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Inphysical systems,dampingis the loss ofenergyof anoscillating systembydissipation.[1][2]Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation.[3]Examples of damping includeviscous dampingin a fluid (seeviscousdrag),surface friction,radiation,[1]resis... | https://en.wikipedia.org/wiki/Damped_sine_wave |
Inmathematics, theFourier transform(FT) is anintegral transformthat takes afunctionas input then outputs another function that describes the extent to which variousfrequenciesare present in the original function. The output of the transform is acomplex-valued function of frequency. The termFourier transformrefers to bo... | https://en.wikipedia.org/wiki/Fourier_transform |
Inmathematics, theharmonic seriesis theinfinite seriesformed by summing all positiveunit fractions:∑n=1∞1n=1+12+13+14+15+⋯.{\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n}}=1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+{\frac {1}{5}}+\cdots .}
The firstn{\displaystyle n}terms of the series sum to approximatelylnn+γ... | https://en.wikipedia.org/wiki/Harmonic_series_(mathematics) |
Theharmonic series(alsoovertone series) is the sequence ofharmonics,musical tones, orpure toneswhosefrequencyis anintegermultiple of afundamental frequency.
Pitchedmusical instrumentsare often based on anacousticresonatorsuch as astringor a column of air, whichoscillatesat numerousmodessimultaneously. As waves travel ... | https://en.wikipedia.org/wiki/Harmonic_series_(music) |
In mathematics, theHelmholtz equationis theeigenvalue problemfor theLaplace operator. It corresponds to theelliptic partial differential equation:∇2f=−k2f,{\displaystyle \nabla ^{2}f=-k^{2}f,}where∇2is the Laplace operator,k2is the eigenvalue, andfis the (eigen)function. When the equation is applied to waves,kis known ... | https://en.wikipedia.org/wiki/Helmholtz_equation |
Instantaneous phase and frequencyare important concepts insignal processingthat occur in the context of the representation and analysis of time-varying functions.[1]Theinstantaneous phase(also known aslocal phaseor simplyphase) of acomplex-valuedfunctions(t), is the real-valued function:
whereargis thecomplex argument... | https://en.wikipedia.org/wiki/Instantaneous_phase |
Asinusoidwithmodulationcan be decomposed into, or synthesized from, twoamplitude-modulatedsinusoids that are inquadrature phase, i.e., with aphase offsetof one-quarter cycle (90 degrees orπ/2 radians). All three sinusoids have the samecenter frequency. The two amplitude-modulated sinusoids are known as thein-phase(I) a... | https://en.wikipedia.org/wiki/In-phase_and_quadrature_components |
Anoscilloscope(formerly known as anoscillograph, informallyscopeorO-scope) is a type ofelectronic test instrumentthat graphically displays varyingvoltagesof one or more signals as a function of time. Their main purpose is capturing information on electrical signals for debugging, analysis, or characterization. The disp... | https://en.wikipedia.org/wiki/Oscilloscope |
Inphysicsandengineering, aphasor(aportmanteauofphase vector[1][2]) is acomplex numberrepresenting asinusoidal functionwhoseamplitudeAandinitial phaseθaretime-invariantand whoseangular frequencyωis fixed. It is related to a more general concept calledanalytic representation,[3]which decomposes a sinusoid into the produc... | https://en.wikipedia.org/wiki/Phasor |
Inpsychoacoustics, apure toneis a sound with asinusoidalwaveform; that is, asinewaveof constantfrequency,phase-shift, andamplitude.[1]By extension, insignal processinga single-frequency tone or pure tone is a purely sinusoidalsignal(e.g., a voltage).
A pure tone has the property – unique among real-valued wave shapes –... | https://en.wikipedia.org/wiki/Pure_tone |
Inmechanicsandphysics,simple harmonic motion(sometimes abbreviated asSHM) is a special type ofperiodicmotionan object experiences by means of arestoring forcewhose magnitude is directlyproportionalto the distance of the object from an equilibrium position and acts towards the equilibrium position. It results in anoscil... | https://en.wikipedia.org/wiki/Simple_harmonic_motion |
Inphysics,mathematics,engineering, and related fields, awaveis a propagating dynamic disturbance (change fromequilibrium) of one or morequantities.Periodic wavesoscillate repeatedly about an equilibrium (resting) value at somefrequency. When the entirewaveformmoves in one direction, it is said to be atravelling wave; b... | https://en.wikipedia.org/wiki/Wave_(physics) |
Thewave equationis a second-order linearpartial differential equationfor the description ofwavesorstanding wavefields such asmechanical waves(e.g.waterwaves,sound wavesandseismic waves) orelectromagnetic waves(includinglightwaves). It arises in fields likeacoustics,electromagnetism, andfluid dynamics.
