Multiple trapping of random walkers on periodic lattices

Formulas are obtained for the mean absorption time of a set ofk independent random walkers on periodic space lattices containingq traps. We consider both discrete (here we assume simultaneous stepping) and continuous-time random walks, and find that the mean lifetime of the set of walkers can be obtained, via a convolution-type recursion formula, from the generating function for one walker on the perfect lattice. An analytical solution is given for symmetric walks with nearest neighbor transitions onN-site rings containing one trap (orq equally spaced traps), for both discrete and exponential distribution of stepping times. It is shown that, asN , the lifetime of the walkers is of the form Ta_kN², whereT is the average time between steps. Values ofa _k, 2 Sk 6, are provided.     

The theory of melting in heteropolymers. I. Random chains

A method is developed for the calculation of the ground-state melting curves ( _o vs.T) for random, infinite heteropolymers. Here _o is the ground-state value of the fraction of melted links ( _o in the strong cooperativity approximation). It is shown that the differential melting curves (d /d T vs.T) can have a fine structure in the form of several peaks on the bell-shaped main curve. Positions, magnitudes, and widths of these peaks are estimated. The accidental fine structure of melting curves, which is caused by a finite length of the polymer, is briefly discussed.Work supported in part by NSF Material Research Laboratory at Case Western Reserve University.Part of this work was submitted to the faculty of the Graduate School at SUNY Buffalo in partial fulfillment of the requirements for the Ph.D. degree.     

A non-Wiener random walk in a two-dimensional Bernoulli environment

For a degenerate random walk in a 2D Bernoulli environment without local traps, computer results show a non-Wiener behavior. For a better exploitation of the memory, the analysis is based on the statistics of the first exit time from a square.     

Stochastic comparisons for bulk queues

We consider two important classes of single-server bulk queueing models: M^(X)/G^(Y)/1 with Poisson arrivals of customer groups, and G^(X)/m^(Y)1 with batch service times having exponential density. In each class we compare two systems and prove that one is more congested than the other if their basic random variables are stochastically ordered in an appropriate manner. However, it must be recognized that a system that appears congested to customers might be working efficiently from the system manager's point of view. We apply the results of this comparison to (i) the family {M/G^(s)/1,s 1} of systems with Poisson input of customers and batch service times with varying service capacity; (ii) the family {G^(s)/1,s 1} of systems with exponential customer service time density and group arrivals with varying group size; and (iii) the family {M/D/s,s 1} of systems with Poisson arrivals, constant service time and varying number of servers. Within each family, we find the system that is the best for customers, but this turns out to be the worst for the manager (or vice versa). We also establish upper (or lower) bounds for the expected queue length in steady state and the expected number of batches (or groups) served during a busy period. The approach of the paper is based on the stochastic comparison of random walks underlying the models.This research was partially supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University.     

A Network Analysis Model for Disambiguation of Names in Lists

In research and application, social networks are increasingly extracted from relationships inferred by name collocations in text-based documents. Despite the fact that names represent real entities, names are not unique identifiers and it is often unclear when two name observations correspond to the same underlying entity. One confounder stems from ambiguity, in which the same name correctly references multiple entities. Prior name disambiguation methods measured similarity between two names as a function of their respective documents. In this paper, we propose an alternative similarity metric based on the probability of walking from one ambiguous name to another in a random walk of the social network constructed from all documents. We experimentally validate our model on actor-actor relationships derived from the Internet Movie Database. Using a global similarity threshold, we demonstrate random walks achieve a significant increase in disambiguation capability in comparison to prior models. Bradley A. Malin is a Ph.D. candidate in the School of Computer Science at Carnegie Mellon University. He is an NSF IGERT fellow in the Center for Computational Analysis of Social and Organizational Systems (CASOS) and a researcher at the Laboratory for International Data Privacy. His research is interdisciplinary and combines aspects of bioinformatics, data forensics, data privacy and security, entity resolution, and public policy. He has developed learning algorithms for surveillance in distributed systems and designed formal models for the evaluation and the improvement of privacy enhancing technologies in real world environments, including healthcare and the Internet. His research on privacy in genomic databases has received several awards from the American Medical Informatics Association and has been cited in congressional briefings on health data privacy. He currently serves as managing editor of the Journal of Privacy Technology. Edoardo M. Airoldi is a Ph.D. student in the School of Computer Science at Carnegie Mellon University. Currently, he is a researcher in the CASOS group and at the Center for Automated Learning and Discovery. His methodology is based on probability theory, approximation theorems, discrete mathematics and their geometries. His research interests include data mining and machine learning techniques for temporal and relational data, data linkage and data privacy, with important applications to dynamic networks, biological sequences and large collections of texts. His research on dynamic network tomography is the state-of-the-art for recovering information about who is communicating to whom in a network, and was awarded honors from the ACM SIG-KDD community. Several companies focusing on information extraction have adopted his methodology for text analysis. He is currently investigating practical and theoretical aspects of hierarchical mixture models for temporal and relational data, and an abstract theory of data linkage. Kathleen M. Carley is a Professor of Computer Science in ISRI, School of Computer Science at Carnegie Mellon University. She received her Ph.D. from Harvard in Sociology. Her research combines cognitive science, social and dynamic networks, and computer science (particularly artificial intelligence and machine learning techniques) to address complex social and organizational problems. Her specific research areas are computational social and organization science, social adaptation and evolution, social and dynamic network analysis, and computational text analysis. Her models meld multi-agent technology with network dynamics and empirical data. Three of the large-scale tools she and the CASOS group have developed are: BioWar a city, scale model of weaponized biological attacks and response; Construct a models of the co-evolution of social and knowledge networks; and ORA a statistical toolkit for dynamic social Network data.     

