Seminars and Colloquiums
for the week of November 4, 2019
Louis Gross, UTK
Betsy Downs, UTK
Jeremy Siegert, UTK
Jan Rosinski, UTK
Jesse Sautel, UTK
Chun Liu, Illinois Institute of Technology
Anna Little, Michigan State University
Theodore Papamarkou, ORNL
Cole Zmurchok, Vanderbilt University
Tea Time - cancelled for this week
3:00 pm – 3:30 pm
Monday, Tuesday, & Wednesday
Room: Ayres 401
MATH BIOLOGY SEMINAR
TITLE: Introduction to Complexity Theory
SPEAKER: Louis Gross, UTK
TIME: 10:10 AM
ROOM: Claxton 105
TITLE: Clifford Algebras
SPEAKER: Betsy Downs, UTK
TIME: 3:35 PM
ROOM: Ayres 114
Tuesday, November 5th
TOPOLOGY/ GEOMETRY SEMINAR
TITLE: Inductive Dimension of Coarse Proximity Spaces
SPEAKER: Jeremy Siegert, UTK
ROOM: Ayres 114
Abstract: In this talk, we define the asymptotic inductive dimension, $asInd$, of coarse proximity spaces. In the case of metric spaces equipped with their metric coarse proximity structure, this definition is equivalent to the definition of $asInd$ given by Dranishnikov for proper metric spaces. We show that if the boundary of a coarse proximity space is completely traceable, then the asymptotic inductive dimension of the space is equal to the large inductive dimension of its boundary. Consequently the large inductive dimension of well known boundaries such as the Gromov boundary and the visual boundary of Cat($0$) spaces is characterized. We also provide conditions on the space under which the boundary is completely traceable. Finally, we use neighborhood filters to define an inductive dimension of coarse proximity spaces whose value agrees with the Brouwer dimension of the boundary.
TITLE: Stochastic Dini's theorem with applications (Part 2)
SPEAKER: Jan Rosinski, UTK
TIME: 2:10 PM-3:25 PM
ROOM: Ayres 112
Abstract: A stochastic version of Dini's theorem was found by Ito and Nisio. It provides a powerful tool to deduce the uniform convergence of stochastic processes from their pointwise convergence. Unfortunately, this tool fails in stronger than uniform modes of convergence, such as Lipschitz or phi-variation convergence, the latter mode being natural for processes processes with jumps. In this work we establish a stochastic version of Dini's theorem in a new framework that covers processes with jumps and strong modes of convergence. We apply these results to Levy driven stochastic differential equations
Wednesday, November 6th
ORAL SPECIALTY EXAMINATION
SPEAKER: Jesse Sautel, UTK
ROOM: A 308H
TIME: 2:30 pm
His committee consist of Professors Richter (Chair), Nicoara, and Sundberg.
TITLE: Energetic Variational Approach in General Diffusion: Boundary and Thermal Effects
SPEAKER: Chun Liu, Illinois Institute of Technology
ROOM: Ayres 405
ABSTRACT: Most biological activities involve transport and distribution of ions and charged particles in complicated biological environments. The coupling and competition between diﬀerent ionic solutions in various biological environments provide the mechanism of the relevant speciﬁcities and selectivities in these systems. These systems are often associated with special biological and chemical conditions, such as the high concentration of speciﬁc species in solutions, which make most of the “ideal” assumptions in classical and conventional approaches irrelevant or unsuitable in the studies of biological problems.
In the talk, I will explore the underlying mechanism governing various diﬀusion processes. We will employ a general framework of energetic variational approaches, consisting of in particular, Onsager’s Maximum Dissipation Principles, and their speciﬁc applications in biology and physiology. I will discuss several extended general diﬀusion systems motivated by the study of ion channels and ionic solutions in biological cells. In particular, I will focus on our recent results in studying the interactions between diﬀerent species, the boundary eﬀects and in some cases, the thermal eﬀects.
TITLE: Robust Statistical Procedures for Noisy, High-dimensional Data
SPEAKER: Anna Little, Michigan State University
ROOM: Ayres 405
Abstract: This talk addresses two topics related to robust statistical procedures for analyzing noisy, high-dimensional data: (I) path-based spectral clustering and (II) robust multi-reference alignment. Both methods must overcome a large ambient dimension and lots of noise to extract the relevant low dimensional data structure in a computationally efficient way. In (I), the goal is to partition the data into meaningful groups, and this is achieved by a novel approach which combines a data driven metric with graph-based clustering. Using a data driven metric allows for strong theoretical guarantees and fast algorithms when clusters concentrate around low-dimensional sets. In (II), the goal is to recover a hidden signal from many noisy observations of the hidden signal, where each noisy observation includes a random translation, a random dilation, and high additive noise. A wavelet based approach is used to apply a data-driven, nonlinear unbiasing procedure, so that the estimate of the hidden signal is robust to high frequency perturbations.
Thursday, November 7th
MATHEMATICAL DATA SCIENCE SEMINAR
TITLE: Challenges in Bayesian inference via Markov chain Monte Carlo for neural networks
SPEAKER: Theodore Papamarkou, ORNL
TIME: 2:10 PM
ROOM: Ayres 111
Abstract: Markov chain Monte Carlo (MCMC) methods and neural networks are instrumental in tackling inferential and prediction problems. However, Bayesian inference based on joint use of MCMC methods and of neural networks is limited. This talk reviews the main challenges posed by neural networks to MCMC developments, including lack of parameter identifiability due to weight symmetries, prior specification effects, and consequently high computational cost and convergence failure. Population and manifold MCMC algorithms are combined to demonstrate these challenges via multilayer perceptron (MLP) examples and to develop case studies for assessing the capacity of approximate inference methods to uncover the posterior covariance of neural network parameters. Some of these challenges, such as high computational cost arising from the application of neural networks to big data and parameter identifiability arising from weight symmetries, stimulate research towards more scalable approximate MCMC methods or towards MCMC methods in reduced parameter spaces.
Friday, November 8th
TITLE: Mathematical modeling of cellular organization: regulatory signaling, cell mechanics, and collective cell behavior
SPEAKER: Cole Zmurchok, Vanderbilt University
ROOM: A 405
ABSTRACT: Cell shape and polarity is regulated by a complex network of cytoskeletal signaling regulators (Rho-family GTPases) and mechanical feedback from the cell itself. I use mathematical modeling, computational approaches, and analysis (PDEs, ODEs, and agent-based models) to probe the cellular behaviors that result from these complex interactions. In this talk, I will discuss (1) how Rho GTPase dynamics can give rise to a diverse set of signaling profiles that match experimentally observed morphologies, (2) how the feedback between mechanics and signaling provides a physical mechanism for cells to adapt to high concentration signaling environments, and (3) how these feedbacks can generate collective cell dynamics seen in tissues. Together, these results help unravel the complex interactions between Rho GTPase signaling and mechanics that organize cell behavior.
If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar.
If you have questions, or a date you would like to confirm, please contact Dr. Christopher Strickland, firstname.lastname@example.org