一种应用于心磁噪声抑制的选择性平均方法研究

在心磁信号探测中, 抑制环境噪声是提取心磁信号的关键. 为了提高心磁信号的信噪比, 信号平均得到了广泛地使用. 然而, 由于局部干扰噪声的存在, 对整段数据进行平均的传统方法不可避免地会带来心磁信号的失真. 本文通过采取模版匹配的方式, 提出了一种选择性平均方法. 结果显示, 本方法能有效剔除带有低频波动、脉冲毛刺等干扰的数据段, 获取高质量的平均心磁信号. 关键词： 心磁 信号平均 噪声抑制 信噪比     

Stationary and multi-self-similar random fields with stochastic volatility

This paper introduces stationary and multi-self-similar random fields which account for stochastic volatility and have type G marginal law. The stationary random fields are constructed using volatility modulated mixed moving average (MA) fields and their probabilistic properties are discussed. Also, two methods for parameterizing the weight functions in the MA representation are presented: one method is based on Fourier techniques and aims at reproducing a given correlation structure, the other method is based on ideas from stochastic partial differential equations. Moreover, using a generalized Lamperti transform we construct volatility modulated multi-self-similar random fields which have type G distribution.     

Risk-sensitive control of continuous time Markov chains

We study risk-sensitive control of continuous time Markov chains taking values in discrete state space. We study both finite and infinite horizon problems. In the finite horizon problem we characterize the value function via Hamilton Jacobi Bellman equation and obtain an optimal Markov control. We do the same for infinite horizon discounted cost case. In the infinite horizon average cost case we establish the existence of an optimal stationary control under certain Lyapunov condition. We also develop a policy iteration algorithm for finding an optimal control.     

Singular control problems in bounded intervals

We consider optimal control problems for one-dimensional diffusion processes y _x (t) = y ^v _x (t), solutions dy _x (t) = g(y _x (t) dt + σ(y _x (t)(dw) + dv _t with y _x(0) = x& isinv;[a,b], the control processes v _t are increasing, positive, and adapted. Several types of expected cost structures associated with each policy v(.) are adopted, e.g. discounted cost, long term average cost and time average cost. Our work is related to [2,6,12,14,16 and 21], where diffusions are allowed to evolve in the whole space, and to [13] and [20], where diffusions evolve only in bounded regions. We shall present some analytic results about value functions, mainly their characterizations, by simple dynamic programming arguments. Several simple examples are explicitly solved to illustrate the singular behaviour of our problems     

A maximal inequality for stochastic convolution integrals on hilbert spaces and space-time regularity of linear stochastic partial differential equations

We consider optimal control problems for one-dimensional diffusion processes [ILM0001] where the control processes υ_t are increasing, positive, and adapted. Several types of expected cost structures associated with each policy υ(.) are adopted, e.g. discounted cost, long term average cost and time average cost. Our work is related to [2,6,12,14,16 and 21], where diffusions are allowed to evolve in the whole space, and to [13] and [20], where diffusions evolve only in bounded regions. We shall present some analytic results about value functions, mainly their characterizations, by simple dynamic programming arguments. Several simple examples are explicitly solved to illustrate the singular behaviour of our problems.     

On circle graphs with girth at least five

Circle graphs with girth at least five are known to be 2-degenerate [A.A. Ageev, Every circle graph with girth at least 5 is 3-colourable, Discrete Math. 195 (1999) 229-233]. In this paper, we prove that circle graphs with girth at least g≥5 and minimum degree at least two contain a chain of g−4 vertices of degree two, which implies Ageev’s result in the case g=5. We then use this structural property to give an upper bound on the circular chromatic number of circle graphs with girth at least g≥5 as well as a precise estimate of their maximum average degree.     

Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation

In this paper, we consider a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation. We show there is a unique positive solution to the system with positive initial value, and mainly investigate the long time behavior of the system. Condition for the system to be extinct is given and persistent condition is established. At last, numerical simulations are carried out to support our results.     

Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications

We study sample approximations of chance constrained problems. In particular, we consider the sample average approximation (SAA) approach and discuss the convergence properties of the resulting problem. We discuss how one can use the SAA method to obtain good candidate solutions for chance constrained problems. Numerical experiments are performed to correctly tune the parameters involved in the SAA. In addition, we present a method for constructing statistical lower bounds for the optimal value of the considered problem and discuss how one should tune the underlying parameters. We apply the SAA to two chance constrained problems. The first is a linear portfolio selection problem with returns following a multivariate lognormal distribution. The second is a joint chance constrained version of a simple blending problem. B.K. Pagnoncelli’s research was supported by CAPES and FUNENSEG. S. Ahmed’s research was partly supported by the NSF Award DMI-0133943. A. Shapiro’s research was partly supported by the NSF Award DMI-0619977.     

Average conditions for Kolmogorov systems

In this paper we consider nonautonomous competitive Kolmogorov systems, which is a generalization of classical Lotka–Volterra competition model. Applying Ahmad and Lazer’s definitions of lower and upper averages of a function, we give the average conditions for the persistence, permanence and global attractivity of the system.     

The precise asymptotics of the complete convergence for moving average processes of <Emphasis Type="Italic">m</Emphasis>-dependent <Emphasis Type="Italic">B</Emphasis>-valued elements

Let {εt;t ∈ Z} be a sequence of m-dependent B-valued random elements with mean zeros and finite second moment. {a3;j ∈ Z} is a sequence of real numbers satisfying ∑j=-∞^∞｜aj｜ 〈 ∞. Define a moving average process Xt = ∑j=-∞^∞aj＋tEj,t ≥ 1, and Sn = ∑t=1^n Xt,n ≥ 1. In this article, by using the weak convergence theorem of { Sn/√ n _〉 1}, we study the precise asymptotics of the complete convergence for the sequence {Xt; t ∈ N}.