Fall 2010

Seminar meets W 3:35 in room 200 LOV. Syllabus for the course.

Seminar schedule

- Aug. 25 no Wed. seminar, go to Friday colloquium of
Nick
Cogan

Speaker: Nick Cogan

Title: Modeling
Biofilm Processes, From Mathematics to Biology

Affiliation: Florida State University

Date: Friday, August 27, 2010

Place and Time: Room 101, Love Building, 3:35-4:30 pm

Refreshments: Room 204, Love Building, 3:00 pm

It is becoming more evident that bacteria outside of the lab setting tend to live is structured communites termed biofilms. This mode of existence is charactarized by aggragates of bacteria enmeshed in a self-produced polymer matrix and imposes constraints on the how the bacteria move, reproduce and react to disinfection external fluid flow. This talk will review the analysis of a sequence of models that explore the impact of these constraints on the bacterial dynamics.

- Sept.
1 Jonathan Bates, Scale-Space Spectral
Representation of Shape

First, we construct a space of representations of shape. In this space, a shape is represented by functions of its intrinsic geometry and the characterization of heat flow on the shape. This representation is called a heat-kernel representation. Second, we equip this space with metrics that derive from spectral representations and the Hausdorff distance. Third, the computational challenge in this shape distance is a minimization problem, which we approach with the Markov chain Monte Carlo algorithm. Fourth, applications are discussed.

- Sept. 8 Margaret Watts, Mechanisms for Full-Length Resets in Pancreatic Islets
- Sept 15 Debbie
Striegel,
Animal Gaits and Symmetry

Patterns arise throughout nature. There are many techniques to better understand biological patterning. Here, the spatio-temporal patterns observed in animal gaits will be reviewed. There are two approaches that are taken. First, a coupled cell system will be used to model patterns observed. Second, group theory will be used to show the possible set of solutions and to give insight to the creation of the patterns observed. Possible applications to cilia will also be discussed.

- Sept 22
Sevgi Sengul, Discrete Fractional
Calculus and its Applicatioin to Tumor Growth

Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real word problems. For instance, one can calculate the "difference" of any function, from 1st order up to the n-th order with some techniques in discrete calculus. However, it is also possible to extend this calculation by means of discrete fractional calculus and consider n any real number such that the ½-th order difference is well defined. In this talk, I demonstrate some basic definitions and properties of discrete fractional calculus while developing the simplest discrete fractional variational theory and the related Euler-Lagrange equation. Also, I will give a proof for Leibniz formula and state and prove the summation by parts formula in discrete fractional calculus. The fractional Gompertz difference equation (FGΔE) will be introduced. I will prove the existence and uniqueness of the solution of (FGΔE) with an initial condition. Then the (FGΔE) will be solved by the method of successive approximation. Finally, some applications will be presented for tumor growth and bacteria growth by use of real data.

- Sept 29 Gregory Toole, Growing Domain Turing
Systems & Cortical Folding

Little is understood about how the folds of the brain's cerebral cortex form and why they are located where they are. One way to investigate cortical folding is by developing a spatio-temporal mathematical model of cortical folding using a Turing reaction-diffusion system on an exponentially growing prolate spheroidal domain. Such a model could be used to make predictions of cortical folding patterns across species and account for cortical folding variability within individuals of a species. In this presentation, I will discuss the growing domain Turing system derived in The effect of growth and curvature on pattern formation (Plaza et al. 2004) and the application of this system to an exponentially growing spherical domain as discussed in Turing patterns on growing spheres: the exponential case (Gjorgjieva and Jacobsen, 2007).

Bursting oscillations are common in neurons and endocrine cells. One type of bursting model with two slow variables has been called "phantom bursting" since the burst period is a blend of the time constants of the slow variables. We describe a measure, which we call the "dominance factor", of the relative contributions of the two slow variables to the bursting produced by a simple phantom bursting model. Using this tool, we demonstrate how the control of different phases of the burst can be shifted from one slow variable to another by changing a model parameter. We then show that the dominance curves obtained as a parameter is varied can be useful in making predictions about the resetting properties of the model cells. We provide experimental data which shows that phase-independent resetting of a burst can be achieved in the electrical activity of pancreatic islets. We demonstrate two mechanisms by which this resetting can be achieved.

