Applied Mathematics Commons^™

Multiscale Modeling Of Microtubule Polarity Mechanisms Following Neuronal Axotomy, Hannah Scanlon

Biology and Medicine Through Mathematics Conference

No abstract provided.

Statistical Mobility Of Aggregated Microswimmers, Yonatan Ashenafi

Biology and Medicine Through Mathematics Conference

No abstract provided.

Local Geometry Of Elementary Visual Computations, Peter Neri

MODVIS Workshop

Visual operators (e.g. edge detectors) are classically modelled using small circuits involving canonical computations, such as template-matching and gain control. Circuit models explain many aspects of the empirical descriptors that are used to characterize local visual operators, from sensitivity to classification images. Notwithstanding their utility, these models fail to provide a unified framework encompassing the variety of effects observed experimentally, such as the impact of contrast, SNR, and attention on the above descriptors. My goal is to start with a simple, plausible geometrical representation of the perceptual operation carried out by the observer, and to show that this representation is …

Improved Rational Approximation Of Near-To-Far Propagation Kernels For The Wave Equation, Sampson Owusu

Mathematics & Statistics ETDs

The 3-space, 1-time dimensional scalar wave equation, or 3+1 wave equation, describes the propagation of scalar or acoustic waves. The unforced homogeneous equation admits a class of outgoing solutions relative to a chosen fixed center, so called “multipole” solutions. This thesis examines near-to-far signal propagation in the context of these multipole solutions. Given a time-series (history of values) for a multipole solution recorded at a radius r1, near- to-far signal propagation recovers the corresponding time-series at larger radius r2 ≫ r1. This propagation takes into account both the appropriate time delay r2 − r1 and corrections to the wave shape. …

Conjugations Of Unitary Operators, I, Javad Mashreghi, Mraek Ptak, William T. Ross

Department of Math & Statistics Faculty Publications

If U is a unitary operator on a separable complex Hilbert space H, an application of the spectral theorem says there is a conjugation C on H (an antilinear, involutive isometry on H) for which CUC= U*. In this paper, we fix a unitary operator U and describe all of the conjugations C which satisfy this property. As a consequence of our results, we show that a subspace is hyperinvariant for U if and only if it is invariant for any conjugation C for which CUC = U*.

H1-Conforming Finite Elements On Nonstandard Meshes, Samuel Edward Reynolds

Dissertations and Theses

We present a finite element method for linear elliptic partial differential equations on bounded planar domains that are meshed with cells that are permitted to be curvilinear and multiply connected. We employ Poisson spaces, as used in virtual element methods, consisting of globally continuous functions that locally satisfy a Poisson problem with polynomial data. This dissertation presents four peer-reviewed articles concerning both the theory and computation of using such spaces in the context of finite elements. In the first paper, we propose a Dirichlet-to-Neumann map for harmonic functions by way of computing the trace of a harmonic conjugate by numerically …

Chemoattractant Distribution In The Drosophila Egg Chamber, Lara Scott

Biology and Medicine Through Mathematics Conference

No abstract provided.

Sperm-Egg Interaction For Fertilization Success, Prajakta P. Bedekar

Biology and Medicine Through Mathematics Conference

No abstract provided.

Impacts Of Hematodinium Infection In A Seasonal Population Model Of The Chesapeake Bay Blue Crab, Gwendolyn R. Sargent, Romuald Lipcius, Leah Shaw, Junping Shi, Jeffrey D. Shields

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Comparative Analysis Of Source Identification Algorithms, Pablo A. Curiel

Biology and Medicine Through Mathematics Conference

No abstract provided.

Incorporating Awareness, Misinformation And Optimal Control In A Model Of Sars-Cov-2, Eric Numfor

Biology and Medicine Through Mathematics Conference

No abstract provided.

Information Feedback Delays Within Epidemic Models And Their Effect On Model Dynamics., Maria K. Bouka, Christopher Strickland Dr

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mathematically Modeling Stoichiometric Drivers Of Nitrogen Fixation, Rebecca Everett, Corday Selden, Mohamed Hatha Abdulla, Jabir Thajudeen, James Powell, Edwin Cruz-Rivera, Luca Schenone, Renn Schipper, Megan Berberich, Halvor Halvorson, Robinson Fulweiler, Amy Marcarelli, Thad Scott

Biology and Medicine Through Mathematics Conference

No abstract provided.

Nidus Idearum. Scilogs, Xiii: Structure / Neutrostructure / Antistructure, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this thirteenth book of scilogs – one may find topics on Neutrosophy, Plithogeny, Physics, Mathematics, Philosophy – email messages to research colleagues, or replies, notes, comments, remarks about authors, articles, or books, spontaneous ideas, and so on. It presents new types of soft sets and new types of topologies.

