Department of Mathematics

Hypernetworks, sometimes called hypergraphs, generalize the concept of a graph by allowing edges to join any number of vertices, gaining the ability to capture multi-way relationships in data. This hy... More

This talk will survey the author's research on social evolution.

The spread of disease is significantly impacted by human behaviour. In particular, homophily ("bird of a feather flock together") and outgroup aversion can affect disease transmission rates and the up... More

The cortical folding of the brain, made up of gyri and sulci, plays a significant role in brain function and is unique to the individual. Abnormalities in cortical folding have been associated with di... More

The outcome of democratic elections rests on individuals' decision-making that is driven by their varying preferences and sets of information. Individuals may prefer consensus to deadlock, or deadlock... More

Mounting empirical research suggests that the stroma, or interface between healthy and cancerous tissue, is a critical determinate of cancer invasion. At the same time, a cancer cell’s location and ... More

In the last two decades, network science has become known as a critical model for understanding complex systems across a wide range of fields. At its core, network science considers a system as a coll... More

Experimentalists have observed that male cicada killer wasps (Sphecius speciosus) will redraw the boundaries of their territories to coincide with wooden dowels randomly scattered in a field. This is ... More

Individuals infected with Human Immunodeficiency Virus (HIV) have a higher risk of developing certain type of cancers, such as Kaposi sarcoma, than individuals not infected with HIV. This is due to th... More

Improvements in drug regimens can make a difference in both clinical trial success and patient outcomes. Optimal control can be used to mathematically optimize regimens, which can then be tested exper... More

I will discuss several aspects of math modeling jobs in the biopharma industry. This includes the types of problems industry math modelers work on, and how their jobs compare with academic jobs. I wil... More

Voluntary vaccination policies are a source of great contention, particularly when individuals weigh self-interests against an already obtained herd immunity. This talk will cover a game theoretical a... More

Voluntary vaccination policies are a source of great contention, particularly when individuals weigh self-interests against an already obtained herd immunity. This talk will cover a game theoretical a... More

Allometric scaling relations, including the 3/4 power law for metabolic rates, are characteristic of all organisms. This talk will discuss a model of scaling relations that predicts structural and fun... More

Stochastic modeling and analysis can help answer pressing medical questions. In this talk, I will attempt to justify this claim by describing recent work on two problems in medicine. The first problem... More

Brain structures change shape dramatically during development. This talk will discuss and review the literature on the tension-based morphogenesis hypothesis, which posits that mechanical tension alon... More

Insulin is secreted in pulses by beta-cells located within regions of the pancreas called islets of Langerhans. The pulsatility is evident in blood insulin measurements, indicating that the islet popu... More

We live in a society. Societies depend on costly cooperation between unrelated individuals who have little prospect for repeated interactions––and thus little clear incentive to cooperate. How can... More

We will have an organizational meeting for the seminar series this semester.

Most pathogens can infect multiple host species, which means that the loss or addition of a host species can alter levels of disease in the community. I use SIR-type epidemiological models to explore ... More

This talk will be a survey of papers on theoretical ecology, particularly covering the interactions of symbionts and hosts. These models have applications to interactions between corals and algae, and... More

Many collective phenomena in Nature emerge from the -partial- synchronization of the units comprising a system. In the case of the brain, this self-organized process allows groups of neurons to fire i... More

In this talk, I will walk through the typical steps I go through to analyze a problem. To do this, I will consider a simple birth-death process. Such a process has a master equation representation and... More

Extraction of information from datasets that are high-dimensional, incomplete and noisy poses significant challenges. Advanced mathematical techniques are under development to address these. One notab... More

We will acquaint the audience with the graph Laplacian matrix, presenting it in both its combinatorial and random walk form. We will then delve into its key spectral properties, demonstrating how it s... More

This talk will be a survey of several papers in social dynamics of biological systems. I will discuss several mathematical models that feature social phenomena including disease spread, reputations, s... More