- Oct. 6 Faculty Showcase
- Oct 13 Arij Daou, From Birdsongs to
Neural Synapses and Mathematical Modeling

Sequences of motor activity are fundamental elements of animal and human behavior. One of the touchstone questions in neuroscience is how the brain learns and generates these complex sequences; this question entails understanding of the underlying complex neural circuitry responsible for producing these patterns. Like humans, songbirds learn to produce highly stereotyped complex sequences of vocal gestures; their songs. This renders the songbird an excellent model system for studying sequential behavior and complex learned patterns. The learned song pattern is generated by the HVC, a telencephalic nucleus that is analogous to pre-motor cortical regions in mammals. The HVC contains three neural populations: neurons that project to the telencephalic motor output for song (RA), neurons that project to the avian striatum (Area X), and interneurons. These three populations are interconnected, with specific patterns of excitatory and inhibitory connectivity. We have developed a simple ionic current-based computational model that replicates this neural architecture, with the goal of understanding the mechanism for the rhythmic firing patterns that occur in all three neural populations during singing. Specifically, extracellular recordings show that during singing HVC neurons that project to RA produce ~10ms bursts that are time-locked to a specific temporal position within the song pattern. In contrast, HVC neurons that project to Area X spike or burst a few times and HVC interneurons spike or burst densely throughout the song pattern. The mathematical model reproduces these patterns, and shows how the sequence of activity can be stored and directed by the specific excitatory and inhibitory connections between these three types of neurons within the HVC microcircuit. We discuss the elements of the model and the assumptions that are required to produce the appropriate rhythmic behaviors.

- Oct 15 Friday: colloquium James A Moorer, Mathematics Goes to Hollywood

In the last two decades, all parts of
the modern audio and video production have moved to digital
computer-based equipment. As a result, technicians in Hollywood no
longer obsess over film dye lots and camera transport mechanisms, but
are just as likely these days to be found discussing the virtue of
dual-quaternion basis functions for smooth character animation.

This talk will illustrate the invasion of mathematics into the creative process by taking a few concrete examples. I will try to show the remarkable diversity of mathematical disciplines that are employed. While the techniques can generally be described as applied mathematics, they sometimes reveal some thorny theoretical issues as well.

This talk will illustrate the invasion of mathematics into the creative process by taking a few concrete examples. I will try to show the remarkable diversity of mathematical disciplines that are employed. While the techniques can generally be described as applied mathematics, they sometimes reveal some thorny theoretical issues as well.

- Oct. 20
no seminar

- Oct. 27 Prof. Qing-Xiang (Amy)
Sang (FSU Chemistry) Macromolecular
Modulators in Cancer, Stroke, and Stem Cell Research

Cardiovascular diseases, cancer, and stroke are major killers of Americans. Identification of biochemical pathways and molecular mechanisms of disease initiation and progression is a major challenge for biochemical and biomedical researchers. For the success of future personalized medicine, scientists, mathematicians, and clinicians must understand factors and biomarkers that are involved in the pathogenesis of the disease. Matrix metalloproteinases (MMPs) are a family of hydrolytic enzymes that require zinc for catalysis and calcium for protein folding and stability. They are able to cleave extra cellular matrix (ECM), pericellular and cell surface proteins such as growth factors and signal receptors. MMPs are macromolecular modulators in tissue 3-D re-structuring, remodeling, embryonic development, morphogenesis, wound healing, and inflammation, and pathologies related to cancer invasion, angiogenesis, and metastasis, as well as stroke, atherosclerosis, and restenosis.

We and others have cloned, discovered, and biochemically characterized human endometase/matrilysin-2/matrix metalloproteinase-26 (MMP-26) using molecular biology, enzymology and medicinal chemistry approaches. We have identified MMP-26 as a novel putative biomarker for preinvasive stage of human breast and prostate cancer tissues. MMP-26 gene and protein expression levels are very low in normal and benign human tissues but the gene is turn on and the protein is highly expressed in many different human carcinoma cells and tissues. MMP-26 might be involved in the progression from an in situ tumor to an invasive cancer. The complex role of MMP-26 in human cancer invasion and progression remains to be further investigated. In collaboration with Drs. Martin A. Schwartz and Yonghao Jin we have designed, synthesized, and tested more than 300 novel MMP inhibitors and used them to investigate the MMP structure and function relationship in biochemical and cellular systems. The potential applications of MMP inhibitors in cancer and cardiovascular disease, stroke, and stem cell research will be discussed. Some problems in cancer, stroke, and stem cell research that mathematicians may help to solve will also be presented. (Supported by NIH, DOD CDMRP Prostate and Breast Cancer Research Programs, Susan G. Komen Breast Cancer Foundation, Florida Breast Cancer Research Coalition Foundation, Elsa U. Pardee Foundation, and the Florida State University)

