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作者：Arnold, Ludwig; Gundlach, Volker Matthias; Demetrius, Lloyd
作者单位：University of Bremen; Harvard University
摘要：We present a formalism to investigate directionality principles in evolution theory for populations, the dynamics of which can be described by a positive matrix cocycle (product of random positive matrices). For the latter, we establish a random version of the Perron-Frobenius theory which extends all known results and enables us to characterize the equilibrium state of a corresponding abstract symbolic dynamical system by an extremal principle. We develop a thermodynamic formalism for random ...
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作者：Arratia, Richard; Waterman, Michael S.
作者单位：University of Southern California; University of Southern California
摘要：We consider a sequence matching problem involving the optimal alignment score for contiguous subsequences, rewarding matches and penalizing for deletions and mismatches. This score is used by biologists comparing pairs of DNA or protein sequences. We prove that for two sequences of length n, as n -> infinity, there is a phase transition between linear growth in n, when the penalty parameters are small, and logarithmic growth in n, when the penalties are large. The results are valid for indepen...
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作者：Athreya, K. B.
作者单位：Iowa State University
摘要：Let {Z(n)}(0)(infinity) be a Galton-Watson branching process with offspring distribution {p(j)}(0)(infinity). We assume throughout that p(0) = 0, pj = 0, p(j) not equal 1 for any j >= 1 and 1 < m = Sigma jp(j) < infinity. Let W-n = Z(n) m (-n) and W-n = lim(n) W-n. In this paper we study the rates of convergence to zero as n -> infinity of P( vertical bar Z(n+1)/z(n) - m vertical bar > epsilon), P(vertical bar W-n - W vertical bar > epsilon), P( vertical bar Z(n+1)/z(n) - m vertical bar > epsi...
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作者：Dupuis, Paul; Oliensis, John
作者单位：Brown University; University of Massachusetts System; University of Massachusetts Amherst
摘要：The main problem considered in this paper is the construction of numerical methods and proofs of their convergence for the problem of shape from shading. In the first part of the paper, it is assumed that the height function that describes the surface to be reconstructed is known at all local minima (or maxima). These points are a subset of the singular points, which are the brightest points in the image. A pair of optimal control problems are defined that provide representations for the heigh...
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作者：Finnoff, William
作者单位：Siemens AG; Siemens Germany
摘要：A model for the activities of a finite number of agents in an economy is presented as the solution to a system of stochastic differential equations driven by general semimartingales and displaying an extended form of strong local interaction. We demonstrate a law of large numbers for the systems of processes as the number of agents goes to infinity under a weak convergence hypothesis on the triangular array of starting values and driving semimartingales which induces the systems of equations. ...
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作者：Perfekt, Roland
作者单位：Lund University
摘要：In this paper the extremal behaviour of real-valued, stationary Markov chains is studied under fairly general assumptions. Conditions are obtained for convergence in distribution of multilevel exceedance point processes associated with suitable families of high levels. Although applicable to general stationary sequences, these conditions are tailored for Markov chains and are seen to hold for a large class of chains. The extra assumptions used are that the marginal distributions belong to the ...
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作者：Fricker, Christine; Robert, Philippe; Saada, Ellen; Tibi, Danielle
作者单位：Inria; Centre National de la Recherche Scientifique (CNRS); Universite de Rouen Normandie; Universite Paris Cite
摘要：In this paper we study a stochastic network model introduced recently in the analysis of neural networks. In this model the interaction between the nodes of the network is local: with each node is associated some real number (the inhibition in the language of neural networks) which is decreasing linearly with time. When this number reaches 0, it sends out some random input to its neighbors (a spike) and restarts with some random value. The state of our network is described as a Markov process....
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作者：Resnick, Sidney I.; Roy, Rishin
作者单位：Cornell University; University of Toronto
摘要：A general framework in an ordinal utility setting for the analysis of dynamic choice from a continuum of alternatives E is proposed. The model is based on the theory of random utility maximization in continuous time. We work with superextremal processes Y = {Y-t, t is an element of (0, infinity)}, where Y-t = {Y-t(tau), tau is an element of E} is a random element of the space of upper semicontinuous functions on a compact metric space E. Here Y-t(tau) represents the utility at time t for alter...
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作者：Anantharam, V.
作者单位：Cornell University
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作者：Pestien, Victor; Ramakrishnan, S.
作者单位：University of Miami
摘要：Assume that k jobs circulate clockwise through a cyclic network of n single-server queues, where at each integer time instant the job at the head of each queue moves with probability p to the next queue, independent of the other jobs. The equilibrium distribution for the associated Markov chain is determined, and an exact expression for the expected number of busy servers is obtained. If n and k are large, a simple approximation for the proportion of busy servers is derived. In a second model,...