This article foc... | https://en.wikipedia.org/wiki/Wave_equation |
Thetilde(/ˈtɪldə/, also/ˈtɪld,-di,-deɪ/)[1]is agrapheme⟨˜⟩or⟨~⟩with a number of uses. The name of the character came intoEnglishfromSpanishtilde, which in turn came from theLatintitulus, meaning 'title' or 'superscription'.[2]Its primary use is as adiacritic(accent) in combination with a base letter. Its freestanding f... | https://en.wikipedia.org/wiki/Tilde#Electronics |
In physics, theJosephson effectis a phenomenon that occurs when twosuperconductorsare placed in proximity, with some barrier or restriction between them. The effect is named after the British physicistBrian Josephson, who predicted in 1962 the mathematical relationships for the current and voltage across the weak link.... | https://en.wikipedia.org/wiki/Josephson_effect |
Inphysics, afluxonis aquantumofelectromagnetic flux. The term may have any of several related meanings.
In the context ofsuperconductivity, intype II superconductorsfluxons (also known asAbrikosov vortices) can form when the applied field lies betweenBc1{\displaystyle B_{c_{1}}}andBc2{\displaystyle B_{c_{2}}}. The fl... | https://en.wikipedia.org/wiki/Fluxon |
Shape wavesare excitations propagating alongJosephson vorticesorfluxons. In the case of two-dimensionalJosephson junctions(thicklong Josephson junctionswith an extra dimension) described by the 2Dsine-Gordon equation, shape waves are distortions of aJosephson vortexline of an arbitrary profile. Shape waves have remarka... | https://en.wikipedia.org/wiki/Shape_waves |
Apitch detection algorithm(PDA) is analgorithmdesigned to estimate thepitchorfundamental frequencyof aquasiperiodicoroscillatingsignal, usually adigital recordingofspeechor a musical note or tone. This can be done in thetime domain, thefrequency domain, or both.
PDAs are used in various contexts (e.g.phonetics,music i... | https://en.wikipedia.org/wiki/Pitch_detection_algorithm |
Instatistical signal processing, the goal ofspectral density estimation(SDE) or simplyspectral estimationis toestimatethespectral density(also known as thepower spectral density) of a signal from a sequence of time samples of the signal.[1]Intuitively speaking, the spectral density characterizes thefrequencycontent of ... | https://en.wikipedia.org/wiki/Spectral_density_estimation#Single_tone |
Inmathematics,Bhāskara I's sine approximation formulais arational expressionin onevariablefor thecomputationof theapproximate valuesof thetrigonometric sinesdiscovered byBhāskara I(c. 600 – c. 680), a seventh-century Indianmathematician.[1]Thisformulais given in his treatise titledMahabhaskariya. It is not known how Bh... | https://en.wikipedia.org/wiki/Bh%C4%81skara_I%27s_sine_approximation_formula |
For smallangles, thetrigonometric functionssine, cosine, and tangent can be calculated with reasonable accuracy by the following simple approximations:
provided the angle is measured inradians. Angles measured indegreesmust first be converted to radians by multiplying them byπ/180{\displaystyle \pi /180}.
These app... | https://en.wikipedia.org/wiki/Small-angle_approximation |
Thedifferentiation of trigonometric functionsis the mathematical process of finding thederivativeof atrigonometric function, or its rate of change with respect to a variable. For example, the derivative of the sine function is written sin′(a) = cos(a), meaning that the rate of change of sin(x) at a particular anglex = ... | https://en.wikipedia.org/wiki/Differentiation_of_trigonometric_functions |
Inmathematics, abivectoror2-vectoris a quantity inexterior algebraorgeometric algebrathat extends the idea ofscalarsandvectors. Considering a scalar as a degree-zero quantity and a vector as a degree-one quantity, a bivector is of degree two. Bivectors have applications in many areas of mathematics and physics. They ar... | https://en.wikipedia.org/wiki/Bivector |
Ingeometry, aplane of rotationis an abstract object used to describe or visualizerotationsin space.
