Friday November 06th, at 11:00AM in Fretwell 315

October 30, 2015 by Duan Chen
Categories: Spring 2022

Chi-Wang Shu, Division of Applied Mathematics, Brown University
Title: High order numerical methods for convection dominated problems

Abstract: Convection dominated partial differential equations are used extensively in applications including fluid dynamics, astrophysics, electro-magnetism, semi-conductor devices, and biological sciences.

High order accurate numerical methods are efficient for solving such partial differential equations, however they are difficult to design because solutions may contain discontinuities and other singularities or sharp gradient regions. In this talk we will survey several types of high order numerical methods for such problems, including weighted essentially non-oscillatory (WENO) finite difference methods, WENO finite volume methods, discontinuous Galerkin finite element methods, and spectral methods. We will discuss essential ingredients, properties and relative advantages of each method, and comparisons among these methods. Recent development and applications of these methods will also be discussed.

 

Wednesday October 28th, at 3:00PM in Fretwell 315

October 20, 2015 by Duan Chen
Categories: Spring 2022
Carlos Castillo-Chavez, Department of Mathematics, Arizona State University
Title: Beyond Ebola: Lessons to mitigate future pandemics
Abstract: It is now just more than a year since the official confirmation of an outbreak of Ebola haemorrhagic fever in West Africa. With new cases occurring at their lowest rate for 2015, and the end of the outbreak in sight for all three countries predominantly affected, now is the time to consider strategies to prevent future outbreaks of this, and other, zoonotic pathogens. The Ebola outbreak, like many other emerging diseases, illustrates the crucial role of the ecological, social, political, and economic context within which diseases emerge. And so, the question remains, what have we learned from this and past outbreaks of emerging diseases? Dispersal, mobility and residence times play a significant role on disease dynamics especially in the case of emergent or re-emergent diseases like Influenza or Ebola. Phenomenological and mechanistic models that highlight the role of these three factors will be presented in order to highlight the impact of, for example, a “cordon sanitaire,” or the fear of Ebola infection on disease dynamics. We will briefly highlight as well the impact of technology on the dynamics, prevention and control of Ebola9.

 

Friday November 20th, at 11:00AM in Fretwell 116

October 20, 2015 by Duan Chen
Categories: Spring 2022
Dewei Wang, Department of Statistics, University of South Carolina, Hosted by Yang Li
Title: Nonparametric goodness-of-fit tests for uniform stochastic ordering
Abstract:In this talk, I will introduce a new nonparametric procedure for testing against uniform stochastic ordering in a two-population setting. Uniform stochastic ordering is stronger than ordinary stochastic ordering but weaker than likelihood ratio ordering. Uniform stochastic ordering is satisfied when the ordinal dominance curve associated with the two distributions is star-shaped. To develop a goodness-of-fit test for this property, we construct test statistics by examining the discrepancy between the empirical ordinal dominance curve and its the least star-shaped majorant. We derive the limiting distribution of these statistics when uniform stochastic ordering is satisfied or not, and further we establish the least favorable distribution that can be used to determine the critical values. We illustrate the performance of our testing procedure through simulation and by applying it to a caffeine study involving premature infants conducted by Palmetto Health Richland in Columbia, SC.

 

Friday November 6th, at 11:00AM in Fretwell 116

October 20, 2015 by Duan Chen
Categories: Spring 2022
Yichao Wu, Department of Statistics, North Carolina State University, Hosted by Shaoyu Li
Title: Variable selection via measurement error model selection likelihoods
Abstract: The measurement error model selection likelihood was proposed in Stefanski, Wu and White (2014) to conduct variable selection. It provides a new perspective on variable selection. The first part of my talk will be a review of the measurement error model selection likelihoods. In the second part, I will present an extension to nonparametric variable selection in kernel regression.

Friday Oct 16, 2015 at 2:00PM in Fretwell 379 (Math Conference Room)

October 12, 2015 by Duan Chen
Categories: Spring 2022
Dr. Wenxiao Pan, Pacific Northwest National Laboratory (PNNL)
Title: Mesoscale Modeling Using Particle-based Methods
Abstract: Recent applications in micro-/nano-technology, material assembly and biological systems demand robust and accurate computational modeling of multiphysical processes at the mesoscale. In this talk, I will focus on mathematical models and numerical schemes that can effectively capture mesoscopic multiphysics using particle-based methods. I will discuss both
top-down and bottom-up approaches. In the top-down approach, the stochastic PDEs with consistent thermal scaling were solved to describe the important effects of thermal fluctuation in mesoscale. In the bottom-up approach, coarse-grained molecular models were developed for modeling complex fluids and soft matters in mesoscale such as concentrate suspensions of colloids, red blood cells, etc.

 

Wed Oct 14, 2015 at 11:00AM in Fretwell 379 (Math Conference Room)

October 07, 2015 by Duan Chen
Categories: Spring 2022

Evgeny Lakshtanov, University of Aveiro, Portugal

Title: On Finiteness in the Card Game of War.

