Spatial-temporal data arises in many applications, for example, environment sciences and disease mapping. This dissertation focuses on Gaussian spatial-temporal data. To make statistical inference for Gaussian spatial-temporal data, we developed a special class of spatial-temporal Gaussian state-space models in which the state vectors are constructed following spatial-temporal Gaussian autoregressions that...
In this dissertation we consider two application specific flow and transport models in porous media at multiple scales: 1) methane gas transport models for hydrate formation and dissociation in the subsurface under two-phase conditions, and 2) coupled flow and biomass-nutrient model for biofilm growth in complex geometries with biofilm, and...
3D vector tomography has been explored and results have been achieved in the last few decades. Among these was a reconstruction formula for the solenoidal part of a vector field from its Doppler transform with sources on a curve. The Doppler transform of a vector field is the line integral...
In this dissertation we develop mathematical treatment for two important applications: (i) evolution of methane in coalbeds with the associated phenomena of adsorption, and (ii) formation of methane hydrates in seabed. We use simplified models for (i) and (ii) since we are more interested in qualitative properties of the solutions...
In this work we consider the dependence of solutions to a partial differential equations system on its data. The problem of interest is a coupled model of nonlinear flow and transport in porous media, with applications, e.g. to environmental modeling. The model of flow we consider is known as the...
Modeling and analyzing the combined effects of disease and population dynamics
is important in understanding the effects of mechanisms such as pathogen transmission
and direct competition between host species on the distribution and abundance of different
species in an ecological community. Mathematical analysis of such models in a
spatially explicit...
Large deviation theory has experienced much development and interest in
the last two decades. A large deviation principle is the exponential decay of the
probability of increasingly rare events and the computation of a rate or entropy
function which measures the rate of decay. Within the probability literature there
has...
Support Vector Machines (SVM) and Random Forests (RF) have
consistently outperformed other machine learning algorithms on a variety of
problems. SVM can be used for classification and regression on many types of
data (e.g. nonlinear, high dimensional), but cannot handle missing or mixed data.
This research implements a permutation-based variable...
In recent years, the rapidly growth of CMOS technology has evolved towards submicron and deep-submicron features. Due to smaller device sizes, and significant demand for low-power designs, the maximum allowable power supply voltage is restricted. So far, two solutions; clock boosting and switched opamp schemes have been proposed. The material...
As the number of weather stations declines globally, ensuring that meteorological monitoring networks efficiently and effectively monitor weather variables becomes increasingly important. Multi-variable weather sensors are becoming more widely available and make monitoring weather phenomena more economical. However, when seeking an optimal spatial distribution of these stations, choosing an objective...