Search results for " Algebra"

showing 10 items of 2082 documents

On Information Processing in the Cat’s Visual Cortex

1986

We assume that the visual system serves for orientation in space, recognition of objects and the interpretation of scenes and scene sequences. This task breaks up into a series of partially interdependent subproblems which are solved by some 13–15 usually retinotopically organized areas. So far it has not been possible to correlate functions and areas unequivocally. One reason for this could be the inadequacy of the questions posed as a basis for experiments. However, we think it more likely that correlating a function with an area is, as a rule, inadmissible since the degree of the coupling in the whole system does not permit a simple divsion. Rather the type and degree of coupling determi…

Basis (linear algebra)business.industryOrientation (computer vision)Computer sciencemedia_common.quotation_subjectInformation processingPattern recognitionTask (project management)ControllabilityObservabilityArtificial intelligencebusinessFunction (engineering)Complement (set theory)media_common
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The pricing capability lifecycle of digital innovations

2021

The pricing capability provides a basis for firms’ competitive advantage. However, to date, the literature has not investigated how this capability forms, develops, and matures. In this study, we define the pricing capability as a dynamic capability consisting of three operational building blocks (tools and data, human and relational resources, and processes, routines, and mechanisms) as well as two dynamic capability building blocks (alertness and responsiveness, and value-based strategic thinking). Furthermore, we propose the pricing capability lifecycle of digital innovations that incorporates insights of the dynamic capabilities view (DCV). Based on a longitudinal multi-case study of fi…

Basis (linear algebra)kilpailukykyComputer sciencepricing capabilityStrategy and ManagementhinnoitteluteknologiayrityksetManagement Science and Operations ResearchCompetitive advantageinnovaatiotinnovaatiotoimintaDynamic capabilitiesdynaamiset kyvykkyydetdigital innovationsdynamic capabilitiesIndustrial organizationcapability lifecycle
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Electric Vehicles and Psychology, Part 2

2021

This paper presents the main psychological attitudes influencing the transition from conventional ICEV to BEV, and it is the continuance of Electric vehicles and psychology, part 1, [1]. This part faces the range anxiety problem, the risk of explosion of batteries, the autonomous silver vehicles and the experience of driving electric vehicles. If the reader is looking for simple answers, the author does not recommend the subsequent reading, since few paradoxes will be solved.

Battery (electricity)egg and chicken paradoxRange anxietyTransition (fiction)media_common.quotation_subjectBatterykey motivators and barriersSimple (abstract algebra)Reading (process)public perceptionContinuancerange anxietyPsychologymedia_commonCognitive psychologyelectric vehicles
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MODELLING USER UNCERTAINTY FOR DISCLOSURE RISK AND DATA UTILITY

2002

In this paper we show how a simple model that captures user uncertainty can be used to define suitable measures of disclosure risk and data utility. The model generalizes previous results of Duncan and Lambert.1 We present several examples to illustrate how the new measures can be used to implement existing optimality criteria for the choice of the best form of data release.

Bayes estimatorArtificial IntelligenceControl and Systems EngineeringComputer scienceSimple (abstract algebra)Data miningcomputer.software_genreInformation theoryData releasecomputerSoftwareInformation SystemsInternational Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
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Splittings of Toric Ideals

2019

Let $I \subseteq R = \mathbb{K}[x_1,\ldots,x_n]$ be a toric ideal, i.e., a binomial prime ideal. We investigate when the ideal $I$ can be "split" into the sum of two smaller toric ideals. For a general toric ideal $I$, we give a sufficient condition for this splitting in terms of the integer matrix that defines $I$. When $I = I_G$ is the toric ideal of a finite simple graph $G$, we give additional splittings of $I_G$ related to subgraphs of $G$. When there exists a splitting $I = I_1+I_2$ of the toric ideal, we show that in some cases we can describe the (multi-)graded Betti numbers of $I$ in terms of the (multi-)graded Betti numbers of $I_1$ and $I_2$.

Binomial (polynomial)Betti numberPrime idealExistential quantificationCommutative Algebra (math.AC)01 natural sciencesCombinatoricsInteger matrixMathematics::Algebraic Geometry0103 physical sciencesFOS: MathematicsGraded Betti numbers; Graphs; Toric idealsMathematics - Combinatorics0101 mathematicsMathematics::Symplectic GeometryMathematicsAlgebra and Number TheorySimple graphIdeal (set theory)Mathematics::Commutative AlgebraGraded Betti numbers Graphs Toric ideals010102 general mathematicsMathematics::Rings and Algebras16. Peace & justiceMathematics - Commutative AlgebraSettore MAT/02 - AlgebraToric ideals13D02 13P10 14M25 05E40Settore MAT/03 - Geometria010307 mathematical physicsCombinatorics (math.CO)Graded Betti numbersGraphs
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Hybrid Quantum Mechanics/Molecular Mechanics Simulations with Two-Dimensional Interpolated Corrections:  Application to Enzymatic Processes

