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Full-Text Articles in Applied Mathematics

Numerical Approximations Of Phase Field Equations With Physics Informed Neural Networks, Colby Wight Aug 2020

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", Paul-Yvann Djamen 4785403, Paul-Yvann Djamen Jul 2020

"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 ...


Dna Complexes Of One Bond-Edge Type, Andrew Tyler Lavengood-Ryan Jun 2020

Dna Complexes Of One Bond-Edge Type, Andrew Tyler Lavengood-Ryan

Electronic Theses, Projects, and Dissertations

DNA self-assembly is an important tool used in the building of nanostructures and targeted virotherapies. We use tools from graph theory and number theory to encode the biological process of DNA self-assembly. The principal component of this process is to examine collections of branched junction molecules, called pots, and study the types of structures that such pots can realize. In this thesis, we restrict our attention to pots which contain identical cohesive-ends, or a single bond-edge type, and we demonstrate the types and sizes of structures that can be built based on a single characteristic of the pot that is ...


Non-Equilibrium Growth Of Metal Clusters On A Layered Material: Cu On Mos2, Dapeng Jing, Ann Lii-Rosales, King C. Lai, Qiang Li, Jaeyoun Kim, Michael C. Tringides, James W. Evans, Patricia A. Thiel May 2020

Non-Equilibrium Growth Of Metal Clusters On A Layered Material: Cu On Mos2, Dapeng Jing, Ann Lii-Rosales, King C. Lai, Qiang Li, Jaeyoun Kim, Michael C. Tringides, James W. Evans, Patricia A. Thiel

Chemistry Publications

We use a variety of experimental techniques to characterize Cu clusters on bulk MoS2 formed via physical vapor deposition of Cu in ultrahigh vacuum, at temperatures ranging from 300 K to 900 K. We find that large facetted clusters grow at elevated temperatures, using high Cu exposures. The cluster size distribution is bimodal, and under some conditions, large clusters are surrounded by a denuded zone. We propose that defect-mediated nucleation, and coarsening during deposition, are both operative in this system. At 780 K, a surprising type of facetted cluster emerges, and at 900 K this type predominates: pyramidal clusters with ...


Modeling The Effects Of Fentanyl And Narcan On The Opioid Epidemic In Allegheny County Using Mathematics, Lindsay Moskal, Lauren Sines, Rachael Neilan Ph.D. May 2020

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, Lindsay Moskal, Lauren Sines, Rachael Neilan Ph.D. May 2020

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++, Sihao Wang May 2020

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, Tracy Stepien, Timothy W. Secomb May 2020

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, Jeffery Demers, Sharon Bewick, Justin M. Calabrese, William F. Fagan May 2020

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, Alyssa Petroski, Lauren M. Childs, Michael Andrew Robert May 2020

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, Evan C. Haskell May 2020

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, Weifan Liu, Minghao Rostami May 2020

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, Melody Walker Ms, Lauren M. Childs, Michael A. Robert May 2020

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, Yirui Chen May 2020

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, Cara J. Sulyok, Judy Day, Suzanne Lenhart May 2020

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, Lihong Zhao May 2020

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, Michael G. Levy, Michael R. Deweese May 2020

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, Emek Kose, Elizabeth Zollinger, Samantha Elliott May 2020

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, Max Mikel-Stites, Anne E. Staples May 2020

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, Maila Brucal-Hallare, Beatriz Cuartas, Anne Fernando, Ana Vivas-Barber May 2020

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, Rayanne Luke May 2020

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, Bernardo Ameneyro May 2020

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.


Using Network Modeling To Understand The Relationship Between Sars-Cov-1 And Sars-Cov-2, Elizabeth Brooke Haywood, Nicole A. Bruce May 2020

Using Network Modeling To Understand The Relationship Between Sars-Cov-1 And Sars-Cov-2, Elizabeth Brooke Haywood, Nicole A. Bruce

Biology and Medicine Through Mathematics Conference

No abstract provided.


Exploring The Effect Of The Nestling Recruitment Curve On Enzootic West Nile Virus Transmission, Emily B. Horton May 2020

Exploring The Effect Of The Nestling Recruitment Curve On Enzootic West Nile Virus Transmission, Emily B. Horton

Biology and Medicine Through Mathematics Conference

No abstract provided.


Decision Tree For Predicting The Party Of Legislators, Afsana Mimi May 2020

Decision Tree For Predicting The Party Of Legislators, Afsana Mimi

Publications and Research

The motivation of the project is to identify the legislators who voted frequently against their party in terms of their roll call votes using Office of Clerk U.S. House of Representatives Data Sets collected in 2018 and 2019. We construct a model to predict the parties of legislators based on their votes. The method we used is Decision Tree from Data Mining. Python was used to collect raw data from internet, SAS was used to clean data, and all other calculations and graphical presentations are performed using the R software.


