Search results for "Linear Algebra"

showing 10 items of 552 documents

A formal proof of the e-optimality of discretized pursuit algorithms

2015

Learning Automata (LA) can be reckoned to be the founding algorithms on which the field of Reinforcement Learning has been built. Among the families of LA, Estimator Algorithms (EAs) are certainly the fastest, and of these, the family of discretized algorithms are proven to converge even faster than their continuous counterparts. However, it has recently been reported that the previous proofs for ??-optimality for all the reported algorithms for the past three decades have been flawed. We applaud the researchers who discovered this flaw, and who further proceeded to rectify the proof for the Continuous Pursuit Algorithm (CPA). The latter proof examines the monotonicity property of the proba…

Learning automataDiscretizationInequalityBasis (linear algebra)Computer sciencemedia_common.quotation_subjectField (mathematics)Monotonic function02 engineering and technologyMathematical proofFormal proof020202 computer hardware & architectureAlgebraArtificial Intelligence0202 electrical engineering electronic engineering information engineeringReinforcement learning020201 artificial intelligence & image processingAlgorithmmedia_common
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Adaptive algorithms robust to impulsive noise with low computational cost using order statistic

2009

Abstract In this paper a family of adaptive algorithms robust to impulsive noise and with low computational cost are presented. Unlike other approaches, no cost functions or filtering of the gradient are considered in order to update the filter coefficients. Its initial basis is the basic LMS algorithm and its sign-error variant. The proposed algorithms can be considered as some sign-error variants of the LMS algorithm. The algorithms are successfully tested in terms of accuracy and convergence in a standard system identification simulation in which an impulsive noise is present. Simulations show that they improve the performance of LMS variants that are robust to impulsive noise.

Least mean squares filterNoiseFilter designIdentification (information)Basis (linear algebra)Control theoryComputer scienceOrder statisticGeneral MedicineFilter (signal processing)Hardware_ARITHMETICANDLOGICSTRUCTURESAlgorithm
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The J-invariant, Tits algebras and Triality

2012

In the present paper we set up a connection between the indices of the Tits algebras of a simple linear algebraic group $G$ and the degree one parameters of its motivic $J$-invariant. Our main technical tool are the second Chern class map and Grothendieck's $\gamma$-filtration. As an application we recover some known results on the $J$-invariant of quadratic forms of small dimension; we describe all possible values of the $J$-invariant of an algebra with orthogonal involution up to degree 8 and give explicit examples; we establish several relations between the $J$-invariant of an algebra $A$ with orthogonal involution and the $J$-invariant of the corresponding quadratic form over the functi…

Linear algebraic groupDiscrete mathematicsInvolution (mathematics)Pure mathematicsAlgebra and Number TheoryChern classTrialityj-invariant010102 general mathematicsMathematics - Rings and Algebras01 natural sciencesMathematics - Algebraic GeometryRings and Algebras (math.RA)0103 physical sciencesFOS: Mathematics010307 mathematical physics0101 mathematicsAlgebraic Geometry (math.AG)Function field20G15 14C25 14L30 16W10 11E04Mathematics
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Algebraic groups as difference Galois groups of linear differential equations

2019

We study the inverse problem in the difference Galois theory of linear differential equations over the difference-differential field $\mathbb{C}(x)$ with derivation $\frac{d}{dx}$ and endomorphism $f(x)\mapsto f(x+1)$. Our main result is that every linear algebraic group, considered as a difference algebraic group, occurs as the difference Galois group of some linear differential equation over $\mathbb{C}(x)$.

Linear algebraic groupPure mathematicsAlgebra and Number TheoryEndomorphism010102 general mathematicsGalois theoryGalois groupField (mathematics)Commutative Algebra (math.AC)Mathematics - Commutative Algebra01 natural sciencesMathematics - Algebraic GeometryLinear differential equationAlgebraic group0103 physical sciencesFOS: Mathematics010307 mathematical physics0101 mathematicsAlgebraic numberAlgebraic Geometry (math.AG)12H10 12H05 34M15 34M50 14L15MathematicsJournal of Pure and Applied Algebra
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Dictionnaire Bilingue, Syntaxe et Sémantique

1995

We have first shown that the conventional and theoretical lexicography has always had a semantic basis which does not permit homogeneous analysis of the items which constitute the entries. We present in this paper a model of bilingual dictionary whose fundamental principles are syntactical. This dictionary is an application of the methods of the Lexique-grammaire des langues romanes adapted to contrastive viewpoint. This contrastive aim implicates that we have to make specific analytic distinctions which we comment here. On the one hand, from a theoretical standpoint, this dictionary may help to establish suitable basis of systematic contrastive (French/Spanish) linguistics, and on the othe…

Linguistics and LanguageBasis (linear algebra)business.industryComputer scienceHomogeneousBilingual dictionaryArtificial intelligencebusinesscomputer.software_genrecomputerNatural language processingLinguisticsLexicographyLingvisticæ Investigationes. International Journal of Linguistics and Language Resources
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Effect ofmconbquark chromomagnetic interaction and on-shell two-loop integrals with two masses

1999

The effect of non-zero c quark mass on b quark HQET Lagrangian, up to 1/mb level, is calculated at two loops. The results are expressed in terms of dilogarithmic functions of mc/mb. This calculation involves on-shell two-loop propagator-type diagrams with two different masses, mb and mc. A general algorithm for reducing such Feynman integrals to the basis of two nontrivial and two trivial integrals is constructed.

