- You are here:
- GT Home
- Home
- News & Events

Wednesday, January 31, 2018 - 11:00 ,
Location: Skiles 006 ,
Prof. Mansoor Haider ,
North Carolina State University, Department of Mathematics & Biomathematics ,
Organizer: Sung Ha Kang

Many biological soft tissues exhibit complex interactions between passive biophysical or biomechanical mechanisms, and active physiological responses. These interactions affect the ability of the tissue to remodel in order to maintain homeostasis, or govern alterations in tissue properties with aging or disease. In tissue engineering applications, such interactions also influence the relationship between design parameters and functional outcomes. In this talk, I will discuss two mathematical modeling problems in this general area. The first problem addresses biosynthesis and linking of articular cartilage extracellular matrix in cell-seeded scaffolds. A mixture approach is employed to, inherently, capture effects of evolving porosity in the tissue-engineered construct. We develop a hybrid model in which cells are represented, individually, as inclusions within a continuum reaction-diffusion model formulated on a representative domain. The second problem addresses structural remodeling of cardiovascular vessel walls in the presence of pulmonary hypertension (PH). As PH advances, the relative composition of collagen, elastin and smooth muscle cells in the cardiovascular network becomes altered. The ensuing wall stiffening increases blood pressure which, in turn, can induce further vessel wall remodeling. Yet, the manner in which these alterations occur is not well understood. I will discuss structural continuum mechanics models that incorporate PH-induced remodeling of the vessel wall into 1D fluid-structure models of pulmonary cardiovascular networks. A Holzapfel-Gasser-Ogden (HGO)-type hyperelastic constitutive law for combined bending, inflation, extension and torsion of a nonlinear elastic tube is employed. Specifically, we are interested in formulating new, nonlinear relations between blood pressure and vessel wall cross-sectional area that reflect structural alterations with advancing PH.

Wednesday, March 15, 2017 - 11:05 ,
Location: Skiles 006 ,
Max Alekseyev ,
George Washington University ,
maxal@gwu.edu ,
Organizer: Torin Greenwood

Genome median and genome halving are combinatorial optimization problems that aim at reconstruction of ancestral genomes by minimizing the number of possible evolutionary events between the reconstructed genomes and the genomes of extant species. While these problems have been widely studied in past decades, their known algorithmic solutions are either not efficient or produce biologically inadequate results. These shortcomings have been recently addressed by restricting the problems solution space. We show that the restricted variants of genome median and halving problems are, in fact, closely related and have a neat topological interpretation in terms of embedded graphs and polygon gluings. Hence we establish a somewhat unexpected link between comparative genomics and topology, and further demonstrate its advantages for solving genome median and halving problems in some particular cases. As a by-product, we also determine the cardinality of the genome halving solution space.

Tuesday, October 18, 2016 - 11:05 ,
Location: Skiles 005 ,
Tandy Warnow ,
The University of Illinois at Urbana-Champaign ,
Organizer: Heather Smith

The estimation of phylogenetic trees from molecular sequences (e.g., DNA, RNA, or amino acid sequences) is a major step in many biological research studies, and is typically approached using heuristics for NP-hard optimization problems. In this talk, I will describe a new approach for computing large trees: constrained exact optimization. In a constrained exact optimization, we implicitly constrain the search space by providing a set X of allowed bipartitions on the species set, and then use dynamic programming to find a globally optimal solution within that constrained space. For many optimization problems, the dynamic programming algorithms can complete in polynomial time in the input size. Simulation studies show that constrained exact optimization also provides highly accurate estimates of the true species tree, and analyses of both biological and simulated datasets shows that constrained exact optimization provides improved solutions to the optimization criteria efficiently. We end with some discussion of future research in this topic. (Refreshments will be served before the talk at 10:30.)

Wednesday, July 6, 2016 - 11:00 ,
Location: Skiles 005 ,
Bradford Taylor ,
School of Biology, Georgia Tech ,
Organizer: Christine Heitsch

When a disease outbreak occurs, mathematical models are used to

estimate the potential severity of the epidemic. The average number of

secondary infections resulting from the initial infection or reproduction

number, R_0, quantifies this severity. R_0 is estimated from the models by

leveraging observed case data and understanding of disease epidemiology.

However, the leveraged data is not perfect. How confident should we be

about measurements of R_0 given noisy data? I begin my talk by introducing

techniques used to model epidemics. I show how to adapt standard models to

specific diseases by using the 2014-2015 Ebola outbreak in West Africa as

an example throughout the talk. Nest, I introduce the inverse problem:

given real data tracking the infected population how does one estimate the

severity of the outbreak. Through a novel method I show how to account for

both inherent noise arising from discrete interactions between individuals

(demographic stochasticity) and from uncertainty in epidemiological

parameters. By applying this, I argue that the first estimates of R_0

during the Ebola outbreak were overconfident because demographic

stochasticity was ignored.

This talk will be accessible to undergraduates.

Wednesday, June 29, 2016 - 11:00 ,
Location: Skiles 005 ,
Elena Dimitrova ,
Clemson University ,
Organizer: Christine Heitsch

Progress in systems biology relies on the use of mathematical and statistical models for system level studies of biological processes. This talk will focus on discrete models of gene regulatory networks and the challenges they present, in particular data selection and model stability. Careful data selection is important for model identification since the process is sensitive to the amount and type of data used as input. We will discuss a criterion for deciding when a set of data points identifies an algebraic model with special
minimality properties. Stability is another important requirement for models of gene regulatory networks. Canalizing functions, a particular class of Boolean functions, show stable dynamic behavior and are thus suitable for expressing gene regulatory relationships. However, in practice, relaxing the canalizing requirement on some variables is appropriate. We will present the class of partially nested canalizing functions and some of their properties and applications.

