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This thesis is interested in the application of statistical physics methods and inference to sparse linear estimation problems. The main tools are the graphical models and approximate message-passing algorithm together with the cavity…
We establish the existence of wave-like solutions to spatially coupled graphical models which, in the large size limit, can be characterized by a one-dimensional real-valued state. This is extended to a proof of the threshold saturation…
We study Ising spin models on finitely connected random interaction graphs which are drawn from an ensemble in which not only the degree distribution $p(k)$ can be chosen arbitrarily, but which allows for further fine-tuning of the topology…
In recent years inelastic spin-flip spectroscopy using a lowtemperature scanning tunneling microscope has been a very successful tool for studying not only individual spins but also complex coupled systems. When these systems interact with…
Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal…
We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible…
The central spin decoherence problem has been researched for over 50 years in the context of both nuclear magnetic resonance and electron spin resonance. Until recently, theoretical models have employed phenomenological stochastic…
Single fault sequential change point problems have become important in modeling for various phenomena in large distributed systems, such as sensor networks. But such systems in many situations present multiple interacting faults. For…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
As massive graphs become more prevalent, there is a rapidly growing need for scalable algorithms that solve classical graph problems, such as maximum matching and minimum vertex cover, on large datasets. For massive inputs, several…
This paper proposes an Adaptive Stochastic Model Predictive Control (MPC) strategy for stable linear time-invariant systems in the presence of bounded disturbances. We consider multi-input, multi-output systems that can be expressed by a…
Sparse coding networks, which utilize unsupervised learning to maximize coding efficiency, have successfully reproduced response properties found in primary visual cortex \cite{AN:OlshausenField96}. However, conventional sparse coding…
We investigate several control strategies for the transport of an excitation along a spin chain. We demonstrate that fast, high fidelity transport can be achieved using protocols designed with differentiable programming. Building on this,…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
Composite systems, where couplings are of two types, a combination of strong dilute and weak dense couplings of Ising spins, are examined through the replica method. The dilute and dense parts are considered to have independent canonical…
Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or…
It is essential for a robot to be able to detect revisits or loop closures for long-term visual navigation.A key insight explored in this work is that the loop-closing event inherently occurs sparsely, that is, the image currently being…
Compressive sensing is a signal acquisition framework based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable recovery. In this paper we introduce a new theory for…
This paper applies Information Theoretic analysis to packet-based random multiple access communication systems. A new channel coding approach is proposed for coding within each data packet with built-in support for bursty traffic…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…