Colloquia & Seminars

Colloquia & seminar talks are scheduled from 1:30pm - 2:30pm on Thursday each week and usually take place in PE 104, unless otherwise noted below. Speakers give 50-minute presentations on various mathematical and statistical topics.

If you would like to meet with a speaker, please contact math@unr.edu to schedule a meeting. To receive email announcements about future talks and events, please subscribe to our email list by sending an email to sympa@lists.unr.edu with a blank subject line and the main body 'subscribe mathstat-announce EmailAddress FirstName LastName'.

We look forward to your participation in our upcoming colloquia!

Colloquia and Seminar Talks Schedule
DateSpeakerInstitutionTitleRoom
Jan. 22, 2019
(Tuesday)
Sneha Jadhav Yale University Pan-disease Clustering Analysis of Trend of Period Prevalence
Click for Abstract...

For most if not all diseases, prevalence has been carefully studied. In the "classic" paradigm, the prevalence of different diseases has usually been studied separately. Accumulating evidences have shown that diseases can be "correlated". The joint analysis of prevalence of multiple diseases can provide significant insights beyond individual-disease analysis, however, has not been well conducted. In this study, we take advantage of the Taiwan National Health Insurance Research Database (NHIRD), which has multiple unique advantages, and conduct a pan-disease analysis of period prevalence trends. The goal is to identify clusters within which diseases share similar period prevalence trends. For this purpose, a novel penalization pursuit approach is developed, which has an intuitive formulation and satisfactory computational and statistical properties. In the analysis of NHIRD data, period prevalence values are computed using records on close to 1 million subjects and 12 years of observation. For 405 diseases, 35 nontrivial clusters (with sizes larger than one) and 27 trivial clusters (with sizes one) are identified. The analysis results differ significantly from those of alternatives. A closer examination suggests that the clustering results have sound medical implications. This study is the first to conduct a pan-disease clustering analysis of disease prevalence trends using the NHIRD data and may have important value in multiple aspects.

PE 104
Jan. 29, 2019
(Tuesday)
Elvan Ceyhan SAMSI & North Carolina State University Classification with a Random Geometric Graph Family
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We employ a geometric graph family called class cover catch digraphs (CCCDs) for classification of data in low to high dimensions. CCCDs are constructed based on spherical proximity regions --- regions that determine the presence and direction of the arcs in the digraph--- and emerged as a graph theoretic solution to the class cover problem. We assess the classification performance of CCCD classifiers by extensive Monte Carlo simulations, comparing them with other classifiers commonly used in the literature. In particular, we show that CCCD classifiers perform well when one class is more frequent than the other in a two-class setting, an example of the class imbalance problem. That is, CCCD classifiers are robust to the class imbalance problem in statistical learning. We also point out the relation between class imbalance and class overlapping problems, and their influence on the performance of CCCD classifiers and other classification methods including some of the state-of-the-art algorithms which are also robust to the class imbalance. CCCDs --- by construction --- tend to substantially under-sample from the majority class while preserving the information on the discarded points during the under-sampling process. While many state-of-the-art methods keep this information by means of ensemble classifiers, CCCDs yield only a single classifier with the same property, making it both simple and fast.

PE 104
Jan. 31, 2019 Hojin Yang University of Texas MD Anderson Cancer Center Functional Regression Analysis of Distributional Data using Quantile Functions
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The aims of this paper are to look at the subject-specific distribution from observing the large number of repeated measurements for each subject and to determine how a set of covariates effects various aspects of the underlying subject-specific distribution, including the mean, median, variance, skewness, heavy-tailedness, and various upper and lower quantiles. To address these, we develop a quantile functional regression modeling framework that models the distribution of a set of common repeated observations from a subject through the quantile function. To account for smoothness in the quantile functions, we introduce custom basis functions that are sparse, regularized, near-lossless, and empirically defined, adapting to the features of a given data set. Then, we build a Bayesian framework that uses nonlinear shrinkage of basis coefficients to regularize the functional regression coefficients and allows fully Bayesian inferences after fitting a Markov chain Monte Carlo. We demonstrate the benefit of the basis space modeling through simulation studies, and illustrate the method using a biomedical imaging data set in which we relate the distribution of pixel intensities from a tumor image to various demographic, clinical, and genetic characteristics. This is joint work with Veerabhadran Baladandayuthapani and Jeffrey S. Morris.

