Physical Sciences and Mathematics Commons^™

Tumor Dynamics Under Immunotherapy: A Time-Delay Revised Predator-Prey Model, Emma A. Turian

Faculty Research and Creative Activities Symposium

Cancer remains a leading cause of death worldwide and traditional treatments such as surgical resection, chemotherapy, and radiotherapy may have limited benefits depending on the type of cancer and the stage at which it is diagnosed. Immunity is the state of protection against foreign pathogens or substances (i.e., antigens). Recent research into novel approaches to treatment has suggested that immunotherapy, which aims to optimize the body’s own natural responses to combating disease through various mechanisms, may be a promising strategy that can improve prognosis for certain cancer types that are refractory to other treatment options. Quantitative models simulating the dynamics …

Internet Searching Behaviors Of Low Literacy Breast Cancer Survivors, Francisco D. Iacobelli, Ginger L. Dragon, Giselle Mazur, Judy Guitelman

Faculty Research and Creative Activities Symposium

Internet searching is a popular tool for patients to find health-related information. However, low literacy individuals are at a disadvantage with respect to their ability to evaluate online health information. When using common web search engines to find health information, behaviors such as misspelling, misappropriation of words and incomplete search queries can result in inadequate results and misleading information. The goal of this research is to understand the search strategies and common mistakes that low-literacy Latina breast cancer survivors exhibit when searching for information online in order to inform future information seeking interfaces. To explore search behaviors online we asked …

Newton’S Iteration At Nonisoated Solutions, Zhonggang Zeng

Faculty Research and Creative Activities Symposium

Newton’s iteration is arguably the most important and fundamental method for solving systems of nonlinear equations with a long and fascinating history. Its local quadratic convergence to isolated nonsingular solutions is well documented in the literature. It is also well-known that the iteration loses its quadratic rate of convergence, if it applies and converges at all, to nonisolated solutions with a dismal attainable accuracy in numerical computation. Even though solving systems of nonlinear equations is a standard topic in textbooks of numerical analysis, the elaboration has always been limited to isolated solutions. Models with nonisolated solutions frequently arise in applications. …

How Good Are Standard Copulas Anyway?, Dragan Radulovic

Mathematics Colloquium Series

First, we will raise a question: How good are standard copulas in capturing the dependency structure? To this end we will offer a series of simulated/numerical examples demonstrating that, more often than not, standard model copulas do not capture the underlying dependency structure. We believe that copula models, unlike other statistical tools, are too readily accepted by practitioners. Rigorous, goodness-of-fit tests are commonly replaced by off-hand statements like: “it works well”. To this end, the second part of the talk offers a theoretical result, an umbrella type theorem tailored for creating numerous Goodness of Fit tests for copulas.

Algebraic Frames And Ultrafilters, Papiya Bhattacharjee

Mathematics Colloquium Series

A frame, also known as pointfree topology, is a complete lattice that satisfies a strong distributive property, known as the 'frame law.' Originally, the study of frames began as studying topological spaces without points, hence the name pointfree topology. Due to this connection, different topological concepts can be generalized to frames, for example, compactness. In the first part of the talk, I will explain the basic notions of frames and their connection with topology. It turns out that we can find frame structure in other categories than topological spaces. For example, given a commutative ring R with identity, the lattice …

How Mathematics Can Help Winning The War Against Cancer?, Peng Feng

Mathematics Colloquium Series

In this talk, I will present a few mathematical models that aims to understand how our immune system interact with cancer cells. In particular, we focus on a model that studies the role or regulatory T cells. Recent advance in the field of regulatory T cell reveals that it plays a vital role during immunotherapy. For example, a higher ratio between regulatory T cells and effector T cells within tumor tissue is associated with worse prognoses in many cancers, including ovarian cancer (Leffers et al., 2009), lung cancer (Tao et al., 2012), glioblastoma (Sayour et al., 2015). On the other …

Sdrap: An Annotation Pipeline For Highly Scrambled Genomes, Jasper Braun

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.

Mathematical Models For Describing Molecular Self-Assembly, Margherita Maria Ferrari

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.

