Numerical Approximations Of Phase Field Equations With Physics Informed Neural Networks, 2020 Utah State University

#### Numerical Approximations Of Phase Field Equations With Physics Informed Neural Networks, Colby Wight

*All Graduate Plan B and other Reports*

Designing numerical algorithms for solving partial differential equations (PDEs) is one of the major research branches in applied and computational mathematics. Recently there has been some seminal work on solving PDEs using the deep neural networks. In particular, the Physics Informed Neural Network (PINN) has been shown to be effective in solving some classical partial differential equations. However, we find that this method is not sufficient in solving all types of equations and falls short in solving phase-field equations. In this thesis, we propose various techniques that add to the power of these networks. Mainly, we propose to embrace the ...

"A Comparison Of Variable Selection Methods Using Bootstrap Samples From Environmental Metal Mixture Data", 2020 University Of New Mexico

#### "A Comparison Of Variable Selection Methods Using Bootstrap Samples From Environmental Metal Mixture Data", Paul-Yvann Djamen 4785403, Paul-Yvann Djamen

*Mathematics & Statistics ETDs*

In this thesis, I studied a newly developed variable selection method SODA, and three customarily used variable selection methods: LASSO, Elastic net, and Random forest for environmental mixture data. The motivating datasets have neuro-developmental status as responses and metal measurements and demographic variables as covariates. The challenges for variable selections include (1) many measured metal concentrations are highly correlated, (2) there are many possible ways of modeling interactions among the metals, (3) the relationships between the outcomes and explanatory variables are possibly nonlinear, (4) the signal to noise ratio in the real data may be low. To compare these methods ...

Modeling The Effects Of Fentanyl And Narcan On The Opioid Epidemic In Allegheny County Using Mathematics, 2020 Duquesne University

#### Modeling The Effects Of Fentanyl And Narcan On The Opioid Epidemic In Allegheny County Using Mathematics, Lindsay Moskal, Lauren Sines, Rachael Neilan Ph.D.

*Undergraduate Research and Scholarship Symposium*

Starting in the 1990s, physicians across the United States have increasingly prescribed opioid pain relievers, which has given rise to the current opioid epidemic. As a result, there has been a drastic increase in the number of overdose fatalities. In 2017, the number of opioid overdose deaths peaked and the U.S. declared the crisis as a public health emergency. One state that has contributed significantly to this epidemic is Pennsylvania, which ranks first for the greatest number of overdose deaths and third for the highest death rate. In fact, Allegheny County has witnessed an overdose death rate that is ...

Modeling The Effects Of Fentanyl And Narcan On The Opioid Epidemic In Allegheny County Using Mathematics, 2020 Duquesne University

#### Modeling The Effects Of Fentanyl And Narcan On The Opioid Epidemic In Allegheny County Using Mathematics, Lindsay Moskal, Lauren Sines, Rachael Neilan Ph.D.

*Undergraduate Research and Scholarship Symposium*

Starting in the 1990s, physicians across the United States have increasingly prescribed opioid pain relievers, which has given rise to the current opioid epidemic. As a result, there has been a drastic increase in the number of overdose fatalities. In 2017, the number of opioid overdose deaths peaked and the U.S. declared the crisis as a public health emergency. One state that has contributed significantly to this epidemic is Pennsylvania, which ranks first for the greatest number of overdose deaths and third for the highest death rate. In fact, Allegheny County has witnessed an overdose death rate that is ...

The Boundary Element Method For Parabolic Equation And Its Implementation In Bem++, 2020 Southern Methodist University

#### The Boundary Element Method For Parabolic Equation And Its Implementation In Bem++, Sihao Wang

*Mathematics Theses and Dissertations*

The goal of this work is to develop a fast method for solving Galerkin discretizations of boundary integral formulations of the heat equation. The main contribution of this work is to devise a new fast algorithm for evaluating the dense matrices of the discretized integral equations.

Similar to the parabolic FMM, this method is based on a subdivision of the matrices into an appropriate hierarchical block structure. However, instead of an expansion of the kernel in both space and time we interpolate kernel in the temporal variables and use of the adaptive cross approximation (ACA) in the spatial variables.

