We present new forensic tools that are capable of detecting traces of tampering in digital images without the use of watermarks or specialized hardware. These tools operate under the assumption that images contain natural properties from a variety...
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...
Spectral theory is the subfield of differential geometry which provided the solution to Kac''s famous question, "Can you hear the shape of a drum?" That is, can we use the Laplace spectrum of a manifold to draw conclusions about its geometry or...
After decades of searching we have yet to find the progenitor systems for type Ia supernovae. In fact most of what we know about this homogeneous class of supernovae is from spectral features associated with the incinerated remains of the C+O white...
Diffuse optical imaging techniques can be combined with standard imaging technologies such as computed tomography (CT) and magnetic resonance (MR) imaging to allow measurement of spectroscopic signals pertaining to the molecular components of...
Coherent states. Quantum field theory. Nonlinear theories.
In this thesis we study the properties of time-dependent, nontopological configurations and their effect on the macroscopic properties of a system described by a nonlinear field theory. These structures seem to be ubiquitous in relativistic field...
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)....
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...
Spatial localization of sound depends on interaural time delay (ITD), level difference, and on the interaction of the source with the head, torso, and pinna. Head-related transfer functions (HRTFs) model the dynamics that are used by listeners to...
A variety of forensic methods have been developed to identify falsified photos, each unified by the ability to estimate and detect properties of a photo that are perturbed by forgery. There exist, however, many photos in which the required...
Brain tissue mechanics are an important biomarker for neurological disorders, yet methods to obtain tissue information yield inconsistent conclusions. These techniques can be invasive or require excised tissue, where tissue function is altered from...
The purpose of this thesis is to describe methods for detecting hidden crevasses on glaciers in Polar regions. Crevasses form in ice sheets as a result of forces imposed upon the brittle ice. The crevasses are hidden from view by bridges of soft...
Nanoparticles have made significant advances in recent years in the realm of cancer therapy. These nanoparticles typically range in size from 10-250nm in diameter, allowing for differential systemic-based biodistribution. The enhanced permeability...
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...
Molecular imaging of cancer features is a critical part of advancing better tools for oncology management and drug discovery, yet it is still evolving as a useful tool. Diffuse Fluorescence Tomography (FT) is one approach to molecular imaging, used...
Medical imaging methods have become increasingly important in diagnosing diseases and assisting therapeutic treatment. In particular, early detection of breast cancer is considered as a critical factor in reducing the mortality rate of women....
Since their discovery in laboratory plasmas in the 1920s, Langmuir waves have been observed to be ubiquitous in plasma environments, particularly in space plasmas. From the greater solar wind to planetary foreshocks and the auroral ionosphere,...
Whistler-mode chorus waves have recently drawn tremendous attention as an important mechanism for controlling the energetic electron flux in Earthâ€™s radiation belt. This dissertation aims to answer questions about whistler-mode chorus waves, such...
Relativity (Physics). ; Anisotropy -- Mathematical models. ; Einstein field equations. ; Newtonian fluids. ; Astrophysics.
We study the effects of anisotropic pressure on the properties of spherically symmetric, gravitationally bound spheres. We consider the full general-relativistic and Newtonian treatment of this problem and obtain exact solutions for various forms...
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...
Proteins -- Structure -- Data processing. Proteins -- Analysis -- Data processing. Nuclear magnetic resonance spectroscopy. Oligomers -- Analysis -- Data processing.
Symmetric homo-oligomers (protein complexes with similar subunits arranged symmetrically) play pivotal roles in complex biological processes such as ion transport and cellular regulation. Structure determination of these complexes is necessary in...