▼ The value of financial derivatives such as options depends, among other things, on the volatility of the underlying asset. Estimating volatility from historic data on asset returns with respect to models of stochastic volatility is inherently difficult due to the fact that volatility states cannot be directly measured. In order to investigate a solution to this problem, we use a sequential method based on particle filters to infer historic volatility from simulated data for a specific discrete approximation of the Hull-White model on stochastic volatility. Advisors/Committee Members: Calvetti, Daniela.

▼ Complex phenomena often feature a large number of coupled variables, whose interdependencies are not clear. One egregious example of a complex system is brain metabolism, which can be represented as a network of biochemical reactions and transports of several interacting species. In this thesis, a detailed multi-compartment mathematical model of brain energy metabolism for steady state becomes the object of data mining applications. In particular, a sample of equilibrium configurations is drawn and self-organizing map and the non-negative matrix factorization are invoked to examine and reveal underlying dependencies between different biochemical processes. The goal of this thesis is to use data mining techniques to let latent dependencies emerge from our data. This, in turn, will make it possible to reduce the degrees of freedom of the system and point to important, yet still unveiled, metabolic relations. Advisors/Committee Members: Calvetti, Daniela.

▼ Communication via diffusible chemical signals is ubiquitous within biology. We explore a model of a biochemical communications channel using a diffusible chemical signal transmitted across a volume. The received signal is attenuated by a combination of diffusion, decay, and counting noise. We find the response of the channel is well fit by an additive Gaussian noise model y = x+z, where x ∈ C is the Fourier component of an arbitrary sinusoidal input at a frequency ω, z ∈ C is complex bivariate Gaussian noise with variance N, and β ∈ C and N ∈ R depend systematically on ω. We impose a natural constraint A on the input amplitude, and find the information capacity on a single frequency, and on several together by waterfilling. We also consider several different coarse grainings of the model and how the loss of detail affects apparent information capacity. Advisors/Committee Members: Thomas, Peter.

▼ Sexual coercion, including date rape, is an issue of major concern on college campuses. Many colleges have instituted date rape programming on their campuses. While these programs seek to increase awareness of the issue of date rape and other forms of sexual coercion, their preventive efforts have been lacking in theoretical depth and attention to developmental design. This study involved methodological development of a preventive intervention to decrease college women's vulnerability to sexual coercion. Based on the foundation of prevention theory, it was guided by a competence-of-women perspective. The research involved a process of design development, implementation, formal measurement, field testing and refinement. It followed a social science developmental research model established to convert an "idea" into a "product." In this study, the resulting product was a sixteen-hour preventive intervention program which aims to decrease college women's vulnerability to sexual coercion. The results of the study indicated that developmental research has utility in the fields of prevention and social work. The program went through several revisions subsequent to the feedback mechanisms built into the design. The study also demonstrate d the applicability of a theoretical construct of competence-of-women to prevention of sexual coercion vulnerability. Advisors/Committee Members: Farkas, Kathleen J.

▼ The brain is a highly metabolic organ, characterized by the presence of different cell types, astrocytes, neurons and endothelial cells, interacting with each other and with specific tasks, whose regulatory mechanisms are still largely unknown. The difficulty in obtaining direct in vivo and in situ cell-type specific measurements of metabolite and intermediate concentrations has left many different hypotheses open on the metabolic role of astrocytes and neurons, in particular on the primary source of energy for brain during stimulation. Computational models of cellular brain metabolism can help sorting out which presumed mechanisms are more likely under various conditions and eventually providing a key to decode information from functional imaging modalities. In this thesis we present new six-compartment computational models of cellular brain metabolism which integrate astrocytes and glutamatergic or GABAergic neurons, extracellular space and blood domains, with detailed biochemical reactions and signalling mechanisms. These models are governed by large systems of nonlinear ordinary differential equations with many degrees of freedom. We study two different kinds of parameter estimation problems, one concerned with steady state and the other with dynamic situations, for which we propose a new Bayesian approach. The complexity of the models, the large discrepancy between the scarcity of available data and the huge number of unknown parameters make the steady state and dynamic parameter estimation inverse problems severely underdetermined and ill-posed. While these features may be an obstacle for classical deterministic methods, they can be overcome in a Bayesian framework, where the unknowns are modelled as random variables and additional information in the form of prior belief about the solutions and the models can be incorporated in the estimation problem. Efficient Markov Chain Monte Carlo sampling techniques are designed and adapted to explore the posterior density, which is the solution of the problem in Bayesian inversion. We will show how this new methodology can be used to test different hypotheses on brain energetics and interpret experimental data in the context of compartmentalized metabolism. The computational results are in remarkable agreement with experimental data and with proposed physiological and biochemical mechanisms on cellular brain metabolism. Advisors/Committee Members: Calvetti, Daniela.

▼ This dissertation concerns the field of values of the inverse of a matrix. Techniques of approximation of this set are considered for large, sparse matrices, and applications are discussed. A new method is presented that is similar in computational cost to previous methods, but may yield better approximations in practice. Also, a new technique for finding eigenvalue inclusion regions is presented, developed from the relationship between the field of values of the inverse and the eigenvalue extraction technique known as harmonic Rayleigh-Ritz. By intersecting these eigenvalue inclusion regions, a new characterization of the spectrum of a matrix is obtained. The technique for generating these regions can be generalized by replacing the field of values with other eigenvalue inclusion sets, and this is demonstrated using the Geršgorin region of a matrix. Advisors/Committee Members: Singer, David A.