Search results for "Symbolic"

showing 10 items of 449 documents

INCIDENCE CONSTRAINTS: A COMBINATORIAL APPROACH

2006

The simplest geometric constraints are incidences between points and lines in the projective plane. This problem is universal, in the sense that all algebraic systems reduce to such geometric constraints. Detecting incidence dependences between these geometric constraints is NP-complete. New methods to prove incidence theorems are proposed, which use strictly no computer algebra but only combinatorial arguments.

Discrete mathematicsIncidence geometryApplied MathematicsCombinatorial proofSymbolic computationTheoretical Computer ScienceAlgebraComputational MathematicsComputational Theory and MathematicsGeometry and TopologyProjective planeAlgebraic numberIncidence (geometry)MathematicsProjective geometryInternational Journal of Computational Geometry & Applications
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Equivalence classes of permutations modulo descents and left-to-right maxima

2014

Abstract In a recent paper [2], the authors provide enumerating results for equivalence classes of permutations modulo excedances. In this paper we investigate two other equivalence relations based on descents and left-to-right maxima. Enumerating results are presented for permutations, involutions, derangements, cycles and permutations avoiding one pattern of length three.

Discrete mathematicsMathematics::CombinatoricsModulo[ MATH.MATH-CO ] Mathematics [math]/Combinatorics [math.CO][MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]CombinatoricsCatalan numberPermutationMotzkin numberComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]MaximaEquivalence classComputingMilieux_MISCELLANEOUSDescent (mathematics)Bell numberMathematicsMathematicsofComputing_DISCRETEMATHEMATICS
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A-Codes from Rational Functions over Galois Rings

2006

In this paper, we describe authentication codes via (generalized) Gray images of suitable codes over Galois rings. Exponential sums over these rings help determine--or bound--the parameters of such codes.

Discrete mathematicsMathematics::Commutative AlgebraApplied MathematicsFundamental theorem of Galois theoryGalois groupRational functionExponential polynomialComputer Science ApplicationsEmbedding problemDifferential Galois theorysymbols.namesakeGalois rings Gray map codesComputer Science::Computer Vision and Pattern RecognitionComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONComputer Science::MultimediasymbolsSettore MAT/03 - GeometriaGalois extensionResolventMathematicsDesigns, Codes and Cryptography
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Polynomial method to study the entanglement of pure N-qubit states

2009

We present a mapping which associates pure N-qubit states with a polynomial. The roots of the polynomial characterize the state completely. Using the properties of the polynomial we construct a way to determine the separability and the number of unentangled qubits of pure N-qubit states.

Discrete mathematicsPhysicsPolynomialQuantum PhysicsQuantum t-designSettore FIS/02 - Fisica Teorica Modelli E Metodi MatematiciCluster stateFOS: Physical sciencesQuantum entanglementQuantum PhysicsPolinomiMeccanica quantisticaAtomic and Molecular Physics and OpticsSettore FIS/03 - Fisica Della MateriaEntanglementSeparable stateComputer Science::Emerging TechnologiesQubitQuantum mechanicsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONW stateHardware_ARITHMETICANDLOGICSTRUCTURESQuantum Physics (quant-ph)Quantum teleportation
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Specification on the interval

1997

We study the consequences of discontinuities on the specification property for interval maps. After giving a necessary and sufficient condition for a piecewise monotonic, piecewise continuous map to have this property, we show that for a large and natural class of families of such maps (including the β \beta -transformations), the set of parameters for which the specification property holds, though dense, has zero Lebesgue measure. Thus, regarding the specification property, the general case is at the opposite of the continuous case solved by A.M. Blokh (Russian Math. Surveys 38 (1983), 133–134) (for which we give a proof).