The main use for planes of rotation is in describing more complex rotations infour-dimensional spaceandhigher dimensions, where they can be used to break down the rotations into simpler parts. This can be done usinggeom... | https://en.wikipedia.org/wiki/Plane_of_rotation |
Computer visiontasks include methods foracquiring,processing,analyzing, and understandingdigital images, and extraction ofhigh-dimensionaldata from the real world in order to produce numerical or symbolic information, e.g. in the form of decisions.[1][2][3][4]"Understanding" in this context signifies the transformation... | https://en.wikipedia.org/wiki/Computer_vision |
Inimage processing,computer visionand related fields, animage momentis a certain particularweighted average(moment) of the image pixels' intensities, or a function of such moments, usually chosen to have some attractive property or interpretation.
Image moments are useful to describe objects aftersegmentation.Simple p... | https://en.wikipedia.org/wiki/Image_moment |
Inatomic physicsandchemistry, anatomic electron transition(also called an atomic transition, quantum jump, or quantum leap) is anelectronchanging from oneenergy levelto another within anatom[1]orartificial atom.[2]The time scale of a quantum jump has not been measured experimentally. However, theFranck–Condon principle... | https://en.wikipedia.org/wiki/Atomic_electron_transition |
In quantummechanicsandcomputing, theBloch sphereis a geometrical representation of thepure statespace of atwo-level quantum mechanical system(qubit), named after the physicistFelix Bloch.[1]
Mathematically each quantum mechanical system is associated with aseparablecomplexHilbert spaceH{\displaystyle H}. A pure state ... | https://en.wikipedia.org/wiki/Bloch_sphere |
Inphysics, in the area ofquantum information theory, aGreenberger–Horne–Zeilinger(GHZ)stateis anentangledquantum statethat involves at least three subsystems (particle states,qubits, orqudits). Named for the three authors that first described this state, the GHZ state predicts outcomes from experiments that directly co... | https://en.wikipedia.org/wiki/Greenberger%E2%80%93Horne%E2%80%93Zeilinger_state |
Theground stateof aquantum-mechanicalsystem is itsstationary stateof lowestenergy; the energy of the ground state is known as thezero-point energyof the system. Anexcited stateis any state with energy greater than the ground state. Inquantum field theory, the ground state is usually called thevacuum stateor thevacuum.
... | https://en.wikipedia.org/wiki/Ground_state |
Quantum mechanicsis the study ofmatterand its interactions withenergyon thescaleofatomicandsubatomic particles. By contrast,classical physicsexplains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the Moon. Classical physics is still used in much of... | https://en.wikipedia.org/wiki/Introduction_to_quantum_mechanics |
Inphysics, theno-cloning theoremstates that it is impossible to create an independent and identical copy of an arbitrary unknownquantum state, a statement which has profound implications in the field ofquantum computingamong others. The theorem is an evolution of the 1970no-go theoremauthored by James Park,[1]in which ... | https://en.wikipedia.org/wiki/No-cloning_theorem |
Inmathematics, particularlylinear algebra, anorthonormal basisfor aninner product spaceV{\displaystyle V}with finitedimensionis abasisforV{\displaystyle V}whose vectors areorthonormal, that is, they are allunit vectorsandorthogonalto each other.[1][2][3]For example, thestandard basisfor aEuclidean spaceRn{\displaystyle... | https://en.wikipedia.org/wiki/Orthonormal_basis |
ThePusey–Barrett–Rudolph(PBR)theorem[1]is ano-go theoreminquantum foundationsdue to Matthew Pusey, Jonathan Barrett, andTerry Rudolph(for whom the theorem is named) in 2012. It has particular significance for how one may interpret the nature of thequantum state.
With respect to certain realisthidden variable theoriest... | https://en.wikipedia.org/wiki/PBR_theorem |
Thequantum harmonic oscillatoris thequantum-mechanicalanalog of theclassical harmonic oscillator. Because an arbitrary smoothpotentialcan usually be approximated as aharmonic potentialat the vicinity of a stableequilibrium point, it is one of the most important model systems in quantum mechanics. Furthermore, it is on... | https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator |
Inquantum computingand specifically thequantum circuitmodel of computation, aquantum logic gate(or simplyquantum gate) is a basic quantum circuit operating on a small number ofqubits. Quantum logic gates are the building blocks of quantum circuits, like classicallogic gatesare for conventional digital circuits.
