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Arbitrary Set (arbitrary + set)

Distribution by Scientific Domains
Mathematics and Statistics40%

Selected Abstracts

A novel key management scheme for dynamic multicast communications

INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 1 2009
Chin-Chen Chang
Abstract Secure multicasting allows the sender to deliver an identical secret to an arbitrary set of recipients through an insecure broadcasting channel, whereas the unintended recipients cannot obtain the secret. A practical approach for securing multicast communications is to apply a session key to encrypt the transmitted data. However, the challenges of secure multicast are to manage the session keys possessed by a dynamic group of recipients and to reduce the overhead of computation and transmission when the membership is changed. In this paper, we propose a new key management scheme for dynamic multicast communication, which is based on privacy homomorphism and Chinese remainder theorem. Our scheme can efficiently and securely deliver an identical message to multiple recipients. In particular, the complexity of the key update process in our scheme is O(1). Copyright © 2008 John Wiley & Sons, Ltd. [source]

The Use of Archimedean Copulas to Model Portfolio Allocations

MATHEMATICAL FINANCE, Issue 2 2002
David A. Hennessy
A copula is a means of generating an n -variate distribution function from an arbitrary set of n univariate distributions. For the class of portfolio allocators that are risk averse, we use the copula approach to identify a large set of n -variate asset return distributions such that the relative magnitudes of portfolio shares can be ordered according to the reversed hazard rate ordering of the n underlying univariate distributions. We also establish conditions under which first- and second-degree dominating shifts in one of the n underlying univariate distributions increase allocation to that asset. Our findings exploit separability properties possessed by the Archimedean family of copulas. [source]

Automorphisms of endomorphism semigroups of reflexive digraphs

MATHEMATISCHE NACHRICHTEN, Issue 7 2010
Joćo Araüjo
Abstract A reflexive digraph is a pair (X, ,), where X is an arbitrary set and , is a reflexive binary relation on X. Let End (X, ,) be the semigroup of endomorphisms of (X, ,). We determine the group of automorphisms of End (X, ,) for: digraphs containing an edge not contained in a cycle, digraphs consisting of arbitrary unions of cycles such that cycles of length ,2 are pairwise disjoint, and some circulant digraphs (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Height and body mass influence on human body outlines: A quantitative approach using an elliptic Fourier analysis

AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY, Issue 1 2010
Alexandre Courtiol
Abstract Many studies use representations of human body outlines to study how individual characteristics, such as height and body mass, affect perception of body shape. These typically involve reality-based stimuli (e.g., pictures) or manipulated stimuli (e.g., drawings). These two classes of stimuli have important drawbacks that limit result interpretations. Realistic stimuli vary in terms of traits that are correlated, which makes it impossible to assess the effect of a single trait independently. In addition, manipulated stimuli usually do not represent realistic morphologies. We describe and examine a method based on elliptic Fourier descriptors to automatically predict and represent body outlines for a given set of predicted variables (e.g., sex, height, and body mass). We first estimate whether these predictive variables are significantly related to human outlines. We find that height and body mass significantly influence body shape. Unlike height, the effect of body mass on shape differs between sexes. Then, we show that we can easily build a regression model that creates hypothetical outlines for an arbitrary set of covariates. These statistically computed outlines are quite realistic and may be used as stimuli in future studies. Am J Phys Anthropol, 2010. © 2009 Wiley-Liss, Inc. [source]

Gauss-Green theorem for weakly differentiable vector fields, sets of finite perimeter, and balance laws

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 2 2009
Gui-Qiang Chen
We analyze a class of weakly differentiable vector fields F : ,n , ,n with the property that F , L, and div F is a (signed) Radon measure. These fields are called bounded divergence-measure fields. The primary focus of our investigation is to introduce a suitable notion of the normal trace of any divergence-measure field F over the boundary of an arbitrary set of finite perimeter that ensures the validity of the Gauss-Green theorem. To achieve this, we first establish a fundamental approximation theorem which states that, given a (signed) Radon measure , that is absolutely continuous with respect to ,N , 1 on ,N, any set of finite perimeter can be approximated by a family of sets with smooth boundary essentially from the measure-theoretic interior of the set with respect to the measure ||,||, the total variation measure. We employ this approximation theorem to derive the normal trace of F on the boundary of any set of finite perimeter E as the limit of the normal traces of F on the boundaries of the approximate sets with smooth boundary so that the Gauss-Green theorem for F holds on E. With these results, we analyze the Cauchy flux that is bounded by a nonnegative Radon measure over any oriented surface (i.e., an (N , 1)-dimensional surface that is a part of the boundary of a set of finite perimeter) and thereby develop a general mathematical formulation of the physical principle of the balance law through the Cauchy flux. Finally, we apply this framework to the derivation of systems of balance laws with measure-valued source terms from the formulation of the balance law. This framework also allows the recovery of Cauchy entropy flux through the Lax entropy inequality for entropy solutions of hyperbolic conservation laws. © 2008 Wiley Periodicals, Inc. [source]