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Colloquia & Seminars

The Department of Mathematics & Statistics colloquium speakers give 50-minute presentations on various mathematical and statistical topics. Colloquia are schedule from 2:30pm - 3:30pm on Thursday unless otherwise noted. If you would like to meet with a speaker, please contact math@unr.edu to schedule a meeting. 

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We look forward to your participation in our upcoming colloquia!

DateSpeakerInstitutionTitleRoomHost
Feb 2 Ania Panorska UNR Statistics and Data Science Graduate Program: a Statistician's Perspective.
Abstract...

As we develop graduate program in Statistics and Data Science (SDS) at UNR it is useful to take a good look at the leading SDS programs in the US. Considering the structure and fit within the university curriculum of the best SDS programs provides data about the national standards for such programs. The purpose of this talk is to present the vision, the underlying principles, and core curriculum of leading SDS programs including those in UC Berkeley, Stanford, the University of Washington, and UNC Chapel Hill. We will also present how these programs are integrated and placed within the universities they reside in. Further, we will discuss the interdisciplinary nature of the leading SDS programs including the role they play in educating students from all disciplines present on campus. Finally, we will propose solutions and ideas for our program based on the lessons learnt from the programs we researched.The talk should leave plenty of time for a discussion of the ideas and making plans for further development of a quality SDS program at UNR.

AB 635
Feb 9 Brandon Levin University of Chicago Congruences between modular forms
Abstract...

The study of congruences between modular forms is a central question in modern number theory which goes back at least to the work of Ramanujan at the beginning of the 20th century. By way of examples, I will first introduce modular forms and their arithmetic counterparts, elliptic curves. In the proof of Fermat's Last Theorem, Wiles together with Taylor introduced a powerful method for constructing congruences between modular forms. I will discuss the relationship between Wiles' work and a 1987 conjecture of Serre about modular forms. Finally, I will describe recent progress on generalizations of these results to higher dimensions.

AB 635
Feb 17 (Fri.) Alfred Grant Schissler University of Arizona Gene set analysis of correlated, paired-sample transcriptome data to enable precision medicine
Abstract...

I will discuss the development of correlation-adjusted analytics of paired-sample transcriptome data. The major emphasis will be on interdisciplinary science, including innovations in single-subject transcriptome (i.e., gene expression data) methodology for precision medicine. Traditional statistical approaches are largely unavailable in this setting due to prohibitive sample size and lack of independent replication. This leads one to rely on informatic devices including knowledgebase integration (e.g., gene set annotations) and external data sources (gene expression warehouses). Common statistical themes include multivariate statistics (such
as Mahalanobis distance and copulas) and large-scale significance testing. Briefly, I'll describe two projects that have led to the development of a clinically-relevant effect size of gene set (pathway) differential expression, the N-of-1-pathways Mahalanobis distance, and a hypothesis testing procedure that accounts for non-trivial, inter-genetic correlation. Time permitting, I will demonstrate an R implementation of the statistics and visualizations developed on real patient data.

SEM 234
Feb 21 (Tues) Xiang (Shawn) Zhan Fred Hutchinson Cancer Research Center A Small-sample Kernel Independence Test with Application to Microbiome Data
Abstract...

The human microbiome, refers to the full collection of genetic materials of all microbes that live in and on the human body, plays an important role in human health and diseases. To fully understand the role of microbiome in human health and diseases, researchers are increasingly interested in assessing the relationship between microbiome composition and host genomic data. The dimensionality of the data as well as complex relationships between microbiota and host genomic data pose considerable challenges for analysis. In this talk, I will present a novel statistical method for testing the global association between microbiome community composition data and multiple outcomes of interest. A kernel-based RV (KRV) coefficient has been proposed, which extends the Pearson-type correlation coefficient to capture more complicated relationships. When kernels are appropriately chosen, our KRV coefficient can also measure the statistical independence between two random vectors. Moreover, to accommodate the relative modest sample size in most current microbiome studies, we study the finite sample distribution of the KRV coefficient and implement a special test design to improve its small-sample performance. The KRV test is demonstrated with simulation studies and real data application.

