All Seminars
| Title: Fast Algorithms for Nonnegative Matrix Factorizations and Applications |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Haesun Park of Georgia Institute of Technology |
| Contact: Veronica Bustamante, vmejia@emory.edu |
| Date: 2011-03-21 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: Nonnegative Matrix Factorization (NMF) has attracted much attention during the past decade as a dimension reduction method in machine learning and data mining. NMF is considered for high dimensional data where each element has a nonnegative value, and it provides a lower rank approximation formed by factors whose elements are also nonnegative. Numerous success stories were reported in application areas including text clustering, computer vision, and chemometrics. In this talk, we review several NMF algorithms available in literature and present our fast algorithms for NMF and their convergence properties. Our algorithms are based on alternating nonnegative least squares (ANLS) and active-set-type methods for non-negativity constrained least squares problem. They can naturally be extended to obtain highly efficient nonnegative tensor factorization (NTF) in the form of the PARAFAC (PARAllel FACtor) model, sparse NMF and NTF with L1 norm regularization. Extensive comparisons of algorithms using various data sets show that the proposed new algorithms outperform existing ones in computational speed. In addition, we introduce fast NMF algorithms with Bregman divergences, adaptive NMF algorithms for changing reduced ranks and data sets, symmetric NMF, and their performances in clustering and video analysis. |
| Title: Computing and Hedge Fund Management |
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| Seminar: Computer Science |
| Speaker: Dr. Tucker Balch of Georgia Institute of Technology |
| Contact: Valerie Summet, valerie@mathcs.emory.edu |
| Date: 2011-03-18 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: Computing pervades today's equity markets. In addition to the electronic infrastructure in the markets to support orders from investors, many investors and traders use algorithmic methods for making trading decisions. I will provide an overview of some of the most popular quantitative tools for assessing portfolios and making trading decisions. I will also demonstrate the QuantSoftware ToolKit, an open source package for automating some of these processes.\\ \\ Bio: Tucker Balch is an associate professor in the School of Interactive Computing at Georgia Tech. He earned a BS and PhD in CS at Georgia Tech before joining the research faculty at CMU's Robotics Institute. He returned to Georgia Tech in 2001. Balch has published more than 140 peer reviewed conference and journal articles in Machine Learning and Robotics. He has a strong interest in finance and investing which led him to spend a sabbatical year as a quantitative analyst at a hedge fund. He is now shifting his teaching and research interests in that direction. |
| Title: Scattering for the cubic Klein Gordon equation in two space dimensions |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Professor Betsy Stovall of University of California, Los Angeles |
| Contact: Shanshuang Yang, syang@mathcs.emory.edu |
| Date: 2011-03-15 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: We will discuss a proof that finite energy solutions to the defocusing cubic Klein Gordon equation scatter, and will discuss a related result in the focusing case. (Don't worry, we will also explain what it means for a solution to a PDE to scatter.) This is joint work with Rowan Killip and Monica Visan. |
| Title: Numerical Solution of the k-Eigenvalue Problem |
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| Defense: Dissertation |
| Speaker: Steven Hamilton of Emory University |
| Contact: Steven Hamilton, sphamil@emory.edu |
| Date: 2011-03-15 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: The k-eigenvalue problem is a generalized eigenvalue problem relevant to the design and analysis of nuclear reactors. The availability of robust and efficient solvers for this problem is an area of active interest in the nuclear engineering community and improved methods may lead to more efficient reactor designs. In this talk we present a survey of existing numerical strategies and offer a new framework based on the Davidson eigensolver which circumvents many standard difficulties. A multigrid-in-energy preconditioner is developed for use with the Davidson method as an alternative to the expensive matrix inversions that must typically be performed. Numerical results using the NEWT radiation transport code provide a comparison between several leading methods and demonstrate the effectiveness of this new approach. |
| Title: Steinberg groups for Jordan pairs |
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| Seminar: Algebra and number theory |
| Speaker: Erhard Neher of University of Ottawa |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2011-03-14 at 3:00PM |
| Venue: W306 |
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| Abstract: In this talk I will describe a concrete construction of groups via matrices or, more generally, as groups of automorphisms of certain Lie algebras and an abstract construction by generators and relations. The concrete groups in question cover most classical groups over rings. The abstract groups generalize the groups defined by Steinberg. The two types of groups are related via central extensions. The main methods to make the general constructions work come from Jordan pairs, but no prior knowledge of Jordan pairs will be assumed. |