Unlike... | https://en.wikipedia.org/wiki/Quantum_logic_gate |
Astationary stateis aquantum statewith allobservablesindependent of time. It is aneigenvectorof theenergy operator(instead of aquantum superpositionof different energies). It is also calledenergy eigenvector,energy eigenstate,energy eigenfunction, orenergyeigenket. It is very similar to the concept ofatomic orbitalandm... | https://en.wikipedia.org/wiki/Stationary_state |
In variousinterpretationsofquantum mechanics,wave function collapse, also calledreduction of the state vector,[1]occurs when awave function—initially in asuperpositionof severaleigenstates—reduces to a single eigenstate due tointeractionwith the external world. This interaction is called anobservationand is the essence... | https://en.wikipedia.org/wiki/Wave_function_collapse |
TheW stateis anentangledquantum stateof threequbitswhich in thebra-ket notationhas the following shape
and which is remarkable for representing a specific type ofmultipartite entanglementand for occurring in several applications inquantum information theory. Particles prepared in this state reproduce the properties of... | https://en.wikipedia.org/wiki/W_state |
In themathematicaldiscipline ofmatrix theory, aJordan matrix, named afterCamille Jordan, is ablock diagonal matrixover aringR(whoseidentitiesare thezero0 andone1), where each block along the diagonal, called a Jordan block, has the following form:[λ10⋯00λ1⋯0⋮⋮⋮⋱⋮000λ10000λ].{\displaystyle {\begin{bmatrix}\lambda &1&0&\... | https://en.wikipedia.org/wiki/Jordan_matrix |
Inmathematics, specificallylinear algebra, theJordan–Chevalley decomposition, named afterCamille JordanandClaude Chevalley, expresses alinear operatorin a unique way as the sum of two other linear operators which are simpler to understand. Specifically, one part ispotentially diagonalisableand the other isnilpotent. Th... | https://en.wikipedia.org/wiki/Jordan%E2%80%93Chevalley_decomposition |
Inlinear algebra, themodal matrixis used in thediagonalization processinvolvingeigenvalues and eigenvectors.[1]
Specifically the modal matrixM{\displaystyle M}for the matrixA{\displaystyle A}is then×nmatrix formed with the eigenvectors ofA{\displaystyle A}as columns inM{\displaystyle M}. It is utilized in thesimilari... | https://en.wikipedia.org/wiki/Modal_matrix |
Inmathematics, inlinear algebra, aWeyr canonical form(or,Weyr formorWeyr matrix) is asquare matrixwhich (in some sense) induces "nice" properties with matrices it commutes with. It also has a particularly simple structure and the conditions for possessing a Weyr form are fairly weak, making it a suitable tool for study... | https://en.wikipedia.org/wiki/Weyr_canonical_form |
Thespectrumof alinear operatorT{\displaystyle T}that operates on aBanach spaceX{\displaystyle X}is a fundamental concept offunctional analysis. The spectrum consists of allscalarsλ{\displaystyle \lambda }such that the operatorT−λ{\displaystyle T-\lambda }does not have a boundedinverseonX{\displaystyle X}. The spectrum... | https://en.wikipedia.org/wiki/Decomposition_of_spectrum_(functional_analysis) |
In mathematics, specifically inspectral theory, adiscrete spectrumof aclosed linear operatoris defined as the set ofisolated pointsof its spectrum such that therankof the correspondingRiesz projectoris finite.
A pointλ∈C{\displaystyle \lambda \in \mathbb {C} }in thespectrumσ(A){\displaystyle \sigma (A)}of aclosed line... | https://en.wikipedia.org/wiki/Discrete_spectrum_(mathematics) |
Inmathematics, theessential spectrumof abounded operator(or, more generally, of adensely definedclosed linear operator) is a certain subset of itsspectrum, defined by a condition of the type that says, roughly speaking, "fails badly to be invertible".
In formal terms, letX{\displaystyle X}be aHilbert spaceand letT{\di... | https://en.wikipedia.org/wiki/Essential_spectrum |
Inmathematics,Fredholm operatorsare certainoperatorsthat arise in theFredholm theoryofintegral equations. They are named in honour ofErik Ivar Fredholm. By definition, a Fredholm operator is abounded linear operatorT:X→Ybetween twoBanach spaceswith finite-dimensionalkernelkerT{\displaystyle \ker T}and finite-dimension... | https://en.wikipedia.org/wiki/Fredholm_operator |
Inmathematics, theresolvent formalismis a technique for applying concepts fromcomplex analysisto the study of thespectrumofoperatorsonBanach spacesand more general spaces. Formal justification for the manipulations can be found in the framework ofholomorphic functional calculus.