Loop Homology Of Bi-Secondary Structures, Andrei Bura

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.

The Energy-Spectrum Of Bicompatible Sequences, Wenda Huang

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

On An Enhancement Of Rna Probing Data Using Information Theory, Thomas J.X. Li, Christian M. Reidys

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Topology And Dynamics Of Gene Regulatory Networks: A Meta-Analysis, Claus Kadelka

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Control Methods To Manage The Sylvatic Plague In Black-Tailed Prairie Dog Towns, David C. Elzinga, Shelby R. Stowe, Leland Russell

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Using Agent-Based Modeling To Investigate The Existence Of Herd Immunity Thresholds For Infectious Diseases On Randomly Generated Contact Networks, Hannah Callender Highlander, Owen Price

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Oscillation In Mathematical Epidemiology, Meredith Greer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Study On Discrete And Discrete Fractional Pharmacokinetics-Pharmacodynamics Models For Tumor Growth And Anti-Cancer Effects, Ferhan Atici, Ngoc Nguyen

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Model For Cross-Institutional Collaboration: Addressing Diminishing Resources In Academia, Claudia Kolakowski

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Research For Educators: Modeling Graph Theory For Nontraditional Math Researchers, Erwin Cornelius

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Using Slow-Fast Dynamical Systems To Understand Regime Shifts In Ecology, Ting-Hao Hsu

Mathematics Colloquium Series

In ecology, regime shifts are continual rapid change between different long-lasting dynamics. For instance, rapid evolutionary changes have been observed in a wide variety of organisms, both in predators and in prey. Another example is disease outbreak, where a system exhibits qualitative changes after long periods of apparent quiescence. Using the theory of slow-fast dynamics, for systems of differential equations with sufficiently large separation of time scales we derive conditions under which regime shifts occur. This is joint work with Shigui Ruan and Gail Wolkowicz.

The Last Digits Of Infinity (On Tetrations Under Modular Rings), William Stowe

Celebration of Learning

A tetration is defined as repeated exponentiation. As an example, 2 tetrated 4 times is 2^(2^(2^2)) = 2^16. Tetrated numbers grow rapidly; however, we will see that when tetrating where computations are performed mod n for some positive integer n, there is convergent behavior. We will show that, in general, this convergent behavior will always show up.

Nonstandard Dice That Both Count For Card Craps, Mark Bollman

International Conference on Gambling & Risk Taking

The Pala Casino in California deals Card Craps using a red die numbered {2; 2; 2; 5; 5; 5} and a blue die numbered {3; 3; 3; 4; 4; 4}. Two cards from a special 36-card deck, which contains one card bearing each of the 36 ways in which two dice can land when rolled, are dealt: one each face down to a red space and a blue space. When the dice are rolled, the higher number determines which of the cards is flipped over.

A moment's reflection reveals that Pala's blue die is unnecessary. The card selection process can …

Lecture 10, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Continuation of Fyodorov--Keating conjectures, connections with random multiplicative functions.

Lecture 9, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Fyodorov--Keating conjectures, connections with random multiplicative functions.

The Weyl Bound For Dirichlet L-Functions, Matthew P. Young

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Abstract: In the 1960's, Burgess proved a subconvexity bound for Dirichlet L-functions. However, the quality of this bound was not as strong, in terms of the conductor, as the classical Weyl bound for the Riemann zeta function. In a major breakthrough, Conrey and Iwaniec established the Weyl bound for quadratic Dirichlet L-functions. I will discuss recent work with Ian Petrow that generalizes the Conrey-Iwaniec bound for more general characters, in particular arbitrary characters of prime modulus.

Extension Of A Positivity Trick And Estimates Involving L-Functions At The Edge Of The Critical Strip, Xiannan Li

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Updated schedule

Abstract: I will review an old trick, and relate this to some modern results involving estimates for L-functions at the edge of the critical strip. These will include a good bound for automorphic L-functions and Rankin-Selberg L-functions as well as estimates for primes which split completely in a number field.

Lecture 8, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Continuation of Extreme values of L-functions.

Lecture 7, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Extreme values of L-functions.