Probability Commons^™

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

Lake Huron Shoreline Analysis, Shubham Satish Nandanwar

Theses and Dissertations (Comprehensive)

Lake Huron is a popular tourist destination and is home to several businesses and residents. Since the shoreline is dynamic and is subject to change over the years due to several factors such as a change in water level, soil type, human encroachment, etc., these locations tend to encounter floods due to increased water levels and wind speed. This causes erosion and loss to the properties along the shoreline.

This study is based on two areas of interest named Pinery Provincial Park and Sauble Beach which are located on the shoreline of Lake Huron where Pinery Provincial Park is a …

First Passage Time Problem For Multivariate Jump-Diffusion Processes: Models, Computation, And Applications In Finance, Di Zhang

Theses and Dissertations (Comprehensive)

The first passage time (FPT) problems are ubiquitous in many applications, from physics to finance. Mathematically, such problems are often reduced to the evaluation of the probability density of the time for a process to cross a certain level, a boundary, or to enter a certain region. While in other areas of applications the FPT problems can often be solved analytically, in finance we usually have to resort to the application of numerical procedures, in particular when we deal with jump-diffusion stochastic processes (JDP). The application of the conventional Monte-Carlo procedure is possible for the solution of the resulting model, …