Theresolventcaptures the spectral prope... | https://en.wikipedia.org/wiki/Resolvent_formalism |
Inmathematics, or more specifically inspectral theory, theRiesz projectoris the projector onto the eigenspace corresponding to a particulareigenvalueof an operator (or, more generally, a projector onto aninvariant subspacecorresponding to an isolated part of the spectrum). It was introduced byFrigyes Rieszin 1912.[1][2... | https://en.wikipedia.org/wiki/Riesz_projector |
Inmathematics, particularly infunctional analysis, thespectrumof abounded linear operator(or, more generally, anunbounded linear operator) is a generalisation of the set ofeigenvaluesof amatrix. Specifically, acomplex numberλ{\displaystyle \lambda }is said to be in the spectrum of a bounded linear operatorT{\displayst... | https://en.wikipedia.org/wiki/Spectrum_(functional_analysis) |
Inmathematics, particularly infunctional analysis, thespectrumof abounded linear operator(or, more generally, anunbounded linear operator) is a generalisation of the set ofeigenvaluesof amatrix. Specifically, acomplex numberλ{\displaystyle \lambda }is said to be in the spectrum of a bounded linear operatorT{\displayst... | https://en.wikipedia.org/wiki/Spectrum_of_an_operator |
Ageographic information system(GIS) consists of integrated computer hardware andsoftwarethat store, manage,analyze, edit, output, andvisualizegeographic data.[1][2]Much of this often happens within aspatial database; however, this is not essential to meet the definition of a GIS.[1]In a broader sense, one may consider ... | https://en.wikipedia.org/wiki/GIS |
GazoPa[1]was an imagesearch enginethat used features from an image tosearch for and identify similar imageswhich closed[2]in 2011.
GazoPa began in TechCrunch50 in 2008 before launching into a state ofopen betain 2009.[3]GazoPa branched out and released a flower photo community site called "GazoPa Bloom" in 2010. This ... | https://en.wikipedia.org/wiki/GazoPa |
Animage retrievalsystem is a computer system used for browsing, searching and retrieving images from a largedatabaseof digital images. Most traditional and common methods of image retrieval utilize some method of addingmetadatasuch ascaptioning,keywords, title or descriptions to the images so that retrieval can be perf... | https://en.wikipedia.org/wiki/Image_retrieval |
This is a list of publicly availablecontent-based image retrieval(CBIR) engines. These image search engines look at the content (pixels) of images in order to return results that match a particular query. | https://en.wikipedia.org/wiki/List_of_CBIR_engines |
Macroglossawas avisual search enginebased on the comparison of images,[1][2]coming from an Italian Group. The development of the project began in 2009. In April 2010 is released the first publicalpha.[3]Users can upload photos or images that they are not sure what they are to determine what the images contain. Macroglo... | https://en.wikipedia.org/wiki/Macroglossa_Visual_Search |
MPEG-7is amultimediacontentdescriptionstandard. It was standardized inISO/IEC15938 (Multimedia content description interface).[1][2][3][4]This description will be associated with the content itself, to allow fast and efficient searching for material that is of interest to the user. MPEG-7 is formally calledMultimedia C... | https://en.wikipedia.org/wiki/MPEG-7 |
Cell lists(also sometimes referred to ascell linked-lists) is a data structure inmolecular dynamicssimulations to find all atom pairs within a given cut-off distance of each other. These pairs are needed to compute the short-range non-bonded interactions in a system, such asVan der Waals forcesor the short-range part o... | https://en.wikipedia.org/wiki/Cell_lists |
Analogical modeling(AM) is a formal theory ofexemplarbased analogical reasoning, proposed byRoyal Skousen, professor of Linguistics and English language atBrigham Young UniversityinProvo, Utah. It is applicable to language modeling and other categorization tasks. Analogical modeling is related toconnectionismandnearest... | https://en.wikipedia.org/wiki/Analogical_modeling |
Multidimensional Expressions(MDX) is aquery languageforonline analytical processing(OLAP) using adatabase management system. Much likeSQL, it is a query language forOLAP cubes.[1]It is also a calculation language, with syntax similar to spreadsheet formulae.
The MultiDimensional eXpressions (MDX) language provides a s... | https://en.wikipedia.org/wiki/MultiDimensional_eXpressions |
Ineconometrics, amultidimensional panel datais data of a phenomenon observed over three or more dimensions. This comes in contrast withpanel data, observed over two dimensions (typically,timeandcross-sections). An example is a data set containing forecasts of one or multiple macroeconomic variables produced by multiple... | https://en.wikipedia.org/wiki/Multidimensional_panel_data |
Adimensionis a structure that categorizesfactsandmeasuresin order to enable users to answer business questions. Commonly used dimensions are people, products, place and time.[1][2](Note: People and time sometimes are not modeled as dimensions.)
