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# Departmental Colloquia

Our department is proud to host weekly colloquium talks featuring research by leading mathematicians from around the world. Most colloquia are held on Fridays at 4pm in Parker Hall, Room 250 (unless otherwise advertised) with refreshments preceding at 3:30pm in Parker Hall, Room 244.

**DMS Colloquium: Julianne Chung**

**Mar 08, 2019 04:00 PM**

Speaker: **Julianne Chung**, Virginia Tech University

Title: Efficient Methods for Large and Dynamic Inverse Problems

Abstract: In many physical systems, measurements can only be obtained on the exterior of an object (e.g., the human body or the earth's crust), and the goal is to estimate the internal structures. In other systems, signals measured from machines (e.g., cameras) are distorted, and the aim is to recover the original input signal. These are natural examples of inverse problems that arise in fields such as medical imaging, astronomy, geophysics, and molecular biology.

In this talk, we describe efficient methods to compute solutions to large, dynamic inverse problems. We focus on addressing two main challenges. First, since most inverse problems are ill-posed, small errors in the data may result in significant errors in the computed solutions. Thus, regularization must be used to compute stable solution approximations, and regularization parameters must be selected. Second, in many realistic scenarios such as in passive seismic tomography or dynamic photoacoustic tomography, the underlying parameters of interest may change during the measurement procedure. Thus, prior information regarding temporal smoothness must be incorporated for better reconstructions, but this can become computationally intensive, in part, due to the large number of unknown parameters. To address these challenges, we describe efficient, iterative, matrix-free methods based on the generalized Golub-Kahan bidiagonalization that allow automatic regularization parameter and variance estimation. These methods can be more flexible than standard methods, and efficient implementations can exploit structure in the prior, as well as possible structure in the forward model. Numerical examples demonstrate the range of applicability and effectiveness of the described approaches.

Faculty host: Yanzhao Cao

**DMS Colloquium: Jan Boronski**

**Mar 18, 2019 04:00 PM**

Speaker: **Jan Boronski**, Technical University in Krakow, Poland, and IT4 Innovations, University of Ostrava, Czech Republic

Title: TBA

Faculty host: Krystyna Kuperberg

**DMS Colloquium: Ferenc Fodor**

**Mar 22, 2019 04:00 PM**

Speaker: **Ferenc Fodor**, University of Szeged (Hungary)

Title: On the \(L_p\) dual Minkowsi problem

Abstract:

Faculty host: Andras Bezdek

**DMS Colloquium: Emanuele Ventura**

**Apr 05, 2019 04:00 PM**

Speaker: **Emanuele Ventura**, Postdoc Texas A&M; Ph.D., Aalto University (Helsinki, Finland) 2017

**DMS Colloquium: Youssef Marzouk**

**Apr 12, 2019 04:00 PM**

Speaker: **Youssef Marzouk**, MIT

Faculty host: Yanzhao Cao

**DMS Colloquium: Frédéric Holweck**

**Apr 19, 2019 04:00 PM**

Speaker: **Frédéric Holweck**, Université de Technologie de Belfort-Montbéliard (France)

Faculty host: Luke Oeding

**DMS Colloquium: Matthias Heikenschloss**

**Apr 26, 2019 04:00 PM**

Speaker: **Matthias Heikenschloss**, Rice University

Title: TBA

**DMS Colloquium: Dr. Chao Huang**

**Feb 15, 2019 04:00 PM**

Speaker: **Dr. Chao Huang**, Department of Biostatistics, University of North Carolina at Chapel Hill

Title: Surrogate Variable Analysis for Multivariate Functional Responses in Imaging Data

Abstract: PLease click here

**DMS Colloquium: Yixi Xu**

**Feb 13, 2019 04:00 PM**

Speaker: **Yixi Xu**, Ph. D. candidate in Purdue University

Title: Weight normalized deep neural networks

**Abstract:** : Deep neural networks (DNNs) have recently demonstrated an amazing performance on many challenging artificial intelligence tasks. DNNs have become popular due to their predictive power and flexibility in model fitting. One of the central questions about DNNs is to explain their generalization ability, even when the number of unknown parameters is much larger than the sample size. In this talk, we study a general framework of norm-based capacity control for \(L_{p,q}\) weight normalized deep neural networks and further propose a sparse neural network. We establish the upper bound on the Rademacher complexities of the \(L_{p,q}\) weight normalized deep neural networks. Especially, with an \(L_{1,\infty}\) normalization, we discuss properties of a width-independent capacity control, where the sample complexity only depends on the depth by a square root term. In addition, for an \(L_{1,\infty}\) weight normalized network with ReLU, the approximation error can be sufficiently controlled by the \(L_1\) norm of the output layer. These results provide theoretical justifications on the usage of such weight normalization to reduce the generalization error. Finally, an easily implemented projected gradient descent algorithm is introduced to practically obtain a sparse neural network via \(L_{1,\infty}\)-weight normalization. Various experiments are performed to validate the theory and demonstrate the effectiveness of the resulting approach.

