Dynamical Systems 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 …

Langevin Dynamic Models For Smfret Dynamic Shift, David Frost, Keisha Cook Dr, Hugo Sanabria Dr

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Geometry Of Competition And Stability For One-Host, Two-Parasitoid Systems With Application To Biocontrol, Michael Kerckhove

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

On The Spectrum Of Quaquaversal Operators, Josiah Sugarman

Dissertations, Theses, and Capstone Projects

In 1998 Charles Radin and John Conway introduced the Quaquaversal Tiling. A three dimensional hierarchical tiling with the property that the orientations of its tiles approach a uniform distribution faster than what is possible for hierarchical tilings in two dimensions. The distribution of orientations is controlled by the spectrum of a certain Hecke operator, which we refer to as the Quaquaversal Operator. For example, by showing that the largest eigenvalue has multiplicity equal to one, Charles Radin and John Conway showed that the orientations of this tiling approach a uniform distribution. In 2008, Bourgain and Gamburd showed that this operator …

Bright Light Therapy And Depression: Assessing Suitability Using Entrainment Maps, Charles A. Mainwaring

Theses

Bright Light Therapy has been shown to be efficacious to mood disorders including Major Depression. Researchers use the Jewett-Forger-Kronauer model of the circadian rhythm with the Unified Model of melatonin including a mathematical term implementing feedback from the melatonin system into the circadian system to quantify the effects of bright light. Early investigations into intrinsic period, light sensitivity, and the circadian pacemaker's sensitivity to blood melatonin concentration may be indicators of subsets of patients with long intrinsic periods exhibiting symptoms of depression.

Computing Brain Networks With Complex Dynamics, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.

Gap Junctions And Synchronization Clusters In The Thalamic Reticular Nuclei, Anca R. Radulescu, Michael Anderson

Biology and Medicine Through Mathematics Conference

No abstract provided.

Effective Non-Hermiticity And Topology In Markovian Quadratic Bosonic Dynamics, Vincent Paul Flynn

Dartmouth College Ph.D Dissertations

Recently, there has been an explosion of interest in re-imagining many-body quantum phenomena beyond equilibrium. One such effort has extended the symmetry-protected topological (SPT) phase classification of non-interacting fermions to driven and dissipative settings, uncovering novel topological phenomena that are not known to exist in equilibrium which may have wide-ranging applications in quantum science. Similar physics in non-interacting bosonic systems has remained elusive. Even at equilibrium, an "effective non-Hermiticity" intrinsic to bosonic Hamiltonians poses theoretical challenges. While this non-Hermiticity has been acknowledged, its implications have not been explored in-depth. Beyond this dynamical peculiarity, major roadblocks have arisen in the search …

Photonic Sensors Based On Integrated Ring Resonators, Jaime Da Silva

Mechanical Engineering Research Theses and Dissertations

This thesis investigates the application of integrated ring resonators to different sensing applications. The sensors proposed here rely on the principle of optical whispering gallery mode (WGM) resonance shifts of the resonators. Three distinct sensing applications are investigated to demonstrate the concept: a photonic seismometer, an evanescent field sensor, and a zero-drift Doppler velocimeter. These concepts can be helpful in developing lightweight, compact, and highly sensitive sensors. Successful implementation of these sensors could potentially address sensing requirements for both space and Earth-bound applications. The feasibility of this class of sensors is assessed for seismic, proximity, and vibrational measurements.

Machine Learning-Based Data And Model Driven Bayesian Uncertanity Quantification Of Inverse Problems For Suspended Non-Structural System, Zhiyuan Qin

All Dissertations

Inverse problems involve extracting the internal structure of a physical system from noisy measurement data. In many fields, the Bayesian inference is used to address the ill-conditioned nature of the inverse problem by incorporating prior information through an initial distribution. In the nonparametric Bayesian framework, surrogate models such as Gaussian Processes or Deep Neural Networks are used as flexible and effective probabilistic modeling tools to overcome the high-dimensional curse and reduce computational costs. In practical systems and computer models, uncertainties can be addressed through parameter calibration, sensitivity analysis, and uncertainty quantification, leading to improved reliability and robustness of decision and …

