Search results for "DUALITY"

showing 10 items of 226 documents

Introduction to General Duality Theory for Multi-Objective Optimization

1992

This is intended as a comprehensive introduction to the duality theory for vector optimization recently developed by C. Malivert and the present author [3]. It refers to arbitrarily given classes of mappings (dual elements) and extends the general duality theory proposed for scalar optimization by E. Balder, S. Kurcyusz and the present author [1] and P. Lindberg.

AlgebraMathematical optimizationVector optimizationStrong dualityWolfe dualityDuality (optimization)Multi-objective optimizationMathematicsScalar optimization
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A class of unitals of order q which can be embedded in two different planes of order q2

1987

By deriving the desarguesian plane of order q2 for every prime power q a unital of order q is constructed which can be embedded in both the Hall plane and the dual of the Hall plane of order q2 which are non-isomorphic projective planes. The representation of translation planes in the fourdimensional projective space of J. Andre and F. Buekenhouts construction of unitals in these planes are used. It is shown that the full automorphism groups of these unitals are just the collineation groups inherited from the classical unitals.

AlgebraPure mathematicsCollineationReal projective planeDuality (projective geometry)Translation planeFinite geometryGeometry and TopologyProjective planeFano planeNon-Desarguesian planeMathematicsJournal of Geometry
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Great Minds Think Alike? Spatial Search Processes Can Be More Idiosyncratic When Guided by More Accurate Information.

2022

Existing research demonstrates that pre-decisional information sampling strategies are often stablewithin a given person while varying greatly across people. However, it remains largely unknown whatdrives these individual differences, that is, why in some circumstances we collect information moreidiosyncratically. In this brief report, we present a pre-registered online study of spatial search. Usinga novel technique that combines machine-learning dimension reduction and sequence alignment algo-rithms, we quantify the extent to which the shape and temporal properties of a search trajectory areidiosyncratic. We show that this metric increases (trajectories become more idiosyncratic) when a p…

Artificial IntelligenceCognitive NeuroscienceVDP::Samfunnsvitenskap: 200::Psykologi: 260IndividualityVisual PerceptionHumansExperimental and Cognitive PsychologyAttentionAlgorithmsCognitive science
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New Twists of 3D Chiral Metamaterials

2018

Rationally designed artificial materials, called metamaterials, allow for tailoring effective material properties beyond ("meta") the properties of their bulk ingredient materials. This statement is especially true for chiral metamaterials, as unlocking certain degrees of freedom necessarily requires broken centrosymmetry. While the field of chiral electromagnetic/optical metamaterials has become rather mature, the field of elastic/mechanical metamaterials is just emerging and wide open. This research news reviews recent theoretical and experimental progress concerning 3D chiral mechanical and optical metamaterials, with special emphasis on work performed at KIT.

Artificial materialsMaterials scienceField (physics)Mechanical EngineeringPhysics::OpticsMetamaterial02 engineering and technologyDegrees of freedom (mechanics)Physics::Classical Physics010402 general chemistry021001 nanoscience & nanotechnologyCentrosymmetry01 natural sciences0104 chemical sciencesDuality (electricity and magnetism)Photonic metamaterialTheoretical physicsMechanics of MaterialsGeneral Materials ScienceBulk ingredient0210 nano-technologyAdvanced Materials
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The mechanically-based approach to 3D non-local linear elasticity theory: Long-range central interactions

2010

Abstract This paper presents the generalization to a three-dimensional (3D) case of a mechanically-based approach to non-local elasticity theory, recently proposed by the authors in a one-dimensional (1D) case. The proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long-range forces exerted by non-adjacent elements. Specifically, the long-range forces are modelled as central body forces depending on the relative displacement between the centroids of the volume elements, measured along the line connecting the centroids. Further, the long-range forces are assumed to be proportional to a proper, material-dependent, dis…

Body forceNon-local elasticityWAVESPROPAGATIONContact forceLattice modelsCentral forcesCentral forceVARIATIONAL-PRINCIPLESMaterials Science(all)Modelling and SimulationVariational formulationsGeneral Materials ScienceVirtual workPLASTICITYSTRAIN-GRADIENT ELASTICITYMathematicsPlane stressDISCRETECONTINUAMechanical EngineeringApplied MathematicsLinear elasticityElastic energySTRAIN-GRADIENT ELASTICITY; VARIATIONAL-PRINCIPLES; CRACK SUBJECT; PROPAGATION; PLASTICITY; DISCRETE; CONTINUA; DEFECTS; LATTICE; WAVESMechanicsDEFECTSCondensed Matter PhysicsLATTICELong-range interactionsClassical mechanicsContact mechanicsStatic–kinematic dualityMechanics of MaterialsModeling and SimulationSettore ICAR/08 - Scienza Delle CostruzioniCRACK SUBJECTInternational Journal of Solids and Structures
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Extropy: Complementary Dual of Entropy

2015

This article provides a completion to theories of information based on entropy, resolving a longstanding question in its axiomatization as proposed by Shannon and pursued by Jaynes. We show that Shannon's entropy function has a complementary dual function which we call "extropy." The entropy and the extropy of a binary distribution are identical. However, the measure bifurcates into a pair of distinct measures for any quantity that is not merely an event indicator. As with entropy, the maximum extropy distribution is also the uniform distribution, and both measures are invariant with respect to permutations of their mass functions. However, they behave quite differently in their assessments…

