Search results for "Discrete"

showing 10 items of 2205 documents

Estimates of maximal functions measuring local smoothness

1999

Letη be a nondecreasing function on (0, 1] such thatη(t)/t decreases andη(+0)=0. Letf ∈L(I n ) (I≡[0,1]. Set $${\mathcal{N}}_\eta f(x) = \sup \frac{1}{{\left| Q \right|\eta (\left| Q \right|^{1/n} )}} \smallint _Q \left| {f(t) - f(x)} \right|dt,$$ , where the supremum is taken over all cubes containing the pointx. Forη=t α (0<α≤1) this definition was given by A.Calderon. In the paper we prove estimates of the maximal functions $${\mathcal{N}}_\eta f$$ , along with some embedding theorems. In particular, we prove the following Sobolev type inequality: if $$1 \leqslant p< q< \infty , \theta \equiv n(1/p - 1/q)< 1, and \eta (t) \leqslant t^\theta \sigma (t),$$ , then $$\parallel {\mathcal{N}}_…

Sobolev spaceDiscrete mathematicsSmoothness (probability theory)General MathematicsMaximal functionType inequalityModulus of continuityMathematicsAnalysis Mathematica
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Locally Supported Wavelets on Manifolds with Applications to the 2D Sphere

1999

Abstract In this paper we present a construction principle for locally supported wavelets on manifolds once a multiresolution analysis is given. The wavelets provide a stable (or unconditional) basis for a scale of Sobolev spaces H s , 0 ≤ s ≤ s . We examine a fast wavelet transform with almost optimal complexity. For the two-dimensional sphere we construct a multiresolution analysis generated by continuous splines that are bilinear with respect to some special spherical grid. In our approach the poles are not exceptional points concerning the approximation power or the stability of the wavelet basis. Finally we present some numerical applications to singularity detection and the analysis o…

Sobolev spaceDiscrete wavelet transformWaveletSingularityLegendre waveletMultiresolution analysisApplied MathematicsMathematical analysisFast wavelet transformContinuous wavelet transformMathematicsApplied and Computational Harmonic Analysis
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Invertibility of Sobolev mappings under minimal hypotheses

2010

Abstract We prove a version of the Inverse Function Theorem for continuous weakly differentiable mappings. Namely, a nonconstant W 1 , n mapping is a local homeomorphism if it has integrable inner distortion function and satisfies a certain differential inclusion. The integrability assumption is shown to be optimal.

Sobolev spaceInverse function theoremDiscrete mathematicsDistortion functionDifferential inclusionIntegrable systemApplied MathematicsLocal homeomorphismDifferentiable functionHomeomorphismMathematical PhysicsAnalysisMathematicsAnnales de l'Institut Henri Poincare (C) Non Linear Analysis
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Clique Percolation Method: Memory Efficient Almost Exact Communities

2022

Automatic detection of relevant groups of nodes in large real-world graphs, i.e. community detection, has applications in many fields and has received a lot of attention in the last twenty years. The most popular method designed to find overlapping communities (where a node can belong to several communities) is perhaps the clique percolation method (CPM). This method formalizes the notion of community as a maximal union of $k$-cliques that can be reached from each other through a series of adjacent $k$-cliques, where two cliques are adjacent if and only if they overlap on $k-1$ nodes. Despite much effort CPM has not been scalable to large graphs for medium values of $k$. Recent work has sho…

Social and Information Networks (cs.SI)FOS: Computer and information sciencesPhysics - Physics and Society[INFO.INFO-SI] Computer Science [cs]/Social and Information Networks [cs.SI][PHYS.PHYS.PHYS-SOC-PH]Physics [physics]/Physics [physics]/Physics and Society [physics.soc-ph][INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]FOS: Physical sciences[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]Computer Science - Social and Information NetworksPhysics and Society (physics.soc-ph)[INFO.INFO-SI]Computer Science [cs]/Social and Information Networks [cs.SI]Computer Science - Information Retrieval[PHYS.PHYS.PHYS-SOC-PH] Physics [physics]/Physics [physics]/Physics and Society [physics.soc-ph][INFO.INFO-IR]Computer Science [cs]/Information Retrieval [cs.IR]Computer Science - Data Structures and AlgorithmsData Structures and Algorithms (cs.DS)[INFO.INFO-IR] Computer Science [cs]/Information Retrieval [cs.IR]Information Retrieval (cs.IR)MathematicsofComputing_DISCRETEMATHEMATICS
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Existence of competitive equilibrium in a non-optimal one-sector economy without conditions on the distorted marginal product of capital

2012

Abstract This paper develops a method for proving the existence of competitive equilibrium in a distorted/non-optimal one-sector economy–a discrete time variant of the Romer model–without conditions on the equilibrium value of the marginal product of capital. Existence is obtained under weaker conditions than in Le Van et al. (2002) . Moreover, we provide an existence result for an economy with a regressive tax studied in Santos (2002) . The proofs rely on ideas of Becker and Boyd (1997) .