This talk will be a survey of several papers in social dynamics of biological systems. I will discuss several mathematical models that feature social phenomena including disease spread, reputations, s... More

Complex dynamical systems in biological domains often show sudden major changes, or tipping points, as the system gradually changes. Examples include mass extinctions in an ecosystem, deforestation, a... More

In this second part, we will discuss how networks are characterized topologically from a statistical standpoint. Specifically, we will explore scale-free networks as an example. Additionally, we will ... More

Evolutionary game theory is applied throughout biomathematics and economics. In this seminar, I will present some fundamental concepts and survey their applications. Of particular interest will be und... More

Network science has emerged as an interdisciplinary field over the last two decades, primarily concerned with the study of complex systems, particularly in the realm of biology. These networks serve a... More

This talk will provide an introduction to game theory and its applications to solving problems in biology and economics. I will cover fundamental ideas of (evolutionary) game theory, including Nash an... More

The organizer will briefly explain the structure of the series of seminars and students will introduce themselves.

Information in the brain is encoded in the timing of electrical impulses generated by neurons, or spike trains. The neural code refers to the rules that transform these electrical impulses into percep... More

The human brain is unique in its folding patterns across individuals in the extent, depth, and shape of the cortical folds and valleys. There is no consensus in neurobiology regarding how or where the... More

Neuronal polarization refers to the common emergence of a single axon and multiple dendrites in a mature neuron from the symmetrically arranged equilateral neurites of a nascent neuron. The polarizati... More

The “slow configuration response” problem has been the bottleneck issue in the field of molecular dynamics sampling. This issue has been significantly limiting actual sampling capability of the en... More

The endocrine cells of the anterior pituitary gland are electrically active when stimulated or, in some cases, when not inhibited. The activity pattern thought to be most effective in releasing hormon... More

Time for students to discuss their work.

Action potentials resulting from periodic stimulation of nerve axons occur at intervals that are irregular at moderate stimulation frequencies. Histograms of the intervals are multimodal, as seen in s... More

This will be a joint seminar with the Undergraduate Mathematics Major Seminar. Note the room change.

The speaker will present the paper of Ha et al. The abstract of the paper follows below:



Type 2 diabetes (T2D) is generally thought to result from the combination of 2 metabolic defects... More

The speaker will discuss the paper "Nonlinear Dynamics of Immunogenic Tumors: Parameter Estimation and Global Bifurcation Analysis" by Kuznetsov et al. The abstract of the paper is:



We ... More

We will give a brief overview of topological data analysis and how it has been applied to biological systems. We'll then discuss work that we did applying topological data analysis to video of C. eleg... More

Human Immunodeficiency Virus (HIV) is a virus that attacks white blood cells in our immune system, specifically the CD4+ T cells, which is used to help fight infections. It turns out that people with ... More

Unlike DNA, RNA is single stranded and folds via bonds between pairs of complementary nucleotides while it is still being synthesized from DNA. One central problem in molecular biology is understandin... More

The Speaker will present the paper "Temperature Dependence of Vegetative Growth and Dark Respiration: A Mathematical Model" by Martin P. N. Gent and Herbert Z. Enoch.



Abstract: A mathe... More

The field of neural decoding studies how neurons transmit information in their electrical signals. Decoding has traditionally been dominated by a rate-oriented perspective, which largely ignores the p... More

Students are encouraged to attend the colloquium talk of Nick Miller instead.

