Safety in transportation systems is a global concern with millions of road accidents happening worldwide every year. Despite sophisticated advancement in automotive design and accident serverity reduction technologies, traffic fatalities continue...
In the late 1960s, Ihara began work that led to the Ihara zeta function, a zeta function which is defined on a finite graph. This function is an interesting graph invariant which gives information on expansion properties of the graph. It also...
Multimedia systems -- Mathematical models. ; Information storage and retrieval systems. ; Machinery -- Alignment.
This thesis introduces multiple media correlation, a new technology for the automatic alignment of multiple media objects such as text, audio, and video. This research began with the question: what can be learned when multiple multimedia components...
For a local field K, we study the affine buildings Ξ n and Δ n naturally associated to SL n ( K ) and Sp n ( K ), respectively. Since Sp n ( K ) is a subgroup of SL 2 n ( K ), we investigate properties of a natural embedding of Δ n in Ξ 2 n ....
Topological graph theory. Aperiodicity. Paths and cycles (Graph theory)
The condition ""every cycle has an entry"" first appeared in the literature in Kumjian, Pask, and Raeburn's paper on Cuntz-Krieger algebras of directed graphs, where it was called Condition (L). It provides a necessary condition for simplicity of...
Bayesian nonparametric methods have become increasingly popular in machine learning for their ability to allow the data to determine model complexity. In particular, Bayesian nonparametric versions of common latent variable models can learn as...
Computer generated 3-D images are proving useful in a wide variety of applications including data visualization, computer animation, virtual reality, telepresence and terrain generation. High-end applications in these fields require images to be...
Proteins, the basic structural and functional building blocks of cellular machinery, evolve under significant constraint. Evolutionary pressures limit the acceptable variation and covariation of amino acids in a protein. As such, these evolutionary...
One of the most distinctive aspects of humans as a species is our propensity to form complex social networks made up of intense, non-reproductive bonds with non-kin. Navigating these networks presents a considerable cognitive challenge that is...
Sensor networks are used in many realtime applications for collecting information from monitored environments and objects, such as moving vehicle tracking, battlefield reconnaissance, and habitat monitoring. Sensor networks are often deployed in...
We associate, to each positive integer n , a Cayley graph to the group PSL(2.Ζ[subscript n]). We then consider the isoperimetric numbers of these graphs. In chapter three we determine upper bounds for the isoperimetric number by a detailed...
Graph algorithms. Nuclear magnetic resonance spectroscopy -- Data processing. Proteins -- Structure -- Mathematical models. Proteins -- Crosslinking -- Mathematical models. Protein folding -- Mathematical models.
The study of three-dimensional protein structures produces insights into protein function at the molecular level. Graphs provide a natural representation of protein structures and associated experimental data, and enable the development of graph...
During our fieldwork with real-world organizations---including those in Public Key Infrastructure (PKI), network configuration management, and the electrical power grid---we repeatedly noticed that security policies and related security artifacts...
This thesis contains material relating to two separate subjects. The first section determines when the C*-algebra affiliated to a directed graph has continuous trace. We use groupoid methods and the focus is on producing conditions on a graph that...
Although genome-wide association studies (GWAS) and other high-throughput initiatives have led to an information explosion in human genetics and genetic epidemiology, the mapping from genotype to phenotype remains challenging as most of the...
This thesis constitutes the first steps in the author's program to investigate the question of when a homotopy of 2-cocycles ω = {ω[subscript t]}[subscript t∊[0,1]] on a locally compact Hausdorff groupoid Ɠ induces an isomorphism of the...
The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C*-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting....
We present aligned hierarchies, a novel solution to the dimension reduction problem, representing high-dimensional and noisy sequential data as a low-dimensional object that encodes relevant information. In this thesis, we motivate our presentation...
Computer input-output equipment. ; Computational grids (Computer systems). ; High performance computing. ; Electronic data processing -- Distributed processing.
High-performance computing increasingly occurs on computational grids composed of heterogeneous and geographically distributed systems of computers, networks, and storage devices that collectively act as a single virtual computer. A key challenge...
This thesis centers around a generalization of the classical discrete Fourier transform. We first present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite...
In this thesis we study 1=k-geodesics, those closed geodesics that minimize on any subinterval of length L=k, where L is the length of the geodesic. These curves arise as critical points of the uniform energy, a function introduced in Morse theory...
In this thesis, we present different approaches to tying knots using robots by enforcing different types of constraints. We attack the problem from three different directions; mechanical design, motion planning with simple control strategies, and...
Networks that model relationships in the real world have attracted much attention in the past few years. The "link prediction problem" plays a central role in the network area. In this thesis, we explore the link prediction problem in a...
Modern distributed systems scatter sensors, storage, and computation throughout the environment. Ideally these devices communicate and share resources, but there is seldom motivation for a device''s owner to yield control to another user. We...
In the Firefighter Problem, a fire starts at a vertex of a graph, and in discrete time units, it spreads from burned vertices to their neighbors, unless they are protected by one of the f firefighters that are deployed every turn. Once burned or...
Shape modeling is an important area in computer vision and medical imaging. Shape models have proved valuable in the tasks of object representation, recognition, and classification. This thesis focuses on shape models of 3D surfaces extracted from...