The ...

Spreading Mechanics And Differentiation Of Astrocytes During Retinal Development, 2020 University of Florida

#### Spreading Mechanics And Differentiation Of Astrocytes During Retinal Development, Tracy Stepien, Timothy W. Secomb

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

The Role Of Diversity Amplification For Personal Protection Control Strategies In Vector-Borne Disease Models, 2020 University of Maryland

#### The Role Of Diversity Amplification For Personal Protection Control Strategies In Vector-Borne Disease Models, Jeffery Demers, Sharon Bewick, Justin M. Calabrese, William F. Fagan

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Density-Dependent Development Impacts The Success Of Wolbachia-Based Mosquito Control Programs, 2020 University of the Sciences in Philadelphia

#### Density-Dependent Development Impacts The Success Of Wolbachia-Based Mosquito Control Programs, Alyssa Petroski, Lauren M. Childs, Michael Andrew Robert

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Attraction-Repulsion Taxis Mechanisms In A Predator-Prey Model, 2020 Nova Southeastern University

#### Attraction-Repulsion Taxis Mechanisms In A Predator-Prey Model, Evan C. Haskell

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Parallel-In-Time Simulation Of Biofluids, 2020 Syracuse University

#### Parallel-In-Time Simulation Of Biofluids, Weifan Liu, Minghao Rostami

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

A Model-Based Investigation Of The Role Of Density Dependence In Juvenile Mosquito Development And Survival, 2020 Virginia Polytechnic Institute and State University

#### A Model-Based Investigation Of The Role Of Density Dependence In Juvenile Mosquito Development And Survival, Melody Walker Ms, Lauren M. Childs, Michael A. Robert

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Mathematical Modeling Of Gliding Motility And Its Regulation In Myxococcus Xanthus, 2020 Virginia Polytechnic Institute and State University

#### Mathematical Modeling Of Gliding Motility And Its Regulation In Myxococcus Xanthus, Yirui Chen

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

A Mathematical Framework To Augment Metrics Of Small Intestinal Health, 2020 University of Tennessee, Knoxville

#### A Mathematical Framework To Augment Metrics Of Small Intestinal Health, Cara J. Sulyok, Judy Day, Suzanne Lenhart

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Eco-Evolutionary Dynamics Of Microbial Communities, 2020 University of Idaho

#### Eco-Evolutionary Dynamics Of Microbial Communities, Lihong Zhao

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Emergence, Mechanics, And Development: How Behavior And Geometry Underlie Cowrie Seashell Form, 2020 University of California Berkeley

#### Emergence, Mechanics, And Development: How Behavior And Geometry Underlie Cowrie Seashell Form, Michael G. Levy, Michael R. Deweese

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Mathematical Modeling Of The Car T-Cell Therapy, 2020 St. Mary's College of Maryland

#### Mathematical Modeling Of The Car T-Cell Therapy, Emek Kose, Elizabeth Zollinger, Samantha Elliott

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Tympanal Asymmetry In A Parasitoid Fly: Small Asymmetries Produce Big Gains, 2020 Virginia Polytechnic Institute and State University

#### Tympanal Asymmetry In A Parasitoid Fly: Small Asymmetries Produce Big Gains, Max Mikel-Stites, Anne E. Staples

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

A Mathematical Model To Study The Crime Dynamics Spread Within Minority Communities, 2020 Norfolk State University

#### A Mathematical Model To Study The Crime Dynamics Spread Within Minority Communities, Maila Brucal-Hallare, Beatriz Cuartas, Anne Fernando, Ana Vivas-Barber

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Parameter Estimation For Tear Film Thinning, 2020 University of Delaware

#### Parameter Estimation For Tear Film Thinning, Rayanne Luke

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

The Role Of Variation In Mate Choice And Wolbachia Infection On Aedes Aegypti Population Dynamics, 2020 University of Tennessee

#### The Role Of Variation In Mate Choice And Wolbachia Infection On Aedes Aegypti Population Dynamics, Bernardo Ameneyro

*Biology and Medicine Through Mathematics Conference*

No abstract provided.