Search results for "Combinatorics"

showing 10 items of 1770 documents

Prototype selection for the nearest neighbour rule through proximity graphs

1997

Abstract In this paper, the Gabriel and Relative Neighbourhood graphs are used to select a suitable subset of prototypes for the Nearest Neighbour rule. Experiments and results are reported showing the effectiveness of the method and comparing its performance to those obtained by classical techniques.

CombinatoricsArtificial IntelligenceGabriel graphSignal ProcessingNearest neighbourTheta graphComputer Vision and Pattern RecognitionNeighbourhood (mathematics)SoftwareMathematics
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A complete characterization of all weakly additive measures and of all valuations on the canonical extension of any finite MV-chain

2010

We consider extensions of the unique additive measure on a finite MV-chain to uncertainty measures on its canonical Girard algebra extension. If the underlying MV-chain has more than two non-trivial elements, in a previous paper we have proved the non-existence of strongly additive measure extensions, where strong additivity is defined as additivity not for all disjoint unions but only restricted to the so-called divisible disjoint unions. This negative result motivates to look for weakly additive measure extensions which are defined to be additive only on all MV-subalgebras of the canonical Girard algebra extension. We obtain a characterization of all such MV-subalgebras which are in fact …

CombinatoricsArtificial IntelligenceLogicWeakly additiveAdditive functionState (functional analysis)MV-algebraDisjoint setsExtension (predicate logic)Characterization (mathematics)Measure (mathematics)MathematicsFuzzy Sets and Systems
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Fuzzy $$\varphi $$ -pseudometrics and Fuzzy $$\varphi $$ -pseudometric Spaces

2017

By replacing the axiom \(m(x,x,t) = 1\) for all \(x\in X, t>0\) in the definition of a fuzzy pseudometric in the sense of George-Veeramani with a weaker axiom \(m(x,x,t) = \varphi (t)\) for all \(x\in X, t>0\) where \(\varphi : {\mathbb R}^+ \rightarrow (0,1]\) is a non-decreasing function, we come to the concept of a fuzzy \(\varphi \)-pseudometric space. Basic properties of fuzzy \(\varphi \)-pseudometric spaces and their mappings are studied. We show also an application of fuzzy \(\varphi \)-pseudometrics in the words combinatorics.

CombinatoricsBaire category theoremPseudometric spaceFunction (mathematics)Space (mathematics)Fuzzy logicAxiomCauchy sequenceMathematics
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Balance Properties and Distribution of Squares in Circular Words

2008

We study balance properties of circular words over alphabets of size greater than two. We give some new characterizations of balanced words connected to the Kawasaki-Ising model and to the notion of derivative of a word. Moreover we consider two different generalizations of the notion of balance, and we find some relations between them. Some of our results can be generalised to non periodic infinite words as well.

CombinatoricsBalance (metaphysics)Distribution (number theory)Settore INF/01 - InformaticaComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Combinatoria delle Parole Parole Sturmiane parole circolari Parole BilanciateComputer Science::Formal Languages and Automata TheoryBinary alphabetWord (group theory)Mathematics
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Monotonicity of Bayes estimators

2013

Let X = (X1; : : : ;Xn) be a sample from a distribution with density (x;θ), θ∈Θ⊂R. In this article the Bayesian estimation of the parameter is considered.We examine whether the Bayes estimators of are pointwise ordered when the prior distributions are partially ordered. Various cases of loss function are studied. A lower bound for the survival function of the normal distribution is obtained.

CombinatoricsBayes' theoremApplied MathematicsEstimatorApplied mathematicsMonotonic functionMathematicsApplicationes Mathematicae
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Weak associativity and restricted rotation

2009

A restricted rotation induced by a weak associative law is introduced. The corresponding equivalence relation is identical to the Glivenko congruence on Tamari lattices, i.e. lattices of binary trees endowed by the well-known rotation operation.

CombinatoricsBinary treeLattice (order)Signal ProcessingEquivalence relationAssociative propertyComputer Science ApplicationsInformation SystemsTheoretical Computer ScienceMathematicsInformation Processing Letters
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Bayesian hypothesis testing: A reference approach

2002

Summary For any probability model M={p(x|θ, ω), θeΘ, ωeΩ} assumed to describe the probabilistic behaviour of data xeX, it is argued that testing whether or not the available data are compatible with the hypothesis H0={θ=θ0} is best considered as a formal decision problem on whether to use (a0), or not to use (a0), the simpler probability model (or null model) M0={p(x|θ0, ω), ωeΩ}, where the loss difference L(a0, θ, ω) –L(a0, θ, ω) is proportional to the amount of information δ(θ0, ω), which would be lost if the simplified model M0 were used as a proxy for the assumed model M. For any prior distribution π(θ, ω), the appropriate normative solution is obtained by rejecting the null model M0 wh…

CombinatoricsBinomial distributionStatistics and ProbabilityBayes' theoremDistribution (mathematics)Prior probabilityStatisticsMultivariate normal distributionContext (language use)Statistics Probability and UncertaintyLindley's paradoxMathematicsStatistical hypothesis testing
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An optimal bound for embedding linear spaces into projective planes

1988

Abstract Linear spaces with υ >n 2 − 1 2 n + 1 points, b⩽n2 + n + 1 lines and not constant point degree are classified. It turns out that there is essentially one class of such linear spaces which are not near pencils and which can not be embedded into any projective plane of order n.

CombinatoricsBlocking setDuality (projective geometry)Discrete Mathematics and CombinatoricsProjective spaceEmbeddingProjective planeFano planeTheoretical Computer ScienceMathematicsDiscrete Mathematics
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A space on which diameter-type packing measure is not Borel regular

1999

We construct a separable metric space on which 1-dimensional diameter-type packing measure is not Borel regular.

CombinatoricsBorel equivalence relationRiesz–Markov–Kakutani representation theoremApplied MathematicsGeneral MathematicsRadon measureStandard probability spaceBaire measureBorel setBorel measureMeasure (mathematics)MathematicsProceedings of the American Mathematical Society
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Nonlocal Cheeger and Calibrable Sets

2019

Given a non-null, measurable and bounded set \(\Omega \subset \mathbb {R}^N\), we define its J-Cheeger constant

CombinatoricsBounded setConstant (mathematics)OmegaMathematics
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