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Department ColloquiaFall 2011 & Spring 2012 |
September 9, 2011
Dr. Graeme Fairweather, Executive Editor Mathematical Reviews, AMS
Title : Mathematical Reviews in its Eighth Decade
Abstract: Mathematical Reviews (MR), a division of the American Mathematical Society, was founded in 1940 by Otto Neugebauer to serve researchers and scholars in the mathematical sciences by providing timely information on articles and books containing new contributions to mathematical research. Since its first issue in January 1940 which contained 176 reviews and consisted of 32 pages, it has grown to a database of over 2.7 million entries. After a brief overview of MR’s history, I will describe the path a published article takes from its arrival at MR until it appears as an MR review. Most users access the MR database using the Web interface MathSciNet. Recent updates and improvements to MathSciNet will be demonstrated.
September 16, 2011
Dr. Craig Zirbel, Bowling Green State University
Title : Predicting the 3D structure of RNA hairpins and internal loops from sequence alone
Abstract : All living organisms have DNA to store their genetic information and use RNA to copy and transmit this information within each cell. But RNA molecules have other important roles as well, which they perform by folding back on themselves to form helices, hairpins, junctions, and internal loops before assembling into a specific 3D structure. The helices are known to be made up of GC and AU Watson-Crick basepairs (very similar to the GC and AT basepairs in DNA), but the hairpins and internal loops have other basepairs which come in 11 additional families. All 12 families of RNA basepairs have characteristic sequence variability, which we see when we compare the same RNA molecule across many species. In this talk, we show that the basepair structure of hairpin and internal loops leads to specific rules for sequence variability for the loop as a whole. We build probabilistic models for this sequence variability using stochastic context-free grammars (SCFG) and Markov random fields (MRF). There are roughly 100 distinct hairpins and 100 distinct internal loops. We show that we can infer the correct hairpin or internal loop from the sequence alone with high accuracy. This will be of great use to biologists studying new RNAs which are known only by their sequences.
September 23, 2011
Dr. Lu Wang, University of Michigan at Ann Arbor
Title : Efficient Estimation in Semiparametric Regression with Missing Data
Abstract : Missing data are common in observational studies, sample surveys, and clinical trials. There is a vast literature on estimation methods in parametric regression models with missing data. However, the functional form of the dependence of an outcome on a covariate is often unknown a priori and can be complicated. In this talk we propose nonparametric and semiparametric methods when the outcome is missing at random (MAR). The inverse probability weighted kernel estimating equations (KEEs) and a class of augmented inverse probability weighted KEEs are developed to estimate the nonparametric regression curve. We also derive the semiparametric efficiency bound and propose weighted Kernel-Profile estimating equations for finite-dimensional parameters in semiparametric regression models under MAR. We study the asymptotic properties of the proposed estimators including asymptotic bias and variance, efficiency, and double robustness. The proposed methods are evaluated through simulations and illustrated using two data examples: the AIDS Costs and Services Utilization Survey data and the two-stage myocardial ischemia screening data.
September 30, 2011
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October 7, 2011
Sarah Wingfield, Wolfram Research Inc
Title : An overview of Mathematica for Education and Research
Abstract :This talk illustrates capabilities in Mathematica 8 that are directly applicable for use in teaching and research on campus. Topics of this technical talk include: • Editing text, generating quizzes, and making presentations • Using free-form input to enter calculations in everyday English • Creating models in Mathematica to investigate classroom concepts • Accessing ready-to-use teaching models in math, physics, chemistry, biology, economics, engineering, music, and other subjects • Utilizing visualization tools and annotated graphics • Experiencing Mathematica's integrated data sources for chemicals, particles, cities and countries, financial instruments, astronomical objects, etc. • Applying and integrating data sources across disciplines and school departments • Using Mathematica's built-in documentation • Exploring the numerous resources available to teachers and researchers • Demonstrations of Digital Image Processing and Parallelization • Built-in Support for GPUs and C-code compilation and generation If you haven't seen Mathematica lately, you will be surprised to see how suitable Mathematica is for projects and course examples in any STEM, business and economics, or liberal arts field. Attendees with no prior experience report that this talk helps with getting started using Mathematica language and workflow. With improvements like the new free-form input and expanded areas like finance, statistics, engineering, software development, and image processing, even the most advanced users report learning quite a bit from Mathematica technical talks. All attendees will receive an electronic copy of the examples, which can be adapted to individual projects.