Multiphase models have been extensively used to describe the dynamics in applications where multicomponent physics play a role. Rather than resolve the components at the microscope, macroscopic closur... More

In this week’s Biomath Seminar, I will discuss multiple topics such as: how I learned of an internship opportunity at Takeda Pharmaceuticals, what my twelve-week, virtual, experience was like, what ... More

Lattice models have a rich history in biological modeling. They provide a valuable framework for modeling complex spatiotemporal dynamics in biological tissues---thereby forming a viable alternative t... More

Pseudomonas aeruginosa biofilms in cystic fibrosis (CF) infections are initiated by individual bacteria that produce various types of extracellular polymeric substances (EPS). The major components of ... More

Insulin is released in pulses from beta cells in pancreatic islets. There are around one million islets in the human pancreas. The fact that we observe clear, high amplitude pulses of insulin in the b... More

In this presentation I will give an overview of my research involving conformal flat maps of the human brain. The functional processing of the brain mainly occurs on the surface, in the cerebral corte... More

Despite many advances in the treatment of triple negative breast cancer, the available treatment options are still quite limited and not broadly successful for improving tumor response. Recent treatme... More

Electrical bursting oscillations in neurons and endocrine cells are activity patterns that facilitate the secretion of neuro-

transmitters and hormones, and have been the focus of study for sev... More

Pituitary cells secrete hormones that regulate most functions of the body. Like neurons, they exhibit electrical activity, and it is this activity that regulates hormone secretion. In particular, burs... More

In this presentation I will give an overview of my research involving cortical pattern formation and conformal flat maps of the human brain. I will discuss some of biological theories of cortical fold... More

An axon is the longest protrusion from a neuron, which can be thousands of times longer than the cell body. A natural question is how the neuron controls the length of the axon. A recently proposed me... More

Canine distemper outbreak modeled in an animal shelter by Dantzler, et al. focused on modeling the spread of the canine distemper virus (CDV) through a local animal shelter. For this presentation, we ... More

In epidemic models, we would like to determine the behavior of an infectious disease (i.e., will we have an epidemic or not). It turns out that you just need to look at a number, called the Basic Repr... More

Merge trees can be a useful tool in topological data analysis. They can be used to extract certain topological features of a dataset for comparison or analysis. For this presentation, we will first ... More

TBA

Please note the date change for this week. Instead of meeting on March 3 at 3:05 pm we will meet on March 4 at 1:20pm.

This talk is designed to explore the relationship between disease spread ... More

This week's seminar will be via a Discussion Board. We will not be meeting in person via Zoom.

For this week's seminar please read the following paper:

Bodner et al. (2021) Ten simple ru... More

The gut microbiota plays a vital role in managing our body's functions -- the microbiota determines health in our gut. Laxative treatment is applied to alleviate the gut problem. Thus, it creates tran... More

In this presentation I will introduce the method of circle packing and how my research group is applying it to create conformal maps of the brain. Motivation for using conformal maps in neuroscience w... More

In this presentation, I will discuss a mathematical model that represents how the visual field is processed by the visual cortex of the visual brain. It turns out that this map is a conformal map and ... More

In this presentation, I will discuss a mathematical model that represents how the visual field is processed by the visual cortex of the visual brain. It turns out that this map is a conformal map and ... More

The human brain is one of the most complex biological geometrical objects. The Human Connectome Project aims to make available an unparalleled compilation of neural functional and structural imaging d... More

One of the great challenges for cancer treatment is the inability to optimize therapy. Without a reasonable mathematical framework, our ability to select treatment regimens for the individual patient ... More

We have developed a new mathematical model of cerebral cortical folding development. The model is time-dependent, nonlinear, 2D, and therefore more biologically relevant than the previous models of ce... More

Inappropriate and excessive food intake-related obesity can contribute to the increased risk of developing diabetes. Diabetes mellitus type 2 has been described as a novel global epidemic characterize... More

Early afterdepolarizations (EADs) are pathological voltage fluctuations that can occur in cardiac cells. These fluctuations have been shown to be a major source of potentially fatal arrhythmias. In th... More

In this seminar, I will describe three focus areas of my research group. We study birds; in particular, the neural basis for song production in the male zebra finch. My group contributes to this study... More

Biochemical reactions are continuously taking place in all living organisms and

most of them involve molecules called enzymes, which act as remarkably efficient

catalysts. Enzymes react... More

Attend Mathematics Colloquium on October 4 as the speaker will be a Biomath speaker.

