Search results for "SAND"

showing 10 items of 2366 documents

Approximate convex hull of affine iterated function system attractors

2012

International audience; In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In additio…

Discrete mathematicsConvex hull0209 industrial biotechnologyGeneral MathematicsApplied Mathematics010102 general mathematicsProper convex functionConvex setMathematicsofComputing_GENERALGeneral Physics and AstronomyStatistical and Nonlinear Physics02 engineering and technology[ INFO.INFO-GR ] Computer Science [cs]/Graphics [cs.GR]01 natural sciences[INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR]020901 industrial engineering & automationAffine hullTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYConvex polytopeOutput-sensitive algorithmConvex combination0101 mathematicsConvex conjugateMathematics
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Minimal forbidden words and symbolic dynamics

1996

We introduce a new complexity measure of a factorial formal language L: the growth rate of the set of minimal forbidden words. We prove some combinatorial properties of minimal forbidden words. As main result we prove that the growth rate of the set of minimal forbidden words for L is a topological invariant of the dynamical system defined by L.

Discrete mathematicsFactorial010102 general mathematics[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]Symbolic dynamicsComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]0102 computer and information sciencesInvariant (physics)16. Peace & justice01 natural sciencesCombinatorics010201 computation theory & mathematicsTheoryofComputation_LOGICSANDMEANINGSOFPROGRAMSInformation complexityFormal language0101 mathematicsComputer Science::Formal Languages and Automata TheoryComputingMilieux_MISCELLANEOUSMathematicsofComputing_DISCRETEMATHEMATICSMathematics
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The computational complexity of the relative robust shortest path problem with interval data

2004

Abstract The paper deals with the relative robust shortest path problem in a directed arc weighted graph, where arc lengths are specified as intervals containing possible realizations of arc lengths. The complexity status of this problem has been unknown in the literature. We show that the problem is NP -hard.

Discrete mathematicsInformation Systems and ManagementGeneral Computer ScienceManagement Science and Operations ResearchIndustrial and Manufacturing EngineeringLongest path problemWidest path problemEuclidean shortest pathShortest Path Faster AlgorithmTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYModeling and SimulationShortest path problemK shortest path routingCanadian traveller problemDistanceMathematicsofComputing_DISCRETEMATHEMATICSMathematicsEuropean Journal of Operational Research
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Collection Principles in Dependent Type Theory

2002

We introduce logic-enriched intuitionistic type theories, that extend intuitionistic dependent type theories with primitive judgements to express logic. By adding type theoretic rules that correspond to the collection axiom schemes of the constructive set theory CZF we obtain a generalisation of the type theoretic interpretation of CZF. Suitable logic-enriched type theories allow also the study of reinterpretations of logic. We end the paper with an application to the double-negation interpretation.

Discrete mathematicsInterpretation (logic)Dependent type theory constructive set theory propositions-as-typesComputer scienceConstructive set theoryIntuitionistic logicIntuitionistic type theoryDependent typeAlgebraMathematics::LogicTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESDependent type theoryType theoryTheoryofComputation_LOGICSANDMEANINGSOFPROGRAMSComputer Science::Logic in Computer ScienceDouble negationSet theoryRule of inferenceAxiom
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Balls into non-uniform bins

2014

Balls-into-bins games for uniform bins are widely used to model randomized load balancing strategies. Recently, balls-into-bins games have been analysed under the assumption that the selection probabilities for bins are not uniformly distributed. These new models are motivated by properties of many peer-to-peer (P2P) networks, which are not able to perfectly balance the load over the bins. While previous evaluations try to find strategies for uniform bins under non-uniform bin selection probabilities, this paper investigates heterogeneous bins, where the "capacities" of the bins might differ significantly. We show that heterogeneous environments can even help to distribute the load more eve…