In adata warehouse, dimensions provide structured labeling information to ... | https://en.wikipedia.org/wiki/Dimension_(data_warehouse) |
Adimensionis a structure that categorizesfactsandmeasuresin order to enable users to answer business questions. Commonly used dimensions are people, products, place and time.[1][2](Note: People and time sometimes are not modeled as dimensions.)
In adata warehouse, dimensions provide structured labeling information to ... | https://en.wikipedia.org/wiki/Dimension_table |
In computer programming contexts, adata cube(ordatacube) is amulti-dimensional ("n-D") arrayof values. Typically, the term data cube is applied in contexts where these arrays are massively larger than the hosting computer's main memory; examples include multi-terabyte/petabytedata warehousesandtime seriesof image data.... | https://en.wikipedia.org/wiki/Data_cube |
Natural-neighbor interpolationorSibson interpolationis a method ofspatial interpolation, developed byRobin Sibson.[1]The method is based onVoronoi tessellationof a discrete set of spatial points. This has advantages over simpler methods of interpolation, such asnearest-neighbor interpolation, in that it provides a smoo... | https://en.wikipedia.org/wiki/Natural_neighbor_interpolation |
Incomputer graphicsanddigital imaging,imagescalingrefers to the resizing of a digital image. In video technology, the magnification of digital material is known as upscaling orresolution enhancement.
When scaling avector graphicimage, the graphic primitives that make up the image can be scaled using geometric transfor... | https://en.wikipedia.org/wiki/Image_scaling |
Akernel smootheris astatisticaltechnique to estimate a real valuedfunctionf:Rp→R{\displaystyle f:\mathbb {R} ^{p}\to \mathbb {R} }as theweighted averageof neighboring observed data. The weight is defined by thekernel, such that closer points are given higher weights. The estimated function is smooth, and the level of s... | https://en.wikipedia.org/wiki/Nearest_neighbor_smoothing |
Thezero-order hold(ZOH) is a mathematical model of the practicalsignal reconstructiondone by a conventionaldigital-to-analog converter(DAC).[1]That is, it describes the effect of converting adiscrete-time signalto acontinuous-time signalby holding each sample value for one sample interval. It has several applications i... | https://en.wikipedia.org/wiki/Zero-order_hold |
Roundingorrounding offmeans replacing anumberwith anapproximatevalue that has a shorter, simpler, or more explicit representation. For example, replacing $23.4476with $23.45, thefraction312/937 with 1/3, or the expression √2 with1.414.
Rounding is often done to obtain a value that is easier to report and communicate t... | https://en.wikipedia.org/wiki/Rounding |
UPGMA(unweighted pair group method with arithmetic mean) is a simple agglomerative (bottom-up)hierarchical clusteringmethod. It also has a weighted variant,WPGMA, and they are generally attributed toSokalandMichener.[1]
Note that the unweighted term indicates that all distances contribute equally to each average that ... | https://en.wikipedia.org/wiki/UPGMA |
WPGMA(WeightedPairGroupMethod withArithmetic Mean) is a simple agglomerative (bottom-up)hierarchical clusteringmethod, generally attributed toSokalandMichener.[1]
The WPGMA method is similar to itsunweightedvariant, theUPGMAmethod.
The WPGMA algorithm constructs a rooted tree (dendrogram) that reflects the structure ... | https://en.wikipedia.org/wiki/WPGMA |
Minimum evolutionis adistance methodemployed inphylogeneticsmodeling. It shares withmaximum parsimonythe aspect of searching for the phylogeny that has the shortest total sum of branch lengths.[1][2]
The theoretical foundations of the minimum evolution (ME) criterion lay in the seminal works of both Kidd and Sgaramell... | https://en.wikipedia.org/wiki/Minimum_Evolution |
Incomputer science, arange treeis anordered treedata structureto hold a list of points. It allows all points within a given range to bereportedefficiently, and is typically used in two or higher dimensions. Range trees were introduced byJon Louis Bentleyin 1979.[1]Similar data structures were discovered independently b... | https://en.wikipedia.org/wiki/Range_tree |
Arange queryis a commondatabaseoperation that retrieves allrecordswhere somevalueis between an upper and lower boundary.[1]For example, list all employees with 3 to 5 years' experience. Range queries are unusual because it is not generally known in advance how many entries a range query will return, or if it will retur... | https://en.wikipedia.org/wiki/Range_query |
Incomputational geometry, aDelaunay triangulationorDelone triangulationof a set of points in the plane subdivides theirconvex hull[1]into triangles whosecircumcirclesdo not contain any of the points; that is, each circumcircle has its generating points on its circumference, but all other points in the set are outside o... | https://en.wikipedia.org/wiki/Delaunay_triangulation |
Inmathematics, themap segmentationproblem is a kind ofoptimization problem. It involves a certain geographic region that has to be partitioned into smaller sub-regions in order to achieve a certain goal. Typical optimization objectives include:[1]
Fair division of land has been an important issue since ancient times, ... | https://en.wikipedia.org/wiki/Map_segmentation |
Thenatural element method (NEM)[1][2][3]is ameshless methodto solvepartial differential equation, where theelementsdo not have a predefined shape as in thefinite element method, but depend on the geometry.[4][5][6]
AVoronoi diagrampartitioning the space is used to create each of these elements.
