous torque and stall torque can vary between motors, and can say something about the motor characteristics (responsiveness versus strength).For comparison, usually around 7-10 Nm is experienced in a street car, and on steering wheels very high torque (e.g. 20 Nm) it may therefore be appropriate to adjust the torque down in the software. However, the stronger motors will often have a faster slew rate (the time an amplifier takes to respond to a signal) which gives better steering response and more realism.
Visual simulation Environmental/context design Augmented_reality_game > Technology > Development > Environmental/context design While accessibility tools are common in basic application design, some consideration should be made when designing time-limited prompts (to prevent unintentional operations), audio cues and overall engagement time. It is important to note that in some situations, the application's functionality may hinder the user's ability. For example, applications that is used for driving should reduce the amount of user interaction and use audio cues instead.
BORO method Presentations BORO_method > Presentations The method has been presented several times, including a tutorial at the Integrated Enterprise Architecture Conference in London in 2008. It was also presented at the UK Ministry of Defence's EKIG conference in October 2009.
Typed set theory Cantor's paradox and Cantorian sets Typed_set_theory > Consequences > Resolution of set-theoretic paradoxes > Cantor's paradox and Cantorian sets The "obvious" bijection x ↦ { x } {\displaystyle x\mapsto \{x\}} from the universe to the one-element sets is not a set; it is not a set because its definition is unstratified. Note that in all known models of NFU it is the case that | P 1 ( V ) | < | P ( V ) | ≪ | V | {\displaystyle |P_{1}(V)|<|P(V)|\ll |V|} ; Choice allows one not only to prove that there are urelements but that there are many cardinals between | P ( V ) | {\displaystyle |P(V)|} and | V | {\displaystyle |V|} . However, unlike in TST, | A | = | P 1 ( A ) | {\displaystyle |A|=|P_{1}(A)|} is a syntactical sentence in NF(U), and as shown above one can talk about its truth value for specific values of A {\displaystyle A} (e.g. when A = V {\displaystyle A=V} it is false). A set A {\displaystyle A} which satisfies the intuitively appealing | A | = | P 1 ( A ) | {\displaystyle |A|=|P_{1}(A)|} is said to be Cantorian: a Cantorian set satisfies the usual form of Cantor's theorem. A set A {\displaystyle A} which satisfies the further condition that ( x ↦ { x } ) ⌈ A {\displaystyle (x\mapsto \{x\})\lceil A} , the restriction of the singleton map to A, is a set is not only Cantorian set but strongly Cantorian.
Infinite geometric series Economics Geometric_series > Applications > Economics In economics, geometric series are used to represent the present value of an annuity (a sum of money to be paid in regular intervals). For example, suppose that a payment of $100 will be made to the owner of the annuity once per year (at the end of the year) in perpetuity. Receiving $100 a year from now is worth less than an immediate $100, because one cannot invest the money until one receives it. In particular, the present value of $100 one year in the future is $100 / (1 + I {\displaystyle I} ), where I {\displaystyle I} is the yearly interest rate.
Functor (type theory) Visual example Functor_(type_theory) > Examples: mapping a list > Visual example Below, you can see a view of each step of the mapping process for a list of integers X = that we want to map into a new list X' according to the function f ( x ) = x + 1 {\displaystyle f(x)=x+1}: The map is provided as part of the Haskell's base prelude (i.e. "standard library") and is implemented as:
Siamese twins Born 21st century Conjoined_twins > Notable people > Born 21st century Share part of their brain and can pass sensory information and thoughts between each other. Trishna and Krishna from Bangladesh were born in December 2006. They are craniopagus twins, joined on the tops of their skulls and sharing a small amount of brain tissue.
Lamina (anatomy) Summary Lamina_(anatomy) The lamina affixa: a layer of epithelium growing on the surface of the thalamus. Lamina cribrosa with two different meanings. == References ==
Random early detection Operation Random_early_detection > Operation RED monitors the average queue size and drops (or marks when used in conjunction with ECN) packets based on statistical probabilities. If the buffer is almost empty, then all incoming packets are accepted. As the queue grows, the probability for dropping an incoming packet grows too. When the buffer is full, the probability has reached 1 and all incoming packets are dropped.
