Department Colloquia

September 21, 2012

Dr. Haiyan Su, Department of Mathematical Sciences, Mont Clair State University

Title: Semiparametric Hybrid Empirical Likelihood Inference for Two-sample Comparison With Censored Data

Abstract: Two-sample comparison problems are often encountered in practical projects and have widely been studied in literature. Owing to practical demands, the research for this topic under special settings such as a semiparametric framework have also attracted great attentions. Zhou and Liang (2005) proposed an empirical likelihood-based semi-parametric inference for the comparison of treatment effects in a two-sample problem with censored data. However, their approach is actually a pseudo-empirical likelihood and the method may not be fully efficient. In this study, we develop a new empirical likelihood-based inference under more general framework by using the hazard formulation of censored data for two sample semi-parametric hybrid models. We demonstrate that our empirical likelihood statistic converges to a standard chi-squared distribution under the null hypothesis. We further illustrate the use of the proposed test by testing the ROC curve with censored data, among others. Numerical performance of the proposed method is also examined.

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September 28, 2012

Dr. Alfredo Hero,  Department of Electrical Engineering and Computer Science, University of Michgan

Learning with entropic graphs

Abstract

Entropy is a higher order extension of second order measures, like
variance and correlation, that characterize uncertainty in terms of the
spread of a distribution or conditional distribution. Entropy
minimization principles can be used to generalize correlation methods
such as principal component analysis (PCA), linear discriminant analysis
(LDA), and other linear models for doing data fusion, feature
extraction, and anomaly detection. Entropy can be estimated using
entropic graphs such as k-nearest neighbor graphs constructed over the
feature space. Entropic graphs have been applied to data analysis tasks
including image registration, intrinsic dimension estimation, spectral
clustering, and anomaly detection.

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October

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October 12, 2012

Dr. Mohammad Khoshneshin, ASOR, BGSU.

Title: Latent Feature Networks for Statistical Relational Learning

Abstract: In this talk,  latent feature networks (LFN) which is an approach for
multi-relational learning via latent variable models will be
presented. Multi-relational learning approaches model multiple
relationships simultaneously. LFN assumes a component for each
relationship. Each component is a latent variable model where a latent
variable is defined for each entity and the relationship is a function
of latent variables. However, if an entity participates in more than
one relationship, then it will have a separate random variable for
each relationship.  LFN can be applied to social network data where
there are heterogeneous relationships. We used LFN for link prediction
in a social network with side information and we showed that using
side information can improve the accuracy of the model drastically.

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Octorber 20, 2012

Dr Reza Medarres, Department of Statistics, George Washington University

Title: Data Depth on Graphs

We represent the observations of a random sample in R^d as vertices of a complete weighted graph and define their depths using several depth functions. We explore the proximity graphs, expose their connection to depth functions and extend this connection to β-skeleton graphs. We define new depth functions on the minimum spanning tree (MST) of the observations and study their properties. The path depth (PD) function of a vector t is the probability that t is on a random path (Xi,...,Xj) of the MST where Xi and Xj are two i.i.d observations from distribution function F . We generalize PD, discuss depth functions based on MST peeling, MST runt, and MST eccentricity and their corresponding multivariate medians. The PD median is the most accessible vertex on the MST, where the PD is maximized. A comparison of the depth functions and associated medians in terms of computational complexity and breakdown point is presented.

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October 26, 2012

Dr. Peter Tingley, Department of Mathematics, MIT

Title:  Various constructions of (affine) Mirkovic-Vilonen polytopes

Kashiwara's crystals are nice combinatorial objects that can be used
to study semi-simple Lie groups, and more generally symmetrizable
Kac-Moody groups. There are a number of explicit realizations of this
combinatorics. In finite type one fruitful realization uses polytopes
defined from the so called ``affine grassmannian" (these are the
Mirkovic-Vilonen polytopes of the title). These same polytopes come up
naturally in several other contexts, including PBW bases, quiver
varieties, and Khovanov-Lauda-Rouquier algebras, all of which make
sense beyond finite type. This gives several ways to extend the
theory. The story is nicest in affine type, and there all the
constructions lead to identical combinatorial objects, which we call
affine MV polytopes. I will explain as much of this as I can and show
some pretty pictures of the resulting combinatorial objects.

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November

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November 2, 2012

Dr. Thomas Kerler, Department of Mathematics, The Ohio State University.

Title: Building 3-Manifolds with Hopf algebras

 In the early 1990's an astonishing confluence of discoveries in statistical mechanics, quantum field
 theory, topology and various algebraic fields led to the construction of a large family of new invariants
 of 3-manifolds starting from certain types of Hopf algebras.

 It turns out that Hopf algebras serve not only as algebraic input data for these constructions, but that,
 in a more abstract sense, Hopf algebras are themselves can be understood as the building blocks
 of 3-manifolds.

 In more precise terms, we will describe a functor from an abstract braided category generated by a
 Hopf algebra object subject to relations given by customary axioms onto the category of 2+1-dimensional
 cobordisms. Well known analogous results on 1+1-dimensions will serve as warm-up. Time permitting
 we will give examples of so presented 3-manifolds, implications for the above mentioned quantum
 invariants, and hint to new developments regarding the injectivity of this functor.

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November 16, 2012

Dr. Manuel Lladser,  Departmenf of Applied Mathematics, Unviersity of Colorado Denver

TITLE: Prediction of the discovery probability of an urn sample.

ABSTRACT: Consider an urn with colored balls but with a completely unknown composition i.e. you do not know
what are the specific colors in the urn nor their relative proportions. Since World War II, various approaches have been
proposed to learn about the urn's composition, based on a sample with replacement from the urn: Turing and Good proposed
predictors for the proportion in the urn of colors observed k-times in the sample to break the Enigma cipher and, more
recently, Mao proposed a predictor for the overall proportion of the colors not observed in the sample to predict the probability
of discovering a new gene from expressed sequence tags in cDNA libraries. In the talk, I will present a new methodology, based
on randomized sample sizes, for the discovery probability of a random sample of size n from an urn. The methodology
leads to conditionally unbiased estimators of this quantity as well as exact prediction intervals. The pros and cons of the
proposed methodology will be discussed and compared against other approaches found in the literature with simulations
from analytic and non-analytic urns. This work is in collaboration with R. Gouet and J. Reeder.

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November 30, 2012

Dr. Asuman Turkmen,  Departmenf of Statistics,  The Ohio State University.

Title: Identification of Common and Rare Variants Associated with Complex Traits

Abstract:
Despite the great successes of genome-wide association studies (GWAS) for complex traits, most common SNVs (single nucleoid variants) identified to date have very small effect sizes, and the proportion of heritability explained is also small for most traits, motivating interest in rare variants that may contribute to genetic risk. Although methods developed for analysis of common variants, such as single-marker tests, can be easily extended to rare variants, they suffer from reduced power due to low frequency of rare variants even in very large samples. Here, we present a robust and powerful statistical method (termed rPLS) that considers a gene as a fundamental unit in the modeling and aggregates information within SNVs to uncover associations that are too weak to be detected individually. The method employs an initial data-mining tool to increase power for detecting associated variants by effectively weeding out irrelevant ones. Furthermore, the proposed methodology allows us to include non-SNV covariates to investigate their interacting effects with genes affecting the trait. Simulation settings based on the 1000 Genomes sequencing data and reflecting real situations are utilized to demonstrate that rPLS performs well compared to existing methods especially when there are a large number of non-causal variants (both rare and common) present in the gene and when causal SNVs have different effect sizes and directions.

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January

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January 11, 2013

Dr. Tullia Dymarz, Department of Mathematics, University of Wisconsin-Madison

Title: Quasisymmetric vs BiLIpschitz maps

Abstract: Quasisymmetric maps are maps that are metrically defined and
closely related to quasiconformal maps.  Quasisymmetric maps of both
euclidean space and the p-adics are abundant but we show that when you
consider the product space of the two all quasisymmetric maps are
biLipschitz.  Furthermore,  our proof does not use any direct analysis
but instead uses coarse topology and results from negative curvature.

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January 14, 2013

Dr. Bangti Jin, Department of Mathematics, Texas A&M University

Title: An Invitation to Fractional Differential Equations

Abstract
In this talk, we consider di_erential equations with a fractional-order deriva-
tive, which arise in many practical applications, e.g., underground ow and ma-
terial science, and have attracted much interest in the past few decades. We will
describe basics of fractional calculus, especially Riemann-Liouville fractional deriva-
tive and Caputo fractional derivative and their properties, and discuss the inuence
of the nonlocal nature of the fractional derivatives on the solution behavior, in-
verse problems and numerical analysis. These di_erent aspects will be illustrated
with two \simple" examples, i.e., time-fractional di_usion problem and fractional
Sturm-Liouville problem.

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January 16, 2013

Dr. Qingshan Chen

Title: Ocean Modeling: The Chalanges and Opportunities

Abstract
The ocean is a critical component of our climate system as it transports water and heat around the globe. Its behavior also has direct impacts on our human society, for which one can mention the example of the sea level rise or the El Nino phenomenon. Hence, an accurate representation of the ocean makes economical sense and also helps us to better understand our climate system. Geophysical fluid dynamics has been studied by mathematicians in the last two decades or so, and yet it is still full of interesting and challenging problems. This talk is oriented to the general mathematical audience. In the first part, a brief introduction to geophysical flows, with the ocean in particular, is given. The second part discusses a set of challenges that mathematicians are likely to be interested in and can make contributions to. The last part of this talk introduces a new co-volume scheme that is suitable for three-dimensional geophysical flows.

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January 18, 2013

Dr. Chris Haruska, Department of Mathematical Sciences, University of Wisconsin-Milwaukee


Title: Cubulating groups

Abstract:
Sageev showed how to construct a nonpositively curved cube complex
dual to a system of "walls" in a space.  If a group acts on this
"wallspace" then the group also acts on the dual cube complex.  The
rich combinatorial structure of this cube complex often has deep
consequences for the structure of the group.  For instance, recent
work of Wise on cube complexes played a key role in Agol's proof of
the Virtual Haken Conjecture for hyperbolic 3-manifolds.  I will give
a gentle introduction to this subject with an emphasis on examples.

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January 23, 2013

Dr. Daniel Munther, York University


Abstract:
In this talk, I will discuss mathematical models of two different problems in mathematical biology: food-borne diseases and population ecology.  The first part of the talk concerns a new model that Jianhong Wu and I developed which focuses on contamination dynamics during the wash procedure in a commercial processing plant. In addition to quantifying these dynamics, we use Monte Carlo methods to link model predictions to issues in disease surveillance. The second part involves the studying the evolution of dispersal via reaction-diffusion-advection models.  Using both analytic and computational approaches, we discuss how the spatial variation of resources influences the movement of species and their ecology.

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January 25, 2013

Dr. Hong Zhu, Division of Biostatistics, the Ohio State University

Title: Inference on bivariate survival data with interval sampling through Kendall's tau: testing and association measure


Abstract:
In many biomedical applications, interest focuses on the occurrence of two or more consecutive failure events and the association between event times. Bivariate survival data with interval sampling arise fre- quently when disease registry or surveillance systems commonly collect data with incidence of disease occurring within a calendar time inter- val. The initiating event is retrospectively confirmed and subsequent failure event is observed during follow-up. In cancer studies, the ini- tiating and two consecutive failure events could correspond to birth, cancer onset and death. Such data represent a non-randomly screened subset of a population and the interval sampling bias needs to be prop- erly adjusted for in analysis. Similar to truncated survival data, the analysis method for this type of data relies on the key assumption of independence, that is, the disease process does not depend on when the initiating event occurs. This paper proposes a nonparametric test of a relatively weaker but sufficient assumption of quasi-independence based on a coordinatewise conditional Kendall’s tau for bivariate sur- vival data with interval sampling. Further, to quantify dependence between bivariate failure times given quasi-independence, a nonpara- metric estimator of Kendall’s tau that uses inverse probability weights is developed, where the contribution of each comparable and order- able pair is weighted by the inverse of the associated probability. Sim- ulation studies demonstrate that the test procedure and association estimator perform well with moderate sample sizes. The methods are applied to ovarian cancer registry data for illustration.

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January 30, 2013

Dr. Joyce Lin, University of Utah

Modeling the Electrical Activity in Cardiac Tissue
 
Abstract: Electrical stimulation of cardiac cells causes an action potential wave to propagate through myocardial tissue, resulting in muscular contraction and pumping blood through the body. Approximately two thirds of unexpected, sudden cardiac deaths, presumably due to ventricular arrhythmias, occur without recognition of cardiac disease. While conduction failure has been linked to arrhythmia, the major players in conduction have yet to be well established. Additionally, recent experimental studies have shown that ephaptic coupling, or field effects, occurring in microdomains may be another method of communication between cardiac cells, bringing into question the classic understanding that action potential propagation occurs primarily through gap junctions. In this talk, I will introduce the mechanisms behind cardiac conduction, give an overview of previously studied models, and present and discuss results from a new model for the electrical activity in cardiac cells with simplifications that afford more efficient numerical simulation, yet capture complex cellular geometry and spatial inhomogeneities that are critical to ephaptic coupling.
 

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February

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February 1, 2013

Safety Instruction

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February 8, 2013

Safety Instruction

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February 15. 2013

1. Grigori Avramidi, the Ohio State University  (1:30pm to 2:20pm)

Title: Isometries of aspherical Riemannian manifolds.

Abstract: The talk will be about isometry groups of aspherical Riemannian manifolds. A manifold is aspherical if it has no higher homotopy groups (equivalently, its universal cover is contractible). A common theme is that much of the geometry and topology of an aspherical manifold is controlled by its fundamental group. It turns out that the symmetries of a Riemannian metric on an aspherical manifold are often constrained by the fundamental group of the manifold. The goal of the talk is to illustrate this phenomenon in some simple examples.

2. Tam Nguyen-Phan, the Ohio State University  (2:30pm t0 3:20pm)

Title: Finite volume, negatively curved manifolds

Abstract: I will talk about the topology of noncompact, complete, finite volume, negatively curved manifolds. Gromov proved that if M is such a manifold and the sectional curvature of M is -1<K(M)<0, then M is the interior of a compact manifold with boundary. I will discuss how different curvature conditions control the topology of the boundary and give examples of different boundaries that arise. I will also discuss new phenomena that happen when the curvature conditions are relaxed.

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February 22. 2013

Rong Liu, University of Toledo


Credit rating via Generalized Additive Partially Linear Model
 
Abstract
 
One central field of modern financial risk management is corporate credit rating in which default prediction plays a vital role. Generalized Additive Partially Linear Model (GAPLM), which is a multivariate semiparametric regression tool for non-Gaussian responses including binary and count data. We use GAPLM to make default prediction and propose spline-backfitted kernel (SBK) estimator with simultaneous confidence bands for the component functions and BIC constructed for components testing and selection.  The SBK technique is both computationally expedient and theoretically reliable, thus usable for analyzing high-dimensional time series. Simulation evidence strongly corroborates with the asymptotic theory. The method is applied to estimate insolvent probability and obtain higher accuracy ratio than previous study.
 
 

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March

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March 15, 2013

Dr. Lingsong Zhang, Department of Statistics, Purdue University


Title: Some Statistical Methods Based on Singular Value Decomposition


Singular Value Decomposition is widely used in analysis of two-way (functional)  data. In this talk, a novel visualization tool will be proposed to highlight important modes of variation. Huang et al (2009) generalized the usual SVD method to regularized SVD (RSVD), which is more suitable for functional data. Note that both SVD and RSVD are sensitive to outliers. We will propose RobSVD  and RobRSVD methods to improve the performance of the above two  methods. Simulation and applications will be used to illustrate the usefulness of these two methods.
 

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March 22, 2013

Dr. Emily Peters, Department of Mathematics, Northwestern University


Title: Planar algebras and evaluation algorithms

Planar algebras are a formalization of "proof by picture" techniques that are used, for instance, in knot theory and subfactor theory.  When one tries to directly construct a planar algebra, by generators and relations, one quickly runs into the standard problems, like:  how do I decide if what I have is just a dressed-up version of the trivial planar algebra? Sometimes, one can answer this type of question by giving an "evaluation algorithm" based on the relations available.  In this talk, I will define planar algebras and give some of my favorite examples of planar algebras with cool evaluation algorithms.

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March 29. 2013

Dr. Yanhong Wu, Department of Mathematics and Statistics, BGSU


Title: Parameter Estimation of Renal Models

A minimal mathematical model of TGF system in a short-looped nephron of the mammalian kidney was developed by Layton, Pitman and Moore. The two crucial parameters of the feedback gain and the time delay  arise  in the bifurcation analysis of the minimal model and  play important role in understanding the autoregulation of renal blood flow in renal hemodynamics. In this talk, an approach  called Bayes linear method  will  be presented  about estimating  these two  important parameters  given a time series of oscillatory behavior of observations.  Likely regions of the estimated parameters are obtained  instead of confidence intervals.
     Bayes linear methods are introduced by Goldstein and Woof. The methods only require the specification of prior expectations, prior covariances and variances for the random quantities we are interested in, without needing the full probability distributions for the random quantities. The random quantities are linearly updated when more information is provided.

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April

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April 5, 2013

Zhonggai Li, Novartis.

Bayesian Analysis for Binary Response Clinical Trial with Imperfect Gold Standard

 
ABSTRACT

Binary response is one of the common end-points for diagnostic tests. A new medical diagnostic instrument usually is required to get regulatory approvals prior to its marketing. If there is an existing instrument with similar functionality in the market already, it is typically used as a reference. This reference is usually not 100% correct, which is called imperfect gold standard. In practice, parts of the discrepant samples from both methods may be sent to further adjudication.  A series of statistical problems are involved over this type of clinical trials, such as multiple tests, multiple sites, multiple stage sampling, sequential trials, and power analysis. There is lack of statistical method that addresses all of these involved statistical problems. In this talk, the statistical problems involved will be discussed. Several Bayesian models proposed to handle one or all of the statistical problems involved will be introduced.  A clinical trial experiment is used as an example to demonstrate the statistical problems and the developed Bayesian models.

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April 12, 2013

Steven, Maceachern, Department of Statistics, the Ohio State University

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April 19, 2013

Dr. Changliang Zou, NanKai University (11:30am-12:20pm)


Dr. Andrew Thomas, Department of Statistics, Carnegie Mellon University (3:45pm-4:45pm)

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