Joint work with RL Hyson, F Johnson, R Bertram.



Abstract:

The resting membrane potential of a neuron is determined primarily by subthreshold currents, including the leakage cur... More

Biofilms are aggregates of bacteria and secreted polymers that form on almost any surface including ship hulls, catheters, teeth and within the mucus lining the lungs. Understanding the interplay betw... More

In this presentation I will give an overview of my research involving cortical pattern formation and conformal flat maps of the human brain. I will discuss some of biological theories of cortical fold... More

Recent Modeling and Simulation Results of a Biomechanical Model of Cortical Folding

In this talk I will discuss the emergence of hyperbolic geometry, how it was developed over time, and its applications.

We will discuss how vision is processed by the brain and formulate a mathematical model that represents the mapping between the visual field and the visual cortex.

Infection with Hepatitis C Virus (HCV) has reached epidemic proportions; it is one of the least tested for, but often one of the most dangerous silent killers among American men. Individuals with chro... More

We will formulate a mathematical model for EEG cortical source localization when the electrical source of brain activity is modeled as a dipole.

The gastric mucus layer is widely recognized to serve a protective function, shielding the stomach wall from the extremely low pH and digestive enzymes present in the stomach lumen.

Often descr... More

The dispersion of passive tracers in laminar shear flow is a classic problem in fluid dynamics. The boost in the tracer dispersion due to the interplay between advection and diffusion was first descri... More

Based on a lecture series by Ran Levi, this talk is a crash course in basic algebraic topology for scientists with a basic background in mathematics. We introduce simplicial complexes, discuss graphs,... More

Based on a lecture series by Ran Levi, this talk is a crash course in basic algebraic topology for scientists with a basic background in mathematics. We introduce simplicial complexes, discuss graphs,... More

The dispersion of passive tracers in laminar shear flow is a classic problem in fluid dynamics. The boost in the tracer dispersion due to the interplay between advection and diffusion was first descri... More

The gastric mucus layer is widely recognized to serve a protective function, shielding the stomach wall from the extremely low pH and digestive enzymes present in the stomach lumen.

Often descr... More

Introduction to multiphase models, how to formulate them and how to simulate/analyze them with emphasis on biomedical applications

Tolerant bacteria enmeshed in a biofilm causes several difficult to treat illnesses like tuberculosis, chronic pneumonia, and chronic inner ear infections. These diseases typically respond poorly to a... More

When the mechanical stress in a structure becomes large, certain n

onlinearities in the material properties force you to abandon linear material mo

dels. The Nonlinear Structural Materia... More

Note the new meeting time for this week only.

Please attend the ATE defense of Canlin Zhang.

Last time, I discussed different conformal invariants that can be

calculated on discrete meshes. We will continue on with this discussion, showing

images and results for external length... More

The Mathematics of Infectious Disease by Herbert W. Hethcote from SIAM Review will be discussed. The abstract for the paper is as follows:



Many models for the spread of infectious disea... More

Methods that are generally applicable and practical procedures for nonlinear finite element analysis will be presented.

Diseases such as tuberculosis, chronic pneumonia, and inner ear infections are caused by bacterial biofilms. Many studies show that it is much more difficult to kill the bacteria in planktonic and bio... More

Circle packing is a quasi-conformal method used with triangulations. By superimposing a triangulated mesh on the cortical surface, we are able to apply this method to create cortical "flat" maps, or m... More

Canine distemper virus (CDV) is a highly contagious virus that can cause outbreaks, specifically in crowding situations, such as an animal shelter, in which a large number of susceptible dogs are brou... More

I will discuss some of the results and research questions regarding conformal mapping and brain mapping that I am working on.

I will discuss some topics that every graduate student should know (but often know one tells you!), including mathematics societies, conferences, travel funding, research databases, etc.

My reearch uses conformal maps to create "flat" maps of the brain. I will discuss some of the mathematics of circle packing and how it can be used to create quasi-conformal maps of the brain.