Sociology and Political ScienceRomerGeneral Social SciencesCompetitive equilibriumMathematical proofMicroeconomicsDiscrete time and continuous timeEconomyValue (economics)EconomicsStatistics Probability and UncertaintyMathematical economicsGeneral PsychologyRegressive taxMarginal product of capitalMathematical Social Sciences
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A Memetic Island Model for Discrete Tomography Reconstruction

2011

Soft computing is a term indicating a coalition of methodologies, and its basic dogma is that, in general, better results can be obtained through the use of constituent methodologies in combination, rather than in a stand alone mode. Evolutionary computing belongs to this coalition, and thus memetic algorithms. Here, we present a combination of several instances of a recently proposed memetic algorithm for discrete tomography reconstruction, based on the island model parallel implementation. The combination is motivated by the fact that, even though the results of the recently proposed approach are finally better and more robust compared to other approaches, we advised that its major drawba…

Soft computingCorrectnessSettore INF/01 - InformaticaComputer sciencebusiness.industryEvolutionary algorithmEvolutionary computationTerm (time)Genetic algorithmMemetic algorithmArtificial intelligencebusinessDiscrete tomographyMemetic algorithm Evolutionary algorithm Discrete tomography Distributed evolutionary algorithm
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Suffix array and Lyndon factorization of a text

2014

Abstract The main goal of this paper is to highlight the relationship between the suffix array of a text and its Lyndon factorization. It is proved in [15] that one can obtain the Lyndon factorization of a text from its suffix array. Conversely, here we show a new method for constructing the suffix array of a text that takes advantage of its Lyndon factorization. The surprising consequence of our results is that, in order to construct the suffix array, the local suffixes inside each Lyndon factor can be separately processed, allowing different implementative scenarios, such as online, external and internal memory, or parallel implementations. Based on our results, the algorithm that we prop…

Sorting suffixes; BWT; Suffix array; Lyndon word; Lyndon factorizationCompressed suffix arraySettore INF/01 - InformaticaSorting suffixesGeneralized suffix treeSuffix arrayOrder (ring theory)Construct (python library)Lyndon wordSorting suffixeTheoretical Computer Sciencelaw.inventionBWTLyndon factorizationComputational Theory and MathematicsFactorizationlawSuffix arrayFactor (programming language)Internal memoryDiscrete Mathematics and CombinatoricsArithmeticcomputerMathematicscomputer.programming_languageJournal of Discrete Algorithms
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Towards Axiomatic Basis of Inductive Inference

2001

The language for the formulation of the interesting statements is, of course, most important. We use first order predicate logic. Our main achievement in this paper is an axiom system which we believe to be more powerful than any other natural general purpose discovery axiom system. We prove soundness of this axiom system in this paper. Additionally we prove that if we remove some of the requirements used in our axiom system, the system becomes not sound. We characterize the complexity of the quantifier prefix which guaranties provability of a true formula via our system. We prove also that if a true formula contains only monadic predicates, our axiom system is capable to prove this formula…

SoundnessDiscrete mathematicsPredicate logicSMorse–Kelley set theoryComputer scienceNon-well-founded set theoryZermelo–Fraenkel set theoryConstructive set theoryInductive reasoningAxiom schemaUrelementScott's trickMonad (functional programming)First-order logicAxiom of extensionalityMathematics::LogicTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESTheoryofComputation_LOGICSANDMEANINGSOFPROGRAMSCalculusAxiom of projective determinacyAxiom of choiceKripke–Platek set theoryAction axiomAxiom
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Special factors and the combinatorics of suffix and factor automata

2011

AbstractThe suffix automaton (resp. factor automaton) of a finite word w is the minimal deterministic automaton recognizing the set of suffixes (resp. factors) of w. We study the relationships between the structure of the suffix and factor automata and classical combinatorial parameters related to the special factors of w. We derive formulae for the number of states of these automata. We also characterize the languages LSA and LFA of words having respectively suffix automaton and factor automaton with the minimal possible number of states.

Special factorGeneral Computer ScienceSpecial factorsFactor automatonBüchi automatonω-automatonTheoretical Computer ScienceCombinatoricsDeterministic automatonTwo-way deterministic finite automatonNondeterministic finite automatonComputer Science::Data Structures and AlgorithmsCombinatorics on wordStandard Sturmian wordsMathematicsDiscrete mathematicsCombinatorics on wordsDAWGPushdown automatonComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Nonlinear Sciences::Cellular Automata and Lattice GasesSuffix automatonProbabilistic automatonSuffix automatonComputer Science::Formal Languages and Automata TheoryComputer Science(all)Theoretical Computer Science
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A comparative empirical assessment of roundabouts operations in rural areas: impacts on congestion-specific vehicle speed profiles, pollutant and noi…

2020

Increasing concern about global warming and air quality has meant an increasing use of energetic and environmental indicators in roundabout design. The main objective of this paper is to compare different rural roundabouts in terms of traffic performance, pollutant and noise emissions through an integrated empirical assessment. Field measurements were carried out with a light duty vehicle in single-lane (SL), compact two-lane (CTL) and multi-lane (ML) roundabouts using Portable Emission Measurements Systems, OBD scan tool and Sound Level Meter, to measure real-world exhaust emissions, engine activity and acoustic data, respectively. Road traffic scene at roundabouts were obtained from video…

Speed profilesOn-road emissionsDiscrete modelsNoiseGeneralLiterature_REFERENCE(e.g.dictionariesencyclopediasglossaries)Roundabouts
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