Digital audio filter design using frequency transformations

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (leaves 80-81).by Chalee Asavathiratham.M.Eng

The influence model : a tractable representation for the dynamics of networked Markov chains

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Includes bibliographical references (p. 186-188).In this thesis we introduce and analyze the influence model, a particular but tractable mathematical representation of random, dynamical interactions on networks. Specifically, an influence model consists of a network of nodes, each with a status that evolves over time. The evolution of the status at a node is according to an internal Markov chain, but with transition probabilities that depend not only on the current status of that node, but also on the statuses of the neighboring nodes. Thus, interactions among the nodes occur probabilistically, starting when a change of status at one node alters the transition probabilities of its neighbors, which then alter those of their neighbors, and so on. More technically, the influence model is a discrete-time Markov process whose state space is the tensor product of the statuses of all the local Markov chains. We show that certain aspects of the dynamics of the influence model can be studied through the influence matrix, a reduced-order matrix whose dimension is the sum rather than the product of the local chain dimensions. We explore the eigenstructure of the influence matrix and explicitly describe how it is related to that of the full-order transition matrix. From the influence matrix, we also obtain the influence graph, which allows the recurrent states of the influence model to be found by graph-theoretic analysis on the reduced-order graph. A nested hierarchy of higher-order influence matrices, obtained from Kronecker powers of the first-order influence matrix, is exposed. Calculations on these matrices allow us to obtain progressively more elaborate statistics of the model at the expense of progressively greater computational burden. As a particular application of the influence model, we analyze the "to link or not to link" dilemma. Suppose that a node is either in a 'healthy' or 'failed' status. Given that connecting to the network makes its status dependent on those of its neighbors, is it worthwhile for a node to connect to the network at all? If so, which nodes should it connect to in order to maximize the 'healthy' time? We formulate these questions in the framework of the influence model, and obtain answers within this framework. Finally, we outline potential areas for future research.by Chalee Asavathiratham.Ph.D

Digital Signal Processing Research Program

Contains table of contents for Section 2, an introduction, reports on twenty-one research projects and a list of publications.U.S. Navy - Office of Naval Research Grant N00014-93-1-0686Lockheed Sanders, Inc. Contract P.O. BY5561U.S. Air Force - Office of Scientific Research Grant AFOSR 91-0034National Science Foundation Grant MIP 95-02885U.S. Navy - Office of Naval Research Grant N00014-95-1-0834MIT-WHOI Joint Graduate Program in Oceanographic EngineeringAT&T Laboratories Doctoral Support ProgramDefense Advanced Research Projects Agency/U.S. Navy - Office of Naval Research Grant N00014-89-J-1489Lockheed Sanders/U.S. Navy - Office of Naval Research Grant N00014-91-C-0125U.S. Navy - Office of Naval Research Grant N00014-89-J-1489National Science Foundation Grant MIP 95-02885Defense Advanced Research Projects Agency/U.S. Navy Contract DAAH04-95-1-0473U.S. Navy - Office of Naval Research Grant N00014-91-J-1628University of California/Scripps Institute of Oceanography Contract 1003-73-5

Network models: growth, dynamics, and failure

This paper reports on preliminary explorations, both empirical and analytical, of probabilistic models of large-scale networks. We rst examine the structure of networks that grow by the addition of nodes and lines, using a class of connection rules motivated by considerations of distance and prior connectivity. Second, we examine the dynamic behavior of the binary in uence model | a particular form of a more general model of networks in which each node has a status (for instance: normal, or failed) that behaves as a Markov chain, but with transitions that are in uenced bythepresent status of each neighboring node. Some interesting in uence model examples are analyzed, including one displaying a power-law relation between the frequency of a failure event and its extensiveness