长程接触过程的快速搅动极限

本文讨论长程接触过程的快速搅动极限，利用长程接触过程的自对偶性以及关于分枝随机游动的几个估计式，证明了长程接触过程的快速搅动极限是下列微分方程的解：     

随机环境中选举模型的Hydrodynamic极限

本文研究随机环境中选举模型的Hydrodynamic极限。首先，我们通过图表示构造出随机环境中的选举模型，然后利用对偶关系得到了该粒子模型的宏观偏微分方程。     

带合作行为的平均场模型的依全变差稳定性

该文考虑一个带合作行为的平均场模型的稳定性问题. 应用耦合方法, 建立了相应于这个平均场模型的扩散过程的依全变差稳定性.     

miR-212 在乳腺浸润性导管癌 组织中的表达及效应分析

本文建立随机环境中具有随机控制函数的两性分枝过程,得到该模型概率母函数之间的关系式.当控制函数上可加时,证明配对单元平均增长率的极限是存在的,同时得到配对单元平均增长率一系列的极限性质,进而推进了前人的研究.     

随机环境中具有随机控制函数两性分枝过程的极限性质(英文)

本文建立随机环境中具有随机控制函数的两性分枝过程,得到该模型概率母函数之间的关系式.当控制函数上可加时,证明配对单元平均增长率的极限是存在的,同时得到配对单元平均增长率一系列的极限性质,进而推进了前人的研究.     

铁电体中介电异常与长程关联的关系

利用双势阱模型研究了铁电体中介电异常的机制 ,结果表明介电常数源于外场造成的偏离中心离子在多位势中的附加的跳跃 .介电常数可分为两部分 :其一与长程关联无关 ,服从 1 /T律 ;其二由长程关联引起 ,可用关联长度很好地描述 .小尺寸样品中介电异常偏离Curie_Weiss定律源于长程关联的减弱 .     

非局部弹性体中的裂纹问题

本文由裂纹的位错塞积模型求解了非局部弹性体中的直线裂纹问题。得到的裂纹尖端应力为有限值。提出在非局部应力边界条件中必须考虑裂纹上、下表面间的长程内聚力。给出了物理意义更加明确的脆断表面能定义。导出了表面能、理论强度、临界断裂判据、裂纹尖端曲率半径等一系列结果。对非局部混合边值问题提出了以经典位移场为基础的求解方案。     

Bethe树和Cayley树上奇偶马尔可夫链场的强极限定理

本文介绍了N元Bethe树TB,N(N元Cayley树TC,N)上的奇偶马尔可夫链场的定义,并通过构造两个非负鞅证得了随机变量序列的强极限定理,应用此强极限定理获得了奇偶马尔可夫链场上的一个强极限定理,作为它的推论得到了状态和状态序偶出现频率的一类强极限定理及其估计,从而推广了关于N元Bethe树上马氏链场和二进树上奇偶马氏链场的部分强极限定理.     

基于最小二乘近似的模型平均方法

本文提出基于最小二乘近似的模型平均方法.该方法可用于线性模型、广义线性模型和分位数回归等各种常用模型.特别地,经典的Mallows模型平均方法是该方法的特例.现存的模型平均文献中,渐近分布的证明一般需要局部误设定假设,所得的极限分布的形式也比较复杂.本文将在不使用局部误设定假设的情形下证明该方法的渐近正态性.另外,本文...     

带跳的平均场随机微分方程的中偏差

平均场随机微分方程是一类在众多工程和科学领域具有广泛应用的随机模型.本文利用弱收敛的方法建立由Poisson随机测度驱动的平均场随机微分方程的中偏差原理.     

Convergence of path measures arising from a mean field or polaron type interaction

Summary We discuss the limiting path measures of Markov processes with either a mean field or a polaron type interaction of the paths. In the polaron type situation the strength is decaying at large distances on the time axis, and so the interaction is of short range in time. In contrast, in the mean field model, the interaction is weak, but of long range in time. Donsker and Varadhan proved that for the partition functions, there is a transition from the polaron type to the mean field interaction when passing to a limit by letting the strength tend to zero while increasing the range. The discussion of the path measures is more subtle. We treat the mean field case as an example of a differentiable interaction and discuss the transition from the polaron type to the mean field interaction for two instructive examples.Research supported by the Swiss National Foundation (21-29833.90)This article was processed by the authors using the Springer-Verlag T_EX ProbTh macro package 1991.     

Continuous Time Finite State Mean Field Games

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.     

Time dependent critical fluctuations of a one dimensional local mean field model

Summary One-dimensional stochastic Ising systems with a local mean field interaction (Kac potential) are investigated. It is shown that near the critical temperature of the equilibrium (Gibbs) distribution the time dependent process admits a scaling limit given by a nonlinear stochastic PDE. The initial conditions of this approximation theorem are then verified for equilibrium states when the temperature goes to its critical value in a suitable way. Earlier results of Bertini-Presutti-Rüdiger-Saada are improved, the proof is based on an energy inequality obtained by coupling the Glauber dynamics to its voter type, linear approximation.     

