All Seminars
| Title: A new tensor framework - theory and applications |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Dr. Misha Kilmer of Tufts University |
| Contact: James Nagy, jnagy@emory.edu |
| Date: 2017-09-22 at 2:00PM |
| Venue: MSC W301 |
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| Abstract: Tensors (aka multiway arrays) can be instrumental in revealing latent correlations residing in high dimensional spaces. Despite their applicability to a broad range of applications in machine learning, speech recognition, and imaging, inconsistencies between tensor and matrix algebra have been complicating their broader utility. Researchers seeking to overcome those discrepancies have introduced several different candidate extensions, each introducing unique advantages and challenges. In this talk, we review some of the common tensor definitions, discuss their limitations, and introduce our tensor product framework which permits the elegant extension of linear algebraic concepts and algorithms to tensors. Following introduction of fundamental tensor operations, we discuss in further depth tensor decompositions and in particular the tensor SVD (t-SVD) and its randomized variant, which can be computed efficiently in parallel. We present details of the t-SVD, theoretical results, and provide numerical results that show the promise of our approach for compression and analysis of operators and datasets, highlighting examples such as facial recognition and model reduction. |
| Title: Unifying relaxed notions of modular forms |
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| Seminar: Algebra |
| Speaker: Martin Raum of Chalmers Technical University, Gothenburg, Sweden |
| Contact: John Duncan, john.duncan@emory.edu |
| Date: 2017-09-21 at 4:00PM |
| Venue: W306 |
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| Abstract: Elliptic modular forms are functions on the complex upper half plane that are invariant under a certain action of the special linear group with integer entries. Their history comprises close to two centuries of amazing discoveries and application: The proof of Fermat's Last Theorem is probably the most famous; The theory of theta functions is among its most frequently employed parts.\\ \\During the past decade it has been à la mode to study relaxed notions of modularity. Relevant keywords that we will discuss are mock modular forms and higher order modular forms. We have witnessed their application, equally stunning as surprising, to conformal field theory, string theory, combinatorics, and many more areas.\\ \\In this talk, we suggest a change of perspective on such generalizations. Most of the novel variants of modular forms (with one prominent exception) can be viewed as components of vector-valued modular forms. This unification draws its charm from the past and the future. On the one hand, we integrate results by Kuga and Shimura that hitherto seemed almost forgotten. On the other hand, we can point out connections, for example, between mock modular forms and so-called iterated integrals that have not yet been noticed. Experts will be pleased to have in the future a ``Petersson pairing'' for mixed mock modular forms at their disposal.\\ \\This is joint work with Michael Mertens |
| Title: On the Birkhoff--von Neumann decomposition and its use in solving sparse linear systems |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Dr. Bora Ucar of CNRS and ENS Lyon, France (visiting GaTech this year) |
| Contact: Michele Benzi, benzi@mathcs.emory.edu |
| Date: 2017-09-15 at 2:00PM |
| Venue: MSC W301 |
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| Abstract: The Birkhoff--von Neumann decomposition expresses a doubly stochastic matrix as a convex combination of permutation matrices. This talk will be an introduction to this decomposition. We are going to see its use in solving sparse linear systems, and investigate some algorithmic and combinatorial problems associated with it. This talk contains results from joint work with Michele Benzi (Emory Univ., Atlanta), Fanny Dufosse (Inria, France), Kamer Kaya (Sabanci Univ, Turkey), and Ioannis Panagiotas (ENS Lyon, France). |
| Title: Linked Fields of Characteristic 2 and their u-Invariant. |
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| Seminar: Algebra |
| Speaker: Dr. Adam Chapman of Tel-Hai Academic College, Israel. |
| Contact: Dr. John Duncan, john.duncan@emory.edu |
| Date: 2017-09-14 at 4:00PM |
| Venue: W306 |
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| Abstract: The u-invariant of a field is the maximal dimension of a nonsingular anisotropic quadratic form over that field, whose order in the Witt group of the field is finite. By a classical theorem of Elman and Lam, the u-invariant of a linked field of characteristic different from 2 can be either 0,1,2,4 or 8. The analogous question in the case of characteristic 2 remained open for a long time.. We will discuss the proof of the equivalent statement in characteristic 2, recently obtained in a joint work by Andrew Dolphin and the speaker. |