Applying Hallgren’S Algorithm For Solving Pell’S Equation To Finding The Irrational Slope Of The Launch Of A Billiard Ball, Sangheon Choi

Mathematical Sciences Technical Reports (MSTR)

This thesis is an exploration of Quantum Computing applied to Pell’s equation in an attempt to find solutions to the Billiard Ball Problem. Pell’s equation is a Diophantine equation in the form of x² − ny² = 1, where n is a given positive nonsquare integer, and integer solutions are sought for x and y. We will be applying Hallgren’s algorithm for finding irrational periods in functions, in the context of billiard balls and their movement on a friction-less unit square billiard table. Our central research question has been the following: Given the cutting sequence of the billiard …

Time Evolution Is A Source Of Bias In The Wolf Algorithm For Largest Lyapunov Exponents, Kolby Brink, Tyler Wiles, Nicholas Stergiou, Aaron Likens

UNO Student Research and Creative Activity Fair

Human movement is inherently variable by nature. One of the most common analytical tools for assessing movement variability is the largest Lyapunov exponent (LyE) which quantifies the rate of trajectory divergence or convergence in an n-dimensional state space. One popular method for assessing LyE is the Wolf algorithm. Many studies have investigated how Wolf’s calculation of the LyE changes due to sampling frequency, filtering, data normalization, and stride normalization. However, a surprisingly understudied parameter needed for LyE computation is evolution time. The purpose of this study is to investigate how the LyE changes as a function of evolution time …

A Visual Tour Of Dynamical Systems On Color Space, Jonathan Maltsman

HMC Senior Theses

We can think of a pixel as a particle in three dimensional space, where its x, y and z coordinates correspond to its level of red, green, and blue, respectively. Just as a particle’s motion is guided by physical rules like gravity, we can construct rules to guide a pixel’s motion through color space. We can develop striking visuals by applying these rules, called dynamical systems, onto images using animation engines. This project explores a number of these systems while exposing the underlying algebraic structure of color space. We also build and demonstrate a Visual DJ circuit board for …

Dynamical Aspects In (4+1)-Body Problems, Ryan Gauthier

Theses and Dissertations (Comprehensive)

The n-body problem models a system of n-point masses that attract each other via some binary interaction. The (n + 1)-body problem assumes that one of the masses is located at the origin of the coordinate system. For example, an (n+1)-body problem is an ideal model for Saturn, seen as the central mass, and one of its outer rings. A relative equilibrium (RE) is a special solution of the (n+1)-body problem where the non-central bodies rotate rigidly about the centre of mass. In rotating coordinates, these solutions become equilibria.

In this thesis we study dynamical aspects of planar (4 + …

On The Spatial Modelling Of Biological Invasions, Tedi Ramaj

Electronic Thesis and Dissertation Repository

We investigate problems of biological spatial invasion through the use of spatial modelling. We begin by examining the spread of an invasive weed plant species through a forest by developing a system of partial differential equations (PDEs) involving an invasive weed and a competing native plant species. We find that extinction of the native plant species may be achieved by increasing the carrying capacity of the forest as well as the competition coefficient between the species. We also find that the boundary conditions exert long-term control on the biomass of the invasive weed and hence should be considered when implementing …

Solving Clostridioides Difficile: Mathematical Models Of Transmission And Control In Healthcare Settings, Cara Sulyok, Max Lewis, Laila Mahrat, Brittany Stephenson, Malen De La Fuente Arruabarrena, David Kovalev, Justyna Sliwinska

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modularity And Boolean Network Decomposition, Matthew Wheeler

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Canalization And Other Design Principles Of Gene Regulatory Networks, Claus Kadelka

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

On Analysis Of Effectiveness Controlling Covid-19 With Quarantine And Vaccination Compartments In Indonesia, Prihantini Prihantini

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Model-Free Identification Of Relevant Variables From Response Data, Alan Veliz-Cuba, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.