Rare Events in Stochastic Partial Differential Equations on Large Spatial Domains

A methodology is proposed for studying rare events in stochastic partial differential equations in systems that are so large that standard large deviation theory does not apply. The idea is to deduce the behavior of the original model by breaking the system into appropriately scaled subsystems that are sufficiently small for large deviation theory to apply but sufficiently large to be asymptotically independent from one another. The methodology is illustrated in the context of a simple one-dimensional stochastic partial differential equation. The application reveals a connection between the dynamics of the partial differential equation and the classical Johnson–Mehl–Avrami–Kolmogorov nucleation and growth model. It also illustrates that rare events are much more likely and predictable in large systems than in small ones due to the extra entropy provided by space.     

利用中值检测方法研究近50年中国极端气温变化趋势

利用中国194个站点1957—2001年的逐日温度观测资料和月平均温度资料,分别采用中值和均值两种极端事件检测方法,检测并比较了中国极端高温事件和极端低温事件的变化趋势和空间分布特征.检测表明,年均极端高温的次数在近50年中趋于上升,而年均极端低温的次数有所减少,这与目前观测结果一致,符合全球变暖的特点.在空间分布上,除西南地区部分站点外,近50年中国大部分地区极端低温事件的年均发生次数趋于减少,而极端高温事件发生频率的变化则呈现出东南沿海地区减少、西北内陆地区增加的分布特点. 关键词： 极端事件 全球增暖 变化趋势 中值     

A modified layered-step interior-point algorithm for linear programming

The layered-step interior-point algorithm was introduced by Vavasis and Ye. The algorithm accelerates the path following interior-point algorithm and its arithmetic complexity depends only on the coefficient matrixA. The main drawback of the algorithm is the use of an unknown big constant in computing the search direction and to initiate the algorithm. We propose a modified layered-step interior-point algorithm which does not use the big constant in computing the search direction. The constant is required only for initialization when a well-centered feasible solution is not available, and it is not required if an upper bound on the norm of a primal—dual optimal solution is known in advance. The complexity of the simplified algorithm is the same as that of Vavasis and Ye. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Research supported in part by ONR contract N00014-94-C-0007 and the Grant-in-Aid for Scientific Research (C) 08680478 and the Grant-in-Aid for Encouragement of Young Scientists (A) 08780227 of the Ministry of Science, Education and Culture of Japan. This research was partially done while S. Mizuno and T. Tsuchiya were visiting IBM Almaden Research Center in the summer of 1995.     

A strong bound on the integral of the central path curvature and its relationship with the iteration-complexity of primal-dual path-following LP algorithms

The main goals of this paper are to: i) relate two iteration-complexity bounds derived for the Mizuno-Todd-Ye predictor-corrector (MTY P-C) algorithm for linear programming (LP), and; ii) study the geometrical structure of the LP central path. The first iteration-complexity bound for the MTY P-C algorithm considered in this paper is expressed in terms of the integral of a certain curvature function over the traversed portion of the central path. The second iteration-complexity bound, derived recently by the authors using the notion of crossover events introduced by Vavasis and Ye, is expressed in terms of a scale-invariant condition number associated with m × n constraint matrix of the LP. In this paper, we establish a relationship between these bounds by showing that the first one can be majorized by the second one. We also establish a geometric result about the central path which gives a rigorous justification based on the curvature of the central path of a claim made by Vavasis and Ye, in view of the behavior of their layered least squares path following LP method, that the central path consists of long but straight continuous parts while the remaining curved part is relatively “short”. R. D. C. Monteiro was supported in part by NSF Grants CCR-0203113 and CCF-0430644 and ONR grant N00014-05-1-0183. T. Tsuchiya was supported in part by Japan-US Joint Research Projects of Japan Society for the Promotion of Science “Algorithms for linear programs over symmetric cones” and the Grants-in-Aid for Scientific Research (C) 15510144 of Japan Society for the Promotion of Science.     

Synthesis and biological evaluation of novel 2,4,5-triaryl-1 H-pyrazol-3(2H)-ones as inhibitors of ALK5

A series of 2,4,5-triaryl substituted 1H-pyrazol-3(2H)-ones,as ALK5 inhibitors,were desigened,synthesized and evaluated in vitro.Most compounds exhibited noticeable ALK5 inhibition activities at 1 μmol/L and displayed no significant cytotoxicities at 30 μmol/L.     

400GeV/c pp碰撞类环事例的产生

利用400GeV/c pp碰撞产生的带电粒子赝快度分布的实验数据,研究了类环事例的产生机制.结果表明在一有限的时间-空间范围内相干胶子辐射是类环事例的一种可能的产生机制,但肯定不是主要的.     

化学探头法与荧光光谱法测定水中溶解氧量

探讨了化学探头法和荧光光谱法测定水中溶解氧的关系。分别用F检验和t检验对两组数据进行了比较,结果表明两组数据的精密度和系统误差都没有显著差异,两种方法测定溶解氧的相对标准偏差(RSD,n=9)分别为0.35%,0.33%。进而又探讨了溶解氧与NaCl含量、温度之间的关系,结果表明溶解氧含量随NaCl含量的增加、温度的升高而逐渐降低。     

一个风险模型的研究

研究了索赔到达过程为平稳无后效流,保单到达过程为平稳无后效流,并带扩散扰动项的盈余过程．讨论了该盈余过程的马尔科夫性和鞅性．然后用鞅方法得到其破产概率的表达式及其相应的Lundberg不等式．     

Importance sampling algorithms for first passage time probabilities in the infinite server queue

This paper applies importance sampling simulation for estimating rare event probabilities of the first passage time in the infinite server queue with renewal arrivals and general service time distributions. We consider importance sampling algorithms which are based on large deviations results of the infinite server queue, and we consider an algorithm based on the cross-entropy method, where we allow light-tailed and heavy-tailed distributions for the interarrival times and the service times. Efficiency of the algorithms is discussed by simulation experiments.     

Initial classification of joint data in EM estimation of latent class joint model

The latent class mixture-of-experts joint model is one of the important methods for jointly modelling longitudinal and recurrent events data when the underlying population is heterogeneous and there are nonnormally distributed outcomes. The maximum likelihood estimates of parameters in latent class joint model are generally obtained by the EM algorithm. The joint distances between subjects and initial classification of subjects under study are essential to finding good starting values of the EM algorithm through formulas. In this article, separate distances and joint distances of longitudinal markers and recurrent events are proposed for classification purposes, and performance of the initial classifications based on the proposed distances and random classification are compared in a simulation study and demonstrated in an example.