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 mapping via EEG activation is a useful tool of basic neuroscience, and has wide clinical applications as well. The mapping is achieved by means of Event Related Potentials (ERPs), task-related changes in EEG time series. The methodology of...
Thermodynamics, and the classic balance between entropy and enthalpy, provides a proverbial zoo of exotic phase behaviour that chemists can harness to create new materials out of simple liquids and polymers. The diversity of self-assembling...
Si/SiGe quantum dots (QDs) are promising candidates for spin-based quantum bits (qubits) as a result of the reduced spin-orbit coupling as well as the Si isotopes with zero nuclear spin. Meanwhile qubit readout is a challenge related to...
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...
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....
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....
Polynomials. Finite fields (Algebra). Algebraic functions. Number theory.
The ring of univariate polynomials over a finite field shares many foundational arithmetic properties with the ring of rational integers. This similarity makes it possible for many problems in elementary number theory to be translated 'through the...
Magnetic nanoparticles are promising candidates for use in biomedical applications as remote sensors of biophysical properties, thermal therapy agents, and detectors of specific biomolecules. Many approaches have been used to model magnetic...
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 accelerated expansion of space in the Universe has been known for two decades. However, finding a plausible theory that describes this expansion is more difficult: Taking general relativity for granted requires us to stipulate the existence of...
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...
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...
This dissertation examines the behavioral and physiological adaptations employed by modern humans to subsist in tropical rainforests. I employ various theoretical and methodological approaches to test hypotheses using empirical data from African...
Three-dimensional imaging in medicine -- Mathematical models. Intraoperative monitoring. Cerebral cortex -- Imaging. Computer vision. Space perception.
Brain deformation models have proven to be a powerful tool in compensating for soft tissue deformation during image-guided neurosurgery. The accuracy of these models can be improved by incorporating intraoperative measurements of brain motion. We...
A mobile agent is an autonomous program that can migrate under its own control from machine to machine in a heterogeneous network. In other words, the program can suspend its execution at an arbitrary point, transport itself to another machine, and...
Two-phase flow -- Mathematical models. ; Gas dynamics -- Mathematical models. ; Kinetic theory of gases.
The kinetic theory based gas-dynamical computational method, due to (Prendergast and Xu, 1993: Xu and Prendergast, 1994) is generalized to two-phase flow computations. The Bhatnagar-Gross-Krook kinetic model is generalized to the case of two...
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...