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Current contacts: Benjamin Seibold or Daniel B. Szyld
The Seminar usually takes place on Wednesdays at 4:00 PM in Room 617 on the sixth floor of Wachman Hall. Click on title for abstract.
Isaac Klapper, Temple University
Sea ice, which covers a significant portion of the earth's surface, is an interestingly complicated material consisting of a mixture of solid ice and liquid brine phases which are coupled by thermodynamic considerations, Among other things, sea ice plays an important role in regulating macroscale heat transport between the ocean and the atmosphere. It also is a platform for microbial life, lots of it in fact, that uses the ice as a sort of shelter though eventually becoming part of the local food chain. A model will be presented that hypothesizes that, in turn, the resident microbial population might impact sea ice structure and, in particular, its transport properties including heat transport.
Kristina Wicke, New Jersey Institute of Technology
Phylogenetic networks are a generalization of phylogenetic trees allowing for the representation of speciation and reticulate evolutionary events such as hybridization or horizontal gene transfer. The inference of phylogenetic networks from biological sequence data is a challenging problem, with many theoretical and practical questions still unresolved. In this talk, I will give an overview of the state of the art in phylogenetic network inference. I will then discuss a novel divide-and-conquer approach for inferring level-1 networks under the network multispecies coalescent model. I will end by discussing some open problems and avenues for future research.
Parts of this talk are based on joint work with Elizabeth Allman, Hector Banos, and John Rhodes.
Matthew Ricci, Hebrew University
Dynamical systems can undergo qualitative, topological changes in their orbit structure called bifurcations when underlying parameters cross a threshold: the "shape" of their behavior alters fundamentally. The development of data-driven tools for modeling these changes holds special promise in the life sciences, from the design of gene regulatory networks to the prediction of catastrophic oscillations in neural circuits. In this talk, I describe an ongoing research program which tackles this challenge by focusing on the realistic case where governing equations are unknown and dynamical behavior must be predicted from prior knowledge given noisy, sparse data. Building on classical work in so-called model manifold theory, our approach learns a shared feature landscape where diverse systems coalesce within a unified embedding space, revealing their underlying qualitative structure. I first describe work which uses such learned universal embeddings of low-dimensional dynamical systems to classify circuits by their function. Next, I demonstrate how a simple autoencoder can learn an implicit notion of topological conjugacy which functions as a robust detector of Hopf bifurcations in single-cell RNA sequencing data from the pancreas. Finally, we generalize to the case of spatiotemporal dynamics, where I outline recent work on building reduced-order parametric models ofpartial differential equations with applications to spatial patterning in the ocellated lizard. We conclude with some future directions, notably extensions to high-dimensional systems and applications to synthetic biology, where engineered organisms and tissues could be designed for stable, predictable functions in dynamic environments.
Francoise Tisseur, University of Manchester
The tropical semiring consists of the real numbers and infinity along with two binary operations: addition defined by the max or min operation and multiplication. Tropical algebra is the tropical analogue of linear algebra, working with matrices with entries on the extended real line. There are analogues of eigenvalues and singular values of matrices, and matrix factorizations in the tropical setting, and when combined with a valuation map these analogues offer `order of magnitude' approximations to eigenvalues and singular values, and factorizations of matrices in the usual algebra. What makes tropical algebra a useful tool for numerical linear algebra is that these tropical analogues are usually cheaper to compute than those in the conventional algebra. They can then be used in the design of preprocessing steps to improve the numerical behaviour of algorithms. In this talk I will review the contributions of tropical algebra to numerical linear algebra and discuss recent results on the selection of Hungarian scalings prior to solving linear systems and eigenvalue problems.
Petr Plechac, University of Delaware
We introduce approximations of ab-initio molecular dynamics derived from quantum mechanics.
Molecular dynamics simulations are often used to approximate canonical quantum correlation
observables in complex nuclei-electron systems. We present shallow random feature neural
networks and provide an analysis of their approximation properties. Furthermore, we describe
an adaptive sampling strategy that ensures a near-optimal distribution of features, thus
enabling controlled approximation of inter-atomic potentials for molecular dynamics simulations.
Finally, we demonstrate that the resulting molecular dynamics accurately approximate correlation observables with quantifiable error estimates.
Henry Brown, Temple University
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