Seminars and Colloquia by Series

Insertions on Double Occurrence Words

Series
Mathematical Biology Seminar
Time
Wednesday, September 25, 2019 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daniel Cruz – Georgia Tech

A double occurrence word (DOW) is a word in which every symbol appears exactly twice; two DOWs are equivalent if one is a symbol-to-symbol image of the other. In the context of genomics, DOWs and operations on DOWs have been used in studies of DNA rearrangement. By modeling the DNA rearrangement process using DOWs, it was observed that over 95% of the scrambled genome of the ciliate Oxytricha trifallax could be described by iterative insertions of the ``repeat pattern'' and the ``return pattern''. These patterns generalize square and palindromic factors of DOWs, respectively. We introduce a notion of inserting repeat/return words into DOWs and study how two distinct insertions into the same word can produce equivalent DOWs. Given a DOW w, we characterize the structure of  w which allows two distinct insertions to yield equivalent DOWs. This characterization depends on the locations of the insertions and on the length of the inserted repeat/return words and implies that when one inserted word is a repeat word and the other is a return word, then both words must be trivial (i.e., have only one symbol). The characterization also introduces a method to generate families of words recursively.

Species network inference under the coalescent model

Series
Mathematical Biology Seminar
Time
Wednesday, September 18, 2019 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hector Banos – Georgia Tech

When hybridization plays a role in evolution, networks are necessary to describe species-level relationships. In this talk, we show that most topological features of a level-1 species network (networks with no interlocking cycles) are identifiable from gene tree topologies under the network multispecies coalescent model (NMSC). We also present the theory behind NANUQ, a new practical method for the inference of level-1 networks under the NMSC.

The geometry of phylogenetic tree spaces

Series
Mathematical Biology Seminar
Time
Wednesday, September 11, 2019 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Bo Lin – Georgia Tech

Phylogenetic trees  are  the fundamental  mathematical  representation  of evolutionary processes in biology. As data objects, they are characterized by the challenges associated with "big data," as well as the  complication that  their  discrete  geometric  structure  results  in  a  non-Euclidean phylogenetic  tree  space,  which  poses  computational  and   statistical limitations.

In this  talk, I  will compare  the geometric  and statistical  properties between a  well-studied framework  -  the BHV  space, and  an  alternative framework that  we  propose, which  is  based on  tropical  geometry.  Our framework exhibits analytic,  geometric, and  topological properties  that are desirable for  theoretical studies in  probability and statistics,  as well  as  increased  computational  efficiency.  I  also  demonstrate  our approach on an example of seasonal influenza data.

Some combinatorics of RNA branching

Series
Mathematical Biology Seminar
Time
Wednesday, September 4, 2019 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Christine Heitsch – Georgia Tech

Understanding the folding of RNA sequences into three-dimensional structures is one of the fundamental challenges in molecular biology.  For example, the branching of an RNA secondary structure is an important molecular characteristic yet difficult to predict correctly.  However, recent results in geometric combinatorics (both theoretical and computational) yield new insights into the distribution of optimal branching configurations, and suggest new directions for improving prediction accuracy.

Organizational meeting

Series
Mathematical Biology Seminar
Time
Wednesday, August 21, 2019 - 11:00 for 30 minutes
Location
Skiles 006
Speaker
Christine Heitsch – Georgia Tech

A brief meeting to discuss the plan for the semester, followed by an informal discussion over lunch (most likely at Ferst Place).

Stochastic models for the transmission and establishment of HIV infection

Series
Mathematical Biology Seminar
Time
Wednesday, March 27, 2019 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dan Coombs – UBC (visiting Emory) –
The likelihood of HIV infection following risky contact is believed to be low. This suggests that the infection process is stochastic and governed by rare events. I will present mathematical branching process models of early infection and show how we have used them to gain insights into the duration of the undetectable phase of HIV infection, the likelihood of success of pre- and post-exposure prophylaxis, and the effects of prior infection with HSV-2. Although I will describe quite a bit of theory, I will try to keep giant and incomprehensible formulae to a minimum.

Inference of evolutionary dynamics of heterogeneous cancer and viral populations

Series
Mathematical Biology Seminar
Time
Wednesday, February 27, 2019 - 11:01 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Pavel Skums – GSU/CDC –

Inference of evolutionary dynamics of heterogeneous cancer and viral populations Abstract: Genetic diversity of cancer cell populations and intra-host viral populations is one of the major factors influencing disease progression and treatment outcome. However, evolutionary dynamics of such populations remain poorly understood. Quantification of selection is a key step to understanding evolutionary mechanisms driving cancer and viral diseases. We will introduce a mathematical model and an algorithmic framework for inference of fitness landscapes of heterogeneous populations from genomic data. It is based on a maximal likelihood approach, whose objective is to estimate a vector of clone/strain fitnesses which better fits the observed tumor phylogeny, observed population structure and the dynamical system describing evolution of the population as a branching process. We will discuss our approach to solve the problem by transforming the original continuous maximum likelihood problem into a discrete optimization problem, which could be considered as a variant of scheduling problem with precedent constraints and with non-linear cumulative cost function.

Exploring the impact of inoculum dose on host immunity and morbidity to inform model-based vaccine design

Series
Mathematical Biology Seminar
Time
Wednesday, January 30, 2019 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Andreas Handel – UGA –
Vaccination is an effective method to protect against infectious diseases. An important consideration in any vaccine formulation is the inoculum dose, i.e., amount of antigen or live attenuated pathogen that is used. Higher levels generally lead to better stimulation of the immune response but might cause more severe side effects and allow for less population coverage in the presence of vaccine shortages. Determining the optimal amount of inoculum dose is an important component of rational vaccine design. A combination of mathematical models with experimental data can help determine the impact of the inoculum dose. We designed mathematical models and fit them to data from influenza A virus (IAV) infection of mice and human parainfluenza virus (HPIV) of cotton rats at different inoculum doses. We used the model to predict the level of immune protection and morbidity for different inoculum doses and to explore what an optimal inoculum dose might be. We show how a framework that combines mathematical models with experimental data can be used to study the impact of inoculum dose on important outcomes such as immune protection and morbidity. We find that the impact of inoculum dose on immune protection and morbidity depends on the pathogen and both protection and morbidity do not always increase with increasing inoculum dose. An intermediate inoculum dose can provide the best balance between immune protection and morbidity, though this depends on the specific weighting of protection and morbidity. Once vaccine design goals are specified with required levels of protection and acceptable levels of morbidity, our proposed framework which combines data and models can help in the rational design of vaccines and determination of the optimal amount of inoculum.

Mathematical models for matrix regeneration and remodeling in biological soft tissues

Series
Mathematical Biology Seminar
Time
Wednesday, January 31, 2018 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Mansoor Haider – North Carolina State University, Department of Mathematics & Biomathematics
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.

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