**DMS Colloquium: Jingyi Zheng**

**Feb 11, 2019 04:00 PM**

Speaker: **Jingyi Zheng**, Ph. D. candidate at the University of California at Davis

Title: A Data-driven Approach to Predict and Classify Epileptic Seizures from Brain-wide Calcium Imaging Video

Abstract: Epilepsy is a neurological disorder in the brain characterized by recurrent, unprovoked seizures. In this talk, we will discuss mainly three aspects of epilepsy study: (epilepsy) classification, (epileptic seizures) prediction, and spatiotemporal structure discovery. Unlike Electroencephalography (EEG) and fMRI data, the calcium imaging video data images the whole brain-wide neurons activities with electrical discharge recorded by calcium fluorescence intensity (CFI). Using zebrafish's brain-wide calcium imaging video data, we first propose a data-driven approach to effectively predict the epileptic seizures. Our approach includes two phases: offline training and online testing. Specifically, during offline training, we confirm the existence of systemic change point, and estimate the ratio of unchanged system duration. For online testing, we implement a statistical model to estimate the change point, and then predict the onset of epileptic seizure. Furthermore, we explore the macroscopic patterns of epileptic and control cases, and then build classifiers using machine learning models. Based on the data structure, we also propose a method to discretize related features, and further visualize the pattern difference using unsupervised learning methods. Finally, we discover the spatial structure based on mutual conditional entropy and recover the temporal system state trajectory that leads to epileptic seizures.

**DMS Colloquium: Prof. Dr. Stefan Friedenberg**

**Feb 08, 2019 04:00 PM**

Speaker: **Prof. Dr. Stefan Friedenberg**, University of Stralsund, Germany

Title: Some footsteps of Ulrich Albrecht in mathematics

Abstract: Since Ulrich Albrecht will retire in the end of May, it is time to shed some light on his mathematical work throughout the last decades. This talk will give a brief overview about his research in several area Algebra, namely Abelian groups, group extensions and his latest work on valuated groups.

Faculty host: Ulrich Albrecht

**DMS Colloquium: Dr. Youngjoo Cho**

**Feb 07, 2019 04:00 PM**

Speaker: **Dr. Youngjoo Cho**, Zilber School of Public Health, University of Wisconsin-Milwaukee

Title: Covariate Adjustment for Treatment Effect On Competing Risks Data in Randomized Clinical Trials

** **Abstract : The double blinded randomization trial is a gold standard for estimating average causal effect (ACE). It does not require adjustment for covariates. However, in most case, adjustment of covariates that are strong predictor of the outcome could improve efficiency for the estimation of ACE. But when covariates are high-dimension, adjust all covariates in the model will lose efficiency or worse, lose identifiability. Recent work has shown that for linear regression, an estimator under risk consistency (e.g., LASSO, Random Forest) for the regression coefficients could always lead to improvement in efficiency. In this work, we studied the behavior of adjustment estimator for competing risk data analysis. Simulation study shows that the covariate adjustment provides the more efficient estimator than unadjusted one.

**DMS Colloquium: Rui Xie**

**Feb 06, 2019 04:00 PM**

PLEASE note room number

Speaker: **Rui Xie**, Ph. D. candidate at the University of Georgia

Title: Online Leverage-based Sequential Sampling Method for Streaming Time Series Data

**Abstract:** Advances in streaming data acquisition technology bring challenges in analyzing large volumes of streaming data. Sampling method as a powerful tool for analyzing large sample data has received significant attention due to the competent estimation accuracy and low computation cost. However, sampling method and its statistical properties for streaming data, especially streaming time series data, are not well studied. In this work, we propose an online leverage-based sequential sampling algorithm for streaming time series data which follows an autoregressive (AR) model. The proposed sequential leveraging sampling (SLS) method samples only one consecutively recorded block from the data stream. The sampling starting point is chosen according to statistical leverage scores of the data, and subsample size is decided by the sequential sampling threshold. We demonstrate that the least squares estimates of model parameters from sequential leveraging subsample are asymptotically normally distributed for non-explosive p-th order autoregressive (AR(p)) model. Simulation studies and real data examples are presented to evaluate the empirical performance of the proposed SLS method.

Last Updated: 09/11/2015