Applied Mathematics Commons^™

Optimal Relaxation Weights For Multigrid Reduction In Time (Mgrit), Masumi Sugiyama

Mathematics & Statistics ETDs

Based on current trends in computer architectures, faster compute speeds must come from increased parallelism rather than increased clock speeds, which are stagnate. This situation has created the well-known bottleneck for sequential time-integration, where each individual time-value (i.e., time-step) is computed sequentially. One approach to alleviate this and achieve parallelism in time is with multigrid. In this work, we consider the scheme known as multigrid-reduction-in-time (MGRIT), but note that there exist other parallel-in-time methods such as parareal and the parallel full approximation scheme in space and time (PFASST). MGRIT is a full multi-level method applied to the time dimension and …

Planck's And Callendar's Blackbody Radiation Formulas And Their Fitness To Experimental Data, Max Tran

Publications and Research

In this paper, we compare the blackbody radiation density formula obtained with classical physics by Hugh L Callendar and the formula obtained by Max Planck using quantization of energy. We use R and Maxima to analyze their fitness on coordinating experimental data and indicate some limitations with experiments in this area.

How Can We Explain Different Number Systems?, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

At present, we mostly use decimal (base-10) number system, but in the past, many other systems were used: base-20, base-60 -- which is still reflected in how we divide an hour into minutes and a minute into seconds -- and many others. There is a known explanation for the base-60 system: 60 is the smallest number that can be divided by 2, by 3, by 4, by 5, and by 6. Because of this, e.g., half an hour, one-third of an hour, all the way to one-sixth of an hour all correspond to a whole number of minutes. In this …

Deep Learning (Partly) Demystified, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

Successes of deep learning are partly due to appropriate selection of activation function, pooling functions, etc. Most of these choices have been made based on empirical comparison and heuristic ideas. In this paper, we show that many of these choices -- and the surprising success of deep learning in the first place -- can be explained by reasonably simple and natural mathematics.

The Graphs That Have Antivoltages Using Groups Of Small Order, Vaidy Sivaraman, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a group Γ of order at most six, we characterize the graphs that have Γ-antivoltages and also determine the list of minor-minimal graphs that have no Γ-antivoltage. Our characterizations yield polynomial-time recognition algorithms for such graphs.

Properly Handling Negative Values In The Calculation Of Binding Constants By Physicochemical Modeling Of Spectroscopic Titration Data, Nathanael P. Kazmierczak, Douglas A. Vander Griend

University Faculty Publications and Creative Works

To implement equilibrium hard-modeling of spectroscopic titration data, the analyst must make a variety of crucial data processing choices that address negative absorbance and molar absorptivity values. The efficacy of three such methodological options is evaluated via high-throughput Monte Carlo simulations, root-mean-square error surface mapping, and two mathematical theorems. Accuracy of the calculated binding constant values constitutes the key figure of merit used to compare different data analysis approaches. First, using singular value decomposition to filter the raw absorbance data prior to modeling often reduces the number of negative values involved but has little effect on the calculated binding constant …

Diabetes And Its Effect On Abdominal Aortic Aneurysm Growth Rate In Hispanic Patients, Monica Betancourt-Garcia, Kristina Vatcheva, Amrit Thakur, Prateek Gupta, Eugene Postevka, Ricardo Martinez, R. Armour Forse

School of Mathematical & Statistical Sciences Faculty Publications

Background

The growth rate of abdominal aortic aneurysms (AAA) can vary depending on age, baseline diameter, blood pressure, race, and history of smoking. Paradoxically, previous studies show evidence of a protective effect of diabetes on the rate of AAA expansion despite its well-established role in the morbidity and mortality of cardiovascular disease. This study aims to investigate the impact diabetes plays on AAA growth within a Hispanic population.

Methods

Data were collected from patients who were predominantly Mexican-American at a single hospital site. Baseline and follow-up measures for AAA diameter were obtained from serial imaging studies. Demographics, medical history, the …

Fluids In Music: The Mathematics Of Pan’S Flutes, Bogdan Nita, Sajan Ramanathan

Department of Mathematics Faculty Scholarship and Creative Works

We discuss the mathematics behind the Pan’s flute. We analyze how the sound is created, the relationship between the notes that the pipes produce, their frequencies and the length of the pipes. We find an equation which models the curve that appears at the bottom of any Pan’s flute due to the different pipe lengths.

Why Does Ramanujan, The Man Who Knew Infinity, Matter?, Ken Ono

Dalrymple Lecture Series

Dr. Ken Ono is the Thomas Jefferson Professor of Mathematics at the University of Virginia, the Asa Griggs Candler Professor of Mathematics at Emory University, and the vice president of the American Mathematical Society.He is an associate producer of the film The Man Who Knew Infinity starring Dev Patel and Jeremy Irons about Srinivasa Ramanujan, a self-trained two-time college dropout who left behind three notebooks filled with equations that mathematicians are still trying to figure out today. Ramanujan claimed that his ideas came to him as visions from an Indian goddess. This lecture is about why Ramanujan matters. The answers …

Mathematics Saves Lives: Models And Signals Enabling Medicine And Biology, Raina Robeva

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Analyzing Student Loan Debt Using Seir Compartmental Model Of Epidemiology, Kavya Ravishankar, Dr. Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Effects Of Excess Nutrients On Tri-Trophic Food Chains In The Aquatic Ecosystem, Lale Asik, Ming Chen, Angela Peace

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Applying Methods Of The Theory Of Heterogeneous Populations To The Problem Of Pathogen Co-Existence, Eric Sarfo Amponsah

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

An Agent-Based Ecological Model Of West Nile Virus For Classroom Use, Stuart Thiel

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

An Agent-Based Modeling Approach For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, Joey Gaudy, Craig Garzella

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Evaluation Of Age- And Risk-Based Mass Drug Administration Policies To Control Soil-Transmitted Helminths: A Mathematical Modeling Study Of Ghana, Mugdha Thakur

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Sperm Motility In Groups, Julie Simons

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Network Structure And Dynamics Of Biological Systems, Deena R. Schmidt

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Parameter Estimation Within An Sir Model Of Chestnut Blight In North America, Anita Davelos Baines, Hope B. Anderson, John S. Mcalister, Robert F. Allen

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Efficient Control Methods For Stochastic Boolean Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Exploring Modeling By Programming: Insights From Numerical Experimentation, Sean Laverty, Brittany E. Bannish

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling And Analysis Of American Chestnut Blight In North America, Robert F. Allen, Anita D. Baines, Hope B. Anderson, John S. Mcalister, Tatum D. Rask, Maia Richards-Dinger

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Network Reconstruction Using Computational Algebra And Gene Knockouts, Matthew Macauley

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Seasonal Dynamics Of Swimmer's Itch And The Efficacy Of Potential Treatment Options, James Peirce

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Quantifying Distribution In Carbon Uptake Across A Global Measurement Network Of Terrestrial Ecosystems, John Zobitz, Madeline Oswood

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Simulating Bacterial Growth, Competition, And Resistance With Agent-Based Models And Laboratory Experiments, Anne E. Yust, Davida S. Smyth

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Effect Of External Perturbations On Ecological Oscillators, Eli Goldwyn

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Beyond The Binary (Part 2): Quantifying Differences In Reproductive Effort Among Life History Strategies In Bromeliaceae, Erin N. Bodine

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Integrating Mathematics And Biology In The Classroom: A Compendium Of Case Studies And Labs, Becky Sanft, Anne Walter

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Design Of Experiments For Unique Wiring Diagram Identification, Elena Dimitrova

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.