Colloquia & Seminars

Colloquia & seminar talks are scheduled from 1:30pm - 2:45pm on Thursday each week, 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!

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Colloquia and Seminar Talks Schedule
DateSpeakerInstitutionTitleRoom
Reschedule for Jan 19 Yifan Cui University of North Carolina at Chapel Hill Tree-based Survival Models and Precision Medicine
Click for Abstract...

In the first part, we develop a theoretical framework for survival tree and forest models. We first investigate the method from the aspect of splitting rules. We show that existing approaches lead to a potentially biased estimation of the within-node survival and cause non-optimal selection of the splitting rules. Based on this observation, we develop an adaptive concentration bound result which quantifies the variance component for survival forest models. Furthermore, we show with three specific examples how these concentration bounds, combined with properly designed splitting rules, yield consistency results. In the second part, we focus on one application of survival trees in precision medicine which estimates individualized treatment rules nonparametrically under right censoring. We extend the outcome weighted learning to right censored data without requiring either inverse probability of censoring weighting or semi-parametric modeling of the censoring and failure times. To accomplish this, we take advantage of the tree-based approach to nonparametrically impute the survival time in two different ways. In simulation studies, our estimators demonstrate improved performance compared to existing methods. We also illustrate the proposed method on a phase III clinical trial of non-small cell lung cancer.

DMSC 102
Jan 23 Colin Grudzien Nansen Environmental and Remote Sensing Center A Dynamically Driven Paradigm for Data Assimilation in Geophysical Models
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, the techniques used to combine these disparate sources of information include methods from Bayesian inference, dynamical systems, numerical analysis and optimal control. While the butterfly effect renders the forecasts 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 --- this is characterized by the unstable-neutral manifold of the state being tracked, with dimension equal to the number of non-negative Lyapunov exponents. The Assimilation in the Unstable Subspace (AUS) methodology of Trevisan et. al. offers mathematical and conceptual tools to understand the mechanisms governing the evolution of uncertainty in ensemble based forecasting, and to exploit the behavior in designing assimilation methods. My research gives a mathematical foundation for AUS, validating its central hypotheses, and extends the assimilation methodology to the presence of stochastic model errors.

AB 635
Jan 25 Jingyu Huang University of Utah Some studies of stochastic heat equations
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Stochastic partial differential equations arise from many disciplines such as physics and biology. In this talk, I will take the stochastic heat equation as an example to talk about some of its basic properties and recent developments. The results are based on joint works with Hu, Khoshnevisan, Le, Nualart and Tindel.

AB 635
Jan 26 Connor Jackman UC Santa Cruz The Jacobi-Maupertuis principle and applications to some N-body problems
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The Jacobi-Maupertuis principle reparameterizes the trajectories of a mechanical system at fixed energy as geodesics on a certain Riemannian manifold. In this talk we will see how this principle applies to planar N-body problems with a '1/r^a potential' i.e. the motion of N point masses under a force that is proportional to the inverse of the mutual distances to the power a+1. In particular we will observe some dynamical consequences due to certain the sectional curvature values of the associated Jacobi-Maupertuis metric.

11am DMSC 104
Jan 30 Sayar Karmakar University of Chicago Simultaneous inference on time-varying models
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The term "time-varying(tv) coefficient models" refers to the collection of statistical models where the unknown coefficients/parameters vary across time. In the first part of my talk, we will highlight the vast applicability of performing simultaneous inference for these parametric functions. The estimation and simultaneous confidence band (SCB) construction will be briefly discussed.
The second half focuses on a specific challenge of exploring the timevarying theme for complicated models such as ARCH, GARCH, ARMAGARCH etc. We solve this problem in its most generality by introducing a framework that accounts for several time-varying regression and autoregression models simultaneously. Such a general treatment calls for a local linear M-estimation of the coefficients and a Bahadur representation to construct the SCB. Bootstrap and sharp Gaussian approximation are used to circumvent logarithmic convergence of theoretical bands. I conclude my talk showing some simulations (time-permitting) and analysis for stock market and currency exchange datasets.