CFA 153
Feb 24 (Fri) Sunyoung Shin University of Wisconsin-Madison Annotation Regression for Genome-Wide Association Studies
Abstract...

Although genome-wide association studies (GWAS) have been successful at identifying many disease-associated genetic variants, these studies are hampered by two obstacles. First, despite ever-increasing sample sizes, these studies are still underpowered for variants with weak effect sizes. Second, and more importantly, a large percentage of identified variants reside in non-coding regions, making them difficult to interpret. In this talk, I will propose a general regression framework utilizing functional annotation data in approaching the challenges. The annotation regression framework for GWAS (ARoG) is based on finite mixture of linear regression models where GWAS association measures are viewed as responses and functional annotations as predictors. This mixture framework addresses heterogeneity of effects of genetic variants by grouping them into clusters and high dimensionality of the functional annotations by enabling annotation selection within each cluster. The framework will be illustrated with computational experiments and analyses of schizophrenia data from Psychiatric Genomics Consortium. I will also discuss an extension of ARoG with multiple phenotypes (multiARoG), which jointly borrows information across phenotypes.

SEM 234
Mar 2 Nilabja Guha Texas A&M Bayesian approaches in inverse problems
and uncertainty quantification
Abstract...

Predictions related to physical systems governed by complex mathematical models depend on underlying model parameters. For example, prediction of oil production is strongly influenced by subsurface properties, such as permeability, porosity and other spatial fields. These spatial fields may be highly heterogeneous and vary over a rich hierarchy of scales. Given the observations from the system (possibly contaminated with errors), inference on the underlying parameter and its uncertainty constitutes the uncertainty quantification of the inverse problem. The inverse problem may be ill-posed. Bayesian methodology provides a natural framework for such problems by imposing regularization through prior distribution. Solution procedures use Markov Chain Monte Carlo (MCMC) or related methodology, where, for each of the proposed parameter values, we solve the underlying forward problem. The solution requires finite element or finite volume techniques. Because of the high computational cost in evaluating the forward models it is important to develop fast, scalable efficient methodology, without sacrificing accuracy.
We focus on various inverse problems and uncertainty quantification techniques. An inverse problem characterization and uncertainty quantification approach under asymmetric skewed error for heat equation is developed. Later, we consider the flow equation and pressure data where estimation of the underlying high dimensional permeability field is of main interest. Based on separable decomposition, we propose a novel MCMC method. Along with MCMC, we approximate the posterior by variational approximation. The convergence of the posterior solution and its approximation is also established.

AB 635
Mar 3 (Fri) Yinghan Chen University of Illinois at Urbana-Champaign Network Motif Detection and Q-matrix Estimation in Cognitive Diagnosis
Abstract...

Network motifs are substructures that appear significantly more often in a given network than in random networks. Motif detection is crucial for discovering new characteristics in biological, developmental, and social networks. I will present a novel sequential importance sampling strategy to estimate subgraph frequencies and detect network motifs. The method is developed by sampling subgraphs sequentially node by node using a carefully chosen proposal distribution. The method generates subgraphs from a distribution close to uniform and performs better than competing methods. I will apply the method to real networks to demonstrate its performance.

Cognitive diagnosis models are partially ordered latent class models and are used to classify students into skill mastery profiles. The deterministic inputs, noisy "AND" gate model (DINA) is a popular psychometric model for cognitive diagnosis. Application of the DINA model requires content expert knowledge of a Q matrix, which maps the test item to its corresponding required attributes or skills. I will propose a Bayesian framework for estimating the DINA Q matrix. The proposed algorithms ensure that the estimated Q matrices always satisfy the identifiability constraints. I will present Monte Carlo simulations to support the accuracy of parameter recovery and apply our algorithms to Tatsuoka's fraction-subtraction dataset.

Mar 9 Jonathan Chávez-Casillas University of Calgary TBA
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Apr 13 TBA TBA TBA
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Apr 20 TBA TBA TBA
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Apr 27 TBA TBA TBA
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May 4 TBA TBA TBA
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