All talks are on different days and different Building and different times.
Organizer: Scott McKinley
October 29
Title: Questionable Cooperation Between Swimming Cells or Molecular Motors
Speaker: Peter Kramer - Rensselaer Polytechnic Institute
Abstract: We examine the effective dynamics of two model systems consisting of stochastically active biological agents coupled together in a manner reflective of natural settings. The first concerns colonies of swimming flagellated cells such as choanoflagellates. We study how the swimming behavior of the colony could be derived from those of the constituent cells, including the effects of taxis and kinesis. Secondly, molecular motors are proteins in biological cells which perform various sorts of biophysical work. For two dissimilar types of kinesin transporting a common cargo, we provide approximate analytical characterizations for how the motors cooperate in carrying the cargo, with attention to incorporating slack in the tether connecting the motor with the cargo. The methodology combine multiscale asymptotic analysis, renewal theory, and first passage time calculations.
Location: Stanley Thomas 316
Time: 11:00
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November 4
Title: Two results in Optimal Transport with applications to biomedical data
Speaker: Natalia Kravtsova - Ohio State
Abstract: This talk presents two results in applied Optimal Transport. The first part of the talk is based on the joint work by N. Kravtsova, R. L. McGee II and A. T. Dawes (https://link.springer.com/article/10.1007/s11538-023-01175-y) and work by N. Kravtsova (https://arxiv.org/abs/2408.06525) on applications of the Gromov-Wasserstein distance defined by F. Memoli in 2011. We modify the NP-hard to compute Gromov-Wasserstein distance to construct a distance between time series that is computable in polynomial time. Our distance retains excellent performance of the Gromov-Wasserstein distance in machine learning tasks, including the ability compare objects in metric spaces with different dimensions. The second part of the talk is based on the work by N. Kravtsova, Asymptotic inference for Multimarginal Optimal Transport cost (submitted). Here we derive the asymptotic distribution of the empirical estimator for the Multimarginal Optimal Transport cost. We use the results to construct statistical inference procedures to compare probability measures. We illustrate the utility of the proposed approach on various datasets, including publicly available real data on cancers in US in 2004 – 2020.
Location: Gibson 126A
Time: 4:00
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November 5
Title: Quantifying approximate symmetries in biological systems
Speaker: Adriana Dawes - Ohio State
Abstract: Symmetry is a fundamental characteristic of natural systems, and is often linked to survival, reproductive success, and evolvability. While symmetry is ubiquitous and often intuitively obvious, biological symmetry is rarely perfect, making it challenging to apply mathematical definitions of idealized symmetry. To address this challenge, we developed a flexible, entropy-based method for quantifying symmetry that requires very little user input. I will highlight some novel insights arising from applications of this measure, including evidence for convergent evolution in flowering plants, classification of biopolymer networks, and visualization of the emergence and loss of symmetries in pattern formation systems.
Location: Stanley Thomas 316
Time: 11:00
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November 12
Title: Modelling Malaria Elimination: Malaria in Zanzibar
Speaker: Nakul Chitnis - Swiss Tropical and Public Health Institute
Abstract: Malaria cases can be classified as imported, introduced or indigenous cases. The World Health Organization’s definition of malaria elimination requires an area to demonstrate that no new indigenous cases have occurred in the last three years. Here, we present a stochastic metapopulation model of malaria transmission that distinguishes between imported, introduced and indigenous cases, and can be used to test the impact of new interventions in a setting with low transmission and ongoing case importation. We use human movement and malaria prevalence data from Zanzibar, Tanzania, to parameterise the model. We test increasing the coverage of interventions such as reactive case detection; implementing new interventions including reactive drug administration and treatment of infected travellers; and consider the potential impact of a reduction in transmission on Zanzibar and mainland Tanzania. We find that the majority of new cases on both major islands of Zanzibar are indigenous cases, despite high case importation rates. Combinations of interventions that increase the number of infections treated through reactive case detection or reactive drug administration can lead to substantial decreases in malaria incidence, but for elimination within the next 40 years, transmission reduction in both Zanzibar and mainland Tanzania is necessary.
Location: Stanley Thomas 316
Time: 11:00
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November 15
Title: Inferring and Interpreting Heterogeneous Models Using Dendrograms
Speaker: Linh Do - (Tulane) and Dat Do - (Michigan)
Abstract: In the new era of big data, modern datasets (e.g., in genomics) are often large-scale and heterogeneous. To meaningfully model such data, scientists use mathematical models to cluster/segment it into a smaller and interpretable number of subpopulations. Long-standing questions involving those models include: (1) In practice, how to select the number of subpopulations; (2) In theory, what happens if that number is misspecified or the model is incorrect. In this talk, we aim to answer these two questions for two popular models of this class named “mixture models” and “changepoint detection.” We take the multiscaling approach to this problem by first overfitting data with a large number of subpopulations and then sequentially projecting it down to smaller subspaces of models. This results in a binary tree representation (a.k.a., dendrogram) of these nested classes of models, which is useful for visualization and model selection. We then study the convergence rate of the vertices and topology of the inferred dendrogram and show it is statistically optimal. Based on this, we propose a novel consistent model selection method named Dendrogram Information Criteria. Several simulation studies are presented to support our theory. We also illustrate the methodology with applications to single-cell RNA sequence analysis and wind turbines data.
Location: Gibson 325 (Computational and Applied Math Seminar)
Time: 3:00
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November 21
Title: Parameter estimation for ordinary differential equations with time warping.
Speaker: John Fricks - Arizona State University
Abstract: Curve registration is a set of techniques to align functional data in the presence of time warping—phase variation in the functional observations. In this talk, we will present a Bayesian framework to estimate the parameters of an ODE model when the observations contain stochastic fluctuations in both amplitude and phase with a Gaussian process defining the time warping model. To facilitate such a framework, a new method for curve registration using Hamiltonian Monte Carlo will be presented along with a hierarchical model that links a basis fit of the data to solutions of an ODE model, allowing for parameter estimation.
Location: Stanley Thomas 316
Time: 11:00 am
