In this thesis, the dynamics of long-lived, time-dependent, coherent field configurations, known as oscillons, are investigated in the presence of an expanding background. In a (1+1)-dimensional expanding spacetime, scalar-field oscillon lifetimes...
Two localized spectroscopic imaging methods were investigated to detect and discriminate microscopic pathologies at the surface of excised breast tissues in order to improve resection completeness during breast conserving surgery. A scanning in...
Diagnostic imaging -- Mathematics. Expectation-maximization algorithms. Imaging systems in medicine -- Mathematics.
We have developed a general-purpose registration algorithm for medical images and volumes. The transformation between images is modeled as locally affine but globally smooth, and explicitly accounts for local and global variations in image...
Motivated by quantum mechanics and geometric optics, it is a long-standing problem whether the length spectrum of a compact Riemannian manifold can be recovered from its Laplace spectrum. One route to proving that the length spectrum depends on the...
Casimir effect. Zero-point field. Electric conductivity. Quantum electrodynamics.
The Casimir force arises from an alteration of boundary condition in vacuum and is often regarded as a manifestation of quantum zero point energy. Considerable progress has been made in the last decade with an impressive achievement of experimental...
Morbidity and complexity involved in lymph node staging via surgical resection and biopsy could ideally be overcome using node assay techniques that are non-invasive. Visible blue dyes, fluorophores and radio-tracers are often used to locate the...
In this thesis, we study the dynamics of magnetic flows on compact nilmanifolds. Magnetic flows are generalizations of geodesic flows. They model the motion of a particle of unit mass and unit charge in a smooth manifold M in the presence of a...
Over the past decade, a pair of instructions called load-linked (LL) and store-conditional (SC) have emerged as the most suitable synchronization instructions for the design of lock-free algorithms. However, current architectures do not support...
Human locomotion -- Computer-assisted instruction. ; Real-time data processing. ; Human-computer interaction.
Teaching physical motions such as riding, exercising, swimming, etc. to human beings is hard. Coaches face difficulties in communicating their feedback verbally and cannot correct the student mid-action; teaching videos are two dimensional and...
We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian...
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...
Partially ordered sets and permutations are combinatorial structures having vast applications in theoretical computer science. In this thesis, we study various computational and algorithmic problems related to these structures. The first chapter of...
In this thesis we review the methods for computation of cosmological correlations in the early universe known as the in-in formalism which are then applied to the problem of magnetogenesis from inflation. For this computation, a power-law single...
Given graded C *-algebras A and B , we define the notion of an admissible pair ([straight phi], D ) for A and B . Associated to an admissible pair ([straight phi], D ) is an equivalence class of asymptotic morphisms from A to B . Under certain...
We examine variations of cops and robbers games on graphs. Our goals are to introduce some randomness into their study, and to estimate (expected) capture time. We show that a cop chasing a random walker can capture him in expected time n + o(n)....
Constructibility (Set theory). Trees (Graph theory).
This thesis investigates possible initial segments of the degrees of constructibility. Specifically, we completely characterize the structure of degrees in generic extensions of the constructible universe L via forcing with Souslin trees. Then we...
Digital integrated circuits -- Testing. Digital integrated circuits -- Testing -- Mathematical models. Digital integrated circuits -- Design and construction.
Electric generators -- Windings. Electric inductors -- Design and construction -- Mathematical models. Electric current converters -- Design and construction -- Mathematical models. Energy dissipation -- Mathematical models.
Magnetic components for high-frequency power conversion applications can have significant losses that compromise the performance of the converter. In particular, winding losses can be large due to high-frequency effects that are difficult to model...
Boundary integral methods have long been used to solve boundary value problems for elliptic partial differential equations with piecewise constant coefficients, since they have several numerical advantages over conventional volume discretization....
The performance of machine learning algorithms largely depends on data representation. As a critical step in machine learning, representation learning (feature learning) learns a transformation of training data to give a new representation that can...
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...
Siegel domains. Modular groups. Hecke algebras. Forms
In the 1960s Satake proved the existence of an isomorphism between the local Hecke algebra and the ring of polynomials invariant under the action of the signed permutation group W n (the Weyl group associated to Sp n over a local field)....
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...
Multiresolution image transformations have become commonplace tools for analyzing images for a number of applications, including enhancement and restoration. Powerful models for these applications have been developed in the transform domain of...