Voter models and external influence

ABSTRACT

In this paper, we extend the voter model (VM) and the threshold voter model (TVM) to include external influences modeled as a jump process. We study the newly-formulated models both analytically and computationally, employing diffusion approximations and mean field approximations. We derive results pertaining to the probability of reaching consensus on a particular opinion and also the expected consensus time. We find that although including an external influence leads to a faster consensus in general, this effect is more pronounced in the VM as compared to the TVM. Our findings suggest the potential importance of external influences in addition to local interactions.     

Consolidation rates for two interacting systems in the plane

Summary This paper is a sequel of a paper of Cox and Griffeath “diffusive clustering in the two dimensional voter model”. We continue our study of the voter model and coalescing random walks on the two dimensional integer lattice. Some exact asymptotics concerning the rate of clustering in the former process and the coalescence rate of the latter are derived. We use these results to prove a limit law, announced in that earlier paper, concerning the size of the largest square centered at the origin which is of solid color at a large time t. Partially supported by the National Science Foundation under Grant DMS-831080 Partially supported by the National Science Foundation under Grant DMS-841317 Partially supported by the National Science Foundation under Grant DMS-830549     

A fuzzy voting scheme for hardware and software fault tolerant systems

Voting algorithms are used to arbitrate between the results of redundant modules in fault-tolerant systems. Inexact majority and weighted average voters have been used in many applications, although both have problems associated with them. Inexact majority voters require an application-specific 'voter threshold’ value to be specified, whereas weighted average voters are unable to produce a benign output when no agreement exists between the voter inputs. Neither voter type is able to cope with uncertainties associated with the voter inputs. This paper introduces a novel voting scheme based on fuzzy set theory. It softens the harsh behaviour of the inexact majority voter in the neighbourhood of the ‘voter threshold’, and handles uncertainty and some multiple error cases in the region defined by the fuzzy input variables. The voter assigns a fuzzy difference value to each pair of voter inputs based on their numerical distance. A set of fuzzy rules then determines a single fuzzy agreeability value for each individual input which describes how well it matches the other inputs. The agreeability of each voter input is then defuzzified to give a weighting value for that input which determines its contribution to the voter output. The weight values are then used in the weighted average algorithm for calculating the voter final output. The voter is experimentally evaluated from the point of view safety and availability, and compared with the inexact majority voter in a Triple Modular Redundant structured framework. The impact of changing some fuzzy variables on the performance of the voter is also investigated. We show that the fuzzy voter gives more correct outputs (higher availability) than the inexact majority voter with small and large errors, less incorrect outputs (higher safety) than the inexact majority voter in the presence of small errors, and less benign outputs than the inexact majority voter. The percentage of the benign outputs of the majority voter that are successfully handled by the fuzzy voter (resulting in correct outputs) is more than the percentage of those that are unsuccessfully resolved by the fuzzy voter (resulting in incorrect outputs). Our results suggest that the fuzzy voter is a viable alternative to a traditional inexact voter in cases where the benefits of a large increase in availability, and a considerable decrease in the number of benign outputs outweighs the cost of a small degradation in the safety performance of the system. The fuzzy voter is also a useful voting algorithm when arbitrating between the responses of dynamic channels of control systems incorporating uncertainties. This is the first reported use of a complete fuzzy voter in the context of fault tolerance.     

A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators

In the limit of a nonlinear diffusion model involving the fractional Laplacian we get a “mean field” equation arising in superconductivity and superfluidity. For this equation, we obtain uniqueness, universal bounds and regularity results. We also show that solutions with finite second moment and radial solutions admit an asymptotic large time limiting profile which is a special self-similar solution: the “elementary vortex patch”.     

Repeated Downsian electoral competition

We analyze an infinitely repeated version of the Downsian model of elections. The folk theorem suggests that a wide range of policy paths can be supported by subgame perfect equilibria when parties and voters are sufficiently patient. We go beyond this result by imposing several suitable refinements and by giving separate weak conditions on the patience of voters and the patience of parties under which every policy path can be supported. On the other hand, we show that only majority undominated policy paths can be supported in equilibrium for arbitrarily low voter discount factors: if the core is empty, the generic case in multiple dimensions, then voter impatience leads us back to the problem of non-existence of equilibrium. We extend this result to give conditions under which core equivalence holds for a non-trivial range of voter and party discount factors, providing a game-theoretic version of the Median Voter Theorem in a model of repeated Downsian elections. J. Duggan was supported by the National Science Foundation, grant number 0213738, is gratefully acknowledged.     

Bose–Einstein Condensates with Non-classical Vortex

Coupled systems of nonlinear Schrödinger equations have been used extensively to describe Bose–Einstein condensates. In this paper, we study a two-component Bose–Einstein condensate (BEC) with an external driving field in a three-dimensional space. This model gives rise to a new kind of vortex–filaments, with fractional degree and nontrivial core structure. We show that vortex–filaments is 1-rectifiable set, and calculate its mean curvature in the strong coupling (Thomas–Fermi) limit. In particular, we show that large strength of the external driving field causes vortex–filaments for a two-component BEC.