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Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
In financial markets under uncertainty, the classical Black-Scholes model cannot explain the empirical facts such as fat tails observed in the probability density. To overcome this drawback, during the last decade, Lévy process and...
Like nerve and many other endocrine cells, pancreatic beta-cells are electrically excitable and produce electrical impulses in response to elevations in glucose. These electrical impulses typically come in the form of bursting. One type...
Methods from shape analysis are used in morphometry, which is the quantitative analysis of macroscopic anatomical features. We assume that anatomy is flexible, and this brings us to the first problem of resolving how ``shape'' should be...
Two numerical methods are developed and analyzed for studying two-phase jet flows. The first numerical method solves the eigenvalue problem for the matrix system that is constructed from the pseudo-spectral discretization of the 3D...
This dissertation presents and evaluates a theoretical method of eradication of invasive species through the use of Trojan Y chromosomes. The mathematical analysis of the Trojan Y chromosome eradication strategy is presented for the ODE...
We have done a few things under Clifford algebra settings. Firstly, one Caccioppoli type estimate is derived for solutions of $A$-Dirac equations in the form $DA(x, Du) = 0$, where $D$ is the Dirac operator. This kind of $A$-Dirac...
The generation, correction, and simplification of brain surfaces from magnetic resonance imaging (MRI) data are important for studying brain characteristics, diseases, and functionality. Changes in cortical surfaces are used to compare...
We construct a framework for the analysis of shapes in Euclidean space of any dimension. In this framework, a shape is represented as a continuous map from a reference Riemannian manifold M. To quantify global shape differences, the...
The mechanism for cortical folding pattern formation is not fully understood. Current models represent scenarios that describe pattern formation through local interactions and one recent model is the intermediate progenitor model. The...
Two stochastic volatility extensions of the Swap Market Model, one with jumps and the other without, are derived. In both stochastic volatility extensions of the Swap Market Model the instantaneous volatility of the forward swap rates...
This dissertation applies knot theory, DNA topology, linear algebra, statistics, probability theory and statistical mechanics to address questions about knotted, double-stranded DNA. The three main investigations are the cellular effects...
The main result in this thesis bounds the combinatorial modulus of a ring in a triangulation graph in terms of the modulus of a related ring. The bounds depend only on how the rings are related and not on the rings themselves. This may...
The sensitivity analysis of options is as important as pricing in option theory since it is used for hedging strategies, hence for risk management purposes. This dissertation presents new sensitivities for options when the underlying...
Plasma insulin measurements from mice, rats, dogs, and humans indicate that insulin levels are oscillatory, reflecting pulsatile insulin secretion from individual islets. An unanswered question, however, is how the activity of a...
We extend the classical Procrustes metric to a new family of shape metrics and introduce a generalized Procrustes shape model. Furthermore, we propose learning models and numerical algorithms for learning metrics by using, guided by the...
Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