Loop (topology)PhysicsNuclear and High Energy PhysicsParticle physicsBasis (linear algebra)BibliographyShell (structure)PropagatorCharm (quantum number)Bottom quarkCharm quarkPhysical Review D
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Faults diagnosis based on proportional integral observer for TS fuzzy model with unmeasurable premise variable

2014

In this work, we focus on the synthesis of a Proportional Integral (PI) observer for the actuators and sensors faults diagnosis based on Takagi-Sugeno (TS) fuzzy model with unmeasurable premise variables. The faults estimation method is based on the assumption that these faults act as unknown inputs under polynomials form whose their kth derivatives are bounded. The convergence conditions of the observer as well as the faults reconstruction are established on the basis of the Lyapunov stability theory and the L 2 optimization technique, expressed as Linear Matrix Inequalities (LMI) constraints. In order to validate the proposed approach, a hydraulic system with two tanks is proposed.

Lyapunov stabilityObserver (quantum physics)Basis (linear algebra)Applied MathematicsTheoretical Computer ScienceArtificial IntelligenceComputer Science::Systems and ControlControl theoryBounded functionConvergence (routing)Hydraulic machineryTheoretical Computer Science; Software; Artificial Intelligence; Applied MathematicsFocus (optics)SoftwareVariable (mathematics)Mathematics2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
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Linus Pauling’s Breakthrough to the Theory of Aromatic Compounds and Hückel’s Reaction

2009

In the mid-1930s Wheland and Pauling set out to find a quantum theoretical basis for Ingold’s general electronic theory of organic reactions. A brief outline of Ingold’s main concepts will provide the necessary background for an evaluation of their contribution and Huckel’s discussion of it.

Magnetic anisotropyTheoretical physicsOrganic reactionBasis (linear algebra)ChemistryPhysical chemistryQuantumMagnetic susceptibilityElectronic theory
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Hyperspectral detection of citrus damage with Mahalanobis kernel classifier

2007

Presented is a full computer vision system for the identification of post-harvest damage in citrus packing houses. The method is based on the combined use of hyperspectral images and the Mahalanobis kernel classifier. More accurate and reliable results compared to other methods are obtained in several scenarios and acquired images.

Mahalanobis distanceContextual image classificationbusiness.industryComputer scienceHyperspectral imagingPattern recognitionObject detectionSupport vector machineKernel (linear algebra)Kernel methodKernel (image processing)Computer visionArtificial intelligenceElectrical and Electronic EngineeringbusinessClassifier (UML)
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When Geometry Constrains Vision: Systematic Misperceptions within Geometrical Configurations.

2016

International audience; How accurate are we in reproducing a point within a simple shape? This is the empirical question we addressed in this work. Participants were presented with a tiny disk embedded in an empty circle (Experiment 1 and 3) or in a square (Experiment 2). Shortly afterwards the disk vanished and they had to reproduce the previously seen disk position within the empty shape by means of the mouse cursor, as accurately as possible. Several loci inside each shape were tested. We found that the space delimited by a circle and by a square is not homogeneous and the observed distortion appears to be consistent across observers and specific for the two tested shapes. However, a com…

MaleEye MovementsVisionPhysiologyVisual SystemVector SpacesSensory PhysiologySocial Scienceslcsh:Medicine[ SCCO.PSYC ] Cognitive science/Psychology050109 social psychologyGeometrySquare (algebra)SymmetryForm perceptionMedicine and Health SciencesPsychologyAttentionlcsh:ScienceMathematicsMultidisciplinaryExperimental Design05 social sciencesSensory SystemsPattern Recognition VisualResearch Design[ SCCO.NEUR ] Cognitive science/Neuroscience[SCCO.PSYC]Cognitive science/PsychologyPhysical SciencesSensory PerceptionFemaleResearch ArticleAdultGeometryResearch and Analysis Methods050105 experimental psychologyYoung AdultPosition (vector)DistortionHumans0501 psychology and cognitive sciencesPoint (geometry)Vision Ocularshape perception perceptual center perceptual force vector field perceptual distortion visual mislocalization Gestalt eye movements[SCCO.NEUR]Cognitive science/Neurosciencelcsh:RCognitive PsychologyBiology and Life SciencesNull (physics)Form PerceptionAlgebraRadiiLinear AlgebraSpace PerceptionContour lineLinear ModelsCognitive Sciencelcsh:QSymmetry (geometry)MathematicsPhotic StimulationNeurosciencePLoS ONE
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