| Title: Souls of some convex surfaces |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Eric Choi of Emory University |
| Contact: Eric Choi, echoi7@emory.edu |
| Date: 2011-03-01 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: The $soul$ of a complete, noncompact, connected Riemannian manifold $(M, g)$ of nonnegative sectional curvature is a compact, totally convex, totally geodesic submanifold such that $M$ is diffeomorphic to the normal bundle of the soul. Hence, understanding of the souls of $M$ can reduce the study of $M$ to the study of a compact set. Also, souls are metric invariants, so understanding how they behave under deformations of the metric is useful to analyzing the space of metrics on $M$. In particular, little is understood about the case when $M = R^2$. Convex surfaces of revolution in $R^3$ are one class of two-dimensional Riemannian manifolds of nonnegative sectional curvature, and I will discuss some results regarding the sets of souls for some of such convex surfaces. % r_h(sis $c = r \sin \phi,$ where $\phi = \angle (\dot \g(t), \dot \sigma)$ ($\sigma$ is the meridian through $\g(t)$.). %the intervals for integration must be broken up as follows: $[r(s_1), r(s_0)), [r(s_0,$ |
| Title: EUMMA Jeopardy Night |
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| Seminar: N/A |
| Speaker: Faculty of Emory |
| Contact: Alex Carstairs, acarsta@emory.edu |
| Date: 2011-02-28 at 6:00PM |
| Venue: MSC W303 |
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| Abstract: |
| Title: List Colorings of Dense Hypergraphs |
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| Seminar: Combinatorics |
| Speaker: Alexander Kostochka of The University of Illinois at Urbana-Champaign |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2011-02-25 at 4:00PM |
| Venue: W306 |
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| Abstract: The {\em list chromatic number} $\chi_{\ell}(G)$ of a hypergraph $G=(V,E)$ is the minimum integer $s$ such that for every assignment of a list $L_v$ of $s$ colors to each vertex $v$ of $G$, there is a vertex coloring of $G$ in which the color of each vertex is in its list and there are no monochromatic edges. In nineties, Alon showed that the list chromatic number of every graph with average degree $d$ is at least $(0.5-o(1))\log_2 d$. In this talk, we discuss two related results by Alon and the speaker on list coloring of uniform hypergraphs. The first of them states that for $r\geq 3$, every $r$-uniform hypergraph in which at least half of the $(r-1)$-vertex subsets are contained in at least $d$ edges has list chromatic number at least $ \frac{\ln d}{(20r)^3}$. When $r$ is fixed, this is sharp up to a constant factor. In particular, $n$-vertex $r$-uniform hypergraphs may have average degree about $(n/r)^{r-2}$ and still be $2$-list-colorable. The second result concerns {\em simple} hypergraphs, that is, the hypergraphs in which any two distinct edges have at most one vertex in common. It is proved that for every fixed $r$, all $r$-uniform hypergraphs with high average degree have ``high" list chromatic number. The result implies that for any finite set of points $X$ in the plane, and for any finite integer $s$, one can assign a list of $s$ distinct colors to each point of the plane so that any coloring of the plane that colors each point by a color from its list contains a monochromatic isometric copy of $X$. |
| Title: Service-Oriented Computing: Emerging Approaches for Web-Based Software Engineering |
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| Colloquium: Computer Science |
| Speaker: M. Brian Blake of University of Notre Dame |
| Contact: Li Xiong, lxiong@mathcs.emory.edu |
| Date: 2011-02-18 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: Emerging technologies facilitate an environment where web-based software or web services have well-defined, open interfaces and are discoverable across the Internet. Service-oriented computing is an emerging approach to software engineering that suggests that new specialized business processes can be created, on-demand, simply by integrating the services provided by others. However, in the real world, software developers tend to create applications that do not conform to consistent developmental practices even if they do use universal interface representations (e.g. the eXtensible Markup Language). Our research utilizes semantic approaches, enhanced syntactical methods, and contextual information to automate the integration of software services that are developed randomly from a wide array of diverse sources. This talk discusses our foundational lines of research and subsequent contributions in the areas of service discovery, composition, and evaluation. The talk will conclude with future work that leverages service-oriented paradigms in areas such as visual analytics, smart grid, and an “Internet of things”. |
| Title: Probabilistic Galois theory |
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| Colloquium: Number Theory |
| Speaker: David Zywina of University of Pennsylvania |
| Contact: Susan Guppy, sguppy@emory.edu |
| Date: 2011-02-17 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: A special case of Hilbert's irreducibility theorem says that a ``random" degree $n$ polynomial with integer coefficients will have the largest possible Galois group (i.e., the symmetric group on $n$ letters). Historically, the notion of ``random" used is that of natural density; the goal of this talk is to discuss alternate approaches that use legitimate probabilistic methods. This will lead us to consider random walks on certain graphs and their connection with the arithmetic of linear algebraic groups. |