Department of

# Mathematics

Seminar Calendar
for Mathematical Biology Seminar events the year of Saturday, November 9, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, November 7, 2019

1:00 pm in 347 Altgeld Hall,Thursday, November 7, 2019

#### Theoretical and Empirical Advances in Large-Scale Species Tree Estimation

###### Tandy Warnow (Computer Science, University of Illinois)

Abstract: The estimation of the "Tree of Life" -- a phylogeny encompassing all life on earth--is one of the big Scientific Grand Challenges. Maximum likelihood (ML) is a standard approach for phylogeny estimation, but estimating ML trees for large heterogeneous datasets is challenging for two reasons: (1) ML tree estimation is NP-hard (and the best current heuristics can use hundreds of CPU years on relatively small datasets, just to find local optima), and (2) the statistical models used in ML tree estimation methods are much too simple, failing to acknowledge heterogeneity across genomes or across the Tree of Life. These two "big data" issues -- dataset size and heterogeneity -- impact the accuracy of phylogenetic methods and have consequences for downstream analyses. In this talk, I will describe a new graph-theoretic "divide-and-conquer" approach to phylogeny estimation that addresses both types of heterogeneity. Our protocol operates as follows: (1) we divide the set of species into disjoint subsets, (2) we construct trees on the subsets (using appropriate statistical methods), and (3) we combine the trees together using auxiliary information, such as a matrix of pairwise distances. I will present three such strategies (all published in the last year) that operate in this fashion, and that improve the theoretical and empirical performance of phylogeny estimation methods. One of the main applications of this work is species tree estimation from multi-locus data sets when gene trees can differ from the species tree due to incomplete lineage sorting. This talk is largely based on joint work with my PhD students, Erin Molloy and Vladimir Smirnov (Illinois).

Thursday, November 21, 2019

1:00 pm in 347 Altgeld Hall,Thursday, November 21, 2019

#### Robust Analysis of Metabolic Pathways

###### Al Holder (Rose-Hulman Institute of Technology)

Abstract: Flux balance analysis (FBA) is a widely adopted computational model in the study of whole-cell metabolisms, often used to identify drug targets, to study cancer, and to engineer cells for targeted purposes. The most common model is a linear program that maximizes cellular growth rate subject to achieving steady metabolic state and to satisfying environmental bounds. Quadratic and integer modifications are also common. Standard stoichiometry decides the preponderance of data in most instances, and hence, the majority of information defining an optimization model is certain. However, several key parts of a model rely on inferred science and are less certain; indeed, the method of deciding several of these values is opaque in the literature. This prompts the question of how the resulting science might depend on our lack of knowledge. We suggest a robust extension of FBA called Robust Analysis of Metabolic Pathways (RAMP) that accounts for uncertain information. We show that RAMP has several mathematical properties concomitant with our biological understanding, that RAMP performs like a relaxation of FBA in practice, and that RAMP requires special numerical awareness to solve.