Assistant Professor, Department of Mathematics and Statistics
AUTHOR

Duan Chen

Friday December 4th, at 11:00AM in Fretwell 116

November 24, 2015 by Duan Chen
Categories: Spring 2022
Jun-Tao Guo, Department of Bioinformatics and Genomics, University of North Carolina at Charlotte, Hosted by Jiancheng Jiang
Title: Structure-based prediction of transcription factor binding sites
Abstract: Transcription factors (TFs) regulate gene expression through binding to specific target DNA sites. Accurate annotation of transcription factor binding sites (TFBSs) at genome scale represents an essential step to our understanding of gene regulation networks. In this talk, I will present our recent work on structure-based prediction of TFBSs using an integrative energy function. The new energy function combines a multi-body statistical potential and two atomic energy terms, hydrogen bond energy and π-interaction energy. This energy function was tested on a set of homeodomains, the second largest transcription factor family in mammals, as well as a non-redundant dataset consisting of transcription factors from different families. Our results show that this integrative energy function improves the prediction accuracy over the knowledge-based, statistical potentials.

 

Thusday November 19th, at 3:30PM in Fretwell 315

November 06, 2015 by Duan Chen
Categories: Spring 2022
Igor Sokolov, Department of Mechanical Engineering, Department of Biomedical Engineering, Department of Physics, Tufts University, Medford, MA
Title: On some emerging mathematical and statistical needs in nanoscience
Abstract: The study of surfaces at the nanoscale (done mostly with atomic force microscopy (AFM) these days) allows imaging not only a sample surface but also mapping its physical and chemical properties. As an example, each set of AFM images/maps can be characterized with up to independent 180 parameters (for example, roughness of the rigidity map, fractal dimension of adhesion, etc.). These parameters are important not only to characterize material but for medical diagnostics. If one considers a combination of these parameters as another parameter, the total number of parameters becomes virtually unlimited. If one adds inevitable noise in each of the images, the problem of classification of the surface parameters and their combinations becomes highly nontrivial.

In this talk I will describe several promising applications in which there is a strong need in the mathematical and statistical tools. A particular emphasis will be given in the early detection of cancerous changes at the single cell level. I will show that the analysis of even one particular parameter might be of big interest, and also can bring the need in new mathematical models. Specifically, the parameter of “multifractality” (deviation of cell geometry from fractal) will be analyzed. I will show how this may have potential implication on understanding of the nature of cancer, and maybe identifying new ways to attack on cancer

 

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.