Interdisciplinary Seminar Series in Mathematical Biology, Spring 2007
Organizing departments: Mathematics, Biology and Computer Science, UMass Dartmouth
Time and Place: Group I Room 218, Wed. 3pm – 4pm
Contacts: Jae-Hun Jung (Mathematics) jjung at umassd dot edu
Eli Stahl (Biology) estahl at umassd dot edu
Li Shen (Computer Science) lshen at umassd dot edu
(Supported by Mathemaitcs Department, Art and Science Dean's Office, UMassD BioMedical Engineering Program)
Schedule
|
Date |
Speaker |
Affiliation |
Research |
Title/Abstract |
Special Time/Place |
|
Feb. 14 |
Cathy Ann Clark |
Mathematics, UMassD
and the Naval Undersea Warfare Center |
Acoustics, Fishery, Schooling |
Modeling population dynamics with difference equations and undersea naval and biological acoustics |
|
|
21 |
Miriam Goldberg |
EpiVac Inc. |
Computational Biology |
|
Cancelled |
|
28 |
Gary Davis |
Mathematics, UMassD |
Nonlinear Time Series Analysis |
Deterministic structure in the chromosome of Mycoplasma genitalium |
|
|
Mar. 14 |
Heng Huang |
Computer Science and Engineering, University of Texas Arlington |
Bio-Medical Imaging, Bio-informatics |
Marker Gene Selection and Gene Regulatory Elements Indentification in Microarray Data Analysis |
* |
|
28 |
Daniel Olmos |
Mathematics, UBC |
Heart Rhythm, Excitable system, Computational Biology |
Numerical studies in equations modelling excitable media based on Pseudospectral methods |
|
|
April 3 |
Gary Livingston |
Computer Science, Umass Lowell |
Machine Learning |
Gene Expression Analysis: Inferring Subpopulation Differences in Variable Interactions and Identifying Putative Transcriptional Regulatory Regions in the PCBV-1 Chlorella Virus Genome |
* |
|
11 |
Alicia Shim |
Mathematics, ASU and Yale |
Epidemiology, Vaccination, Game Theory |
Mathematical modeling of rotavirus epidemic in the presence of maternal antibodies and vaccination |
|
|
18 |
Jessica Libertini |
Applied Mathematics, Brown |
Tumor Growth |
Investigations of the Two-Compartment Dynamic Imaging Model for Measuring Cancer Growth |
|
|
25 |
Li Shen |
Computer Science, UMass Dartmouth |
Bio-medical Imaging |
Parametric Surface Modeling and Morphometric Pattern Analysis |
* |
|
May 2 |
Eli Stahl |
Biology, UMass Dartmouth |
Computational Genetics |
Statistical Genetics in the Stahl Laboratory in Biology |
|
|
3 |
Nathaniel Whitaker |
Mathematics
UMass Amherst |
Fluid Mechanics,
Mathematical Biology |
Some Mathematical Models in Biology |
** |
* Special Time and Place: Dion 101, 2pm – 3pm
** Special Time: Thursday Group I, 218 3pm - 4pm
Abstracts
Modeling population dynamics with difference equations and undersea naval and biological acoustics
Cathy Ann Clark (Mathematics, UMass Dartmouth and the Naval Undersea Warfare center, Newport, RI)
We introduce the theory of Difference Equations which can be considered as a discrete analogue of Differential Equations, and discuss a few examples of modeling population dynamics. We also give an overview of a selection of topics involving biologics and the propagation of sound in undersea environments. An overview of the latter topic can be found by selecting the "Animals and Sound in the Sea" option at http://www.dosits.org (Discovery of Sound in the Sea).
Deterministic Structure in the Chromosome of Mycoplasma Genitalium
Gary Davis (Mathematics, UMass Dartmouth)
We will utilize various techniques of time series analysis to look for evidence of deterministic structure in the gene MG468 of the bacterium Mycoplasma genitalium. This bacterium is distinguished by having a very small genome, and MG468 is one of its largest genes. We are looking for evidence that the sequence of codons in gene MG468 is not random.
Marker Gene Selection and Gene Regulatory Elements Identification in Microarray Data Analysis
Heng Huang (Computer Science and Engineering, University of Texas Arlington)
Microarray gene expression techniques have recently made it possible to offer phenotype classification of many diseases. One problem in this analysis is that each sample is represented by quite a large number of genes, and many of them are insignificant or redundant to clarify the disease problem. The previous work has shown that selecting informative genes from microarray data can improve the accuracy of classification. We proposed to use a heuristic K-means+ based clustering method to group similar genes and select informative genes from them to avoid redundancy and extract biological information from them. Empirical results on both public data sets and on data sets in the MAGIC database (Dartmouth Medical School) have shown that our methods can successfully select good candidate marker genes that lead to better classification accuracy than other methods. Meanwhile we also presented a new test environment in which synthetic data is perturbed to simulate possible variations in gene expression values. The goal is for the generated data to have appropriate properties that match natural data, and that are appropriate for use in testing the sensitivity of feature selection algorithms and validating the robustness of selected marker genes.
On the other research work, we study the organization of protein binding sites (cis-regulatory elements) in sets of co-regulated genes. The identification of potential cis-regulatory elements in the upstream regions of genes is key to understanding the mechanisms that regulate gene expression. We presented the efficient algorithms -- beam-search enumerative algorithm for motif finding, which aimed at the discovery of cis-regulatory elements in the DNA sequences upstream of a related group of genes. This algorithm dramatically limits the search space of expanded sequences, converting the problem from one that is exponential in the length of motifs sought to one that is linear. Unlike sampling algorithms, our algorithms converge and are capable of finding statistically overrepresented motifs with a low failure rate.