Natural neighbor inter... | https://en.wikipedia.org/wiki/Natural_element_method |
Incomputational geometry, apower diagram, also called aLaguerre–Voronoi diagram,Dirichlet cell complex,radical Voronoi tesselationor asectional Dirichlet tesselation, is a partition of theEuclidean planeintopolygonalcells defined from a set of circles. The cell for a given circleCconsists of all the points for which th... | https://en.wikipedia.org/wiki/Power_diagram |
Incomputational geometry, the positive and negativeVoronoi polesof acellin aVoronoi diagramare certain vertices of the diagram, chosen in pairs in each cell of the diagram to be far from the site generating that pair. They have applications insurface reconstruction.
LetV{\displaystyle V}be the Voronoi diagram for a se... | https://en.wikipedia.org/wiki/Voronoi_pole |
Curveletsare a non-adaptivetechnique for multi-scaleobjectrepresentation. Being an extension of thewaveletconcept, they are becoming popular in similar fields, namely inimage processingandscientific computing.
Wavelets generalize theFourier transformby using a basis that represents both location and spatial frequency.... | https://en.wikipedia.org/wiki/Curvelet |
Digital cinemais thedigitaltechnology used within thefilm industrytodistributeorprojectmotion picturesas opposed to the historical use of reels ofmotion picture film, such as35 mm film. Whereas film reels have to be shipped tomovie theaters, a digital movie can be distributed to cinemas in a number of ways: over theInt... | https://en.wikipedia.org/wiki/Digital_cinema |
Insignal processing, afilter bank(orfilterbank) is an array ofbandpass filtersthat separates the input signal into multiple components, each one carrying asub-bandof the original signal.[1]One application of a filter bank is agraphic equalizer, which can attenuate the components differently and recombine them into a mo... | https://en.wikipedia.org/wiki/Filter_bank |
Fractal compressionis alossy compressionmethod fordigital images, based onfractals. The method is best suited for textures and natural images, relying on the fact that parts of an image often resemble other parts of the same image.[1]Fractalalgorithmsconvert these parts into mathematical data called "fractal codes" whi... | https://en.wikipedia.org/wiki/Fractal_compression |
Inmathematics, in the area ofharmonic analysis, thefractional Fourier transform(FRFT) is a family oflinear transformationsgeneralizing theFourier transform. It can be thought of as the Fourier transform to then-th power, wherenneed not be aninteger— thus, it can transform a function to anyintermediatedomain between tim... | https://en.wikipedia.org/wiki/Fractional_Fourier_transform |
Gabor waveletsarewaveletsinvented byDennis Gaborusing complex functions constructed to serve as a basis forFourier transformsininformation theoryapplications. They are very similar toMorlet wavelets. They are also closely related toGabor filters. The important property of thewaveletis that it minimizes the product of i... | https://en.wikipedia.org/wiki/Gabor_wavelet#Wavelet_space |
TheHuygens–Fresnel principle(named afterDutchphysicistChristiaan HuygensandFrenchphysicistAugustin-Jean Fresnel) states that every point on awavefrontis itself the source of spherical wavelets, and the secondary wavelets emanating from different points mutuallyinterfere.[1]The sum of these spherical wavelets forms a ne... | https://en.wikipedia.org/wiki/Huygens%E2%80%93Fresnel_principle |
Non-separable waveletsare multi-dimensionalwaveletsthat are not directly implemented astensor productsof wavelets on some lower-dimensional space.