AB 635
Feb 8 Boris Kalinin Pennsylvania State University Rigidity Properties of Commuting Differentiable Maps
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We will consider actions of Z^k and R^k on compact manifolds by commuting hyperbolic diffeomorphisms and flows. Algebraic examples of such actions include actions by automorphisms of tori and by homogeneous flows on cosets of Lie groups. In contrast to hyperbolic actions of Z and R, i.e. hyperbolic diffeomorphisms and flows, actions of Z^k and R^k exhibit various rigidity properties. We will give an overview of results in this area focusing on rigidity of invariant measures for algebraic actions and smooth non-uniformly hyperbolic actions.

AB 635
Feb 9 Victoria Sadovskaya Pennsylvania State University Cocycles Over Hyperbolic Dynamical Systems
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We consider linear and group-valued cocycles over a hyperbolic dynamical system. An important motivation comes from the differential of a hyperbolic diffeomorphism or its restriction to an invariant sub-bundle. We will focus on the conclusions that can be made based on the values of the cocycle at the periodic points of the system. In particular, we will consider the questions when two cocycles are cohomologous and when a cocycle is cohomologous to one with values in a smaller group.

DMSC 102
Feb 13 Shih-Kang Chao Purdue University Distributed Inference for Quantile Regression Processes
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The increased availability of massive data provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big data, I will discuss a two-step procedure: (i) estimate conditional quantile functions at different levels in a parallel computing environment; (ii) construct a conditional quantile regression process through projection based on these estimated quantile curves. Using simple linear model for the conditional quantile as a working model, I will show that the proposed procedure does not sacrifice any statistical inferential accuracy provided that the number of distributed computing units and quantile levels are chosen properly. In particular, a sharp upper bound for the former and a sharp lower bound for the latter are derived to capture the minimal computational cost from a statistical perspective. As an important application, I will describe computationally efficient approaches to construct confidence intervals in the distributed setting. Those approaches directly utilize the availability of estimators from sub-samples and can be carried out at almost no additional computational cost to the two-step procedure described above. Simulation results confirm our theory.

AB 635
Feb 15 Andrey Sarantsev UC Santa Barbara Competing Brownian Particles
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A model of Brownian particles on the real line interacting
through their ranks was created for financial modeling in (Banner, Fernholz, Karatzas, 2005). In this model, each Brownian particle has drift and diffusion coefficients dependent on their current rank relative to other particles. We can consider both finite and infinite systems of such particles. In this talk, we survey recent developments and propose unsolved questions.

TBA
Feb 20 Shuwen Lou University of Illinois at Chicago Brownian Motion on Spaces with Varying Dimension
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The first part of this talk will be an introduction to the relationship between electrical networks in physics and Dirichlet forms. As a matter of fact, Dirichlet forms are sometimes called "energy forms" because they characterize the energy consumed by electrical networks when they are charged. In particular, we give the Dirichlet form characterization for electrical networks with shorting. In the second part, we present a class of probabilistic models of our interest: Brownian motion constructed on spaces with varying dimension, using the idea of "shorting". Brownian motion on spaces with varying dimension has an intrinsic interplay with the geometry of the underlying spaces, and therefore reveals many non-trivial and interesting phenomena. We give an overview of their properties with an emphasis on the two sided heat kernel estimates.

TBA
Mar 15 TBA TBA
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TBA

Mar 29 Carla Farsi University of Colorado Boulder Representations, Wavelets, and Spectral Triples for K-graphs: An Infinite Path Space Approach
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After a heuristic introduction to (finite) graphs and k-graphs, I will detail the construction of their infinite path space. I will also outline why and how this object is so central to many aspects of their theory and C*-algebras. No expertise in the area needed, as I will introduce all the relevant concepts from scratch. This talk touches upon and highlights joint work with Gillaspy, Kang, Jorgensen, Julien, and Packer.

AB 635
Apr 5 Petr Lukas Charles University, Prague Adaptive Techniques in SOLD methods
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TBA

AB 635
Apr 12 Danny Ruberman Stanford University / Brandeis University TBA
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TBA

AB 635
Apr 19 Noorie Hyun Medical College of Wisconsin TBA
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TBA

AB 635
Apr 26 Jing-Jing Huang  UNR TBA
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TBA

AB 635
May 3 Jesse Levitt USC TBA
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TBA

AB 635