This is a collection of expository articles about various topics at the interface between enumerative combinatorics and stochastic processes. These articles expand on a course of lectures given at the École d’Été de Probabilités de St. Flour in July 2002. The articles are called ’chapters ’ and numbered according to the order of these chapters in a printed volume to appear in Springer Lecture Notes in Mathematics. Each chapter is fairly self-contained, so readers with adequate background can start reading any chapter, with occasional consultation of earlier chapters as necessary. Following this Chapter 0, there are 10 chapters, each divided into sections. Most sections conclude with some Exercises. Those for which I don’t know solutions are called Problems. Acknowledgments Much of the research reviewed here was done jointly with David Aldous. Much credit is due to him, especially for the big picture of continuum approximations to large combinatorial structures. Thanks also to my other collaborators in this work, especially Jean Bertoin, Michael Camarri, Steven

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ing with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works, requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept, ACM Inc., 1515 Broadway, New York, NY 10036 USA, fax 1 (212) 869-0481, or permissions@acm.org. ACM Transactions on Computer-Human Interactions, Vol.5, No.1, March 1998, Pages 63-108. 2 \Delta Chengzheng Sun, et al. 1. INTRODUCTION Cooperative editing systems are very useful groupware tools in the rapidly expanding areas of CSCW (Computer-Supported Cooperative Work) [Ellis et al. 1991], They can be used to allow physically dispersed people to edit a shared textual document [Ellis and Gibbs 1989

Concurrency control and group undo are important issues in the design of groupware, especially for interactive group editors. We present an improved version of an existing distributed algorithm for concurrency control that is based on operation transformations. Since the usability of the algorithm relies on its formal correctness, we present a set of necessary and sufficient conditions to be satisfied in order to ensure consistency in a replicated architecture. We identify desirable properties of operation transformations and show how our approach can be employed to implement group undo. The approach has been applied to build a prototypical group editor for text; some experiences gained are presented. Keywords Concurrency Control, Group Editors, Group Undo, Groupware, Interaction Model, Operation Transformation. INTRODUCTION Groupware systems, i.e., multi-user applications for cooperative work [2, 5], present remarkable challenges for application designers. Concurrency control and ...

this paper draws quite heavily on Ressel et al. (adOPTed), and we use their formal treatments and notation throughout, quoting their statement of the algorithm in Figures 3 -- 4

on this approach are able to satisfy the mandatory correctness properties T P1 and T P2 defined in the Ressel’s framework. This paper addresses this correctness issue by proposing a new way to model shared state by retaining tombstones when elements are removed. An instantiation of the proposed model for a linear

Many advances in the development of Krylov subspace methods for the iterative solution of linear systems during the last decade and a half are reviewed. These new developments include different versions of restarted, augmented, deflated, flexible, nested, and inexact methods. Also reviewed are methods specifically tailored to systems with special properties such as special forms of symmetry and those depending on one or more parameters.

This paper presents a general framework based on reproducing kernel Hilbert spaces (RKHS) to mathematically describe and manipulate spike trains. The main idea is the definition of inner products to allow spike train signal processing from basic principles while incorporating their statistical

Novel Frameworks for Dark Matter and Neutrino Masses The established light neutrino masses and the Dark Matter of the Universe both require physics beyond the Standard Model for their theoretical explanation. Models that provide a common framework for these two issues are very attractive

Abstract—Privacy has become a critical topic in the engi-neering of electric systems. This work proposes an approach for smart-grid-specific privacy requirements engineering by extend-ing previous general privacy requirements engineering frame-works. The proposed extension goes one step further