Stable Diffusion Summary Stable_Diffusion Stable Diffusion is a deep learning, text-to-image model released in 2022 based on diffusion techniques. It is primarily used to generate detailed images conditioned on text descriptions, though it can also be applied to other tasks such as inpainting, outpainting, and generating image-to-image translations guided by a text prompt. It was developed by researchers from the CompVis Group at Ludwig Maximilian University of Munich and Runway with a compute donation by Stability AI and training data from non-profit organizations.Stable Diffusion is a latent diffusion model, a kind of deep generative artificial neural network. Its code and model weights have been released publicly, and it can run on most consumer hardware equipped with a modest GPU with at least 8 GB VRAM. This marked a departure from previous proprietary text-to-image models such as DALL-E and Midjourney which were accessible only via cloud services.
RAFOS float Of the importance of measuring ocean currents RAFOS_float > Introduction > Of the importance of measuring ocean currents The underwater world is still mostly unknown. The main reason for it is the difficulty to gather information in situ, to experiment, and even to reach certain places. But the ocean nonetheless is of a crucial importance for scientists, as it covers about 71% of the planet. Knowledge of ocean currents is of crucial importance.
Category utility What purpose do concepts serve? Category_utility > Category "goodness": models and philosophy > What purpose do concepts serve? Mill here seems to be suggesting that the best category structure is one in which object features (properties) are maximally informative about the object's class, and, simultaneously, the object class is maximally informative about the object's features. In other words, a useful classification scheme is one in which category knowledge can be used to accurately infer object properties, and property knowledge can be used to accurately infer object classes. One may also compare this idea to Aristotle's criterion of counter-predication for definitional predicates, as well as to the notion of concepts described in formal concept analysis.
Procedural Reasoning System Extensions Procedural_Reasoning_System > Extensions The following list the major implementations and extensions of the PRS architecture. UM-PRS OpenPRS (formerly C-PRS and Propice) AgentSpeak Distributed Multi-Agent Reasoning System (dMARS) GORITE JAM JACK Intelligent Agents SRI Procedural Agent Realization Kit (SPARK) PRS-CL
Inhibitor of apoptosis Bcl-2 family Inhibitor_of_apoptosis > Bcl-2 family The Bcl-2 family of proteins can either inhibit or promote apoptosis and members are characterized by the Bcl-2 homologous domains BH1, BH2, BH3, and BH4. The combinations of the domains in the proteins determine its role in the apoptosis process. Members of the family that inhibit apoptosis include Bcl-2 itself, Bcl-XL, and Bcl-w, which possess all four of the domains. Bcl-2 is the most well known of the anti-apoptotic members, and is classified as an oncogene. Studies have shown that the Bcl-2 oncogene may inhibit apoptosis in two ways; either by directly controlling the activation of caspases, or by disrupting the channels that allow proapoptotic factors from leaving the mitochondria.
Euler–Lagrange equations Statement Euler–Lagrange_equation > Statement Let ( X , L ) {\displaystyle (X,L)} be a mechanical system with n {\displaystyle n} degrees of freedom. Here X {\displaystyle X} is the configuration space and L = L ( t , q , v ) {\displaystyle L=L(t,{\boldsymbol {q}},{\boldsymbol {v}})} the Lagrangian, i.e. a smooth real-valued function such that q ∈ X , {\displaystyle {\boldsymbol {q}}\in X,} and v {\displaystyle {\boldsymbol {v}}} is an n {\displaystyle n} -dimensional "vector of speed". (For those familiar with differential geometry, X {\displaystyle X} is a smooth manifold, and L: R t × T X → R , {\displaystyle L:{\mathbb {R} }_{t}\times TX\to {\mathbb {R} },} where T X {\displaystyle TX} is the tangent bundle of X ) . {\displaystyle X).}
Poincaré dodecahedral space Summary Poincaré_homology_sphere In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n ≥ 1 {\displaystyle n\geq 1} . That is, H 0 ( X , Z ) = H n ( X , Z ) = Z {\displaystyle H_{0}(X,\mathbb {Z} )=H_{n}(X,\mathbb {Z} )=\mathbb {Z} } and H i ( X , Z ) = { 0 } {\displaystyle H_{i}(X,\mathbb {Z} )=\{0\}} for all other i.Therefore X is a connected space, with one non-zero higher Betti number, namely, b n = 1 {\displaystyle b_{n}=1} . It does not follow that X is simply connected, only that its fundamental group is perfect (see Hurewicz theorem). A rational homology sphere is defined similarly but using homology with rational coefficients.