| Title: Spectrum of singularities, exponential sums and the irreducibility of polynomials in two variables |
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| Seminar: Algebra |
| Speaker: Jorge Jimenez Urroz of U. Politecnica, Catalunya |
| Contact: John Duncan, john.duncan@emory.edu |
| Date: 2017-08-29 at 4:00PM |
| Venue: W306 |
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| Abstract: In order to control the spectrum of singularities of the generalized Riemann function, we need to find sharp bounds for certain kind of Gauss sums with frequencies on polynomials. This can be achieved by Weil bounds on completely irreducible algebraic curves, which lead us to prove some theorems on irreducibility of polynomials in two variables. We will prove a general theorem in this field. An example of the theorem is the absolute irreducibility of p(x)-p(y)+1, for any p(x) with integer coefficients. |
| Title: Topics in Tropical and Analytic Geometry |
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| Defense: Dissertation |
| Speaker: Charles Morrissey of Emory University |
| Contact: Charles Morrissey, cjmorr3@emory.edu |
| Date: 2017-08-10 at 2:00PM |
| Venue: W306 |
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| Abstract: In this thesis, the author proves theorems on the existence and mapping properties of tropical stacks that arise from result concerning toric Artin stacks. The author also provides a generalization, using the same ideas from the toric Artin stacks, of recent work involving analytic stacks and their tropicalizations. The author also proves results on the notion of a tropical jet space. |
| Title: Application of the DIKW Model in Malaria Systems Biology: From NGS Data to Disease Progression Insight |
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| Defense: N/A |
| Speaker: Jung-Ting Chien of Emory University |
| Contact: Jung-Ting Chien, jchien2@emory.edu |
| Date: 2017-07-07 at 10:00AM |
| Venue: W306 |
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| Abstract: The data, information, knowledge and wisdom (DIKW) model has been widely used in data science fields to generate a comprehensive view of each domain. It provides a hierarchical representation of the understanding of the domain knowledge; the DIKW model can reveal insights in systems biology by integrating different types of –omics data to form a comprehensive understanding.\\ \\The foundation of systems biology is mining genomics data with machine learning. As the use of high-throughput, next-generation sequencing (NGS) applications grows, research in genomics enters the “big data” era. NGS applications can be divided into two major categories, short-read and long-read techniques, which are based on the principle differences in generating “reads”. A “read” is the fundamental element of genomic information. Short-read applications have been widely applied in several fields of genomics research, while long-read applications just came to market in 2011. Long-read applications have shown the potential to handle several areas of genomic questions. However, obtaining a well-defined genome still has a number of challenges in malaria systems biology research, and these challenges block researchers’ understanding the mechanism of the malaria disease progression.\\ \\To tackle these challenges, we built a novel long-read NGS pipeline with third party modules and modified them to solve complicated Plasmodium genome assembly questions. These techniques provided a solution where traditional, short-read technologies could not because of the Plasmodium genome’s highly repetitive nature. We also implemented infrastructure to solve data management difficulties and developed several novel and robust pipelines to process and analyze the data. We host this pipeline along with other third party applications for data quality control, generic data visualization and data management tools. Our pipeline is also scalable and flexible to combine different technologies (long reads and short reads) to assemble the Plasmodium genome and conduct downstream annotations.\\ \\This dissertation describes an overview of –omics research in the big data era and reveals the possibility of applying DIKW models through mining genomics data. A detailed discussion on how to apply our platform to solve questions, including multiple Plasmodium genome assemblies and annotations, and an initial discussion of applying machine learning approaches in a host-pathogen transcriptome analysis and its data mining applications are also provided. |
| Title: Perfect Secrecy vs. Computational Security in Private Key Encryption Schemes |
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| Seminar: Computer Science |
| Speaker: Steven La Fleur of Emory University |
| Contact: TBA |