Wednesday, June 22, 2016 - 11:00 ,
Location: Skiles 005 ,
Emily Rogers ,
Georgia Tech ,
Organizer: Christine Heitsch

Although DNA forensic evidence is widely considered objective and infallible, a great deal of subjectivity and bias can still exist in its
interpretation, especially concerning mixtures of DNA. The exact degree of variability across labs, however, is unknown, as DNA forensic examiners are primarily trained in-house, with protocols and quality control up to the discretion of each forensic laboratory. This talk uncovers the current state of forensic DNA mixture interpretation by analyzing the results of a groundbreaking DNA mixture interpretation study initiated by the Department of Defense's Defense Forensic Science Center (DFSC) in the summer of 2014. This talk will be accessible to undergraduates.

Thursday, June 16, 2016 - 11:00 ,
Location: Skiles 005 ,
Lenore Cowen ,
Tufts University ,
Organizer: Christine Heitsch

In protein-protein interaction (PPI) networks, or more general protein-protein association networks, functional similarity is often
inferred based on the some notion of proximity among proteins in a local neighborhood. In prior work, we have introduced diffusion state distance (DSD), a new metric based on a graph diffusion property, designed to capture more fine-grained notions of similarity from the neighborhood structure that we showed could improve the accuracy of network-based function-prediction algorithms. Boehnlein, Chin, Sinha and Liu have recently shown that a variant of the DSD metric has deep connections to Green's function, the normalized Laplacian, and the heat kernel of the graph.
Because DSD is based on random walks, changing the probabilities of the underlying random walk gives a natural way to incorporate experimental error and noise (allowing us to place confidence weights on edges), incorporate biological knowledge in terms of known biological pathways, or weight subnetwork importance based on tissue-specific expression levels, or known disease processes. Our framework provides a mathematically natural way to integrate heterogeneous network data sources for classical function prediction and disease gene prioritization problems.
This is joint work with Mengfei Cao, Hao Zhang, Jisoo Park, Noah Daniels, Mark Crovella and Ben Hescott.

Wednesday, April 13, 2016 - 11:05 ,
Location: Skiles 005 ,
Cameron Browne ,
U. of Louisiana ,
Organizer:

Mathematical modeling of viruses, such as HIV, has been an extensive
area of research over the past two decades. For HIV, some important
factors that aﬀect within-host dynamics include: the CTL (Cytotoxic T
Lymphocyte) immune response, intra-host diversity, and heterogeneities
of the infected cell lifecycle. Motivated by these factors, I consider
several extensions of a standard virus model. First, I analyze a cell
infection-age structured PDE model with multiple virus strains. The main
result is that the single-strain equilibrium corresponding to the virus
strain with maximal reproduction number is a global attractor, i.e.
competitive exclusion occurs. Next, I investigate the eﬀect of CTL
immune response acting at diﬀerent times in the infected-cell lifecycle
based on recent studies demonstrating superior viral clearance eﬃcacy of
certain CTL clones that recognize infected cells early in their
lifecycle. Interestingly, explicit inclusion of early recognition CTLs
can induce oscillatory dynamics and promote coexistence of multiple
distinct CTL populations. Finally, I discuss several directions of
ongoing modeling work attempting to capture complex HIV-immune system interactions suggested by experimental
data.

Wednesday, March 16, 2016 - 11:05 ,
Location: Skiles 005 ,
June Zhang ,
CDC. ,
Organizer:

Accounting for Heterogenous Interactions in the Spread Infections, Failures, and Behaviors_ The
scaled SIS (susceptible-infected-susceptible) network process that we
introduced extends traditional birth-death process by accounting for
heterogeneous interactions between individuals. An edge in the network
represents contacts between two individuals, potentially leading to
contagion of a susceptible by an infective. The inclusion of the network
structure introduces combinatorial complexity, making such processes
difficult to analyze. The scaled SIS process has a closed-form
equilibrium distribution of the Gibbs form. The network
structure and the infection and healing rates determine susceptibility
to infection or failures. We study this at steady-state for three
scales: 1) characterizing susceptibility of individuals, 2)
characterizing susceptibility of communities, 3) characterizing
susceptibility of the entire population. We show that the
heterogeneity of the network structure results in some individuals
being more likely to be infected than others, but not necessarily the
individuals with the most number of interactions (i.e., degree). We also
show that "densely connected" subgraphs are more vulnerable to
infections and determine when network structures include these more
vulnerable communities.

Wednesday, February 17, 2016 - 11:00 ,
Location: Skiles 006 ,
Professor David Gurarie ,
CWRU ,
dxg5@case.edu ,
Organizer:

Schistosoma is a parasitic worm that circulates between human and snail hosts. Multiple biological and ecological factors contribute to its spread and persistence in host populations. The infection is widespread in many tropical countries, and WHO has made control of schistosomiasis a priority among neglected tropical diseases.Mathematical modeling is widely used for prediction and control analysis of infectious agents. But host-parasite systems with complex life-cycles like Schistosoma, pose many challenges. The talk will outline the basic biology of Schistosoma, and the principles employed in mathematical modeling of macro parasites. We shall review conventional approaches to Schistosomiasis starting with the classical work of MacDonald, and discuss their validity and implications. Then we shall outline more detailed “stratified worm burden approach”, and show how combining mathematical and computer tools one can explore real-world systems and make reliable predictions for long term control outcomes and the problem of elimination.