PE 104
Feb. 1, 2019
(Friday)
Ruy Exel UFSC (Brazil) Weak Cartan inclusions and non-Hausdorff groupoids
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Given a non-necessarily Hausdorff, topologically free, twisted étale groupoid (G,L), we consider its "essential groupoid C*-algebra", denoted C*ess(G,L), obtained by completing Cc(G,L) with the smallest among all C*-seminorms coinciding with the uniform norm on Cc(G0). The inclusion of C*-algebras "C0(G0) ⊆ C*ess(G,L)" is then proven to satisfy a list of properties characterizing it as what we call a "weak Cartan inclusion". We then prove that every weak Cartan inclusion (A,B), with B separable, is modeled by a twisted étale groupoid, as above. This talk is based on joint work with D. Pitts.

DMSC 104
Feb. 5, 2019
(Tuesday)
Yue Zhao KU Leuven, Belgium The Normal Scores Estimator for the High-Dimensional Gaussian Copula Model
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The (semiparametric) Gaussian copula model consists of distributions that have dependence structure described by Gaussian copulas but that have arbitrary marginals. A Gaussian copula is in turn determined by a Euclidean parameter R called the copula correlation matrix. In this talk we study the normal scores (rank correlation coefficient) estimator, also known as the van der Waerden coefficient, of R in high dimensions. It is well known that in fixed dimensions, the normal scores estimator is the optimal estimator of R, i.e., it has the smallest asymptotic covariance. Curiously though, in high dimensions, nowadays the preferred estimators of R are usually based on Kendall's tau or Spearman's rho. We show that the normal scores estimator in fact remains the optimal estimator of R in high dimensions. More specifically, we show that the approximate linearity of the normal scores estimator in the efficient influence function, which in fixed dimensions implies the optimality of this estimator, holds in high dimensions as well.

PE 104
Feb. 7, 2019 Lynna Chu UC Davis Asymptotically Distribution-Free Change-Point Detection For Multivariate And Non-Euclidean Data
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We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of multivariate or non-Euclidean observations. While the change-point problem has been extensively studied for low-dimensional data, advances in data collection technology have produced data sequences of increasing volume and complexity. Motivated by the challenges of modern data, we study a non-parametric framework that can be effectively applied to various data types as long as an informative similarity measure on the sample space can be defined. The existing approach along this line has low power and/or biased estimates for change-points under some common scenarios. To address these problems, we present new tests based on similarity information that exhibit substantial improvements in detecting and estimating change-points. In addition, under some mild conditions, the new test statistics are asymptotically distribution free under the null hypothesis of no change. Analytic p-value approximation formulas to the significance of the new test statistics are derived, making the new approaches easy off-the-shelf tools for large datasets. The effectiveness of the new approaches are illustrated in an analysis of New York taxi data. This is based on joint work with Hao Chen.

PE 104
Feb. 8, 2019 (Friday) Marcy Robertson University of Melbourne An action of the Grothendieck-Teichmüller group on stable curves of genus zero
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The Grothendieck-Teichmüller group is an explicitly defined group introduced by Drinfeld which is closely related to (and conjecturally equal to) the absolute Galois group. The idea was based on Grothendieck's suggestion that one should study the absolute Galois group of the rationals by relating it to its action on the Teichmüller tower of fundamental groupies of the moduli stacks of genus g curves
with n marked points.
In this talk, we give a reimagining of the genus zero Teichmüller tower in terms of a profinite completion of the framed little 2-discs operad. Using this reinterpretation, we show that the homotopy automorphisms of this model for the Teichmüller tower is isomorphic to the (profinite) Grothendieck-Teichmüller group. We then show a non-trivial action of the absolute Galois group on our tower.
This talk will be aimed at a general audience and will not assume previous knowledge of the Grothendieck-Teichmüller group or operads.
This is joint work with Pedro Boavida and Geoffroy Horel.

DMSC 104
Feb. 12, 2019 (Tuesday) Whitney Huang SAMSI & Canadian Statistical Sciences Institute & University of Victoria Estimating Precipitation Extremes Using The Log-Histospline
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One of the commonly used approaches to modeling extremes is the peaks-over-threshold (POT) method. The POT method models exceedances over a threshold that is sufficiently high so that the exceedance has approximately a generalized Pareto distribution (GPD). This method requires the selection of a threshold that might affect the estimates. Here we propose an alternative method, the Log-Histospline (LHSpline), to explore modeling the tail behavior and the remainder of the density in one step using the full range of the data. LHSpline applies a smoothing spline model to a finely binned histogram of the log transformed data to estimate its log density. By construction, a LHSpline estimation is constrained to have polynomial tail behavior, a feature commonly observed in daily rainfall observations. We illustrate the LHSpline method by analyzing the precipitation data collected in Houston, Texas. This is based on joint work with Doug Nychka and Hao Zhang.