2006

Hybrid quantum mechanics/molecular mechanics (QM/MM) techniques are widely used to study chemical reactions in large systems. Because of the computational cost associated with the high dimensionality of these systems, the quantum description is usually restricted to low-level methods, such as semiempirical Hamiltonians. In some cases, the description obtained at this computational level is quite poor and corrections must be considered. We here propose a simple but efficient way to include higher-level corrections to be used in potential energy surface explorations and in the calculation of potentials of mean force. We evaluate a correction energy term as the difference between a high-level …

BiophysicsCatechol O-MethyltransferaseMethylationCatalysisSimple (abstract algebra)Quantum mechanicsMaterials ChemistryComputer SimulationPhysical and Theoretical ChemistryWave functionQuantumChemistry PhysicalChemistryFunction (mathematics)Models TheoreticalEnzymesSurfaces Coatings and FilmsClassical mechanicsModels ChemicalPotential energy surfaceChorismate mutaseQuantum TheoryThermodynamicsBicubic interpolationEnergy (signal processing)Bacillus subtilisChorismate MutaseThe Journal of Physical Chemistry B
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Iterative sparse matrix-vector multiplication for accelerating the block Wiedemann algorithm over GF(2) on multi-graphics processing unit systems

2012

SUMMARY The block Wiedemann (BW) algorithm is frequently used to solve sparse linear systems over GF(2). Iterative sparse matrix–vector multiplication is the most time-consuming operation. The necessity to accelerate this step is motivated by the application of BW to very large matrices used in the linear algebra step of the number field sieve (NFS) for integer factorization. In this paper, we derive an efficient CUDA implementation of this operation by using a newly designed hybrid sparse matrix format. This leads to speedups between 4 and 8 on a single graphics processing unit (GPU) for a number of tested NFS matrices compared with an optimized multicore implementation. We further present…

Block Wiedemann algorithmComputer Networks and CommunicationsComputer scienceGraphics processing unitSparse matrix-vector multiplicationGPU clusterParallel computingGF(2)Computer Science ApplicationsTheoretical Computer ScienceGeneral number field sieveMatrix (mathematics)Computational Theory and MathematicsFactorizationLinear algebraMultiplicationComputer Science::Operating SystemsSoftwareInteger factorizationSparse matrixConcurrency and Computation: Practice and Experience
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CCSDT calculations of molecular equilibrium geometries

1997

Abstract CCSDT equilibrium geometries of CO, CH2, F2, HF, H2O and N2 have been calculated using the correlation-consistent cc-pVXZ basis sets. Similar calculations have been performed for SCF, CCSD and CCSD(T). In general, bond lengths decrease when improving the basis set and increase when improving the N-electron treatment. CCSD(T) provides an excellent approximation to CCSDT for bond lengths as the largest difference between CCSDT and CCSD(T) is 0.06 pm. At the CCSDT/cc-pVQZ level, basis set deficiencies, neglect of higher-order excitations, and incomplete treatment of core-correlation all give rise to errors of a few tenths of a pm, but to a large extent, these errors cancel. The CCSDT/…

Bond lengthBasis (linear algebra)Computational chemistryChemistryGeneral Physics and AstronomyPhysical and Theoretical ChemistryMolecular physicsBasis setChemical Physics Letters
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Analysis of Spatially and Temporally Overlapping Events with Application to Image Sequences

2006

Counting spatially and temporally overlapping events in image sequences and estimating their shape-size and duration features are important issues in some applications. We propose a stochastic model, a particular case of the nonisotropic 3D Boolean model, for performing this analysis: the temporal Boolean model. Some probabilistic properties are derived and a methodology for parameter estimation from time-lapse image sequences is proposed using an explicit treatment of the temporal dimension. We estimate the mean number of germs per unit area and time, the mean grain size and the duration distribution. A wide simulation study in order to assess the proposed estimators showed promising resul…

Boolean modelEstimation theorybusiness.industryStochastic modellingApplied MathematicsProbabilistic logicEstimatorFunctional data analysisImage processingBoolean algebrasymbols.namesakeComputational Theory and MathematicsArtificial IntelligencesymbolsComputer visionComputer Vision and Pattern RecognitionArtificial intelligencebusinessAlgorithmSoftwareMathematicsIEEE Transactions on Pattern Analysis and Machine Intelligence
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Exacus: Efficient and Exact Algorithms for Curves and Surfaces

2005

We present the first release of the Exacus C++ libraries. We aim for systematic support of non-linear geometry in software libraries. Our goals are efficiency, correctness, completeness, clarity of the design, modularity, flexibility, and ease of use. We present the generic design and structure of the libraries, which currently compute arrangements of curves and curve segments of low algebraic degree, and boolean operations on polygons bounded by such segments.

Boolean operations on polygonsModularity (networks)CorrectnessTheoretical computer scienceExact algorithmGeneric programmingComputer scienceBounded functionCompleteness (order theory)Algebraic numberAlgorithmCylindrical algebraic decomposition
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