# Upcoming Seminars

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Title: Data Warehousing and Ensemble Learning of Omics Data
Speaker: Xiaobo Sun of Emory University
Contact: TBA
Date: 2018-04-20 at 1:00PM
Venue: Room GCR311 of Department of Biostatistics
Abstract:
The development and application of high-throughput genomics technologies has resulted in massive quantities of diverse omics data that continue to accumulate rapidly. These rich datasets offer unprecedented and exciting opportunities to address long standing questions in biomedical research. However, our ability to explore and query the content of diverse omics data is very limited. Existing dataset search tools rely almost exclusively on the metadata. A text-based query for gene name(s) does not work well on datasets where the vast majority of their content is numeric. To overcome this barrier, we have developed Omicseq, a novel web-based platform that facilitates the easy interrogation of omics datasets holistically, beyond just metadata to improve findability. The core component of Omicseq is trackRank, a novel algorithm for ranking omics datasets that fully uses the numerical content of the dataset to determine relevance to the query entity. The Omicseq system is supported by a scalable and elastic, NoSQL database that hosts a large collection of processed omics datasets. In the front end, a simple, web-based interface allows users to enter queries and instantly receive search results as a list of ranked datasets deemed to be the most relevant. Omicseq is freely available at http://www.omicseq.org.
Title: The maximum number of cycles in a graph
Seminar: Combinatorics
Speaker: Andrii Arman of The University of Manitoba
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2018-04-20 at 4:00PM
Venue: W301
Abstract:
The problem of bounding the total number of cycles in a graph is more than a century old. In 1897, Ahrens proved bounds on the number of cycles using the cyclomatic number of the graph and since then many results have appeared on the maximum number of cycles in graphs with different restrictions.

In this talk I will consider a problem of maximizing the number of cycles for three classes of graphs: graphs with given number of edges (and unrestricted number of vertices), graphs with a given average degree, and graphs without a clique of a specific size. For the first two classes I will show that the maximum number of cycles in a graph has bounds exponential in the number of edges of the graph. I will also present exponentially tight bounds for the maximum number of cycles in a multigraph with a fixed number of vertices and edges.
Title: A proof of a conjecture of Erd\H{o}s et al. about subgraphs of minimum degree k
Seminar: Combinatorics
Speaker: Lisa Sauermann of Stanford University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2018-04-23 at 4:00PM
Venue: W301
Abstract:
Erd\H{o}s, Faudree, Rousseau and Schelp observed the following fact for every fixed integer $k \geq 2$: Every graph on $n \geq k-1$ vertices with at least $(k-1)(n-k+2)+(k-2)(k-3)/2$ edges contains a subgraph with minimum degree at least k. However, there are examples in which the whole graph is the only such subgraph. Erdos et al. conjectured that having just one more edge implies the existence of a subgraph on at most $(1-\epsilon_k)n$ vertices with minimum degree at least $k$, where $\epsilon_k>0$ depends only on $k$. In this talk, we will sketch a proof of this conjecture. The proof relies on ideas from a paper of Mousset, Noever and $\check{S}kori\acute{c}$. We will discuss these ideas and how they can be extended to give a proof of the full conjecture.
Title: Lattice Point Counting and Arithmetic Statistics
Seminar: Algebra
Speaker: Frank Thorne of University of South Carolina
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2018-04-24 at 4:00PM
Venue: W304
Abstract:
The Gauss Circle Problem asks how many lattice points are contained in a circle centered at the origin or radius R. A simple geometric argument establishes that this count is approximated by the area $\pi R^2$, with an error bounded by the perimeter $O(R)$. \\ Arithmetic statistics" is about arithmetic objects -- number fields, ideal class groups, and so on. Bhargava and many others have recently proved spectacular theorems by parametrizing such objects in terms of lattice points, and then using geometry to counting the lattice points. \\ Meanwhile, harmonic analysts have long known that you can do better than an error of $O(R)$ in Gauss's circle problem. I will describe a program to import such improvements into arithmetic statistics, and give an overview of the number theoretic results we hope to obtain. \\ This is ongoing joint work with Theresa Anderson and Takashi Taniguchi.
Title: Optimization Methods for Training Neural Networks
Colloquium: Computational Mathematics
Speaker: Jorge Nocedal of Northwestern University
Contact: Lars Ruthotto, lruthotto@emory.edu
Date: 2018-04-27 at 3:00PM
Venue: MSC E208
Abstract:
Most high-dimensional nonconvex optimization problems cannot be solved to optimality. It has been observed, however, that deep neural networks have a benign geometry that permits standard optimization methods to find acceptable solutions. However, solution times can be exorbitant. In addition, not all minimizers of the neural network loss functions are equally desirable, as some lead to prediction systems with better generalization properties than others. In this talk we discuss classical and new optimization methods in the light of these observations, and conclude with some open questions

BIO:
Jorge Nocedal is the Walter P. Murphy Professor in the Department of Industrial Engineering and Management Sciences at Northwestern University. His research is in optimization, both deterministic and stochastic, and with emphasis on very large-scale problems. His current work is driven by applications in machine learning. He is a SIAM Fellow, was awarded the 2012 George B. Dantzig Prize, and the 2017 Von Neumann Theory Prize for contributions to theory and algorithms of optimization.