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作者：Lange, Kenneth; Zhao, Hongyu; Speed, Terence P.
作者单位：University of Michigan System; University of Michigan; Yale University; University of California System; University of California Berkeley
摘要：The Poisson-skip model introduced in this paper generalizes the chi-quare model of crossover interference. Both models are constructed from the random points of a Poisson process occurring along a meiotic bundle of four chromatids. The points of the Poisson process are divided into X points and o points, with X points corresponding to crossovers. In the chi-square model, a fixed number of o points intervene between every adjacent pair of X points; in the Poisson-skip model, a random number of ...
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作者：Boehm, W.; Mohanty, S. G.
作者单位：McMaster University
摘要：In this paper we present some interesting results which follow from the celebrated determinant formulas for noncoincidence probabilities of Markov processes discovered by Karlin and McGregor. The first theorem is a determinant formula for the probability that a Markov jump process will avoid a certain finite set of points. From this theorem a simple solution of the moving boundary problem for certain types of Markov processes can be obtained. The other theorems deal with noncoincidence probabi...
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作者：Bertoin, Jean
作者单位：Sorbonne Universite
摘要：Consider a completely asymmetric Levy process which has absolutely continuous transition probabilities. We determine the exponential decay parameter rho and the quasistationary distribution for the transition probabilities of the evy process killed as it exits from a finite interval, prove that the killed process is rho-positive and specify the rho-invariant function and measure.
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作者：O'Neill, Philip
作者单位：University of Bradford
摘要：This paper is concerned with a model for the spread of an epidemic in a closed, homogeneously mixed population in which new infections occur at rate beta(z)xy/(x+y), where x, y and z denote, respectively, the numbers of susceptible, infective and removed individuals. Thus the infection mechanism depends upon the number of removals to date, reflecting behavior change in response to the progress of the epidemic. For a deterministic version of the model, a recurrent solution is obtained when beta...
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作者：Bouton, Catherine; Pages, Gilles
作者单位：heSam Universite; Universite Pantheon-Sorbonne; Sorbonne Universite; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：The competitive learning vector quantization (CLVQ) algorithm with constant step epsilon > 0-also known as the Kohonen algorithm with 0 neighbors-is studied when the stimuli are i.i.d. vectors. Its first noticeable feature is that, unlike the one-dimensional case which has n! absorbing subsets, the CLVQ algorithm is irreducible on open sets whenever the stimuli distribution has a path-connected support with a nonempty interior. Then the Doeblin recurrence (or uniform ergodicity) of the algorit...
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作者：Chassaing, Philippe
作者单位：Universite de Lorraine
摘要：We are given a set of n elements, some of them red, the others blue, but their colors are hidden. We are to determine the composition of this set, or to determine an element of the majority color, by making pairwise comparisons of elements from which we obtain the information the colors of these two elements are the same,'' or they are different.'' Let tau(n), respectively, mu(n), be the optimal average number of comparisons needed to solve these two problems. We give an explicit expression of...
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作者：Ossiander, Mina; Waymire, Ed; Zhang, Qing
作者单位：Oregon State University
摘要：Consider a rooted labelled tree graph tau(n) having a total of n vertices. The width function counts the number of vertices as a function of the distance to the root phi. In this paper we compute large n asymptotic behavior of the width functions for two classes of tree graphs (both random and deterministic) of the following types: (i) Galton-Watson random trees tn conditioned on total progeny and (ii) a class of deterministic self-similar trees which include an expected Galton-Watson tree in ...
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作者：Flatto, L.
作者单位：AT&T; Nokia Corporation; Nokia Bell Labs
摘要：The M / M / 1 queue is considered in the case in which customers are served in random order. A formula is obtained for the distribution of the waiting time w in the stationary state. The formula is used to show that P(w > l) similar to alpha l (-5/6) exp( -beta l - gamma l(1/3)) as l -> infinity, with the constants alpha, beta, and gamma expressed as functions of the traffic intensity p. The distribution of w for the random order discipline is compared to that of the first in, first out discip...
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作者：Bean, N. G.; Bright, L.; Latouche, G.; Pearce, C. E. M.; Pollett, P. K.; Taylor, P. G.
作者单位：University of Adelaide; Universite Libre de Bruxelles; University of Queensland
摘要：For evanescent Markov processes with a single transient communicating class, it is often of interest to examine the limiting probabilities that the process resides in the various transient states, conditional on absorption not having taken place. Such distributions are known as quasi-stationary (or limiting-conditional) distributions. In this paper we consider the determination of the quasi-stationary distribution of a general level-independent quasi-birth-and-death process (QBD). This distrib...
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作者：Jones, Owen Dafydd
作者单位：University of Sheffield
摘要：Using the ergodic theory of nonnegative matrices, conditions are obtained for the L-2 and almost sure convergence of a supercritical multitype branching process with varying environment, normed by its mean. We also give conditions for the extinction probability of the limit to equal that of the process. The theory developed allows for different types to grow at different rates, and an example of this is given, taken from the construction of a spatially inhomogeneous diffusion on the Sierpinski...
