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# 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!

Date | Speaker | Institution | Title | Room |
---|---|---|---|---|

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 Click for Abstract... 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 Click for Abstract... 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 Click for Abstract... Given a non-necessarily Hausdorff, topologically free, twisted étale groupoid (G,L), we consider its "essential groupoid C*-algebra", denoted C* |
DMSC 104 |

Feb. 5, 2019 (Tuesday) |
Yue Zhao | KU Leuven, Belgium | The Normal Scores Estimator for the High-Dimensional Gaussian Copula Model Click for Abstract... 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 |
PE 104 |

Feb. 7, 2019 | Lynna Chu | UC Davis | Asymptotically Distribution-Free Change-Point Detection For Multivariate And Non-Euclidean Data Click for Abstract... 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 Click for Abstract... 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 |
DMSC 104 |

Feb. 12, 2019 (Tuesday) | Whitney Huang | SAMSI & Canadian Statistical Sciences Institute & University of Victoria | Estimating Precipitation Extremes Using The Log-Histospline Click for Abstract... 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 Click for Abstract... 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 Click for Abstract... 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 Click for Abstract... 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 Click for Abstract... 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 Click for Abstract... 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. |
AB 110 |

Mar. 7, 2019 | Chi-Kwong Li | College of William and Mary | Quantum States and Quantum Channels Click for Abstract... 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 Click for Abstract... 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 Click for Abstract... 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 Click for Abstract... 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 Click for Abstract... 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 Click for Abstract... TBA |
PE 104 |