Numerical studies in equations modelling excitable media based on Pseudospectral methods
Daniel Olmos (Mathematics, University of British Columbia)
In this talk, I present a numerical scheme for solving equations of the reaction diffusion type with multiple spatiotemporal scales. The method, which is based on Chebyshev polynomials, is tested for the classical FitzHugh-Nagumo equations where a comparison with traditional methods is presented. The algorithm based on Chebyshev polynomials, is also considered for numerical experiments in a more realistic physiological model given by Beeler and Reuter (1977). The phenomena of spiral meandering and effects of the boundary are discussed.
Gene Expression Analysis: Inferring Subpopulation Differences in Variable Interactions and Identifying Putative Transcriptional Regulatory Regions in the PCBV-1 Chlorella Virus Genome
Gary Livingston (Computer Science, UMass Lowell)
Gene expression micro-array technology provides biologists with the technology to simultaneously measure the rate of expression of thousands of genes. Bayesian network learning and other methods have been adapted to infer gene interactions from microarray data, but these methods do not infer differences in variable interactions between subpopulations (e.g., gene A’s expression is positively correlated with gene B’s expression in normal liver tissue, but gene A’s expression is negatively correlated with gene B’s expression in cancerous liver tissue). The first portion of this talk will present network-based method for inferring interactions among variables that differ between subpopulations and results from evaluating the method using artificially generated data and breast cancer promoter data. The second portion on this talk will discuss methods for using gene expression data to identify putative transcriptional regulatory regions in genomes using data obtained from the PCBV-1 Chlorella virus as an example.
Mathematical modeling of rotavirus epidemic in the presence of maternal antibodies and vaccination
Alicia Shim (Mathematics, ASU and Yale)
Rotavirus (RV) is the most common cause of severe diarrhoea in children worldwide and diarrhoeal deaths in children in developing countries. Two live oral RV vaccines have been developed and approved. They are being implemented in developed and developing nations and clinical studies have shown that they can reduce RV morbidity and mortality. An age-structured epidemiological model is used to explore the population-level impact on RV dynamics of various vaccine regimes. Theoretical work is followed by the evaluation of specific vaccine schedule. It is shown that the large-scale implementation of recommended age-vaccine schedules have a differential impact in developed and developing countries. In developed nations the impact is significant while in nations with high growth rate the impact is dramatic. At a global scale, RV epidemics support clear seasonal patterns. Knowledge of the patterns can be used to improve the impact of vaccine schedules. Data from Australia are fitted to a model that incorporates the effect of seasonality in the transmission process in order to highlight the impact of temporary and partially effective vaccines on such patterns.
Investigations of the Two-Compartment Dynamic Imaging Model for Measuring Cancer Growth
Jessica Libertini (Applied Mathematics, Brown University)
Cancer is one of the leading causes of death in the civilized world. Many of the leading cancer-fighting drugs on the market target the blood supply to the tumor, but due to the use of static imaging techniques, patients often have to undergo several months of treatments before the efficacy can be measured. Using dynamic imaging techniques and a simplified two-compartment model, we hope to measure factors that indicate the level of blood flow, specifically the perfusion coefficient and the permeability-surface area product. In addition to presenting some past work on this model using a simplification by Morales and Smith, I will show results which raise serious questions about the use of this simplifying assumption. I will also show some recent results which do not require the use of this simplification.
Parametric Surface Modeling and Morphometric Pattern Analysis
Li Shen (Computer and Information Science, University of Massachusetts Dartmouth)
Statistical morphometric analysis is used in biomedical imaging to study various structures of interest, and aims to identify morphometric abnormalities associated with a particular condition in order to aid diagnosis and treatment. We present computational techniques for surface-based morphometry, where two key issues are (1) how to model 3D surfaces and (2) how to perform statistical analysis with these surface models. We employ the spherical harmonic (SPHARM) method for surface modeling, and then perform high-dimensional pattern classification and statistical inference based on random field theory to localize regionally specific shape changes between groups of 3D objects. Although SPHARM has been shown to be promising, algorithmic problems related to its robustness and scalability need to be solved before it can be of broad use. To address these issues, we present new methods usable in three crucial steps for modeling SPHARM surfaces: (1) spherical parameterization, (2) 3D shape registration, and (3) spherical harmonic expansion. We demonstrate these techniques by applying them to several studies in computational neuroscience and imaging genetics.
Statistical Genetics in the Stahl Laboratory in Biology
Eli Stahl (Biology, University of Massachusetts Dartmouth)
This seminar will provide an overview of the Dr. Eli Stahl's research in the Biology Department at UMass Dartmouth, with an emphasis on bioinformatic/computational projects. These include inference under evolutionary models of post-glacial population expansion and of metapopulation extinction/re-colonization dynamics, analysis of a model of the effects of metapopulation dynamics on evolutionary adaptation, and analysis of functional genomic data on plant adaptation to drought. The presentation will be non- mathematical, but will highlight numerous opportunities for projects integrating mathematical, computer science and biological approaches to complex biological problems.
Some Mathematical Models in Biology
Nathaniel Whitaker (Mathematics, University of Massachusetts Amherst)
In this talk, I will discuss some mathematical models in biology. In the first part, I will present a model to simulate and inhibit tumor growth. A tumor releases chemical stimuli attracting endothelial cells towards it which eventually form a network of blood vessels. This network provides it with oxygen and nutrients which allows it to grow as well as providing a means of transport to other parts of the body. The mathematical model will simulate the proliferation of this network. In the second part of this talk, we will present a model for the processing of blood in the kidney. In particular, the transport and processing of blood in the loop of Henle will be modeled. I will show how dynamical systems theory can be used to predict oscillations in certain important variables.
Last Updated On: 4/27/07