Author: cyang3

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Variable selection in mixture models: Uncovering cluster structures and relevant features

Speaker: Dr. Mahlet Tadesse

Time: March 4, 2022 04:00 PM Central Time (US and Canada)

Abstract: Identifying latent classes and component-specific relevant predictors can shed important insights when analyzing high-dimensional data. In this talk, I will present methods we have proposed to address this problem in a unified manner by  combining ideas of mixture models and variable selection in different contexts. In particular, I will discuss (1) a bi-clustering approach that allows clustering on subsets of variables by introducing latent variable selection indicators in finite or infinite mixture models, (2) an integrative model to relate two high-dimensional datasets by fitting multivariate mixture of regression models using stochastic partitioning, and (3) a mixture of regression trees approach to uncover homogeneous subgroups and their associated predictors accounting for non-linear relationships and interaction effects. I will illustrate the methods with various genomic applications.

Bio: Dr. Mahlet Tadesse is Professor and Chair of the Department of Mathematics and Statistics at Georgetown University. She is an elected member of the International Statistical Institute and an elected fellow of the American Statistical Association. Her research focuses on the development of statistical and computational tools for the analysis of high-dimensional data with an emphasis on -omic applications.

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Ergodic Th Seminar

Speaker: Szu Ting Kitty Yang

Time: Jan 28, 2022 01:00 PM Central Time (US and Canada)

Abstract: In the study of dynamical systems, an important class of examples consists of subshifts. By coding the orbits of points. you can model any dynamical system with a subshift. In this talk, we will focus on substitution subshifts, which arise by iterating a finite substitution. Given a subshift, we can associate various groups, including the automorphism group and the mapping class group, which reflect dynamical properties of its subshift. We will end the talk with a result that characterizes the mapping class group of a substitution subshifts, and look at various examples.

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Special Colloquium Lecture: Zarankiewicz, VC-dimension, and incidence geometry

Title: Zarankiewicz, VC-dimension, and incidence geometry

Speaker: Dr. Cosmin Pohoata, Yale University
For your reference, here is Dr. Pohoata’s website: https://pohoatza.wordpress.com/

Time: Jan 28, 2022 04:00 PM Central Time (US and Canada)

Abstract:  The Zarankiewicz problem is a central problem in extremal graph theory, which lies at the intersection of several areas of mathematics. It asks for the maximum number of edges $\operatorname{ex}(n,K_{s,t})$ in a bipartite graph on $2n$ vertices, where each side of the bipartition contains $n$ vertices, and which does not contain the complete bipartite graph $K_{s,t}$ as a subgraph. One of the reasons this problem is particularly interesting is that, for various (rather mysterious) reasons, the extremal graphs seem to have to be of algebraic nature, which is not always the case for Tur\’an-type problems. The most tantalizing case is by far the symmetric problem where $s=t:=k$, for which the value of $\operatorname{ex}(n,K_{k,k})$ is completely unknown for most values of $k$. In this talk, we will discuss a rather surprising new phenomenon related to an important variant of this problem, which is the analogous question in bipartite graphs with VC-dimension at most $d$, where $d$ is a fixed integer such that $k \geq d \geq 2$. We will also present a few consequences of our result in incidence geometry, which improve upon classical results. Based on joint work with Oliver Janzer (ETH).

Location: Join Zoom Meeting
https://memphis.zoom.us/j/87547314942?pwd=aWFsbVpHZGg1ZjJVMVFFNmo5ZTg4QT09

Meeting ID: 875 4731 4942
Passcode: 220994

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Special Colloquium Lecture: Splitting quasi-transitive infinite graphs

Title: Splitting quasi-transitive infinite graphs

Speaker: Dr. Matthias Hamann, University of Warwick
For you reference, attached is the CV of Dr. De Boeck, and the following is a link to his webpage.
www.math.uni-hamburg.de/home/hamann/

Time: Jan 27, 2022 01:00 PM Central Time (US and Canada)

Location: see the link below.