PE 104
Feb. 14, 2019 Yanglei Sang University of Illinois, Urbana-Champaign Asymptotically Optimal Multiple Testing With Streaming Data
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The problem of testing multiple hypotheses with streaming (sequential) data arises in diverse applications such as multi-channel signal processing, surveillance systems, multi-endpoint clinical trials, and online surveys. In this talk, we investigate the problem under two generalized error metrics. Under the first one, the probability of at least k mistakes, of any kind, is controlled. Under the second, the probabilities of at least k1 false positives and at least k2 false negatives are simultaneously controlled. For each formulation, we characterize the optimal expected sample size to a first-order asymptotic approximation as the error probabilities vanish, and propose a novel procedure that is asymptotically efficient under every signal configuration. These results are established when the data streams for the various hypotheses are independent and each local log-likelihood ratio statistic satisfies a certain law of large numbers. Further, in the special case of iid observations, we quantify the asymptotic gains of sequential sampling over fixed- sample size schemes.

PE 104
Feb. 22, 2019 (Friday) Alex Suciu Northeastern Topology and combinatorics of hyperplane arrangements
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Much of the fascination with arrangements of complex hyperplanes comes from the rich interplay between the combinatorics of the intersection lattice and the algebraic topology of the complement. A key bridge between the two is provided by the geometry of two sets of algebraic varieties associated to the complement: the resonance varieties of the cohomology ring and the characteristic varieties of the fundamental group.

DMSC 104
Feb. 27, 2019 (Wed 12-1pm) Noah Forman University of Washington Projections of a Random Walk on a Space of Binary Trees
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Consider the Markov process in the space of binary trees in which, at each step, you delete a random leaf and then grow a new leaf in a random location on the tree. In 2000, Aldous conjectured that it should have a continuum analogue, which would be a continuum random tree-valued diffusion. We will discuss a family of projectively consistent Markov chains that are projections of this tree, and discuss how these representations can be passed to the continuum. This is joint work with Soumik Pal, Douglas Rizzolo, and Matthias Winkel.

SEM 234
Feb. 28, 2019 Colin Grudzien UNR A dynamical systems framework for ensemble based filtering: a problem partially solved
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In physical applications, dynamical models and observational data play dual roles in prediction and uncertainty quantification, each representing sources of incomplete and inaccurate information. In data rich problems, first-principle physical laws constrain the degrees of freedom of massive data sets, utilizing our prior insights to complex processes. Respectively, in data sparse problems, dynamical models fill spatial and temporal gaps in observational networks. The dynamical chaos characteristic of these process models is, however, among the primary sources of forecast uncertainty in complex physical systems. Observations are thus required to update predictions where there is sensitivity to initial conditions and uncertainty in model parameters. Broadly referred to as data assimilation, or stochastic filtering, the techniques used to combine these disparate sources of information include methods from Bayesian inference, dynamical systems and optimal control. While the butterfly effect renders the forecasting problem inherently volatile, chaotic dynamics also put strong constraints on the evolution of errors. It is well understood in the weather prediction community that the growth of forecast uncertainty is confined to a much lower dimensional subspace corresponding to the directions of rapidly growing perturbations. The Assimilation in the Unstable Subspace (AUS) methodology of Trevisan et al. has offered understanding of the mechanisms governing the evolution of uncertainty in ensemble forecasting, exploiting this dimensional reduction prescribed by the dynamics. With my collaborators, I am studying the mathematical foundations of ensemble based filtering in the perspective of smooth and random dynamical systems.