October 14, 2011
Dr. Mike Davis, The Ohio State University
Title : Coxeter groups and buildings
Abstract : Around 1960, Jacques Tits defined the notion of a Coxeter group or an "abstract reflection group" in connection with his theory of buildings. Classically, algebraists were almost exclusively interested in buildings where the associated Coxeter group was either a finite spherical reflection group or a Euclidean reflection group. More recently, Kac Moody groups and buildings for more or less arbitrary Coxeter groups have been discovered. I will explain the natural construction of a cell complex associated to any Coxeter group or building. These spaces are of independent interest in geometric group theory.
Octorber 20, 2011
Dr Fred Rickey, United States Military Academy
Title: The impact of ballistics on mathematics. The work of Robins and Euler in the eighteenth-century
Abstract : In the first half of the 18th century, Benjamin Robins, a British mathematician and military engineer, invented the ballistic pendulum. This device allowed for fairly accurate estimates of the muzzle velocities of muskets and other artillery. Through this experimental work he discovered that air resistance should not be neglected. In 1742 he published these results in New Principles of Gunnery, the first book to deal extensively with external ballistics. This book motivated a deeper analysis of projectile motion — a topic tackled by Leonhard Euler and Daniel Bernoulli. Subsequently, Frederick the Great encouraged Euler to translate this work of Robins. Euler, true to form, tripled the length of the work with his annotations and published them in 1745. The annotated text was translated back into English in 1777, which, two and a half centuries later, brings us to our theme here.
October 21, 2011
Dr. Linxiong Li, University of New Orleans
Title :DISTRIBUTIONS OF COTTON FIBER LENGTHS
Abstract : Fiber length is one of the most important properties of cotton in marketing and yarn processing. In the past decades, cotton industry and researchers have been trying to develop efficient methods to measure the length of cotton. However, nearly all efforts were focused on the distribution of the projecting fiber length. Studies on the distribution of actual fiber lengths, due to, we believe, technical difficulties, have not been done successfully. Since knowing the distribution of the actual fiber length is of great practical interest, we in this study are trying to develop a method that estimates the distribution of the actual fiber length based on the observed projecting length. In particular, we have obtained two results: (1) We found the distribution of fiber lengths which is a mixture of two Weibull distributions, and (2) we used partial least squares regression to estimate the distribution of the actual fiber length based on that of the projecting fiber length. Calculations show that the method works well.
October 28, 2011
Dr. Ji Zhu, University of Michigan
Title : Joint Estimation of Multiple Graphical Models
Abstract :Gaussian graphical models explore dependence relationships between random variables, through estimation of the corresponding inverse covariance matrices. In this paper we develop an estimator for such models appropriate for data from several graphical models that share the same variables and some of the dependence structure. In this setting, estimating a single graphical model would mask the underlying heterogeneity, while estimating separate models for each category does not take advantage of the common structure. We propose a method which jointly estimates the graphical models corresponding to the different categories present in the data, aiming to preserve the common structure, while allowing for differences between the categories. This is achieved through a hierarchical penalty that targets the removal of common zeros in the inverse covariance matrices across categories. We establish the asymptotic consistency and sparsity of the proposed estimator in the high-dimensional case, and illustrate its superior performance on a number of simulated networks. An application to learning semantic connections between terms from webpages collected from computer science departments is also included. This is joint work with Jian Guo, Elizaveta Levina, and George Michailidis.
November 4, 2011
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November 18, 2011
Dr. Gary McDonald, Oakland University
Reflections on Ridge Regression
Abstract : Ridge regression refers to a class of biased linear estimators used in a multiple linear regression context when the explanatory variables are highly correlated. In such instances, the optimal least squares estimator often yields regression coefficient estimates that have large variances. In addition, the direction of the least squares estimates may be reversed from prior knowledge and thus rendered meaningless from a practical perspective. Ridge regression is one approach to statistical estimation within this context. The motivations for considering this methodology will be reviewed reflecting the speakers’ experience using such methods for over three decades. Ridge regression estimators are rational functions in the so-called ridge parameter and this property leads to useful insights into the behavior of a ridge trace, i.e., a plot of ridge regression coefficients as a function of the ridge parameter. Several illustrative examples will be used to highlight various properties of the ridge estimator.