| Date: 2017-05-22 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: As evidenced by recent events, privacy and security of data is increasingly important. There is a lot of interest in the ability to securely encrypt and send messages between two parties in such a way that any potential eavesdropper will be unable to read the message. But what does "security" of an encryption scheme mean, and how do we measure how secure a given scheme is?\\ \\In this talk we will investigate formal definitions for security of an encryption schemes, and what it means to prove that an encryption scheme is secure using these definitions. We will consider the practical drawbacks of "perfect secrecy" and how the definitions and assumptions made for computational security fix these drawback while still maintaining secrecy from attackers of different strengths.\\ \\The talk is intended for undergraduate students who have taken a course in discrete mathematics for computer science and have a basic understanding of probability, theory of computation and rigorous proof. |
| Title: Efficient and Adaptive Skyline Computation |
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| Defense: Dissertation |
| Speaker: Jinfei Liu of Emory University |
| Contact: Jinfei Liu, jliu253@emory.edu |
| Date: 2017-05-10 at 1:00PM |
| Venue: MSC E406 |
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| Abstract: Skyline, also known as Maxima in computational geometry or Pareto in business management field, is important for many applications involving multi-criteria decision making. The skyline of a set of multi-dimensional data points consists of the points for which no other point exists that is better in at least one dimension and at least as good in every other dimension. Although skyline computation and queries have been extensively studied in both computational geometry and database communities, there are still many challenges need to be fixed, especially in this big data ear. In this dissertation, I present several efficient and adaptive skyline computation algorithms. First, I show a faster output-sensitive skyline computation algorithm which is the state-of-the-art algorithm from the theoretical aspect. Second, traditional skyline computation is inadequate to answer queries that need to analyze not only individual points but also groups of points. To address this gap, I adapt the original skyline definition to the novel group-based skyline (G-Skyline), which represents Pareto optimal groups that are not dominated by other groups. Third, to facilitate skyline queries, I propose a novel concept Skyline Diagram, which given a set of points, partitions the plane into a set of regions, referred to as skyline polyominos. Similar to kth-order Voronoi diagram commonly used to facilitate k nearest neighbor (kNN) queries, any query points in the same skyline polyomino have the same skyline query results. |
| Title: Non-backtracking walk centrality for directed networks |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Francesca Arrigo of University of Strathclyde |
| Contact: Michele Benzi, benzi@mathcs.emory.edu |
| Date: 2017-04-28 at 1:00PM |
| Venue: MSC W301 |
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| Abstract: The talk is motivated by a practical issue: walk-based centrality measures regard all walks of the same length as being equally important, whereas it is intuitively reasonable to rule out certain classes of walk. We focus here on non-backtracking walks. The theory of zeta functions provides an expression for the generating function of non-backtracking walk counts on a directed network. This expression can be used to produce a centrality measure that eliminates backtracking walks at no cost. The new centrality measure may be interpreted as standard Katz on a modified network, where self loops are added, and where non-reciprocated edges are augmented with negative weights. We also give a multilayer interpretation of the new centrality measure, where (negatively) weighted walks between layers compensate for backtracking walks on the only non-empty layer. We further show that the radius of convergence of the generating function is determined by the spectrum of a three-by-three block matrix involving the original adjacency matrix. This gives a means to choose appropriate values of the attenuation parameter and, in particular, we show that we obtain a larger range of choices for the attenuation parameter than that obtained for standard Katz. By studying the effect of pruning operations on the network (i.e., removing nodes), we show that there is potential for the non-backtracking centrality to be computed more cheaply than Katz for appropriate network structures. Studying the limit as the attenuation parameter approaches its upper bound allows us to propose an eigenvector-based non-backtracking centrality measure in this directed network setting. We illustrate the centrality measure on a synthetic network, where it is shown to eliminate a localization effect present in standard Katz centrality. We also give results for real networks. Finally, we discuss some preliminary results on the non-backtracking version of the total communicability and of some alternating walk-based centrality measures.\\ \\This talk is based on joint work with Prof. Peter Grindrod (University of Oxford, UK), Prof. Desmond J. Higham (University of Strathclyde, UK), and Dr. Vanni Noferini (University of Essex, UK). |