PE 104
Mar. 4, 2019 (Mon 12-1pm) Hailin Sang University of Mississippi Some Recent Developments On Linear Processes and Linear
Random Fields
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The linear processes and linear random fields are tools for studying stationary time series and stationary random fields. One can have a better understanding of many important time series and random fields by studying the corresponding linear processes and linear random fields.
In this talk we survey some recent developments on linear processes and linear random fields. One part is the moderate and large deviations under different conditions. This part research plays an important role in many applied fields, for instance, the premium calculation problem, risk management in insurance, nonparametric estimation and network information theory. We also study the memory properties of transformations of linear processes which have application in econometrics and financial data analysis when the time series observations have non-Gaussian heavy tails. Entropy is widely applied in the fields of information theory, statistical classification, pattern recognition and so on since it is a measure of uncertainty in a probability distribution. At the end, we focus on the estimation of the quadratic entropy for linear processes. With a Fourier transform on the kernel function and the projection method, it is shown that, the kernel estimator has similar asymptotical properties as the i.i.d. case if the linear process has the defined short range dependence. Part of the results are confirmed by simulation studies. We also obtain very promising results in some real data analysis.

AB 110
Mar. 7, 2019 Chi-Kwong Li College of William and Mary Quantum States and Quantum Channels
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In the Hilbert space formulation, quantum states are density matrices, i.e., positive semi-definite matrices with trace one, and quantum channels are trace preserving completely positive linear maps on matrices. In this talk, we will present some results on the existence of quantum channels that send certain quantum states to other quantum states. Additional requirement on the quantum channels may be imposed under certain optimization criteria. Additional results and problems in this direction will be mentioned. (No quantum mechanics background is needed.)

PE 104
Mar. 28, 2019 Ryan Grady Montana State Invariants via Quantizing Algebroids
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Finding topological invariants of manifolds and submanifolds, e.g., knots or links, is a classical problem. Work of Atiyah, Donaldson, Floer, Hitchin, Witten, and others from the 1980s illustrated the power of quantum field theory (QFT) in addressing this problem. In this talk, I will describe a mathematical framework for QFT and describe several examples of sigma models; a sigma model studies the space of maps between a pair of manifolds. I will then extract topological and representation theoretic invariants from the quantization of these sigma models.

PE 104
Apr. 4, 2019 Shilin Yu Texas A&M Deformation Quantization of Coadjoint Orbits
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The coadjoint orbit method/philosophy suggests that irreducible unitary representations of a Lie group can be constructed as quantization of coadjoint orbits of the group. I will propose a geometric way to understand orbit method using deformation quantization, in the case of noncompact real reductive Lie groups. This approach combines recent studies on quantization of symplectic singularities and their Lagrangian subvarieties. This is joint work with Conan Leung.

PE 104
Apr. 11, 2019 Jonathan Brown University of Dayton Orbit Equivalence and Groupoids
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A directed graph gives rise to a dynamical system by considering the shift on the space of infinite paths. It is possible for two different directed graphs to give rise to dynamical systems with the same orbits. We call such graphs "orbit equivalent". It can be difficult in general to see when two graphs are orbit equivalent. However, recent results of Brownlowe, Carlsen, and Whittaker characterize when two graphs satisfying Condition L are orbit equivalent, using both C*-algebras and groupoids. This talk introduces graph groupoids and C*- algebras with the aim of explaining Brownlowe et al.'s remarkable result.

PE 104
Apr. 18, 2019 Piotr Hajac IMPAN, Polish Academy of Sciences & University of Colorado, Boulder Operator Algebras That One Can See
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Operator algebras are the language of quantum mechanics just as much as differential geometry is the language of general relativity. Reconciling these two fundamental theories of physics is one of the biggest scientific dreams. It is a driving force behind efforts to geometrize operator algebras and to quantize differential geometry. One of these endeavors is noncommutative geometry, whose starting point is natural equivalence between commutative operator algebras (C*-algebras) and locally compact Hausdorff spaces. Thus noncommutative C*-algebras are thought of as quantum topological spaces, and are researched from this perspective. However, such C*- algebras can enjoy features impossible for commutative C*-algebras, forcing one to abandon the algebraic-topology based intuition. Nevertheless, there is a class of operator algebras for which one can develop new ("quantum") intuition. These are graph algebras, C*-algebras determined by oriented graphs (quivers). Due to their tangible hands-on nature, graphs are extremely efficient in unraveling the structure and K-theory of graph algebras. We will exemplify this phenomenon by showing a CW- complex structure of the Vaksman-Soibelman quantum complex projective spaces, and how it explains their K-theory.

PE 104
Apr. 25, 2019 TBA TBA TBA
Click for Abstract...

TBA

PE 104
May. 2, 2019 Walter Piegorsch University of Arizona TBA
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TBA

PE 104