December 2, 2011
Dr. Xiaoli Gao, Oakland University
Title : Estimation and Selection Properties of the LAD Fused Lasso Signal Approximator
Abstract The fused lasso is an important method for signal processing when the hidden signals are sparse and blocky. It is often used in combination with the squared loss function. However, the squared loss is not suitable for heavy tail error distributions nor is robust against outliers which arise often in practice. The least absolute deviations (LAD) loss provides a robust alternative to the squared loss. In this paper, we study the asymptotic properties of the fused lasso estimator with the LAD loss for signal approximation. We refer to this estimator as the LAD fused lasso signal approximator, or LAD-FLSA. We investigate the estimation consistency properties of the LAD-FLSA and provide sufficient conditions under which the LAD-FLSA is sign consistent. We also construct an unbiased estimator for the generalized degrees of freedom (GDF) of the LAD-FLSA for any given tuning parameters. Both simulation studies and real data analysis are conducted to illustrate the performance of the LAD-FLSA and the effect of the unbiased estimator of GDF. :
December 9, 2011
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January 13, 2012
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January 20, 2012
Dr. Reinhard Laudenbacher, Virginia Bioinformaticis Institute and Virginia Tech.
Title : Algebraic models in systems biology
Abstract:Progress in systems biology relies on the use of mathematical and statistical models for system level studies of biological processes. Several different modeling frameworks have been used successfully, including traditional differential equations based models, a variety of stochastic models, agent-based models, and Boolean networks, to name some common ones. This talk will focus on several types of discrete models, and will describe a common mathematical approach to their comparison and analysis, which relies on computational algebraic geometry. This talk is suitable for undergraduates.
January 27, 2012
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February 3, 2012
Dr. Huixia Judy Wang, NCSU
Title : Estimation of high conditional quantiles for heavy-tailed distributions
Abstract:Estimation of conditional quantiles at very high or low tails is of interest in numerous applications. Quantile regression provides a convenient and natural way of quantifying the impact of covariates at di erent quantiles of a response distri- bution. However, high tails are often associated with data sparsity, so quantile regression estimation can su er from high variability at tails especially for heavy- tailed distributions. In this paper, we develop new estimation methods for high conditional quantiles by rst estimating the intermediate conditional quantiles in a conventional quantile regression framework, and then extrapolating these estimates to the high tails based on reasonable assumptions on tail behaviors. We establish the asymptotic properties of the proposed estimators, and demonstrate through simulation studies that the proposed methods enjoy higher accuracy than the con- ventional quantile regression estimates. In a real application involving statistical downscaling of daily precipitation in the Chicago area, the proposed methods pro- vide more stable results quantifying the chance of heavy precipitation in the area.
February 10, 2012
Kevin O'Malley, The Lubrizol Corporation, OH.
Title :Reaching Beyond Classical Statistical Approaches Innovative, non-classical approaches are needed to solve complex industry problems. Experimentation often requires designs that are highly customized to fit the needs of the project. Important steps when creating such designs are highlighted through an example of developing a superior paint. An experimental strategy is also introduced to shed light on how to develop designed experiments when the levels of the factors are unknown. Finally, a case study is used to show complexities in modeling when the response is estimated using a nonlinear function and the factors in the model are both mixture and process variables. These examples are only a glimpse into the variety of interesting problems facing industry statisticians.