- Nov. 3 Rafael Martinez-Vega, Is the inability of hearing the shape of drums enough to be no way able to trace out the shape of objects?
- Nov.
10 Matt Donahue Modeling the
Interaction Between Fluid Flow in Plant Xylem and Biofilm Formation by
Xylella Fastidiosa in Pierce's Disease

There has been a recent explosion of interest in biofilm infections due to the prevalence of the biofilm mode of life as well as the inability to fully eliminate the bacteria within the biofilm. Significant discoveries in biofilm formation involve advances in the understanding of quorum sensing and biofilm "genes". However there has been little attention paid to the formation and development of biofilm diseases in plants; specifically Pierce's Disease which affect grape vines, citrus plants, and some fruit trees. This bacterial infection greatly reduces the amount and quality of produce before eventually killing the plant itself. After a primer on the formation of biofilms and the subsequent complications including the formation of Pierce's Disease, a modeling framework will be proposed using multiphase physics. An investigation of the system will follow featuring linearization and perturbation analysis.

- Nov. 17 Raghu Kanumalla Simple Models of the
Heart, Circulation, and Cardiovascular Diseases

With heart disease and other cardiovascular anomalies threatening the lives of more and more people, understanding this vital organ and its related structures is crucial in the theory and practice of Medicine. Early models of the heart and circulation were formulated by Peskin using simple ideas from electric circuit theory, differential equations and related numerical discretization techniques.

Using Peskin's work as a starting point, one can expand them to understand cardiovascular diseases. One notable disease is Dilated Cardiomyopathy (DCM), which results in weakened cardiac muscle that is unable to efficiently pump blood. This disease affects many people as a result of congenital defects, drug and alcohol abuse, or as a result of illness or other diseases.

Further research using these simple models can be applied to the interaction of the cardiovascular system with other organs such as the lungs and kidneys, and even further to fluid flow problems in obstructed arteries.

- Nov. 24
no seminar
- Dec. 1 Prof. Edward Bernat (FSU Psychology) Time-frequency approaches to disentangling brain processes associated with cognition, emotion, and impulse dysregulation psychopathology.

The 1966 paper "Can one hear the shape of a drum?" by Mark Kac brought up a rather interesting question regarding if the shape of an object can be partially determined by its sound or the sound that it makes (musicians must know something of this by heart!) and its response in 1992 "One cannot hear the shape of a drum" by Gordon, et al... arises interesting modifications to the original question. Rather than just analyzing the Wave Equation, the research done on the Heat Equation has come with rather interesting results that address this topic. A bit about this will be discussed briefly, focusing more on the facts that can be used from its partial responses to the original question as practical tools for image recognition needed for several issues in medical sciences. The use of diverse analytical mathematical tools for surface registration will be described.

Electroencephalographic (EEG)
event-related potential (ERP) measures have attracted renewed interest
in recent years. This is due to several factors. First,
evidence now indicates that EEG and functional magnetic resonance
imaging (fMRI) both index local field potential activity, EEG with
greater time resolution and fMRI with greater spatial resolution.
Second, developments in source localization models now offer reasonable
approaches to inferring neural sources underlying observed EEG/ERP
activity. Finally, new methods, including time-frequency (TF)
analysis, now offer stronger approaches to disentangling neural
activity that overlaps in time but not frequency. The presented
work utilizes these advances to better delineate cognitive and
emotional processes generally, and to assess for disruptions in these
processes related to impulse dysregulation (ID) psychopathology.
For example, reductions in the amplitude of the P300 ERP component are
perhaps the most widely studied neurophysiological indicator of impulse
dysregulation. Unfortunately, standard time-domain measures have
not produced useful decompositions of this activity to make clear
inferences about disruptions in underlying cognitive, emotional, or
neurophysiological processes. P300 and related data will be
presented from both community and incarcerated offender samples that
vary in ID. These analyses will show how multiple processes
concomitant with P300 can be disentangled using TF approaches,
providing a clearer assessment of ID-related activity.