Abstract: The game of war is a popular international children’s card game. In the beginning of the game, the deck is split into two parts, then each player reveals their top card. The player having the highest card collects both and returns them to the bottom of their hand. The player left with no cards loses. It is often wrongly assumed that this game is deterministic and the result is set once the cards have been dealt. However, this is not so; the rules of the game do not prescribe the order in which the winning player will place their cards on the bottom of the hand. First, we provide an example of a cycling game with fixed rules and then assume that each player can seldom but regularly change the returning order. We have proved that in this case the mathematical expectation of the length of the game is finite. In principle it is equivalent to the graph of the game, which has edges corresponding to all acceptable transitions, having the following property: from each initial configuration there is at least one path to the end of the game. (Joint work with V. Roshchina)

Friday October 2nd, at 11:00AM in Fretwell 116

September 17, 2015 by Duan Chen
Categories: Spring 2022
Grace Yi, Department of Statistics and Actuarial Sciences, University of Waterloo, Canada, Hosted by Yangqing Sun
Title: Analysis of High Dimensional Longitudinal Data with Measurement Error and Missing Observations
Abstract: Longitudinal studies have proven to be useful in studying changes of response over time, and have been widely conducted in practice. It is common that longitudinal studies collect a large number of covariates, some of which are unimportant in explaining the response. Including such covariates in modelling and inferential procedures would greatly degrade the quality of the results. Moreover, longitudinal data analysis is challenged by the presence of measurement error and missing observations. In this talk, I will discuss the issues induced from these features, and describe simultaneous variable selection and estimation procedures that handle high dimensional longitudinal data with missingness and measurement error.

Wednesday September 16th, at 11:00AM in Math Conference Room

September 09, 2015 by Duan Chen
Categories: Spring 2022
Chunmei Wang, Georgia Tech
Title: Weak Galerkin Finite Element Methods for PDEs
Abstract: Weak Galerkin (WG) is a new finite element method for partial differential equations where the differential operators (e.g., gradient, divergence, curl, Laplacian etc) in the variational forms are approximated by weak forms as generalized distributions. The WG discretization procedure often involves the solution of inexpensive problems defined locally on each element. The solution from the local problems can be regarded as a reconstruction of the corresponding differential operators. The fundamental  difference between the weak Galerkin finite element method and other existing methods is the use of weak functions and weak derivatives (i.e., locally reconstructed differential operators) in the design of numerical schemes based on existing variational forms for the underlying PDE problems. Weak Galerkin is, therefore, a natural extension of the conforming Galerkin finite element method. Due to its great structural flexibility, the weak Galerkin finite element method is well suited to most partial differential equations by providing the needed stability and accuracy in approximation.

In this talk, the speaker will introduce a general framework for WG methods, WG mixed finite element methods, and a hybridized formulation of WG by using the second order elliptic problem as an example.  Furthermore, the speaker will present WG finite element methods for several model PDEs, including the linear elasticity, biharmonic, and time-harmonic Maxwell’s equations. The talk should be accessible to graduate students with adequate training in computational mathematics.

 

Friday May 1, 2015 at 11:00am in Friday 132

April 03, 2015 by Michael Grabchak
Categories: Spring 2022
 Hongyu Zhao, Yale University
Title: Spatial Temporal Modeling of Gene Expression Dynamics During Human Brain Development
Abstract: Human neurodevelopment is a highly regulated biological process, and recent technological advances allow scientists to study the dynamic changes of neurodevelopment at the molecular level through the analysis of gene expression data from human brains. In this talk, we focus on the analysis of data sampled from 16 brain regions in 15 time periods of neurodevelopment. We will introduce a two-step statistical inferential procedure to identify expressed and unexpressed genes and to detect differentially expressed genes between adjacent time periods. Markov Random Field (MRF) models are used to efficiently utilize the information embedded in brain region similarity and temporal dependency in our approach. We develop and implement a Monte Carlo expectation-maximization (MCEM) algorithm to estimate the model parameters. Simulation studies suggest that our approach achieves lower misclassification error and potential gain in power compared with models not incorporating spatial similarity and temporal dependency. We will also describe our methods to infer dynamic co-expression networks from these data. This is joint work with Zhixiang Lin, Stephan Sanders, Mingfeng Li, Nenad Sestan, and Matthew State.

 

Friday April 10, 2015 at 11:00am in Friday 132

April 03, 2015 by Michael Grabchak
Categories: Spring 2022
Lianming Wang, University of South Carolina
Title: Nonhomogeneous Poisson models for panel count data and interval-censored failure time data
Abstract: In many epidemiological and medical studies, subjects are examined at regular or irregular follow-up visits. Panel count data arise when the response of interest is the count of some repeated events between consecutive examination times, while interval-censored data arise when the response of interest is the time to some particular event and only the status of the event is known at each examination time. Poisson process has been popular to model the panel count data in the literature. In this talk, we propose a gamma-frailty nonhomogeneous Poisson process model for analyzing panel count data to account for the within-subject correlation and develop an easy estimation method using EM algorithm. We also propose a computationally efficient method for analyzing general interval-censored data under the PH model using an EM algorithm. We developed a novel data augmentation by introducing a latent nonhomogeneous Poisson process to expand the observed likelihood. Both approaches have shown excellent performance in terms of estimation accuracy and computational advantages, such as being robust to initial values, converging fast, and providing variance estimates in closed-form. A joint modeling of panel count responses and the interval-censored failure time of a terminal event is discussed as a generalization of the proposed approaches.