Abstract: We will look at multi-ended quasi-transitive graphs and obtain results for them that are generalisations of major theorems from geometric group theory such as Stallings’ splitting theorem of multi-ended groups or
Dunwoody’s accessibility theorem of finitely presented groups.

The central notion that we will use is due to Mohar: tree amalgamations. Starting with two quasi-transitive graphs, it allows us to construct a new quasi-transitive graph. We will consider the question whether the reverse also holds, i.e. whether every multi-ended quasi-transitive graph is a tree amalgamation of two other quasi-transitive graphs. To
answer this, we will use canonical tree-decompositions and their recently obtained theory and we will see how tree amalgamations and tree-decompositions relate to each other.

Location: Join Zoom Meeting
https://memphis.zoom.us/j/82607051522?pwd=RzBGbkQ4b1VjUHdmR2RYTG9kWE1vQT09
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Special Colloquium Lecture: Neumaier graphs

Title: Neumaier graphs

Speaker: Dr. Maarten De Boeck, University of Rijeka

Time: Jan 26, 2022 01:00 PM Central Time (US and Canada)

Abstract:  This is joint work with A. Abiad, W. Castryck, J. Koolen and S. Zeijlemaker.

A Neumaier graph is an edge-regular graph with a regular clique. A lot of strongly regular graphs (but clearly not all of them) are indeed Neumaier, but in [3] it was asked whether there are Neumaier graphs that are not strongly regular. This question was only solved recently (see [2]), so now we know there are so-called strictly Neumaier graphs. In this talk I will discuss several new results on (strictly) Neumaier graphs, including (non)-existence results. I will focus on a new construction producing an infinite number of strictly Neumaier graphs, described in [1]. The proofs rely on several results from number theory. I will also discuss a few directions for future research about Neumaier graphs.

References

[1] A. Abiad and W. Castryck and M. De Boeck and J.H. Koolen and S. Zeijlemaker, An infinite class of Neumaier graphs and non-existence results, arXiv:2109.14281 (2021), 22 pp.
[2] G.R. Greaves and J.H. Koolen, Edge-regular graphs with regular cliques, European J. Combin. 71(2018), 194–201.
[3] A. Neumaier, Regular cliques in graphs and special 1 1/2-designs, Finite Geometries and Designs, London Math. Soc. Lecture Note Series vol. 49 (1981), 244–25

Location: Join Zoom Meeting
https://memphis.zoom.us/j/86824870127?pwd=OHU3RTFWUUozR21mTVJ3OWllSnpVQT09
Meeting ID: 868 2487 0127
Passcode: 561211
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Special Colloquium Lecture: H-percolation

Title: H-percolation

Speaker: Bret Kolesnik , UCSD,
For your reference, here is Dr. Kolesnik’s website: https://mathweb.ucsd.edu/~bkolesnik/

Abstract: A graph G is said to H-percolate if all missing edges can be added eventually by iteratively completing copies of H minus an edge. This process was introduced by Bollobás (1967) and studied more recently by Balogh, Bollobás and Morris (2012) in the case that G is the Erdős–Rényi graph G(n,p). In this talk, we will discuss our recent work with Zsolt Bartha, which locates the critical percolation threshold p_c for all “reasonably balanced” graphs H.

Time: Jan 21, 2022 05:00 PM Central Time (US and Canada)

Join Zoom Meeting: https://memphis.zoom.us/j/89379811191?pwd=SDBQS3pnSUVTMmFmcEN1Z2NsNXJPQT09

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The Dirichlet Problem

Speaker 

Professor Wolfgang Arendt, University of Ulm, Germany

Abstract

The Dirichlet problem has a long history: Dirchlet tried to solve it by variational methods, Perron found an ingenious weak solution, Wiener obtained a characterization of well posedness in terms of his famous capacity condition, Stampacchia – in the light of the Di Giorgi-Nash result – investigated the Dirichlet problem for general elliptic operators.

We will tell the story of this fascinating problem explaining also some very new results in cases where the maximum principle does not hold. We also explain how the solution of the Dirichlet problem can be used to solve a parabolic problem via semigroup theory.