Physical Sciences and Mathematics 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 …

Statistical Models For Decision-Making In Professional Soccer, Sean Hellingman

Theses and Dissertations (Comprehensive)

As soccer is widely regarded as the most popular sport in the world there is high interest in methods of improving team performances. There are many ways teams and individual athletes can influence their own performances during competition. This thesis focuses on developing statistical methodologies for improving competition-based decision-making for soccer so as to allow professional soccer teams to make better informed decisions regarding player selection and in-game decision-making.

To properly capture the dynamic actions of professional soccer, Markov chains with increasing complexity are proposed. These models allow for the inclusion of potential changes in the process caused by goals …

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 …

Self-Exciting Point Process For Modelling Terror Attack Data, Siyi Wang

Theses and Dissertations (Comprehensive)

Terrorism becomes more rampant in recent years because of separatism and extreme nationalism, which brings a serious threat to the national security of many countries in the world. The analysis of spatial and temporal patterns of terror data is significant in containing terrorism. This thesis focuses on building and applying a temporal point process called self-exciting point process to fit the terror data from 1970 to 2018 of 10 countries. The data come from the Global Terrorism database. Further, an application in predicting the number of terror events based on the self-exciting model is another main innovative idea, in which …

Modeling Multivariate Hopfield-Transformer Hawkes Process: Application To Sovereign Credit Default Swaps, Mohsen Bahremani

Theses and Dissertations (Comprehensive)

Hawkes process was evolved so that the past events contribute to the occurrence time of future events by self-exciting or mutually exciting. However, many real-world data do not follow the Hawkes process's assumptions (i.e., positivity, additivity, and exponential decay) and become more complex to be modeled by the traditional Hawkes processes, so the neural Hawkes process was developed to tackle the challenges. However, Recurrent Neural Networks (RNN) fail to capture long-term dependencies among multiple point processes, and Transformer Hawkes processes only address temporal characteristics of Hawkes processes. In this thesis, we proposed a combination of neural networks and Hawkes processes …

Aggregate Loss Model With Poisson-Tweedie Loss Frequency, Si Chen

Theses and Dissertations (Comprehensive)

The aggregate loss model has applications in various areas such as financial risk management and actuarial science. The aggregate loss is the summation of all random losses occurred in a period, and it is governed by both the loss severity and the loss frequency. While the impact of the loss severity on aggregate loss is well studied, less focus is paid on the influence of loss frequency on aggregate loss, which motivates our study. In this thesis, we enrich the aggregate loss framework by introducing the Poisson-Tweedie distribution as a candidate for modelling loss frequency, prove the closedness of Poisson-Tweedie …

Estimation Of Multivariate Asset Models With Jumps, Angela Loregian, Laura Ballotta, Gianluca Gianluca Fusai, Marcos Fabricio Perez

Business Faculty Publications

We propose a consistent and computationally efficient two-step methodology for the estimation of multidimensional non-Gaussian asset models built using Levy processes. The proposed framework allows for dependence between assets and different tail behaviors and jump structures for each asset. Our procedure can be applied to portfolios with a large number of assets as it is immune to estimation dimensionality problems. Simulations show good finite sample properties and significant efficiency gains. This method is especially relevant for risk management purposes such as, for example, the computation of portfolio Value at Risk and intra-horizon Value at Risk, as we show in detail …

Toward Using High-Frequency Coastal Radars For Calibration Of S-Ais Based Ocean Vessel Tracking Models, Ben Freidrich

Theses and Dissertations (Comprehensive)

Most of the world relies on ships for transportation, shipping, and tourism. Automatic Identification System messages are transmitted from ships and provide a wealth of positional data on these open ocean vessels. This data is being utilized to determine the optimal path for ships, as well as predicting where a ship may be going in the near future. It has only been in the past decade that Automatic Identification Systems (AIS) signals have been easily received with satellites (S-AIS) so there have been few studies that look at using available information and pairing it with the new abundance of ship …

Spatial Modelling And Wildlife Health Surveillance: A Case Study Of White Nose Syndrome In Ontario, Lauren Yee

Theses and Dissertations (Comprehensive)

Wildlife data is often limited by survey effort, small sample sizes, and spatial biases associated with collection and missing data. These factors can create unique challenges from a surveillance perspective when trying to extract spatial patterns of habitat suitability and disease distributions for conservation and management purposes. This thesis examined data quality from a wildlife health database in the context of spatial analysis of wildlife disease. Spatial analysis of the data to predict habitat suitability of bats and white nose syndrome afflicted bats was examined by using the MaxEnt modelling method. Methods to reduce spatial bias were examined and specific …

Space-Time Modelling Of Emerging Infectious Diseases: Assessing Leptospirosis Risk In Sri Lanka, Cameron C F Plouffe

Theses and Dissertations (Comprehensive)

In this research, models were developed to analyze leptospirosis incidence in Sri Lanka and its relation to rainfall. Before any leptospirosis risk models were developed, rainfall data were evaluated from an agro-ecological monitoring network for producing maps of total monthly rainfall in Sri Lanka. Four spatial interpolation techniques were compared: inverse distance weighting, thin-plate splines, ordinary kriging, and Bayesian kriging. Error metrics were used to validate interpolations against independent data. Satellite data were used to assess the spatial pattern of rainfall. Results indicated that Bayesian kriging and splines performed best in low and high rainfall, respectively. Rainfall maps generated from …

A Localized Approach To The Origins Of Pottery In Upper Mesopotamia, Elizabeth Gibbon

The Partisan

No abstract provided.

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, …

Identifying Directional Properties Of Spatial Point Patterns An Investigation Of Two Methods, Rolf Puchtinger

Theses and Dissertations (Comprehensive)

Analyses of spatial point patterns tend to focus on deviations from randomness by either clustering or regularity. One assumption of these analyses implies that the point generating process is equal in all directions. However, the association of the location of points with a process biased in one or more directions is widely neglected due to a lack of appropriate statistical procedures. This is surprising, since patterns generated by directional processes are important in Geography. The purpose of this thesis is to investigate the blunt-triangle method and the third moment method for their potential of identifying directionality in spatial point patterns. …