Analysis 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 …

Understanding Impact Of Educational Awareness And Vaccines As Optimal Control Mechanisms For Changing Human Behavior In Disease Epidemics, Manal Badgaish, Dr. Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Effects Of Persistent Post-Concussion Syndrome, Jackson Flemming, Olivia Schleifer, Megan Powell

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

On A Stationary Random Knot, Andrey A. Dorogovtsev

Journal of Stochastic Analysis

No abstract provided.

Backward Stochastic Differential Equations In A Semi-Markov Chain Model, Robert J. Elliott, Zhe Yang

Journal of Stochastic Analysis

No abstract provided.

Are The Cans In The Store “Volume Optimized”? [Mathematics], Bukurie Gjoci

Open Educational Resources

This is one of LaGuardia’s Project Connexion STEM Team’s experiential learning activities. Project Connexion's purpose is to promote creative thinking on how to engage students in the classroom. As part of this, the STEM team developed Experiential/co-curricular activities that demonstrated to students how their work in class connects to the world around them. These activities were embedded into the syllabus to ensure the participation of all students. Each professor designed a Co-curricular activity for their courses, ensuring that the Co-curricular activity directly linked course material to the outside world.

This Calculus I Experiential Learning Project aligns with one of the …

An Analysis Of The Sequence Xn+2 = I M Xn+1 + Xn, David Duncan, Prashant Sansgiry, Ogul Arslan, Jensen Meade

Journal of the South Carolina Academy of Science

We analyze the sequence Xn+2 = imXn+1 + Xn, with X1 = X2 = 1 + i, where i is the imaginary number and m is a real number. Plotting the sequence in the complex plane for different values of m, we see interesting figures from the conic sections. For values of m in the interval (−2, 2) we show that the figures generated are ellipses. We also provide analysis which prove that for certain values of m, the sequence generated is periodic with even period.

Double Barrier Backward Doubly Stochastic Differential Equations, Tadashi Hayashi

Journal of Stochastic Analysis

No abstract provided.

Symmetric Functions Algebras (Sfa) Iii: Stochastic And Constant Row Sum Matrices, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.

Using Geographic Information To Explore Player-Specific Movement And Its Effects On Play Success In The Nfl, Hayley Horn, Eric Laigaie, Alexander Lopez, Shravan Reddy

SMU Data Science Review

American Football is a billion-dollar industry in the United States. The analytical aspect of the sport is an ever-growing domain, with open-source competitions like the NFL Big Data Bowl accelerating this growth. With the amount of player movement during each play, tracking data can prove valuable in many areas of football analytics. While concussion detection, catch recognition, and completion percentage prediction are all existing use cases for this data, player-specific movement attributes, such as speed and agility, may be helpful in predicting play success. This research calculates player-specific speed and agility attributes from tracking data and supplements them with descriptive …

Secondary Features Of Importance For A Url Ranking, Atajan Abdyyev

Dissertations and Theses

This paper investigates the impact of secondary ranking factors on webpage relevance and rankings in the context of Search Engine Optimization (SEO), focusing on the jewelry domain within the United States e-commerce market. By generating a keyword list related to jewelry and retrieving top URLs from Google's search results, the study employs machine learning models including XGBoost, CatBoost, and Linear Regression to identify key features influencing webpage relevance and rankings.The findings highlight specific optimal ranges for features like Outlinks, Unique Inlinks, Flesch Reading Ease Score, and others, indicating their significant impact on better rankings. Notably, Random Forest model performed best …

Concentration Theorems For Orthonormal Sequences In A Reproducing Kernel Hilbert Space, Travis Alvarez

All Dissertations

Let H be a reproducing kernel Hilbert space with reproducing kernel elements {Kx} indexed by a measure space {X,mu}. If H can be embedded in L2(X,mu), then H can be viewed as a framed Hilbert space. We study concentration of orthonormal sequences in such reproducing kernel Hilbert spaces.

Defining different versions of concentration, we find quantitative upper bounds on the number of orthonormal functions that can be classified by such concentrations. Examples are shown to prove sharpness of the bounds. In the cases that we can add "concentrated" orthonormal vectors indefinitely, the growth rate of doing so is shown.