Random Walks Associated with Non-Divergence Form Elliptic Equations

This paper is concerned with the study of the diffusion process associated with a nondivergence form elliptic operator in d dimensions, d2. The authors introduce a new technique for studying the diffusion, based on the observation that the probability of escape from a d–1 dimensional hyperplane can be explicitly calculated. They use the method to estimate the probability of escape from d–1 dimensional manifolds which are C ^1, , and also d–1 dimensional Lipschitz manifolds. To implement their method the authors study various random walks induced by the diffusion process, and compare them to the corresponding walks induced by Brownian motion.     

The shapes of bowed interfaces in the two-dimensional Ising model

We show that properly normalized net energy fluctuations associated with interfaces in two-dimensional Ising models are described, asymptotically, by random walk partition functions. Two examples are investigated: one is a droplet on a wall, and the other is two nearby, ideally parallel interfaces; the mean shapes of the interfaces in both cases prove to be elliptic, bowed outward from the wall or from each other, the semiminor axis of the latter ellipse being 1/2 that of the former, in accord with random walk results.     

Diffusion in lattices with anisotropic scatterers

We study diffusion in lattices with periodic and random arrangements of anisotropic scatterers. We show, using both analytical techniques based upon our previous work on asymptotic properties of multistate random walks and computer calculation, that the diffusion constant for the random arrangement of scatterers is bounded above and below at an arbitrary density by the diffusion constant for an appropriately chosen periodic arrangement of scatterers at the same density. We also investigate the accuracy of the low-density expansion for the diffusion constant up to second order in the density for a lattice with randomly distributed anisotropic scatterers. Comparison of the analytical results with numerical calculations shows that the accuracy of the density expansion depends crucially on the degree of anisotropy of the scatterers. Finally, we discuss a monotonicity law for the diffusion constant with respect to variation of the transition rates, in analogy with the Rayleigh monotonicity law for the effective resistance of electric networks. As an immediate corollary we obtain that the diffusion constant, averaged over all realizations of the random arrangement of anisotropic scatterers at density, is a monotone function of the density.     

拉力诱导下的紧密高分子链相变行为

采用相互作用自回避行走(interacting self-avoiding walks,ISAWS)模型研究了一端固定的紧密高分子链在拉伸过程中的低温相变行为,观察到在拉伸过程中当温度T<0.1时平均拉力会出现一个震荡,随着温度的升高这种震荡现象又渐渐消失,这是由于紧密高分子链在低温时类似于β折叠的"冻结构象"被拉开而引起的.比较吸附条件下和无吸附作用下平均拉力、自由能以及相变行为的差别,发现在吸附条件下在拉伸的初始阶段为了克服表面吸附的相互作用,拉力会出现一个峰.吸附作用也使得外界作用到高分子链上的实际有效拉力减小,造成崩塌相态(collapsed phase)区域面积减少.另外发现在吸附条件下平均拉力还受温度变化的影响.在拉伸的初期由于单体间存在体积排除效应,平均拉力是随着温度的升高而降低,随着拉伸的深入当末端距到达一定长度时平均拉力是随着温度的升高而增加.并同Kumar等人在不考虑吸附作用下拉伸紧密高分子链得到的结果进行了比较.这些研究对于进一步研究外力诱导下吸附紧密高分子的相变有一定的参考价值.