Second symmetric derivative Summary Second_symmetric_derivative A well-known counterexample is the absolute value function f(x) = |x|, which is not differentiable at x = 0, but is symmetrically differentiable here with symmetric derivative 0. For differentiable functions, the symmetric difference quotient does provide a better numerical approximation of the derivative than the usual difference quotient.The symmetric derivative at a given point equals the arithmetic mean of the left and right derivatives at that point, if the latter two both exist. : 6 Neither Rolle's theorem nor the mean-value theorem hold for the symmetric derivative; some similar but weaker statements have been proved.
Hash code Customised hash function Hash_functions > Hashing integer data types > Customised hash function A hash function can be designed to exploit existing entropy in the keys. If the keys have leading or trailing zeros, or particular fields that are unused, always zero or some other constant, or generally vary little, then masking out only the volatile bits and hashing on those will provide a better and possibly faster hash function. Selected divisors or multipliers in the division and multiplicative schemes may make more uniform hash functions if the keys are cyclic or have other redundancies.
Workload Cognitive workload in time-critical decision-making processes Workload > Theory and modelling > Cognitive workload in time-critical decision-making processes Work conducted by K Tara Smith has defined some terms relating to the workload in this area. The two main concepts relating to workload are: workload debt - which is when an individual's cognitive workload is too high to complete all relevant tasks in the time available, and they decide (either consciously or subconsciously) to postpone one or more tasks (usually low priority tasks) to enable them to decide on the required timeframe. workload debt cascade - when, because of the high workload, the postponed tasks mount up so that the individual cannot catch up with the tasks they are required to do, causing failure in subsequent activities.
Seismic microzonation Effect of site conditions on earthquake ground motion Seismic_microzonation > Effect of site conditions on earthquake ground motion Similar kinds of site amplification of ground motion were observed in the Loma Prieta earthquake in October 1989. Deep clay deposits underlying sites around the perimeter of the San Francisco Bay area amplified the ground motion tremendously in the San Francisco and Oakland area causing severe damage. The San Francisco-Oakland Bay Bridge, founded on a deep clay site, was extensively damaged in this earthquake. The site amplification phenomenon observed during these earthquakes clearly highlighted the possibility of severe ground motions on sites with soft soil profiles located at large distance from causative faults and underscored the importance of site specific risk analysis.
Small nucleolar RNA CD11 Summary Small_nucleolar_RNA_CD11 In molecular biology, CD11 is a member of the C/D class of snoRNA which contain the C (UGAUGA) and D (CUGA) box motifs. Most of the members of the box C/D family function in directing site-specific 2'-O-methylation of substrate RNAs.
Information privacy law Summary Information_privacy_law The European Union has the General Data Protection Regulation (GDPR), in force since May 25, 2018. The United States is notable for not having adopted a comprehensive information privacy law, but rather having adopted limited sectoral laws in some areas like the California Consumer Privacy Act (CCPA).These laws are based on fair information practice guidelines developed by the U.S. Department for Health, Education and Welfare (HEW) (later renamed Department of Health & Human Services (HHS)), by a Special Advisory Committee on Automated Personal Data Systems, under the chairmanship of computer pioneer and privacy pioneer Willis H. Ware.
