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In network tomography, we seek to infer link status parameters (delay, congestion, loss rates etc.) inside a network through end-to-end measurements at (external) boundary nodes. As can be expected, such approaches generically suffer from identifiability problems; i.e., status of links in a large number of network topologies is not identifiable. We introduce an innovative approach based on linear...
We examine the role played by a linear dynamical network's topology in inference of its eigenvalues from noisy impulse-response data. Specifically, for a canonical linear time-invariant network dynamics, we relate the Cramer-Rao bounds on eigenvalue estimator performance (from impulse-response data) to structural properties of the transfer function, and in turn to the network's topological structure...
We obtain an explicit formula for the absolute difference between two eigenvector components for a weighted graph's Laplacian matrix, in terms of the the Laplacian's eigenvalues as well as the eigenvalues of matrices associated with certain coalesced graphs. We then briefly illustrate two uses of this formula, in analyzing graph modifications.
We take a structural approach to the problem of designing the edge weights in an undirected graph subject to an upper bound on their total, so as to maximize the algebraic connectivity. Specifically, we first characterize the eigenvector(s) associated with the algebraic connectivity at the optimum, using optimization machinery together with eigenvalue sensitivity notions. Using these characterizations,...
We motivate the problem of designing a subset of the edge weights in a graph, to shape the spectrum of an associated linear time-invariant dynamics. We address a canonical design problem of this form by applying time-scale assignment methods, and give graph-theoretic characterizations of the designed dynamics.
We develop and characterize a dynamical network model for activity-dependent sleep regulation. Specifically, in accordance with the activity-dependent theory for sleep, we view organism sleep as emerging from the local sleep states of functional units known as cortical columns; these local sleep states evolve through integration of local activity inputs, loose couplings with neighboring cortical columns,...
Motivated by network controller design applications, we develop several majorization results for the dominant eigenvector of an irreducible nonnegative matrix.
In this work we apply graph theoretic tools to provide a close bound on a frontier relating the number of line outages in a grid to the power disrupted by the outages. This frontier describes the boundary of a space relating the possible severity of a disturbance in terms of power disruption, from zero to some maximum on the boundary, to the number line outages involved in the event. We present the...
Social networks refer to structures made of nodes that represent people or other entities embedded in a social context, and whose edges represent interaction between entities. Typical examples of social networks are collaboration networks in a research community, networks arising out of interaction between colleagues of large organization etc. Social networks are highly dynamic objects that evolve...
Low-density parity-check codes using the belief-propagation decoding algorithm tend to exhibit a high error floor in the bit error rate curves, when some problematic graphical structures, such as the so-called trapping sets, exist in the corresponding Tanner graph. This paper presents a joint row-column decoding algorithm to lower the error floor, in which the column processing is combined with the...
We propose a new and flexible hierarchical multibaseline stereo algorithm that features a non-uniform spatial decomposition of the disparity map. The visibility computation and refinement of the disparity map are integrated into a single iterative framework that does not add extra constraints to the cost function. This makes it possible to use a standard efficient stereo matcher during each iteration...
We propose a partitioning problem in a power system context that weighs the two objectives of minimizing cuts between partitions and maximizing the power imbalance between partitions. We then pose the problem in a purely graph theoretic sense. We offer an approximate solution through relaxation of the integer problem and suggest refinement using stochastic methods. Results are presented for the IEEE...
We envision a future where thousands to millions of small sensors for self-organizing wireless networks. As it provides solutions to many needs such as wireless communication, remote monitoring, surveillance etc. wireless networking will likely become widespread. Most applications will be done where wiring is impossible to install, or too expensive or where operating and supporting costs are prohibitively...
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