Discrete mathematicsMathematical optimizationComputational complexity theoryComputer Networks and CommunicationsComputer scienceDistributed computingAstrophysics::Cosmology and Extragalactic AstrophysicsPhysics::Data Analysis; Statistics and ProbabilityLoad balancing (computing)BinTheoretical Computer ScienceLoad managementCapacity planningArtificial IntelligenceHardware and ArchitectureTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYBounded functionBall (bearing)Resource allocationHardware_ARITHMETICANDLOGICSTRUCTURESGame theorySoftwareMathematicsMathematicsofComputing_DISCRETEMATHEMATICS2010 IEEE International Symposium on Parallel & Distributed Processing (IPDPS)
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Deciding reachability for planar multi-polynomial systems

1996

In this paper we investigate the decidability of the reachability problem for planar non-linear hybrid systems. A planar hybrid system has the property that its state space corresponds to the standard Euclidean plane, which is partitioned into a finite number of (polyhedral) regions. To each of these regions is assigned some vector field which governs the dynamical behaviour of the system within this region. We prove the decidability of point to point and region to region reachability problems for planar hybrid systems for the case when trajectories within the regions can be described by polynomials of arbitrary degree.

Discrete mathematicsPolynomialReachability problemReachabilityTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYHybrid systemState spaceVector fieldFinite setMathematicsofComputing_DISCRETEMATHEMATICSDecidabilityMathematics
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Discrete Mathematics in Lower School Grades? Situation and Possibilities in Italy

2017

This paper presents an overview of the Italian situation in teaching discrete mathematics in primary and middle school, taking into account the national teaching guidelines and their connection with the subject. We describe research conducted with about 150 teachers, interviewed in a preliminary questionnaire. The data collected shows, for all teaching grades, interest in having more discrete mathematics in the school curriculum even if there are some difficulties in teaching it and in inserting it in the usual mathematical activities at school, mostly related to teachers’ knowledge and self-confidence about the subject. We also discuss results and future plans for a continuing research pro…

Discrete mathematicsResearch designProcess (engineering)Computational thinkingComputingMilieux_COMPUTERSANDEDUCATIONSubject (documents)Design research Computational thinking Algorithms Programming UnpluggedSettore MAT/04 - Matematiche ComplementariPsychologyCurriculum
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Counting in the Two Variable Guarded Logic with Transitivity

2005

We show that the extension of the two-variable guarded fragment with transitive guards (GF+TG) by functionality statements is undecidable. This gives immediately undecidability of the extension of GF+TG by counting quantifiers. The result is optimal, since both the three-variable fragment of the guarded fragment with counting quantifiers and the two-variable guarded fragment with transitivity are undecidable. We also show that the extension of GF+TG with functionality, where functional predicate letters appear in guards only, is decidable and of the same complexity as GF+TG. This fragment captures many expressive modal and description logics.

Discrete mathematicsTransitive relationGuarded logicTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESFragment (logic)Description logicFunctional predicateTheoryofComputation_LOGICSANDMEANINGSOFPROGRAMSExtension (predicate logic)Undecidable problemMathematicsDecidability
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Incorporation of learning strategies into adult distance learning

2008

Incorporation of learning strategies into adult distance learning The paper is based on a study of a group of adult students in a distance learning environment. The focus of the study is on the student comprehension of particular learning strategies. The students' experiences are documented by using case study method and interviews, as well as a quantitative analysis of the results of a survey. The conclusions are that a direct teaching component for learning strategies in a distance learning course may improve the students' strategy awareness as well as contribute to the empowerment of adult students as autonomous learners by reducing their anxiety dealing with new learning situations, by …

Distance educationPedagogyComputingMilieux_COMPUTERSANDEDUCATIONPsychologyExperiential learningStudies for the Learning Society
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Researching Classrooms in Search of Learning: Theoretical and Methodological Considerations

2019

The chapter gives a background to research and research traditions on teaching and learning in classrooms. In the post-war period, a large number of research approaches have been developed in order to capture the complexities of classroom life. Much of this research has documented traditional patterns of communication in classrooms that seem to be fairly stable across time and educational systems. The introduction of video documentation provided new means of following and understanding the dynamics of instructional patterns. Video also made it possible to analyze the activities from different perspectives, including how students are able to follow, contribute to and make sense of classroom …

DocumentationProcess (engineering)Dynamics (music)ComputingMilieux_COMPUTERSANDEDUCATIONMathematics educationStudent activitiesPsychologyPeriod (music)Educational systems
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