Recovering Coefficients Of Second-Order Hyperbolic And Plate Equations Via Finite Measurements On The Boundary, Scott Randall Scruggs

All Dissertations

Abstract In this dissertation, we consider the inverse problem for a second-order hyperbolic equation of recovering n + 3 unknown coefficients defined on an open bounded domain with a smooth enough boundary. We also consider the inverse problem of recovering an unknown coefficient on the Euler- Bernoulli plate equation on a lower-order term again defined on an open bounded domain with a smooth enough boundary. For the second-order hyperbolic equation, we show that we can uniquely and (Lipschitz) stably recover all these coefficients from only using half of the corresponding boundary measurements of their solutions, and for the plate equation, …

Asymptotic Cones Of Quadratically Defined Sets And Their Applications To Qcqps, Alexander Joyce

All Dissertations

Quadratically constrained quadratic programs (QCQPs) are a set of optimization problems defined by a quadratic objective function and quadratic constraints. QCQPs cover a diverse set of problems, but the nonconvexity and unboundedness of quadratic constraints lead to difficulties in globally solving a QCQP. This thesis covers properties of unbounded quadratic constraints via a description of the asymptotic cone of a set defined by a single quadratic constraint. A description of the asymptotic cone is provided, including properties such as retractiveness and horizon directions.

Using the characterization of the asymptotic cone, we generalize existing results for bounded quadratically defined regions with …

Bayesian Optimization With Switching Cost: Regret Analysis And Lookahead Variants, Peng Liu, Haowei Wang, Wei Qiyu

Research Collection Lee Kong Chian School Of Business

Bayesian Optimization (BO) has recently received increasing attention due to its efficiency in optimizing expensive-to-evaluate functions. For some practical problems, it is essential to consider the path-dependent switching cost between consecutive sampling locations given a total traveling budget. For example, when using a drone to locate cracks in a building wall or search for lost survivors in the wild, the search path needs to be efficiently planned given the limited battery power of the drone. Tackling such problems requires a careful cost-benefit analysis of candidate locations and balancing exploration and exploitation. In this work, we formulate such a problem as …

On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson

Rose-Hulman Undergraduate Mathematics Journal

We provide solutions of a first order, linear partial differential equation of two variables where the nonhomogeneous term is a two-dimensional Dirac delta function. Our results are achieved by applying the unilateral Laplace Transform, solving the subsequently transformed PDE, and reverting back to the original space-time domain. A discussion of existence and uniqueness of solutions, a derivation of solutions of the PDE coupled with a boundary and initial condition, as well as a few worked examples are provided.

Some New Techniques And Their Applications In The Theory Of Distributions, Kevin Kellinsky-Gonzalez

LSU Doctoral Dissertations

This dissertation is a compilation of three articles in the theory of distributions. Each essay focuses on a different technique or concept related to distributions.

The focus of the first essay is the concept of distributional point values. Distribu- tions are sometimes called generalized functions, as they share many similarities with ordi- nary functions, with some key differences. Distributional point values, among other things, demonstrate that distributions are even more akin to ordinary functions than one might think.

The second essay concentrates on two major topics in analysis, namely asymptotic expansions and the concept of moments. There are many variations …

The Existence Of Solutions To A System Of Nonhomogeneous Difference Equations, Stephanie Walker

Rose-Hulman Undergraduate Mathematics Journal

This article will demonstrate a process using Fixed Point Theory to determine the existence of multiple positive solutions for a type of system of nonhomogeneous even ordered boundary value problems on a discrete domain. We first reconstruct the problem by transforming the system so that it satisfies homogeneous boundary conditions. We then create a cone and an operator sufficient to apply the Guo-KrasnoselâA˘Zskii Fixed Point Theorem. The majority of the work involves developing the constraints ´ needed to utilized this fixed point theorem. The theorem is then applied three times, guaranteeing the existence of at least three distinct solutions. Thus, …

Schur Analysis And Discrete Analytic Functions: Rational Functions And Co-Isometric Realizations, Daniel Alpay, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

We define and study rational discrete analytic functions and prove the existence of a coisometric realization for discrete analytic Schur multipliers.

Solving The Cable Equation, A Second-Order Time Dependent Pde For Non-Ideal Cables With Action Potentials In The Mammalian Brain Using Kss Methods, Nirmohi Charbe

Master's Theses

In this thesis we shall perform the comparisons of a Krylov Subspace Spectral method with Forward Euler, Backward Euler and Crank-Nicolson to solve the Cable Equation. The Cable Equation measures action potentials in axons in a mammalian brain treated as an ideal cable in the first part of the study. We shall subject this problem to the further assumption of a non-ideal cable. Assume a non-uniform cross section area along the longitudinal axis. At the present time, the effects of torsion, curvature and material capacitance are ignored. There is particular interest to generalize the application of the PDEs including and …