Discrete mathematicsProperty (philosophy)Lebesgue measureApplied MathematicsGeneral MathematicsSymbolic dynamicsPiecewiseMonotonic functionInterval (mathematics)Classification of discontinuitiesNatural classMathematicsTransactions of the American Mathematical Society
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An exact and efficient approach for computing a cell in an arrangement of quadrics

2006

AbstractWe present an approach for the exact and efficient computation of a cell in an arrangement of quadric surfaces. All calculations are based on exact rational algebraic methods and provide the correct mathematical results in all, even degenerate, cases. By projection, the spatial problem is reduced to the one of computing planar arrangements of algebraic curves. We succeed in locating all event points in these arrangements, including tangential intersections and singular points. By introducing an additional curve, which we call the Jacobi curve, we are able to find non-singular tangential intersections. We show that the coordinates of the singular points in our special projected plana…

Discrete mathematicsPure mathematicsArrangementsControl and OptimizationFunction field of an algebraic varietyAlgebraic curvesMathematicsofComputing_NUMERICALANALYSISComputational geometryComputer Science ApplicationsComputational MathematicsComputational Theory and MathematicsJacobian curveAlgebraic surfaceComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONReal algebraic geometryAlgebraic surfacesExact algebraic computationAlgebraic functionGeometry and TopologyAlgebraic curveAlgebraic numberRobustnessMathematicsSingular point of an algebraic varietyComputational Geometry
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Trading off accuracy for efficiency by randomized greedy warping

2016

Dynamic Time Warping (DTW) is a widely used distance measure for time series data mining. Its quadratic complexity requires the application of various techniques (e.g. warping constraints, lower-bounds) for deployment in real-time scenarios. In this paper we propose a randomized greedy warping algorithm for finding similarity between time series instances. We show that the proposed algorithm outperforms the simple greedy approach and also provides very good time series similarity approximation consistently, as compared to DTW. We show that the Randomized Time Warping (RTW) can be used in place of DTW as a fast similarity approximation technique by trading some classification accuracy for ve…

Dynamic time warpingSeries (mathematics)Computer sciencebusiness.industryPattern recognitionData_CODINGANDINFORMATIONTHEORY02 engineering and technologyMeasure (mathematics)TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESComputingMethodologies_PATTERNRECOGNITIONSimilarity (network science)Computer Science::Sound020204 information systemsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processingArtificial intelligenceImage warpingbusinessGeneralLiterature_REFERENCE(e.g.dictionariesencyclopediasglossaries)Computer Science::DatabasesProceedings of the 31st Annual ACM Symposium on Applied Computing
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Feigenbaum graphs: a complex network perspective of chaos

2011

The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map…

Dynamical systems theoryScienceSymbolic dynamicsFOS: Physical sciencesLyapunov exponentFixed pointBioinformatics01 natural sciences010305 fluids & plasmasStatistical Mechanicssymbols.namesake0103 physical sciencesAttractorEntropy (information theory)Statistical physics010306 general physicsChaotic SystemsCondensed-Matter PhysicsCondensed Matter - Statistical MechanicsPhysicsMultidisciplinaryStatistical Mechanics (cond-mat.stat-mech)Applied MathematicsPhysicsQRComplex SystemsComplex networkNonlinear Sciences - Chaotic DynamicsDegree distributionNonlinear DynamicssymbolsMedicineChaotic Dynamics (nlin.CD)MathematicsAlgorithmsResearch Article
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"Table 2" of "A measurement of alpha(s) from the scaling violation in e+ e- annihilation."

1996

alpha_s was evaluated from the scaling violation of the fragmentation func tions. The data from other experiments are used for the fitting procedure.

E+ E- --> DQBAR DQHigh Energy Physics::PhenomenologyE+ E- --> CQBAR CQE+ E- --> BQBAR BQE+ E- --> UQBAR UQALPHASE+ E- --> CHARGED-HADRON XInclusiveE+ E- --> SQBAR SQE+ E- ScatteringComputer Science::General LiteratureExclusiveComputer Science::Symbolic ComputationHigh Energy Physics::Experiment29.0
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"Table 4" of "Inclusive production of neutral vector mesons in hadronic Z decays"

1995

Average multiplicity per hadronic event. Extrapolation to the full X range.

E+ E- --> OMEGA XInclusiveHigh Energy Physics::LatticeE+ E- ScatteringHigh Energy Physics::ExperimentComputer Science::Symbolic Computation91.2Nuclear ExperimentComputer Science::Distributed Parallel and Cluster ComputingMULT
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