Noise (signal processing) Noise in specific kinds of signals Noise_(signal_processing) > Noise in specific kinds of signals Noise may arise in signals of interest to various scientific and technical fields, often with specific features: Noise (audio), such as "hiss" or "hum", in audio signals Background noise, due to spurious sounds during signal capture Comfort noise, added to voice communications to fill silent gaps Electromagnetically induced noise, audible noise due to electromagnetic vibrations in systems involving electromagnetic fields Noise (video), such as "snow" Noise (radio), such as "static", in radio transmissions Image noise, affects images, usually digital ones Salt and pepper noise or spike noise, scattered very dark or very light pixels Fixed pattern noise, that is tied to pixel sensors Shadow noise, made visible by increasing brightness or contrast Speckle noise, typical of radar imaging and interferograms Film grain in analog photography Compression artifacts or "mosquito noise" around edges in JPEG and other formats Noise (electronics) in electrical signals Johnson–Nyquist noise, in semiconductors Quantum noise Quantum 1/f noise, a disputed theory about quantum systems Generation-recombination noise, in semiconductor devices Oscillator phase noise, random fluctuations of the phase of an oscillator Barkhausen effect or Barkhausen noise, in the strength of a ferromagnet Spectral splatter or switch noise, caused by on/off transmitter switching Ground noise, appearing at the ground terminal of audio equipment Synaptic noise, observed in neuroscience Neuronal noise, observed in neuroscience Transcriptional noise in the transcription of genes to proteins Cosmic noise, in radioastronomy Phonon noise in materials science Internet background noise, packets sent to unassigned or inactive IP addresses Fano noise, in particle detectors Mode partition noise in optical cables Seismic noise, spurious ground vibrations in seismology Cosmic microwave background, microwave noise left over from the Big Bang
Second polar moment of area Summary Second_polar_moment_of_area The second polar moment of area, also known (incorrectly, colloquially) as "polar moment of inertia" or even "moment of inertia", is a quantity used to describe resistance to torsional deformation (deflection), in objects (or segments of an object) with an invariant cross-section and no significant warping or out-of-plane deformation. It is a constituent of the second moment of area, linked through the perpendicular axis theorem. Where the planar second moment of area describes an object's resistance to deflection (bending) when subjected to a force applied to a plane parallel to the central axis, the polar second moment of area describes an object's resistance to deflection when subjected to a moment applied in a plane perpendicular to the object's central axis (i.e. parallel to the cross-section). Similar to planar second moment of area calculations ( I x {\displaystyle I_{x}} , I y {\displaystyle I_{y}} , and I x y {\displaystyle I_{xy}} ), the polar second moment of area is often denoted as I z {\displaystyle I_{z}} .
Sun crack Formation of mudcrack Mudcrack > Formation of mudcrack Naturally forming mudcracks start as wet, muddy sediment dries up and contracts. A strain is developed because the top layer shrinks while the material below stays the same size. When this strain becomes large enough, channel cracks form in the dried-up surface to relieve the strain. Individual cracks spread and join up, forming a polygonal, interconnected network of forms called "tesselations."
Second-order logic Expressive power Second_order_predicate_calculus > Expressive power In second-order logic, it is possible to write formal sentences that say "the domain is finite" or "the domain is of countable cardinality." To say that the domain is finite, use the sentence that says that every surjective function from the domain to itself is injective. To say that the domain has countable cardinality, use the sentence that says that there is a bijection between every two infinite subsets of the domain.
Gaseous hydrogen Covalent and organic compounds Molecular_hydrogen > Properties > Compounds > Covalent and organic compounds While H2 is not very reactive under standard conditions, it does form compounds with most elements. Hydrogen can form compounds with elements that are more electronegative, such as halogens (F, Cl, Br, I), or oxygen; in these compounds hydrogen takes on a partial positive charge. When bonded to a more electronegative element, particularly fluorine, oxygen, or nitrogen, hydrogen can participate in a form of medium-strength noncovalent bonding with another electronegative element with a lone pair, a phenomenon called hydrogen bonding that is critical to the stability of many biological molecules. Hydrogen also forms compounds with less electronegative elements, such as metals and metalloids, where it takes on a partial negative charge.
Viable population Extinction Viable_population > Extinction Unlike demographic and genetic stochasticity, environmental stochasticity tends to affect populations of all sizes. Natural catastrophes An extension of environmental stochasticity, natural disasters are random, large scale events such as blizzards, droughts, storms, or fires that directly reduce a population within a short period of time. Natural catastrophes are the hardest events to predict, and MVP models often have difficulty factoring them in.
Hunting oscillation Energy balance Hunting_oscillation > Railway wheelsets > Energy balance The outer wheel velocity is given by: The kinetic energy is: for the inner wheel it is where m is the mass of both wheels. The increase in kinetic energy is: The motion will continue at constant amplitude as long as the energy extracted from the forward motion, and manifesting itself as increased kinetic energy of the wheel set at zero yaw, is equal to the potential energy lost by the lowering of the axle load at maximum yaw. Now, from the kinematics: but The translational kinetic energy is The total kinetic energy is: The critical speed is found from the energy balance: Hence the critical speed is given by This is independent of the wheel taper, but depends on the ratio of the axle load to wheel set mass.
