Consider a random Hamiltonian for We assume that the family is jointly Gaussian centered and that for =ξ(N?1∑i?Nσ1iσ2i) for a certain function ξ on . F. Guerra proved the remarkable fact that the free energy of the system with Hamiltonian is bounded below by the free energy of the Parisi solution provided that ξ is convex on . We prove that this fact remains (asymptotically) true when the function ξ is only assumed to be convex on . This covers in particular the case of the p-spin interaction model for any p. To cite this article: M. Talagrand, C. R. Acad. Sci. Paris, Ser. I 337 (2003).相似文献
Given a subset E of convex functions from
into
which satisfy growth conditions of order p>1 and an open bounded subset
of
, we establish the continuity of a map μΦμ from the set of all Young measures on
equipped with the narrow topology into a set of suitable functionals defined in
and equipped with the topology of Γ-convergence. Some applications are given in the setting of periodic and stochastic homogenization. 相似文献
The stable admissions polytope– the convex hull of the stable assignments of the university admissions problem – is described by a set of linear inequalities.
It depends on a new characterization of stability and arguments that exploit and extend a graphical approach that has been
fruitful in the analysis of the stable marriage problem.
Received: April 10, 1998 / Accepted: June 3, 1999?Published online January 27, 2000 相似文献
Let (Y,,,T) be an ergodic dynamical system. LetA be an nonempty subset ofL2() such that
, whereA=sup{||sȒt||2
,s, tA} andN(A, u) is the smallest number ofL2()-open balls of radiusu, centered inA, enough to coverA. Let
. We prove as a consequence of a more general result, thatC(A) is aGB subset ofL2(). 相似文献
A novel architecture for an optical time-division switch is investigated and demonstrated at a bit rate of 625 Mbit/s. The self-clocked configuration eliminates some of the limitations found in previous optical implementations of time-division switches: the switch operation is asynchronous, no read gate is required, and an optimal number of delay lines is used. Furthermore, this paper reports the first experimental demonstration of optical space-sorting demultiplexing. 相似文献
Acquisition of acoustic data from ocean observatories is expected to play a key role for the long-term monitoring of marine mammals and anthropogenic noise. It typically requires processing of a large volume of acoustic data and it must rely on automated identification of signals. We present an algorithmic framework for the detection of short tonal sounds (e.g. cetacean calls, anthropogenic pings) intended to act as a first stage in a system for the automated real-time detection, classification, and localisation of acoustic sources. The algorithm was validated under a diversity of scenarios expected at ocean observatories. Using simulated signals that emulate a variety of cetacean call-types, perfect identification of signal position was obtained for signal to noise ratios of ?15 to ?5 dB, depending on the signal-type. Separation of real-world data segments with short tonal sounds (mainly cetacean calls) from segments with other sounds or noise resulted in Area Under the ROC Curve values between 0.96 and 0.98. The algorithm can be used to automatically identify cetacean calls and anthropogenic short tonal sounds much faster than in real-time, thereby reducing the burden put on data transmission, storage, or processing by classification and localisation algorithms. 相似文献
We consider the asymptotic behavior for large time of solutions to reaction-diffusion systems modeling reversible chemical reactions. We focus on the case where multiple equilibria exist. In this case, due to the existence of so-called "boundary equilibria", the analysis of the asymptotic behavior is not obvious. The solution is understood in a weak sense as a limit of adequate approximate solutions. We prove that this solution converges in L^1 toward an equilibrium as time goes to infinity and that the convergence is exponential if the limit is strictly positive. 相似文献
We address the problem of determining a robust maximum flow value in a network with uncertain link capacities taken in a polyhedral
uncertainty set. Besides a few polynomial cases, we focus on the case where the uncertainty set is taken to be the solution
set of an associated (continuous) knapsack problem. This class of problems is shown to be polynomially solvable for planar
graphs, but NP-hard for graphs without special structure. The latter result provides evidence of the fact that the problem
investigated here has a structure fundamentally different from the robust network flow models proposed in various other published
works. 相似文献
We consider a network of infinite-server queues where the input process is a Cox process of the following form: The arrival rate is a vector-valued linear transform of a multivariate generalized (i.e., being driven by a subordinator rather than a compound Poisson process) shot-noise process. We first derive some distributional properties of the multivariate generalized shot-noise process. Then these are exploited to obtain the joint transform of the numbers of customers, at various time epochs, in a single infinite-server queue fed by the above-mentioned Cox process. We also obtain transforms pertaining to the joint stationary arrival rate and queue length processes (thus facilitating the analysis of the corresponding departure process), as well as their means and covariance structure. Finally, we extend to the setting of a network of infinite-server queues.
This article studies a model of coalition formation for the joint production (and finance) of public projects, in which agents may belong to multiple coalitions. We show that, if projects are divisible, there always exists a stable (secession-proof) structure, i.e., a structure in which no coalition would reject a proposed arrangement. When projects are indivisible, stable allocations may fail to exist and, for those cases, we resort to the least core in order to estimate the degree of instability. We also examine the compatibility of stability and fairness in metric environments with indivisible projects, where we also explore the performance of well-known solutions, such as the Shapley value and the nucleolus. 相似文献