Long‐range dependence and performance in telecom networks

Telecommunications systems have recently undergone significant innovations. These call for suitable statistical models that can properly describe the behaviour of the input traffic in a network. Here we use fractional Brownian motion (FBM) to model cumulative traffic network, thus taking into account the possible presence of long‐range dependence in the data. A Bayesian approach is devised in such a way that we are able to: (a) estimate the Hurst parameter H of the FBM; (b) estimate the overflow probability which is a parameter measuring the quality of service of a network: (c) develop a test for comparing the null hypothesis of long‐range dependence in the data versus the alternative of short‐range dependence. In order to achieve these inferential results, we elaborate an MCMC sampling scheme whose output enables us to obtain an approximation of the quantities of interest. An application to three real datasets, corresponding to three different levels of traffic, is finally considered. Copyright © 2004 John Wiley & Sons, Ltd.     

障碍平方期权的定价

本讨论了一种变异期权——收益结构为平方的障碍期权，在股票价格服从几何布朗运动的模型下，由带单侧吸收壁的布朗运动的密度和分布函数得到连续障碍平方期权的定价公式．     

Creation, Dissipation and Recycling of Resources in Non-Equilibrium Systems

In this article, we define stochastic dynamics for a system coupled to reservoirs. The rules for forward and backward transitions are related by a generalized detailed balance identity involving the system and its reservoirs. We compare the variation of information and of entropy. We define the Carnot dissipation and prove that it can be expressed in terms of cyclic transformations. Lower bounds for partial dissipations are also studied, as well as the effect of switching off certain reservoirs. We also study the near degeneracy of the stochastic matrix, relate it to phase transitions and we show that the reduced dynamics on the set of phases is a permutation. Finally, we relate these concepts to heat, work and more generally to the dissipation and creation of resources, in general systems.     

束流线性耦合效应的初步研究

在储存环的束流传输系统中,斜四极场和纵向螺线管场是引起束流线性耦合的主要原因.由于这种耦合,使得束流的幅度和发射度发生交换,引起束流横向包络的增大,严重的将造成束流损失.从Betatron运动方程出发研究了斜四极场和螺线管场存在时束流的幅度耦合效应,分析了斜四极场存在时束流发射度的变化.     

Super-Brownian motion with reflecting historical paths. II. Convergence of approximations

We prove that the sequence of finite reflecting branching Brownian motion forests defined by Burdzy and Le Gall ([1]) converges in probability to the “super-Brownian motion with reflecting historical paths.” This solves an open problem posed in [1], where only tightness was proved for the sequence of approximations. Several results on path behavior were proved in [1] for all subsequential limits–they obviously hold for the unique limit found in the present paper.Mathematics Subject Classification (2000): Primary 60H15, Secondary 35R60Supported in part by NSF Grant DMS-0071486, Israel Science Foundation Grants 12/98 and 116/01 - 10.0, and the U.S.-Israel Binational Science Foundation (grant No. 2000065).     

Formula 1 – A Mathematical Microworld with CAS: Analysis of Learning Opportunities and Experiences with Students

In this article we describe a mathematical microworld for investigating car motion on a racing course and its use with a group of grade 12 students. The microworld is concerned with the mathematical construction of courses and functions which describe car motion. It is implemented in the computer algebra system, Maple^®, which provides the means to represent courses and functions symbolically and graphically. We describe the learning opportunities offered by the microworld in relation to the research literature on functions. Various facets and layers of the function concept are addressed in the microworld, and we suggest how work in the microworld might help in overcoming some well-known misconceptions.This revised version was published online in September 2005 with corrections to the Cover Date.     

Ergodicity for the Dissipative Boussinesq Equations with Random Forcing

We study the stationary measure for the two-dimensional Boussinesq equation with random forcing. We prove the ergodicity for the two-dimensional stochastically forced Boussinesq equation. We also study the Galerkin truncations of the three-dimensional Boussinesq equations under degenerate stochastic forcing. We follow closely the previous results on the stochastically forced Navier–Stokes equations.     

Quadratic Integrals of Motion for the Systems of Identical Particles

The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in Hamilton-Jacobi equation is clarified.     

Duffing-van der Pol振子随机分岔的全局分析

应用广义胞映射方法研究了参激和外激共同作用的Duffing-van der Pol振子的随机分岔.以 系统参数通过某一临界值时，如果系统的随机吸引子或随机鞍的形态发生突然变化，则认为 系统发生随机分岔为定义，分析了参激强度和外激强度的变化对于随机分岔的影响.揭示了 随机分岔的发生主要是由于系统的随机吸引子与系统的随机鞍碰撞产生的.分析表明，广义 胞映射方法是分析随机分岔的有力工具，这种全局分析方法可以清晰地给出随机分岔的发生 和发展. 关键词： 随机分岔 全局分析 广义胞映射方法 随机吸引子 随机鞍     

Threshold‐Based Camera Motion Characterization of MPEG Video

We propose an efficient scheme for camera motion characterization in MPEG‐compressed video. The proposed scheme detects six types of basic camera motions through threshold‐based qualitative interpretation, in which fixed thresholds are applied to motion model parameters estimated from MPEG motion vectors (MVs). The efficiency and robustness of the scheme are validated by the experiment with real compressed video sequences.