Bregman divergenceFOS: Computer and information sciencesStatistics and ProbabilitySettore MAT/06 - Probabilita' E Statistica MatematicaKullback–Leibler divergenceComputer Science - Information TheoryGeneral MathematicsFOS: Physical sciencesBinary numberMathematics - Statistics TheoryStatistics Theory (math.ST)Kullback–Leibler divergenceBregman divergenceproper scoring rulesGini index of heterogeneityDifferential entropyBinary entropy functionFOS: MathematicsEntropy (information theory)Statistical physicsDual functionAxiomMathematicsdifferential and relative entropy/extropy Kullback- Leibler divergence Bregman divergence duality proper scoring rules Gini index of heterogeneity repeat rate.Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniDifferential and relative entropy/extropyInformation Theory (cs.IT)Probability (math.PR)repeat ratePhysics - Data Analysis Statistics and ProbabilitydualityStatistics Probability and UncertaintySettore SECS-S/01 - StatisticaMathematics - ProbabilityData Analysis Statistics and Probability (physics.data-an)Statistical Science
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ChPT parameters from tau-decay data

2015

Using the updated ALEPH V-A spectral function from tau decays, we determine the lowest spectral moments of the left-right correlator and extract dynamical information on order parameters of the QCD chiral symmetry breaking. Uncertainties associated with violations of quark-hadron duality are estimated from the data, imposing all known short-distance constraints on a resonance-based parametrization. Employing proper pinched weight functions, we obtain an accurate determination of the effective chiral couplings L10 and C87 and the dimension-six and -eight contributions in the Operator Product Expansion.

Chiral anomalyPhysicsQuantum chromodynamicsNuclear and High Energy PhysicsParticle physicsChiral perturbation theory010308 nuclear & particles physicsHigh Energy Physics::PhenomenologyFOS: Physical sciencesDuality (optimization)01 natural sciencesHigh Energy Physics - PhenomenologyHigh Energy Physics - Phenomenology (hep-ph)[PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph]Nambu–Jona-Lasinio model0103 physical sciencesHigh Energy Physics::ExperimentOperator product expansion010306 general physicsChiral symmetry breakingParametrization
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On Duality in Learning and the Selection of Learning Teams

1996

AbstractPrevious work in inductive inference dealt mostly with finding one or several machines (IIMs) that successfully learn collections of functions. Herein we start with a class of functions and considerthe learner setof all IIMs that are successful at learning the given class. Applying this perspective to the case of team inference leads to the notion ofdiversificationfor a class of functions. This enable us to distinguish between several flavours of IIMs all of which must be represented in a team learning the given class.

Class (computer programming)business.industryPerspective (graphical)Duality (mathematics)InferenceInductive reasoningMachine learningcomputer.software_genreTheoretical Computer ScienceComputer Science ApplicationsTeam learningComputational Theory and MathematicsSelection (linguistics)Artificial intelligencebusinesscomputerMathematicsInformation SystemsInformation and Computation
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Are locally finite MV-algebras a variety?

2021

We answer Mundici's problem number 3 (D. Mundici. Advanced {\L}ukasiewicz calculus. Trends in Logic Vol. 35. Springer 2011, p. 235): Is the category of locally finite MV-algebras equivalent to an equational class? We prove: (i) The category of locally finite MV-algebras is not equivalent to any finitary variety. (ii) More is true: the category of locally finite MV-algebras is not equivalent to any finitely-sorted finitary quasi-variety. (iii) The category of locally finite MV-algebras is equivalent to an infinitary variety; with operations of at most countable arity. (iv) The category of locally finite MV-algebras is equivalent to a countably-sorted finitary variety. Our proofs rest upon th…

Class (set theory)Pure mathematicsAlgebra and Number Theory06D35 (Primary) 18C05 (Secondary)Duality (mathematics)Mathematics - Category TheoryMathematics - LogicArityMathematical proofComputer Science::Logic in Computer ScienceMathematics::Category TheoryFOS: MathematicsCountable setFinitaryCategory Theory (math.CT)Variety (universal algebra)Logic (math.LO)Categorical variableMathematics
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The hidden group structure of quantum groups: strong duality, rigidity and preferred deformations

1994

A notion of well-behaved Hopf algebra is introduced; reflexivity (for strong duality) between Hopf algebras of Drinfeld-type and their duals, algebras of coefficients of compact semi-simple groups, is proved. A hidden classical group structure is clearly indicated for all generic models of quantum groups. Moyal-product-like deformations are naturally found for all FRT-models on coefficients andC∞-functions. Strong rigidity (H bi 2 ={0}) under deformations in the category of bialgebras is proved and consequences are deduced.

Classical groupPure mathematicsQuantum groupDeformation theoryLie groupStatistical and Nonlinear PhysicsHopf algebra17B37Algebra81R50Compact groupMathematics::Quantum AlgebraStrong dualityDual polyhedron16W30Mathematical PhysicsMathematics
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