Prostate cancer is the second most common cancer in neared there is currently no cure. Many different treatments are used to slow its progression, prevent and delay relapse, and provide a better quali... More

In a paper published in Human Brain Mapping this past May, Papenberg et. al conducted an experiment using magnetic resonance imaging data to investigate one aspect of the brain maintenance hypothesis,... More

In this presentation, I will give pointers and tips of some of the

things I wish I had been told as a graduate student to help me prepare for a future job. Topics will include C.V.s, resumes, g... More

The dynamics of oscillating bubbles has been studied since Lord Rayleigh's original 1917 paper. Back then, the focus of bubble research was largely Naval-based. For example, how to reduce the drag pro... More

This talk will be an overview of topics in modeling of biofilms.

Glioblastoma is by far the most common and most malignant of glial tumors. With standard treatment, the median survival of adults diagnosed with high-grade gliomas is only 12 ? 14.6 months.

... More

In this presentation, I will give an overview of some of biological theories of cortical folding pattern formation. I will then discuss some of the mathematical models I am developing to help answer q... More

Understanding the genetic basis of phenotypic variation in organisms is a central problem in developmental and evolutionary biology. In plant science, to gain insights on such problems as how plants r... More

Traditional descriptors such as the mean and the covariance matrix give useful global summaries of data and probability measures. Nevertheless, when distributions with more complex topological and ge... More

While the immune system is extraordinarily complex and powerful, and medical advancements are more spectacular than ever, in recent history we have seen the unfortunate failure of both processes (immu... More

While contests can help an individual secure access to vital resources, the energy or time necessary to engage in contest behavior can be detrimental. Consequently, several factors play a role in deci... More

Johnna Barnaby will discuss "A Simple Mathematical Model Based on the Cancer Stem Cell Hypothesis Suggests Kinetic Commonalities in Solid Tumor Growth", by R. Molina-Pena et. al, PLoS One, 7: e26233, ... More

Knotted and linked DNA cause complications during DNA replication and transcription, and therefore simplifying these topological forms is essential. DNA topology simplification is usually mediated by ... More

In shape classification problems the main objective is to separate different groups away from each other while keeping the samples belong to same class as close as possible. In this talk, we will intr... More

Striegal and Hurdal have previously developed a mathematical model for cortical folding pattern formation during development. In this model, a Turing reaction-diffusion system and a prolate spheroid d... More

Classical game theory predicts that respect for ownership "Bourgeois" behavior can arise as an arbitrary convention to avoid costly fights. The same theory also predicts that disrespect for ownership ... More

The groups in some networks may have the overlap. We temporarily call these kind of groups as "covers".However, none of the methodologies of identifying the modules can identify covers.We propose a me... More

We study a mathematical model based on two cell phenotypes,

one more migratory and the other more proliferative, with transition between them. This presentation has two parts. First, we presen... More

Quantitative analysis of gene expression domains and investigation of relationships between gene expression and developmental and phenotypic outcomes are central to advancing our understanding of the ... More

My goals for this talk are to explain the two major classes of models that are used in theoretical work on competition, and to provide an example of each type of model and what they can be used for vi... More

Alopecia areata is an autoimmune disease characterized by the formation of distinct patterns of hair loss. The causes of the disease are not completely understood, and treatment is often problematic. ... More

Winner and loser effect is a phenomenon prevails in animal behavior that aggressive behavior may be affected by prior contest experiences. For example a winner in the current contest is more likely to... More

Modeling papers on (i) facial landmarks and (ii) immune system dynamics will be discussed.

A basic two strategy six player game modeling spatial decision making in African Elephants is extended to include multiple spatial and temporal strategies and an arbitrary population. Data from Ambose... More

The data processing pipeline from MRI acquisition to conformal brain maps involves many steps, each one being a research field in their own right. In this presentation, I will give an overview of anat... More