They have been studied since 1992.[1]They offer a few important advantages. Notably, using non-separable filters leads to more parameters in design, and consequently better ... | https://en.wikipedia.org/wiki/Non-separable_wavelet |
In applied mathematical analysis,shearletsare a multiscale framework which allows efficient encoding ofanisotropicfeatures inmultivariateproblem classes. Originally, shearlets were introduced in 2006[1]for the analysis andsparse approximationof functionsf∈L2(R2){\displaystyle f\in L^{2}(\mathbb {R} ^{2})}. They are a n... | https://en.wikipedia.org/wiki/Shearlet |
Ultra-wideband(UWB,ultra wideband,ultra-wide bandandultraband) is aradio technologythat can use a very low energy level for short-range, high-bandwidth communications over a large portion of the radio spectrum.[1]UWB has traditional applications in non-cooperativeradar imaging. Most recent applications target sensor da... | https://en.wikipedia.org/wiki/Ultra_wideband |
Waveletsare often used to analyse piece-wise smooth signals.[1]Wavelet coefficients can efficiently represent a signal which has led to data compression algorithms using wavelets.[2]Wavelet analysis is extended formultidimensional signal processingas well. This article introduces a few methods for wavelet synthesis and... | https://en.wikipedia.org/wiki/Wavelet_for_multidimensional_signals_analysis |
Inmathematics, a sequencea=(a0,a1, ...,an)of nonnegative real numbers is called alogarithmically concave sequence, or alog-concave sequencefor short, ifai2≥ai−1ai+1holds for0 <i<n.
Remark:some authors (explicitly or not) add two further conditions in the definition of log-concave sequences:
These conditions mirror th... | https://en.wikipedia.org/wiki/Logarithmically_concave_sequence |
Inmathematics, aBorel measureμonn-dimensionalEuclidean spaceRn{\displaystyle \mathbb {R} ^{n}}is calledlogarithmically concave(orlog-concavefor short) if, for anycompact subsetsAandBofRn{\displaystyle \mathbb {R} ^{n}}and 0 <λ< 1, one has
whereλA+ (1 −λ)Bdenotes theMinkowski sumofλAand (1 −λ)B.[1]
TheBrunn–Minkowski ... | https://en.wikipedia.org/wiki/Logarithmically_concave_measure |
"AI slop", often simply "slop", is a derogatory term for low-quality media, including writing and images, made usinggenerative artificial intelligencetechnology, characterized by an inherent lack of effort, logic, or purpose.[1][4][5]Coined in the 2020s, the term has a pejorative connotation akin to "spam".[4]
It has ... | https://en.wikipedia.org/wiki/AI_slop |
Artificial intelligence(AI) has been used in applications throughout industry and academia. In a manner analogous to electricity or computers, AI serves as ageneral-purpose technology. AI programs are designed to simulate human perception and understanding. These systems are capable of adapting to new information and r... | https://en.wikipedia.org/wiki/Applications_of_artificial_intelligence#Art |
Artificial intelligence in architecturedescribes the use ofartificial intelligencein automation, design and planning in the architectural process or in assisting human skills in the field of architecture.[1]Artificial Intelligenceis thought to potentially lead to and ensue major changes in architecture.[2][3][4]
AI's ... | https://en.wikipedia.org/wiki/Artificial_intelligence_in_architecture |
Computational creativity(also known asartificial creativity,mechanical creativity,creative computingorcreative computation) is a multidisciplinary endeavour that is located at the intersection of the fields ofartificial intelligence,cognitive psychology,philosophy, andthe arts(e.g.,computational artas part ofcomputatio... | https://en.wikipedia.org/wiki/Computational_creativity |
Cybernetic artiscontemporary artthat builds upon the legacy ofcybernetics, wherefeedbackinvolved in the work takes precedence over traditionalaestheticand material concerns. The relationship between cybernetics and art can be summarised in three ways: cybernetics can be used to study art, to create works of art or may ... | https://en.wikipedia.org/wiki/Cybernetic_art |
Deepfakes(aportmanteauof'deep learning'and'fake'[1]) are images, videos, or audio that have been edited or generatedusing artificial intelligence, AI-based tools or AV editing software. They may depict real or fictional people and are considered a form ofsynthetic media, that is media that is usually created by artific... | https://en.wikipedia.org/wiki/Deepfakes |
Many notable artificial intelligence artists have created a wide variety ofartificial intelligence artfrom the 1960s to today. These include:
Thisartificial intelligence-related article is astub. You can help Wikipedia byexpanding it. | https://en.wikipedia.org/wiki/List_of_artificial_intelligence_artists |
Music and artificial intelligence(music and AI) is the development ofmusic softwareprograms which useAIto generate music.[1]As with applications in other fields, AI in music also simulates mental tasks. A prominent feature is the capability of an AI algorithm to learn based on past data, such as in computer accompanime... | https://en.wikipedia.org/wiki/Music_and_artificial_intelligence |
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