Yevgeniy Kovchegov

Design and Analysis of Delay-Tolerant Sensor Networks for Monitoring and Tracking Free-Roaming Animals

This paper is concerned with the design and analysis of delay-tolerant networks (DTNs) deployed for free-roaming animal monitoring, wherein information is either transmitted or carried to static access-points by the animals whose movement is assumed to be random. Specifically, in such mobility-aided applications where routing is performed in a store-carry-and-drop manner, limited buffer capacity of a carrier node plays a critical role, and data loss due to buffer overflow heavily depends on access-point density. Driven by this fact, our focus in this paper is on providing sufficient conditions on access-point density that limit the likelihood of buffer overflow. We first derive sufficient access-point density conditions that ensure that the data loss rates are statistically guaranteed to be below a given threshold. Then, we evaluate and validate the derived theoretical results through comparison with both synthetic and real-world data.

Mixing Times for the Mean-Field Blume-Capel Model via Aggregate Path Coupling

We investigate the relationship between the mixing times of the Glauber dynamics of a statistical mechanical system with its thermodynamic equilibrium structure. For this we consider the mean-field Blume-Capel model, one of the simplest statistical mechanical models that exhibits the following intricate phase transition structure: within a two-dimensional parameter space there exists a curve at which the model undergoes a second-order, continuous phase transition, a curve where the model undergoes a first-order, discontinuous phase transition, and a tricritical point which separates the two curves. We determine the interface between the regions of slow and rapid mixing. In order to completely determine the region of rapid mixing, we employ a novel extension of the path coupling method, successfully proving rapid mixing even in the absence of contraction between neighboring states.

Tokunaga and Horton self-similarity for level set trees of Markov chains

Abstract The Horton and Tokunaga branching laws provide a convenient framework for studying self-similarity in random trees. The Horton self-similarity is a weaker property that addresses the principal branching in a tree; it is a counterpart of the power-law size distribution for elements of a branching system. The stronger Tokunaga self-similarity addresses so-called side branching. The Horton and Tokunaga self-similarity have been empirically established in numerous observed and modeled systems, and proven for two paradigmatic models: the critical Galton–Watson branching process with finite progeny and the finite-tree representation of a regular Brownian excursion. This study establishes the Tokunaga and Horton self-similarity for a tree representation of a finite symmetric homogeneous Markov chain. We also extend the concept of Horton and Tokunaga self-similarity to infinite trees and establish self-similarity for an infinite-tree representation of a regular Brownian motion. We conjecture that fractional Brownian motions are also Tokunaga and Horton self-similar, with self-similarity parameters depending on the Hurst exponent.

RAPID MIXING OF GLAUBER DYNAMICS OF GIBBS ENSEMBLES VIA AGGREGATE PATH COUPLING AND LARGE DEVIATIONS METHODS

In this paper, we present a novel extension to the classical path coupling method to statistical mechanical models which we refer to as aggregate path coupling. In conjunction with large deviations estimates, we use this aggregate path coupling method to prove rapid mixing of Glauber dynamics for a large class of statistical mechanical models, including models that exhibit discontinuous phase transitions which have traditionally been more difficult to analyze rigorously. The parameter region for rapid mixing for the generalized Curie–Weiss–Potts model is derived as a new application of the aggregate path coupling method.

The aggregate path coupling method for the Potts model on bipartite graph

In this paper, we derive the large deviations principle for the Potts model on the complete bipartite graph

Distributed Data Replenishment

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Adiabatic Times for Markov Chains and Applications

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HORTON LAW IN SELF-SIMILAR TREES

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Data Loss Modeling and Analysis in Partially-Covered Delay-Tolerant Networks

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A P2P Video Delivery Network (P2P-VDN)

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