Microscopic polyangiitis Causes Microscopic_polyangiitis > Causes While the mechanism of the disease has yet to be fully elucidated, the leading hypothesis is that AAV (ANCA Associated Vasculitis) develops in patients with a genetic predisposition when an unknown cause triggers the production of p-ANCA. These antibodies will circulate at low levels until an environmental trigger—such as infection, malignancy, or drug therapy, causes the upregulation of neutrophils. The neutrophils bind to p-ANCAs and subsequently release inflammatory cytokines, reactive oxygen species and lytic enzymes that cause endothelial injury resulting to inflammation and necrosis of the small vessels. The damage that is caused in the kidneys is specifically called necrotizing and crescentic glomerulonephritis.
Distributed processing Models Distributed_processing > Theoretical foundations > Models A commonly used model is a graph with one finite-state machine per node.In the case of distributed algorithms, computational problems are typically related to graphs. Often the graph that describes the structure of the computer network is the problem instance. This is illustrated in the following example.
Kinetic Isotope Effects of RuBisCO Summary Intrinsic_KIE_of_RuBisCO The kinetic isotope effect (KIE) of ribulose-1,5-bisphosphate carboxylase oxygenase (RuBisCO) is the isotopic fractionation associated solely with the step in the Calvin-Benson cycle where a molecule of carbon dioxide (CO2) is attached to the 5-carbon sugar ribulose-1,5-bisphosphate (RuBP) to produce two 3-carbon sugars called 3-phosphoglycerate (3 PGA). This chemical reaction is catalyzed by the enzyme RuBisCO, and this enzyme-catalyzed reaction creates the primary kinetic isotope effect of photosynthesis. It is also largely responsible for the isotopic compositions of photosynthetic organisms and the heterotrophs that eat them. Understanding the intrinsic KIE of RuBisCO is of interest to earth scientists, botanists, and ecologists because this isotopic biosignature can be used to reconstruct the evolution of photosynthesis and the rise of oxygen in the geologic record, reconstruct past evolutionary relationships and environmental conditions, and infer plant relationships and productivity in modern environments.
Vector magnetometer Archaeology Magnetometer > Uses > Archaeology Caesium and Overhauser magnetometers are also very effective when used as gradiometers or as single-sensor systems with base stations. The TV program Time Team popularised 'geophys', including magnetic techniques used in archaeological work to detect fire hearths, walls of baked bricks and magnetic stones such as basalt and granite. Walking tracks and roadways can sometimes be mapped with differential compaction in magnetic soils or with disturbances in clays, such as on the Great Hungarian Plain. Ploughed fields behave as sources of magnetic noise in such surveys.
Small perturbations History Perturbation_methods > History Perturbation theory in quantum mechanics is fairly accessible, as the quantum notation allows expressions to be written in fairly compact form, thus making them easier to comprehend. This resulted in an explosion of applications, ranging from the Zeeman effect to the hyperfine splitting in the hydrogen atom. Despite the simpler notation, perturbation theory applied to quantum field theory still easily gets out of hand.
ADE classification Binary polyhedral groups ADE_classification > Binary polyhedral groups Note that the ADE correspondence is not the correspondence of Platonic solids to their reflection group of symmetries: for instance, in the ADE correspondence the tetrahedron, cube/octahedron, and dodecahedron/icosahedron correspond to E 6 , E 7 , E 8 , {\displaystyle E_{6},E_{7},E_{8},} while the reflection groups of the tetrahedron, cube/octahedron, and dodecahedron/icosahedron are instead representations of the Coxeter groups A 3 , B C 3 , {\displaystyle A_{3},BC_{3},} and H 3 . {\displaystyle H_{3}.}
In-memory computing Data structures In-memory_processing > Disk-based business intelligence > Data structures Another drawback is that SQL is designed to efficiently fetch rows of data, while BI queries usually involve fetching of partial rows of data involving heavy calculations. To improve query performance, multidimensional databases or OLAP cubes - also called multidimensional online analytical processing (MOLAP) - are constructed. Designing a cube is an elaborate and lengthy process, and changing the cube's structure to adapt to dynamically changing business needs may be cumbersome. Cubes are pre-populated with data to answer specific queries and although they increase performance, they are still not suitable for answering ad-hoc queries.Information technology (IT) staff spend substantial development time on optimizing databases, constructing indexes and aggregates, designing cubes and star schemas, data modeling, and query analysis.