February 17, 2012
Dr. Peng Zhang, Peking University
Title : Statistical Analyses of Evaluating the Clinical Utility of Quantitative Real-Time Loop-Mediated Isothermal Amplification for Diagnosis of Lower Respiratory Tract Infections
Abstract: Quantitative real-time loop-mediated isothermal amplification (qrt-LAMP) provides a new way to rapidly amplify and quantify the amount of multiple types of bacterial pathogens simultaneously. In this article, we propose a novel statistical approach to evaluating the clinical utility of qrt-LAMP for diagnosis of lower respiratory tract infections (LRTI), which has long been known for lack of a good diagnostic method. Partially, difficulty lies in the fact that multiple types of bacterial pathogens can inhabit the host system, while it is hard to distinguish the pathogens that colonize without causing problems versus those that rapidly grow and cause infection. New statistical methods are needed to differentiate bacterial colonization from infection and thus recommend the right choice/dosage of antibiotic treatments. This can be done using data collected through qrt-LAMP. We first utilize zero-inflated mixture models to estimate the prevalence of bacterial pathogens of interest through LAMP, and demonstrate that LAMP, utilized first time in detecting pathogens in sputum samples for diagnosis of LRTI, shows consistency with results from standard culture methods. We then employ a zero-inflated Tobit model to adjust for the effects of baseline covariates on both the probabilities of carrying pathogens and the quantities of pathogens for carriers. Clear clinical interpretations of such results further validate the applicability of utilizing qrt-LAMP to test for pathogens in sputum samples. Finally, we propose a novel framework to identify disease-causing pathogens by combining information from absolute quantities of pathogens and their symbiosis information, both of which are essential in eventually causing infection, to form G-scores to represent bacterial growth status. Change-point detection methods clearly reveal two change-points of these G-scores, which are closely related to three phases of bacterial growth — lag phase, log phase, and stationary phase. Piecewise-linear regression is used to identify such change-points.
February 24, 2012
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March 16, 2012
Dr. Yan Ma, Weill Medical College of Cornell University, NY
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March 23, 2012
Dr. Louis Kauffman, University of Illinois at Chicago
Title :Virtual Knot Theory
Abstract: This talk is an introduction to virtual knot theory, and is a self-contained introduction to combinatorial knot theory based on the Reidemeister moves. A knot is an embedding of a closed curve (called a link if there are multiple curves) into three dimensional space. Knots are usually taken up to ambient isotopy in three-space, meaning that two knots are equivalent if there is a continuous family of embeddings starting with one knot and ending with the other. In the 1920's Kurt Reidemeister initiated an approach to the theory of knots in three dimensional space based on taking a projection of the knot to a plane with transversal self intersections. Such a projection appropriately labeled at the crossings (the self-intersections) can be used to reconstruct the embedding from which it was projected, up to ambient isotopy. Reidemeister discovered a set of moves on the projections so that two labeled projections (called knot diagrams) represent the same knot-type if and only if they are related by the Reidemeister moves. Thus began combinatorial knot theory. In the 1980's the Jones polynomial was constructed via a purely diagrammatic definition. To this day, there is no other satisfactory definition of the Jones polynomial. At the present time conbinatorial knot theory is a very rich subject due to a host of constructions of invariants that use Reidemeister's method and due to its extension to virtual knot theory. We will illustrate examples and discuss the Jones polynomial and its natural extension to knots embedded in thickened surfaces. This leads directly to virtual knot theory, which is a combinatorial approach to the study of knots in thickened surfaces, part of the wider subject of knots in three dimensional manifolds.
March 30, 2012
Dr. Mei Wang, University of Chicago
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April 6, 2012
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April 13, 2012
Dr. Shiming Zheng, College of Public Health, East Tennessee State University
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April 20, 2012
Dr. Hammou Elbarmi, Baruch College, City University of New York
Title : Inference for uniform stochastic using empirical likelihood
Abstract: Let T1,T2,...,Tk be survival functions of life distributions. They are said to be uniformly stochastically ordered, T1 <=uso T2 <=uso<=... <=uso Tk, if Ti=Ti+1 is a survival function for 1 <= i <= k-1: The nonparametric maximum likelihood estimators of the survival functions subject to the ordering constraint, based on independent random samples, are known to be inconsistent in general for cases other than the multinomials with a common support. Consistent estimators were developed in the case of k = 2 in the early 1990's; however, the general k-sample case had been elusive. In this talk I will provide consistent estimators in the k-sample case with no restrictions on the survival functions. They are applicable to both the uncensored and censored cases and they are strongly uniformly consistent. I will also developed a test of homogeneity against uniform stochastic ordering. Some real life data will be used to illustrate the theoretical results. 1
April 27, 2010
Dr. Masoud Khalkhali, The University of Western Ontario
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