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961.
962.
963.
964.
965.
Maria Deijfen Henri van den Esker Remco van der Hofstad Gerard Hooghiemstra 《Arkiv f?r Matematik》2009,47(1):41-72
In this paper, a random graph process {G(t)}
t≥1 is studied and its degree sequence is analyzed. Let {W
t
}
t≥1 be an i.i.d. sequence. The graph process is defined so that, at each integer time t, a new vertex with W
t
edges attached to it, is added to the graph. The new edges added at time t are then preferentially connected to older vertices, i.e., conditionally on G(t-1), the probability that a given edge of vertex t is connected to vertex i is proportional to d
i
(t-1)+δ, where d
i
(t-1) is the degree of vertex i at time t-1, independently of the other edges. The main result is that the asymptotical degree sequence for this process is a power
law with exponent τ=min{τW,τP}, where τW is the power-law exponent of the initial degrees {W
t
}
t≥1 and τP the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze. 相似文献
966.
967.
Ronald DeVore Gerard Kerkyacharian Dominique Picard Vladimir Temlyakov 《Foundations of Computational Mathematics》2006,6(1):3-58
Let ρ be an unknown Borel measure defined on the space Z := X × Y with X ⊂ ℝd and Y = [-M,M]. Given a set z of m samples zi =(xi,yi) drawn according to ρ, the problem of estimating a regression function fρ using these samples is considered. The main focus
is to understand what is the rate of approximation, measured either in
expectation or probability, that can be obtained under a given prior
fρ ∈ Θ, i.e., under the assumption that fρ is in the set
Θ, and what are possible algorithms for obtaining optimal or
semioptimal (up to logarithms) results. The optimal rate of decay in terms
of m is established for many priors given either in terms of smoothness of
fρ or its rate of approximation measured in one of several ways. This optimal rate is determined by two types of results.
Upper bounds are established using various tools in approximation such as entropy, widths, and linear and nonlinear approximation.
Lower bounds are proved using
Kullback-Leibler information together with Fano inequalities and a certain type
of entropy. A distinction is drawn between algorithms which employ knowledge
of the prior in the construction of the estimator and those that do not.
Algorithms of the second type which are universally optimal for a certain range
of priors are given. 相似文献
968.
We show how to compute the optical response of a Quantum Disk (QDisk) to an electromagnetic wave as a function of the incident
wave polarization, in the energetic region of interband transitions. Both the TM and TE polarization in guided-wave geometry
are analyzed. The method uses the microscopic calculation of Quantum Disk eigenfunctions and the macroscopic real density
matrix approach to compute the effective QDisk susceptibility, taking into account the valence band structure of the QDisk
material and the Coulomb interaction between the electron and the hole. Analytical expressions for the QDisk susceptibility
are obtained for a certain model electron — hole potential. Using these expressions, all optical functions can be computed.
Results for the absorption coefficient are computed for InAs/GaAs QDisks. Fair agreement with experiments is obtained. 相似文献
969.
Let T be an order bounded disjointness preserving operator on an Archimedean vector lattice. The main result in this paper shows
that T is algebraic if and only if there exist natural numbers m and n such that n ≥ m, and Tn!, when restricted to the vector sublattice generated by the range of Tm, is an algebraic orthomorphism. Moreover, n (respectively, m) can be chosen as the degree (respectively, the multiplicity of 0 as a root) of the minimal polynomial of T. In the process of proving this result, we define strongly diagonal operators and study algebraic order bounded disjointness
preserving operators and locally algebraic orthomorphisms. In addition, we introduce a type of completeness on Archimedean
vector lattices that is necessary and sufficient for locally algebraic orthomorphisms to coincide with algebraic orthomorphisms. 相似文献
970.
Jean Derks Gerard van der Laan Valery Vasil’ev 《Mathematical Methods of Operations Research》2006,64(1):155-163
A Harsanyi payoff vector (see Vasil’ev in Optimizacija Vyp 21:30–35, 1978) of a cooperative game with transferable utilities is obtained by some distribution of the Harsanyi dividends of all coalitions among its members. Examples of Harsanyi payoff vectors are the marginal contribution vectors. The random order values (see Weber in The Shapley value, essays in honor of L.S. Shapley, Cambridge University Press, Cambridge, 1988) being the convex combinations of the marginal contribution vectors, are therefore elements of the Harsanyi set, which refers to the set of all Harsanyi payoff vectors.The aim of this paper is to provide two characterizations of the set of all sharing systems of the dividends whose associated Harsanyi payoff vectors are random order values. The first characterization yields the extreme points of this set of sharing systems and is based on a combinatorial result recently published (Vasil’ev in Discretnyi Analiz i Issledovaniye Operatsyi 10:17–55, 2003) the second characterization says that a Harsanyi payoff vector is a random order value iff the sharing system is strong monotonic.This work was partly done whilst Valeri Vasil’ev was visiting the Department of Econometrics at the Free University, Amsterdam. Financial support from the Netherlands Organisation for Scientific Research (NWO) in the framework of the Russian-Dutch programme for scientific cooperation, is gratefully acknowledged. The third author would also like to acknowledge partial financial support from the Russian Fund of Basic Research (grants 98-01-00664 and 00-15-98884) and the Russian Humanitarian Scientific Fund (grant 02-02-00189a). 相似文献