Exchanging ideas with Mohammad Abobala, Ishfaq Ahmad, Ibrahim M. Almanjahie, Fatimah Alshahrani, Nizar Altounji, Muhammad Aslam, Said Broumi, Victor Christianto, R. Diksh, Feng Liu, Frank Julian Gelli, Erick Gonzalez Caballero, Riad Hamido, Yaser Al-Hasan, Ahmed Hatip, Yasin Karmouta, Nivetha Martin, Preda Mihăilescu, V. Lakshmana Gomathi Nayagam, Ze Carlos Tiago de …

Analysis And Computation Of Constrained Sparse Coding On Emerging Non-Von Neumann Devices, Kyle Henke

Mathematics & Statistics ETDs

This dissertation seeks to understand how different formulations of the neurally inspired Locally Competitive Algorithm (LCA) represent and solve optimization problems. By studying these networks mathematically through the lens of dynamical and gradient systems, the goal is to discern how neural computations converge and link this knowledge to theoretical neuroscience and artificial intelligence (AI). Both classical computers and advanced emerging hardware are employed in this study. The contributions of this work include:

1. Theoretical Work: A comprehensive convergence analysis for networks using both generic Rectified Linear Unit (ReLU) and Rectified Sigmoid activation functions. Exploration of techniques to address the binary …

Effect Of Recommending Users And Opinions On The Network Connectivity And Idea Generation Process, Sriniwas Pandey, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

The growing reliance on online services underscores the crucial role of recommendation systems, especially on social media platforms seeking increased user engagement. This study investigates how recommendation systems influence the impact of personal behavioral traits on social network dynamics. It explores the interplay between homophily, users’ openness to novel ideas, and recommendation-driven exposure to new opinions. Additionally, the research examines the impact of recommendation systems on the diversity of newly generated ideas, shedding light on the challenges and opportunities in designing effective systems that balance the exploration of new ideas with the risk of reinforcing biases or filtering valuable, unconventional …

Robust Prediction Of Charpy Toughness Of Additively Manufactured Kovar Using Deep Convolutional Neural Networks, Nathan R. Bianco

Mathematics & Statistics ETDs

Understanding the reason for mechanical failures of manufactured parts in their operating environments is critical to prevention of future failures. However, in-situ post-mortem evaluation of physical properties, such as fracture toughness, is time consuming and alters the condition of the material, leading to potentially misleading findings. In this study, additively manufactured test coupons were produced over a wide range of process conditions to test the impact toughness of a material. The Charpy V-Notch toughness was measured on over 200 samples alongside corresponding optical images of both sides of the fracture surface. Convolutional neural network models were trained to correlate fracture …

Duality Of Ensemble Systems Through Moment Representations, Vignesh Narayanan, Wei Zhang, Jr-Shin Li

Publications

Controlling large-scale dynamic population systems, known as ensemble control, is a pervasive and essential task in many emerging applications from diverse scientific domains. Previous focuses in the area of ensemble control have been placed on seeking open-loop control strategies due to unavailability of state feedback information for each individual system in the ensemble. In this paper, we develop a foundational framework for analysis and control of ensemble systems with closed feedback control loops. We introduce the notion of ensemble moments and construct moment systems associated with the ensemble systems. By extending the classical moment problem in mathematical analysis and statistics, …

Analytical And Numerical Analysis Of The Sirs Model, Catherine Nguyen

Departmental Honors & Graduate Capstone Projects

Mathematical models in epidemiology describe how diseases affect and spread within a population. By understanding the trends of a disease, more effective public health policies can be made. In this paper, the Susceptible-Infected-Recovered-Susceptible (SIRS) Model was examined analytically and numerically to compare with the data for Coronavirus Disease 2019 (COVID-19). Since the SIRS model is a complex model, analytical techniques were used to solve simplified versions of the SIRS model in order to understand general trends that occur. Then by Euler's Method, the Runge-Kutta Method, and the Predictor-Corrector Method, computational approximations were obtained to solve and plot the SIRS model. …

Non-Contact Wind Turbine Blade Crack Detection Using Laser Doppler Vibrometers, Ali Zabihi, Farhood Aghdasi, Chadi Ellouzi, Nand Kishore Singh, Ratneshwar Jha, Chen Shen

Henry M. Rowan College of Engineering Departmental Research

In response to the growing global demand for both energy and a clean environment, there has been an unprecedented rise in the utilization of renewable energy. Wind energy plays a crucial role in striving for carbon neutrality due to its eco-friendly characteristics. Despite its significance, wind energy infrastructure is susceptible to damage from various factors including wind or sea waves, rapidly changing environmental conditions, delamination, crack formation, and structural deterioration over time. This research focuses on investigating non-destructive testing (NDT) of wind turbine blades (WTBs) using approaches based on the vibration of the structures. To this end, WTBs are first …