Gene transfer agent GTA genes and evolution Gene_transfer_agent > GTA genes and evolution One alternative explanation is that GTA genes persist because GTAs are genetic parasites that spread infectiously to new cells. However this is ruled out because GTA particles typically are too small to contain the genes that encode them.
Earthquake prediction Evaluating earthquake predictions Earthquake_prediction > Evaluating earthquake predictions Following the 2009 L'Aquila Earthquake, seven scientists and technicians in Italy were convicted of manslaughter, but not so much for failing to predict the earthquake, where some 300 people died, as for giving undue assurance to the populace – one victim called it "anaesthetizing" – that there would not be a serious earthquake, and therefore no need to take precautions. But warning of an earthquake that does not occur also incurs a cost: not only the cost of the emergency measures themselves, but of civil and economic disruption. False alarms, including alarms that are canceled, also undermine the credibility, and thereby the effectiveness, of future warnings.
240 (number) Summary 240_(number) a Harshad number in bases 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15 (and 73 other bases). the aliquot sum of 120 and 57121. part of the 12161-aliquot tree. The aliquot sequence starting at 120 is: 120, 240, 504, 1056, 1968, 3240, 7650, 14112, 32571, 27333, 12161, 1, 0.
PAS capacitor Activated carbon PAS_capacitor > Materials > Electrodes > Electrodes for EDLCs > Activated carbon Activated carbon was the first material chosen for EDLC electrodes. Even though its electrical conductivity is approximately 0.003% that of metals (1,250 to 2,000 S/m), it is sufficient for supercapacitors.Activated carbon is an extremely porous form of carbon with a high specific surface area — a common approximation is that 1 gram (0.035 oz) (a pencil-eraser-sized amount) has a surface area of roughly 1,000 to 3,000 square metres (11,000 to 32,000 sq ft) — about the size of 4 to 12 tennis courts. The bulk form used in electrodes is low-density with many pores, giving high double-layer capacitance. Solid activated carbon, also termed consolidated amorphous carbon (CAC) is the most used electrode material for supercapacitors and may be cheaper than other carbon derivatives.
Brouwer Fixed Point Theorem A combinatorial proof Brouwer's_fixed-point_theorem > Proof outlines > A combinatorial proof Because the sum of the coordinates of P {\displaystyle P} and f ( P ) {\displaystyle f(P)} must be equal, all these inequalities must actually be equalities. But this means that: f ( P ) = P . {\displaystyle f(P)=P.} That is, P {\displaystyle P} is a fixed point of f . {\displaystyle f.}
Solar car Solar array Solar-powered_car > Solar array integrated. Some vehicles cover every available surface with solar cells.
Large deviation theory Large deviations and entropy Large_deviation_theory > Applications > Large deviations and entropy The rate function is related to the entropy in statistical mechanics. This can be heuristically seen in the following way. In statistical mechanics the entropy of a particular macro-state is related to the number of micro-states which corresponds to this macro-state. In our coin tossing example the mean value M N {\displaystyle M_{N}} could designate a particular macro-state.
Ockham's razor Probability theory and statistics Principle_of_Parsimony > Uses > Probability theory and statistics Marcus Hutter's universal artificial intelligence builds upon Solomonoff's mathematical formalization of the razor to calculate the expected value of an action. There are various papers in scholarly journals deriving formal versions of Occam's razor from probability theory, applying it in statistical inference, and using it to come up with criteria for penalizing complexity in statistical inference. Papers have suggested a connection between Occam's razor and Kolmogorov complexity.One of the problems with the original formulation of the razor is that it only applies to models with the same explanatory power (i.e., it only tells us to prefer the simplest of equally good models). A more general form of the razor can be derived from Bayesian model comparison, which is based on Bayes factors and can be used to compare models that do not fit the observations equally well.
Permutation matrix Permutation of rows and columns Permutation_matrix > Examples > Permutation of rows and columns When a matrix M is multiplied by a permutation matrix P on the left to make PM, the product is the result of permuting the rows of M. As a special case, if M is a column vector, then PM is the result of permuting the entries of M: When instead M is multiplied by a permutation matrix on the right to make MP, the product is the result of permuting the columns of M. As a special case, if M is a row vector, then MP is the result of permuting the entries of M: