Tuesday, May 15, 2015
University of Nebraska-Lincoln
Title: Cluster analysis of High dimensional data
Abstract: We discuss the high dimensional data that the distance between objects become degenerate,
we present a technique for clustering categorical data by generating many dissimilarity matrices. We begin by demonstrating our technique on low dimensional categorical data and comparing it to several other techniques. The proposed methods are the extension of ensembling approach that pool several random models to draw the inference. We discuss couple of examples to study the performance of proposed methods.
Tuesday, May 12, 2015, AB635 at 2:30pm
Alexander Kirpich (Guest Speaker )
Department of Biostatistics, Colleges of Medicine and Public Health Professions, University of Florida
Title: Cholera Transmission in Ouest department of Haiti: Dynamic modeling and prediction.
Abstract: The goal of this analysis is to build a comprehensive compartmental model for cholera transmission and to apply it to the analysis of the data collected in Haiti. The challenge with cholera modeling, like with many other infectious diseases, is the course of the dis-ease. The majority of the infections remain asymptomatic and, therefore, unobserved. Un-derreporting is another issue, i.e. not everyone who develops symptoms is actually properly recorded. Disease transmission mechanisms are not completely understood at the moment, but it is believed that external water reservoirs of bacteria and environmen-tal factors such as temperature and precipitation play significant roles in triggering trans-mission and facilitating further spread of the epidemic. All that should be addressed in the analysis. We propose the model that will incorporate the incidence and the environ-mental data that are typically available from surveillance, and apply our model to the da-ta collected in Haiti. When a new epidemic arises it is crucial to react appropriately. Prop-er public health measures such as vaccination campaigns or improved access to purified or bottled water can curb the epidemic or even stop it completely. We evaluate the effec-tiveness of the vaccination campaigns in our model by producing the epidemic outcomes under vaccine intervention. We also look at the behavior of the model in the long run over a period of ten years and evaluate the possibility of future outbreaks.
Thursday, April 23, 2015, AB 634 at 2:30pm
Kirsten Morris, Applied Mathematics Department, University of Waterloo
Title: Sensors & actuators in control of partial differential equations
Abstract: For control of systems that vary in space, there is generally choice in the type of actuator and sensors used and also their locations. Performance depends on the location of controller hardware, the sensors and actuators. The best locations may be different from those chosen based on physical intuition. Since it is often difficult to move hardware, and trial-and-error may not be effective when there are multiple sensors and actuators, analysis is crucial. Similarly, better estimation can be obtained with carefully placed sensors. Proper placement when there are disturbances present is in general different from that appropriate for reducing the response to an initial condition, and both are quite different from locations based on optimizing controllability or observability. The choice of actuator and sensor and their models are also factors in controller design. The models for these systems will be coupled ordinary/partial differential equations (PDE's). Approximations to the governing equations, often of very high order, are required and this complicates both controller design and optimization of the hardware locations. Numerical algorithms and issues will be briefly discussed.
Thursday, April 16, 2015, AB 634 at 2:30pm
Hal Smith, School of Mathematical and Statistical Sciences, Arizona State University
How Nested Infection Networks in Bacteria-Virus Communities Come To Be
Abstract. This talk is essentially motivated by a series of recent papers from J. Weitz's group on phage-bacteria infection networks in natural ecosystems. Their work showed that phage-bacteria infection networks in natural ecosystems, describing which phage infect which bacteria, often have a nested structure in which phage strains can be ordered according to the extent to which they are specialists or generalists at infecting bacterial strains and where bacterial strains infected by a more specialist phage are also infected by a more generalist phage. In a recent paper, Weitz et al raised the question of whether a Lotka-Volterra-like model of a phage-bacteria community with nested infection network is permanent provided that bacterial strains that grow faster devote the least effort to defence against infection and virus strains that are the most efficient at infecting host have the smallest host range. Motivated by these works, grad student Dan Korytowski and I show that a mathematical model of a phage-bacteria community in which the bacterial strains compete for a single limiting nutrient in a chemostat setting and for which the infection network is perfectly nested is permanent, a.k.a. uniformly persistent, provided that bacteria strains that are superior competitors for nutrient devote the least effort to defence against infection and virus strains that are the most efficient at infecting host have the smallest host range. In addition, we answer the question in the title by showing that a permanent bacteria-phage community with an arbitrary number of bacteria and phage types for which the infection network is nested can arise through a succession of permanent sub-communities, each with a nested infection network, by the successive addition of one new population.
Thursday, April 9, 2015 , in AB 634 at 2:30pm.
Angelica Osorno, Mathematics Department, Reed College
Why do algebraic topologists care about categories?
Abstract. The study of category theory was started by Eilenberg and MacLane, in their effort to codify the axioms for homology. Category theory provides a language to express the different structures that we see in topology, and in most of mathematics. Categories also play another role in algebraic topology. Via the classifying space construction, topologists use categories to build spaces whose topology encodes the algebraic structure of the category. This construction is a fruitful way of producing important examples of spaces used in algebraic topology. In this talk we will describe how this process works, starting from classic examples and ending with some recent work.
Friday, April 3, 2015, DMSC 102 at 2:30pm
Dr.Jing-Jing Huang, Department of Mathematics, University of Toronto
From counting rational points to diophantine approximation
Abstract: The distribution of rational points on algebraic varieties is a central problem in number theory. An even more general problem is to investigate rational points near manifolds, where the algebraic condition is replaced with the non-vanishing curvature condition. I establish, for the first time, a sharp asymptotic formula for the rational points of a giv-en height and within a given distance to a hypersurface. This has surprising applications to counting rational points lying on the manifold; indeed setting the distance to zero, I am able to prove an analogue of Serre's Dimension Growth Conjecture (originally stated for projective varieties) in this general setup, which roughly says that the number of rational points of a given height on the manifold is bounded above by the height to the power of the dimension of the manifold. In the second half of the talk, I will focus on metric diophantine approximation on manifolds and its connection with the counting problem described above. A long standing conjecture in this area is the Generalized Baker-Schmidt Problem, a beautiful Zero versus Infinity law for the Hausdorff measure of well-approximable points on the manifold in terms of an arbitrary approximation function. As another consequence of the main counting result above, I settle this problem for all hypersurfaces with non-vanishing Gaussian curvatures. Final-ly, if time permits, I will briefly elaborate on the main ideas behind the proof.
Tuesday, March 31, 2015, in AB 634 at 2:30pm
Dr. Daniel Vallieres, Department of Mathematical Sciences, Binghamton University
Abelian Artin L-functions at zero
Abstract: In the early 1970s, Harold Stark formulated a conjecture about the first non-vanishing Taylor coefficient at zero of Artin L-functions. About 10 years later, he refined his conjecture for abelian L-functions having order of vanishing one at zero, under certain hy-potheses. In 1996, Karl Rubin extended this last refinement of Stark to the higher order of vanishing setting. In this expository talk for a general audience, we will give a survey of this area of research and present a more general conjecture, which we formulated in the past few years. At the end, we will present evidence for our conjecture and indicate one possible direction for further research.
Monday, March 30, 2015, DMSC 105 at 2:30pm
Daniel Szpruch, Department of Mathematics, Indiana University
Shahidi local coefficients and irreducibility results on coverings of p-adic SL(2).
Abstract: The Langlands-Shahidi method has proven to be one of the most powerful tools to study L-functions. This method is based on a certain uniqueness theorem known as unique-ness of Whittaker functional which gives rise to a family of meromorphic functions called Shahidi local coefficients. Among the local applications of the Langlands-Shahidi method one finds a criteria for irreducibility of unitary parabolic induction on quasi-split reductive algebraic groups in terms of poles of automorphic L-functions. In this talk we shall sur-vey the definition of Shahidi local coefficients in the basic and important example of p-adic SL(2) and discuss the irreducibility question. We shall then discuss a similar prob-lem for coverings of SL(2). Coverings of linear groups, sometimes called metaplectic groups, are nowadays studied by many representation and number theorists. One of the main difficulties in studying these non-algebraic groups is the failure of uniqueness of the Whittaker functional. Neither background on p-adic numbers nor knowledge on rep-resentation theory beyond basics is required for this talk. This is joint work with David Goldberg.
Friday, March 27, 2015, in DMSC 102 at 2:30pm
Minsun Song, Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, NIH
Testing for Genetic Associations in Arbitrarily Structured Populations
Abstract. We present a new statistical test of association between a trait and genetic markers, which we theoretically and practically prove to be robust to arbitrarily complex population structure. The statistical test involves a set of parameters that can be directly estimated from large-scale genotyping data, such as that measured in genome-wide associations studies (GWAS). We also derive a new set of methodologies, called a genotype-conditional association test (GCAT), shown to provide accurate association tests in populations with complex structures, manifested in both the genetic and environmental contributions to the trait. Our proposed framework provides a substantially different approach to the problem from existing methods. We provide some discussion on the popular methods for correcting population structure including the linear mixed model and principal component approaches.
Thursday, March 26, 2015, AB 634 at 2:30pm
Qing Nie, Department of Mathematics, University of California, Irvine
Stem Cells: From Simple Model to Big Data
Abstract. In developing and renewing tissues, terminally differentiated cell types are typically specified through the actions of multistage cell lineages. Such lineages commonly include a stem cell and multiple progenitor cell stages, which ultimately give rise to terminally differentiated cells. In this talk, I will present several modeling frameworks with different complexity on multistage cell lineages driven by stem cells, which account for diffusive signaling molecules, regulatory networks, individual cells, mechanics, and evolution.
Questions of our interest include role of feedbacks in regeneration, stem cell niche for tissue spatial organization, crosstalk between epigenetic and genetic regulations. In addition, I will discuss our recent effort on connecting modeling and big data by integrating prior knowledge and heterogeneous spatial and temporal data for elucidating developing tissues.
Friday, March 13, 2015, in DMSC 102 at 2:30pm
Apratim Ganguly, Department of Mathematics and Statistics, Boston University
Local Neighborhood Fusion in Locally Constant Gaussian Graphical Models
Abstract. Sparsity in the precision matrix of a multivariate Gaussian random variable is a direct consequence of conditional independence among a significant proportion of its univariate component pairs. In most modern applications of high dimensional statistical learning in Gaussian graphical models, unavailability of a large enough sample led researchers to think about alternatives to classical statistical procedures. Neighborhood selection using lasso (Meinshausen & Buhlmann), block-coordinate descent algorithm to estimate the covariance matrix (Banerjee et al.), graphical lasso (Tibshirani et al.) are some of the most popular ones. In this talk, I will present an alternative method for model selection, leveraging on the local information in Gaussian graphical models on a manifold. This is inspired by the idea of local constancy, introduced by Honorio et al. (2009) who incorporated the spatial information in model selection. However, the notion was introduced very intuitively and no theoretical analysis in support of its superiority over traditional methods have been found in the literature. The algorithm we proposed extended the Meinshausen-Buhlmann's idea of node-wise regression by a generalized version of fused lasso penalty. This is referred as Neighborhood- Fused Lasso algorithm. We have shown by simulation and proved theoretically the asymptotic model selection consistency of the proposed method and established faster "convergence" to the ground truth, comparing its performance with Meinshausen-Buhlmann analogue with no local neighborhood penalty, under the assumption of local constancy. We further investigated the compatibility issues in our proposed mechanism and derived bounds on estimated coefficients and quadratic prediction error. This is a joint work with my PhD supervisor, Dr. Wolfgang Polonik.
Thursday, March 12, 2015, in AB 205 at 2:30pm.
Cornel Pasnicu, Department of Mathematics, University of Texas at San Antonio
Noncommutative zero dimensional topological space
Abstract. A C*-algebra can be thought as a noncommutative topological space or as a collection of infinite matrices of complex numbers endowed with an interesting algebraic and topological structure. The C*- algebras have significant applications in different areas of mathematics (geometry, topology, ergodic theory), parts of physics (quantum mechanics and statistical mechanics) and other sciences. Understanding the structure and classification of C*-algebras was and continues to be one of the most important research directions in Operator Algebras (G. A. Elliott and E. Kirchberg, I.C.M. 1994, M. Rordam, I.C.M. 2006). First, I will present, in a natural context and giving basic definitions and examples, a joint result with M. Rordam in which we characterize, in the separable case, for a large and important class of C*-algebras that are "infinite" in some specific sense (introduced by E. Kirchberg and M. Rordam) a certain condition of noncommutative zero dimensionality (introduced by L. G. Brown and G. K. Pedersen) that proved to be very successful in Elliott's well known Classification Program for C*-algebras (I.C.M. 1994). (Many C*-algebras of interest happen - sometimes surprisingly - to satisfy this condition). Some interesting consequences of this result that concern the structure of C*-algebras will be also presented. Our theorem strongly generalizes a result of F. Perera and M. Rordam (J. Funct. Anal. 2004) and, in the separable case, a result of S. Zhang. I will also discuss several permanence properties of some classes of "noncommutative zero dimensional topological spaces" (C*-algebras which have the ideal property) that are also "infinite" in the above sense (of E. Kirchberg and M. Rordam), obtained jointly with N. C. Phillips.
Friday, March 6, 2015, in AB 205 at 2:30pm
Reinier Broker, Department of Mathematics, Brown University
Constructing Elliptic Curves of Prescribed Order
Abstract. Elliptic curves have become increasingly important during the last 20 years. They play a key role in Wiles' proof of Fermat's last theorem, and they are one of the foundations of modern cryptography: every cell phone contains an elliptic curve nowadays. There are various efficient algorithms to count the number of points of a given elliptic curve over a finite field. In this talk I will consider the inverse problem of constructing elliptic curves of prescribed order. I¹ll present a solution that easily handles the sizes occurring in cryptographic practice. Many examples will be given.
Monday, March 2, 2015, in DMSC 105 at 2:30pm
Sang Yun Oh, Computational Research Division, Lawrence Berkeley National Lab
Principled and Scalable Methods for High Dimensional Graphical Model Selection
Abstract. Learning high dimensional graphical models is a topic of contemporary interest. A popular approach is to use L1 regularization methods to induce sparsity in the inverse covariance estimator, leading to sparse partial covariance/correlation graphs. Such approaches can be grouped into two classes: (1) regularized likelihood methods and (2) regularized regression-based, or pseudo-likelihood, methods. Regression based methods have the distinct advantage that they do not explicitly assume Gaussianity. One major gap in the area is that none of the popular approaches proposed for solving regression based objective functions guarantee the existence of a solution. Hence it is not clear if resulting estimators actually yield correct partial correlation/partial covariance graphs. To this end, we propose a new regression based graphical model selection method that is both tractable and has provable convergence guarantees, leading to well-defined estimators. In addition, we demonstrate that our approach yields estimators that have good large sample proper-ties and computational complexity. The methodology is illustrated on both real and simulated data. We also present a novel unifying framework that places various pseudo-likelihood graphical model selection methods as special cases of a more general formulation, leading to important insights. (Joint work with Bala Rajaratnam and Kshitij Khare)
Thursday, February 26, 2015, in AB 634
Jon Marshall, EMPLOYERS
Actuarial Internship Information Meeting
All UNR undergraduate and graduate students are welcome.
Learn about the Summer 2015 actuarial internship program at EMPLOYERS Insurance Group, based in Reno.
Get a brief introduction to Property and Casualty Insurance and the P&C actuarial profession.
Learn about planned projects and the people working on them.
Get application and other info about the internship.
Speak with a previous internship program participant who is now working in a full-time actuarial role.
Thursday, February 12, 2015, in AB 634 at 2:30pm
Maxim Arnold, Department of Mathematical Sciences, University of Texas at Dallas
Stochastically driven Self-organization
Abstract. Problem of constructing the shortest path with given geometric and topological constraints is known to be very hard from the computational point of view. However, simple organisms perform quite well solving problems of this kind. I will show how one can address the construction of various minimal structures using very simple stochastic dynamics. The talk will be accessible for undergraduate mathematics/statistics students.
Thursday, February 5, 2015, in AB 634 at 2:30pm
Dr. Elizabeth Gillaspy, Department of Mathematics, University of Colorado Boulder
K-theory and twisted groupoid C*-algebras
Abstract. A number of fundamental results in C*-algebra theory (such as Bott periodicity and the rotation algebras) can be viewed as instances where a homotopy of 2-cocycles gives rise to a family of twisted group C*-algebras that, while not isomorphic, are sufficiently similar that their K-theory groups are isomorphic. In this talk, we discuss the extent to which this phenomenon -- that of a homotopy of 2-cocycles giving rise to K-isomorphic twisted C*-algebras -- extends to more general groupoids. In particular, we will focus on the groupoids associated to higher-rank graphs, transformation groups, and vector bundles.
Thursday, January 29, 2015, in AB 634 at 2:30pm
Bruce Blackadar, Department of Mathematics and Statistics, University of Nevada, Reno
Junior Colloquium: What does "Obvious" mean in mathematics? (and why do we have to prove things?)
Abstract. We will discuss a number of examples of things that may appear "obvious" at first in mathematics, but which turn out to be anything but obvious (and sometimes not even true!) Some examples we will discuss are: areas of sets in the plane, apportionment of representatives, calculus, Euclidean geometry, the definition of π, and counterexamples to the four-color theorem. In some instances the problem is a matter of drawing unwarranted conclusions or using hidden assumptions, and in other instances the problem is one of making insufficiently careful definitions or statements of results.
This will be a "junior colloquium" designed to be accessible to undergraduates. The examples we discuss should all be understandable to anyone who has been through Math 283. But the issues we will discuss are important ones for all mathematicians up through research level, and I will try to make the talk interesting to all faculty and graduate students as well as undergraduates.