Hadamard Well-Posedness For Two Nonlinear Structure Acoustic Models, Andrew Becklin May 2020

Hadamard Well-Posedness For Two Nonlinear Structure Acoustic Models, Andrew Becklin

Dissertations, Theses, and Student Research Papers in Mathematics

This dissertation focuses on the Hadamard well-posedness of two nonlinear structure acoustic models, each consisting of a semilinear wave equation defined on a smooth bounded domain $\Omega\subset\mathbb{R}^3$ strongly coupled with a Berger plate equation acting only on a flat portion of the boundary of $\Omega$. In each case, the PDE is of the following form: \begin{align*} \begin{cases} u_{tt}-\Delta u +g_1(u_t)=f(u) &\text{ in } \Omega \times (0,T),\\[1mm] w_{tt}+\Delta^2w+g_2(w_t)+u_t|_{\Gamma}=h(w)&\text{ in }\Gamma\times(0,T),\\[1mm] u=0&\text{ on ...


Non-Linear Modifications Of Black-Scholes Pricing Model With Diminishing Marginal Transaction Cost, Kaidi Wang May 2020

Non-Linear Modifications Of Black-Scholes Pricing Model With Diminishing Marginal Transaction Cost, Kaidi Wang

Undergraduate Honors Theses

In the field of quantitative financial analysis, the Black-Scholes Model has exerted significant influence on the booming of options trading strategies. Publishing in their Nobel Prize Work in 1973, the model was generated by Black and Scholes. Using Ito’s Lemma and portfolio management methodology, they employed partial differential equation to provide a theoretical estimate of the price of European-style options.

This paper is interested in deriving non-linear modifications of the Black-Scholes model with diminishing marginal transaction cost.


Stage-Structured Blue Crab Population Model With Fishing, Predation And Cannibalism, Fangming Xu May 2020

Stage-Structured Blue Crab Population Model With Fishing, Predation And Cannibalism, Fangming Xu

Undergraduate Honors Theses

Blue crab is a species of crab commonly found in the waters of the western Atlantic Ocean. It is one of the most important shellfish in the Chesapeake Bay. The blue crab fishing industry has a notable impact on the local economy, and blue crabs form a key link in the Chesapeake Bay food web. Between the mid-1990s and 2004, the blue crab population dropped by two thirds. Factors such as habitat loss, harvest pressure and climate change may have contributed to the decline. However, there hasn’t been enough research on the long term dynamic equilibrium, making it difficult ...


Dynamics Of Sensory Integration Of Olfactory And Mechanical Stimuli Within The Response Patterns Of Moth Antennal Lobe Neurons, Harrison Tuckman May 2020

Dynamics Of Sensory Integration Of Olfactory And Mechanical Stimuli Within The Response Patterns Of Moth Antennal Lobe Neurons, Harrison Tuckman

Undergraduate Honors Theses

Odors emanating from a biologically relevant source are rapidly embedded within a windy, turbulent medium that folds and spins filaments into fragmented strands of varying sizes. Environmental odor plumes therefore exhibit complex spatiotemporal dynamics, and rarely yield an easily discernible concentration gradient marking an unambiguous trail to an odor source. Thus, sensory integration of chemical input, encoding odor identity or concentration, and mechanosensory input, encoding wind speed, is a critical task that animals face in resolving the complex dynamics of odor plumes and tracking an odor source. In insects, who employ olfactory navigation as their primary means of foraging for ...


Learning & Planning For Self-Driving Ride-Hailing Fleets, Jack Morris May 2020

Learning & Planning For Self-Driving Ride-Hailing Fleets, Jack Morris

Undergraduate Honors Theses

Through simulation, we demonstrate that incorporation of self-driving vehicles into ride-hailing fleets can greatly improve urban mobility. After modeling existing driver-rider matching algorithms including Uber’s Batched Matching and Didi Chuxing’s Learning and Planning approach, we develop a novel algorithm adapting the latter to a fleet of Autos – self-driving ride-hailing vehicles – and Garages – specialized hubs for storage and refueling. By compiling driver-rider matching, idling, storage, refueling, and redistribution decisions in one unifying framework, we enable a system-wide optimization approach for self-driving ride-hailing previously unseen in the literature. In contrast with existing literature that labeled driverless taxis as economically infeasible ...