Fall 2017
Time & Location: All talks are on Wednesdays in Gibson Hall 414 at 3:00 PM unless otherwise noted.
Organizer: Scott McKinley
September 13
Topic: A hop, skip, and jump-diffusion through some models of intracellular transport
Chris Miles | University of Utah, Mathematics Department (Host: Scott McKinley)
Abstract:
The movement of cargo within cells by small teams of molecular motors is a critical ingredient of many cellular functions. Both at the individual motor and ensemble levels, stochasticity is fundamentally unavoidable and diverse in its manifestation. Thus, fully elucidating the behavior of these systems requires disentangling a variety of noises at different temporal and spatial scales, providing a rich platform for not only biological intrigue, but also mathematical. In this talk, I'll briefly discuss some of my work modeling motor systems. The first project, inspired by motor stepping dynamics, provides some mathematical results on statistics of general jump-diffusion processes with state dependent jump rates. The second, a collaboration with experimentalists, attempts to unravel underlying sources of diffusive noise in observed transport data. Lastly, I'll mention how these projects relate to on-going work modeling transport by a curious type of motor incapable of taking many steps.
September 20
Long-term dynamics of particles undergoing active transport
Veronica Ciocanel | Mathematical Biosciences Institute (Host: Scott Mckinley)
Abstract:
In many developing organisms, such as frog oocytes, mRNAs and other proteins get transported to specific cell locations to ensure that healthy asymmetric cell division can occur. The dynamics often include diffusion, bidirectional transport, and stationary states, and may be influenced by the spatial distribution of filaments inside the cell. To determine the long-term displacement of the particles, we derive their effective velocity and diffusion using dynamical systems techniques for certain PDE systems. We also outline an alternative (and potentially equivalent) stochastic approach for deriving these large-time transport quantities using renewal reward theory.
November 8
Classification on the space of persistence diagrams
Vasileios Maroulas | University of Tennessee-Knoxville (Host:Scott McKinley)
Abstract:
In this talk, we consider the problem of signal classification by considering their associated persistence diagrams. We endow the data space of persistence diagrams with a new metric. In contrast with the Wasserstein distance, this metric accounts for changes in small persistence and cardinality. Pulling back to the space of signals, this corresponds to detecting differences in a signal’s periodicity, underlying noise, and geometry. The metric space of persistence diagrams is proved to admit statistical structure in the form of Fréchet means and variances. The new classification method using this distance is benchmarked on both synthetic data and real acoustic signals provided by the US Army Research Lab.
November 29
A Bayesian Approach to Estimating Background Flows from a Passive Scalar
Justin Krometisi | Virginia Tech, Mathematics Department
Abstract:
We consider the statistical inverse problem of estimating a background flow field from the partial and noisy observation of a passive scalar - e.g., estimating wind patterns by measuring a pollutant in the air. Here our unknown is a vector field that is specified by large or infinite number of degrees of freedom. Our work expands on frameworks developed in recent years for infinite-dimensional Bayesian inference. The talk will begin with some of the background required to formulate and analyze this problem: the advection-diffusion equation, ill-posed inverse problems, Bayesian inference, and Markov Chain Monte Carlo (MCMC). We then approach the inference both analytically and computationally, developing Metropolis-Hastings type algorithms to generate unbiased samples from the posterior distribution.
December 4
Special Statistics Seminar
Bayesian Experimental Design and Hierarchical Model for Quantitative and Qualitative Responses
Lulu Kang | Illinois Institute of Technology Statistical and Applied Mathematical Sciences Institute (SAMSI)
Abstract:
In many science and engineering systems both quantitative and qualitative output observations are collected. For short, we call such a system QQ system. In this talk, I will talk about a systematical approach for the experimental design and data analysis for the QQ system.
Classic experimental design methods are not suitable here because they often focus on one type of responses. We develop both Bayesian D and A-optimal design methods for experiments with one continuous and one binary responses. Both noninformative and conjugate informative prior distributions on the unknown parameters are considered. The proposed design criterions has meaningful interpretations in terms of the optimality for the models for both types of responses. Efficient design construction algorithms are developed to construct the local D-and A-optimal designs for given parameter values.
To capture a correlation between the two types of responses, we propose a Bayesian hierarchical modeling framework to jointly model a continuous and a binary response. Compared with the existing methods, the Bayesian method overcomes two restrictions. First, it solves the problem in which the model size (specifically, the number of parameters to be estimated) exceeds the number of observations for the continuous response. Second, the Bayesian model can provide statistical inference on the estimated parameters and predictions. Gibbs sampling scheme is used to generate accurate estimation and prediction for the Bayesian hierarchical model. Both simulation and real case study are shown to illustrate the proposed method.
Location: Gibson 414
Time: 3:00 PM
December 13
Probability and Statistics
Using Remote Sensing, Weather, and Demographic Data to Create Risk Maps for Zika, Dengue, and Chikungunya in Brazil
Carrie Manore | Los Alamos National Laboratory
Abstract:
Mosquito-borne diseases such as Zika, dengue, and chikungunya viruses have dynamics coupled to weather, ecology, human infrastructure, socio-economic demographics, and behavior. We use both mechanistic process-based models and statistical models to understand risk for Zika and dengue. Using deterministic and stochastic models, we quantified Zika risk in the eastern United States and estimated outbreak size in Central and South American countries. Time-varying remote sensing and weather data, along with demographics and internet data were used to predict risk through time for dengue outbreaks in Brazil with distributed lag methods, quantifing the lag between outbreaks and weather. Our statistical and mechanistic models indicate that the relationships between the variables are complex, but that quantifying risk is possible with the right data at appropriate spatio-temporal scales.
