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Mathematics & Statistics

Colloquia — Fall 2015

Friday, November 13, 2015

Title

Speaker

Time
Place
Sponsor

First Passage processes — from molecular transport to populations extinctions
Anton Zilman
University of Toronto
3:00pm-4:00pm
CMC 130
Razvan Teodorescu

Abstract

Many aspects of the behaviors of physical, chemical and biological systems can be understood simply in terms of the dynamics of averaged state variables and their deterministic evolution equations. However, in some scenarios, random fluctuations not just add some negligible noise to the averaged dynamics, but instead give rise to fundamentally different behaviors. It is increasingly appreciated that for biological systems at the cellular scale, fluctuations can lead to single-cell behaviors that considerably deviate from naive ensemble-averaged expectations.

Often irreversible changes in cellular behavior are triggered by threshold events, i.e., the attainment of a threshold value of a relevant cellular dynamical variable. Such processes are known as “first passage” (FP) processes, referring to the event when the random variable first passes the threshold value. Even seemingly simple processes, such as the transport of a molecule through a nano-channel or population extinction fall under the FP rubric. Tremendous advances in measurement techniques are providing direct insights into the stochastic dynamics of processes on the cellular and molecular scales. These developments bring the applications of FP formalism to the forefront of research in cellular and molecular biology.

I will review the fundamentals of the FP formalism — which were pioneered several decades ago, in the context of non-equilibrium physical chemistry and chemical physics — and discuss our recent results in two specific contexts: molecular transport through nanochannels and population dynamics.

Title
Speaker


Time
Place
Sponsor

Cellular automata and groups
Tullio Ceccherini-Silberstein
Università del Sannio
Italy
1:30pm-2:30pm
CMC 130
Dima Savchuk

Abstract

Cellular automata were introduced by von Neumann (around 1930) as theoretical models for self-reproducing machines: the Theory of Cellular Automata is now a central theme in Symbolic Dynamics and in Theoretical Computer Science. The seemingly unrelated notion of an amenable group was also introduced by von Neumann (1929) and originated from the study of the Banach-Tarski paradox: nowdays it plays a prominent role in the Theory of Dynamical Systems and Ergodic Theory as well as in Harmonic and Functional Analysis.

In this talk, I wish to present the “Garden of Eden Theorem for cellular automata over amenable groups” (1997): this provides a characterization of amenability in terms of cellular automata.

Also, I wish to discuss the notions of soficity (due to Gromov and B. Weiss) and surjunctivity (due to Gottschalk) and present some recent results and connections between the Theory of Cellular Automata and the Theory of Group Rings (e.g., the solution of the Kaplansky conjecture on stable finiteness of the group ring of sofic groups).

Friday, October 23, 2015

Title
Speaker

Time
Place
Sponsor

Machine Learning in Medical Imaging
Feng Shi
University of North Carolina, Chapel Hill
3:00pm-4:00pm
CMC 130
Dan Shen

Abstract

Machine learning provides methods, techniques, and tools that can help solving diagnostic and prognostic problems in a variety of medical domains. In this talk, I will present my recent work of applying machine learning approaches in medical imaging computing. In the first part, I will introduce our brain segmentation framework on first-year infants by using random forest technique with multi-modality features. In the second part, I will demonstrate an image enhancement method reconstructing 7T-like images from 3T inputs by using sparse models and paired dictionaries. In the last part, I will talk about computer-aided prediction of autistic risk on 6-month infants by using multi-kernel support vector machine (SVM) with features from brain white matter connectomics.

Friday, September 25, 2015

Title
Speaker


Time
Place
Sponsor

Pfaffianization of a semi-discrete KP equation and matrix integrals
Chun-Xia Li
College of Charleston, USA
and Capital Normal University, China
3:00pm-4:00pm
CMC 130
Wen-Xiu Ma

Abstract

In this talk, I'd like to first explore a semi-discrete KP equation whose solutions can be expressed in terms of both Wronskian determinants and Grammian determinants. Through the procedure of Pfaffianization, we are able to derive the coupled system for the semi-discrete KP equation. Due to the close connections between matrix integrals and integrable systems, we manage to obtain matrix integral solutions to the semi-discrete KP equation and its coupled system.

Friday, September 18, 2015

Title
Speaker


Time
Place
Sponsor

Pattern Mixture Weighted GEE Models for Survey Nonresponses
Ming Ji
Professor of Biostatistics
USF College of Nursing
3:00pm-3:30pm
CMC 130
Lesɫaw Skrzypek

Abstract

Survey nonresponses is an epic issue for social and behavioral research. There has been methodological development on survey nonresponse in the past decades which resulted in statistical methods such as multiple imputation and inverse probability weighting. In biostatistics research, there has been decades of research development on handling missing data from longitudinal studies such as clinical trials which yielded statistical methods such as pattern mixture models. In this talk, we will first demonstrate the equivalence of complex survey logistic and Generalized Estimating Equation (GEE) logistic regression. Based on this equivalence of the two classes of models from the fields of survey and biostatistics research, we discuss how to implement pattern mixture GEE models to analyze survey nonresposnes which follows the exponential distribution family.

Title
Speaker


Time
Place
Sponsor

Big Data and Health Research — A Statistician's Perspective
Ming Ji
Professor of Biostatistics
USF College of Nursing
3:30pm-4:00pm
CMC 130
Lesɫaw Skrzypek

Abstract

It is without doubt that we are currently in a revolution brought by big data. Big data challenges the limits of the existing technology and scientific methods to process and analyze data. In this talk, I will briefly review the big data revolution and its impact on health research from the perspective of a statistician. I will discuss what big data is, the characteristics of big data, the challenges of big data to data sciences, and my personal views on several key areas for big data research, successful applications of big data in health research and how to use big data in our own research.

Friday, August 28, 2015

Title
Speaker


Time
Place
Sponsor

Inversible fibrations, globalization and triviality of maps
Nigar Tuncer
Bahcesehir University
Istanbul, Turkey
3:00pm-4:00pm
CMC 108
Nataša Jonoska

Abstract

Dyer and Eilenberg (1988) in “Globalizing Fibrations by schedules” defined inversible fibration and prove a globalization theorem for these kind of fibrations, then they asked whether a locally trivial maps over contractible space is trivial. In this talk, we provide some further details concerning inversible fibrations and we define also inversible Hurewicz Fibrations, relate these to the inversible fibrations of Dyer and Eilenberg and study inversibility for path space fibrations. An affirmative answer to a special case of the Dyer and Eilenberg question is given.