All Seminars
| Title: A Parameter Decomposition Scheme for Iteratively Regularized Gauss-Newton |
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| Type: AWM Event |
| Speaker: Dr. Alexandra Smirnova of Georgia State University |
| Contact: Kinnari Amin, kinnari.amin@emory.edu |
| Date: 2008-12-08 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: A new convergence result for an Iteratively Regularized Gauss Newton (IRGN) algorithm with a Tikhonov regularization term using a seminorm generated by a linear operator will be presented [SRK07]. The convergence theorem uses an a posteriori stopping rule and a modified source condition, without any restriction on the nonlinearity of the operator. The theoretical results are illustrated by simulations for a 2D version of the exponentially ill-posed optical tomography inverse problem for the diffusion and absorption coefficient spatial distributions. The modified Tikhonov regularization performs the mapping of the minimization variables, which are the coefficients of the spline expansions for the diffusion and absorption, to physical space. This incorporates the inherently differing scales of these variables in the minimization, and also suggests relative weighting of the regularization terms with respect to each parameter space. The modified IRGN allows greater flexibility for implementations of iteratively regularized solutions of ill-posed inverse problems in which differing scales in physical space hinder standard IRGN inversions. |
| Title: Sentry Selection |
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| Seminar: Combinatorics |
| Speaker: Paul Balister of University of Memphis |
| Contact: Michal Karonski, michal@mathcs.emory.edu |
| Date: 2008-12-05 at 4:00PM |
| Venue: W306 |
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| Abstract: Suppose we have a collection of sensors in a large region, each of which can detect events within a disk of radius 1. We wish to devise a schedule so that each sensor can sleep for much of the time, while making sure that the whole region is covered by the sensors that are awake. A natural way of doing this is to partition the sensors into k subsets, each subset of sensors covering the whole region. Then in time slot t we activate all the sensors in subset (t mod k). If this is possible we say the sensors are k-partitionable. An obvious necessary condition is that each point in the region is covered by at least k sensors (k-coverage), but this is not in general sufficient. We show that for random deployments of sensors k-coverage usually implies k-partitionability, and identify the most likely obstructions to k-partitionability when this fails. This leads to some natural unsolved problems involving k-partitionability of (deterministic) configurations of disks. This is joint work with B. Bollobas, A. Sarkar, and M. Walters. |
| Title: Sign Pattern Matrices |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Dr. Zhongshan Li of Georgia State University, Dept. of Mathematics & Statistics |
| Contact: Raya Horesh, rshindm@emory.edu |
| Date: 2008-12-03 at 3:00PM |
| Venue: W304 |
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| Abstract: |
| Title: Invariants of orthogonal involutions |
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| Seminar: Algebra |
| Speaker: Jean-Pierre Tignol of Universite catholique de Louvain, Belgium |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2008-11-25 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: For central simple algebras of even degree with orthogonal involutions, invariants modeled on the discriminant and Clifford algebra of quadratic forms were defined by Jacobson and Tits, and a relative cohomological invariant of degree 3 is defined by using the Rost invariant of Spin groups when the first two invariants vanish. Its properties and computation will be discussed in the particular case where the algebra has degree 8 and index 4, in relation with properties of 8-dimensional quadratic forms in $I^2$. (Joint work with Anne Qu\'eguiner-Mathieu). |
| Title: Contextualized Computing Education |
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| Seminar: Computer Science |
| Speaker: Dr. Mark Guzdial of Georgia Institute of Technology |
| Contact: James J. Lu, jlu@mathcs.emory.edu |
| Date: 2008-11-21 at 3:00PM |
| Venue: MSC W201 |
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| Abstract: One of the most powerful tools for improving success rates in introductory computing courses is the incorporation of context -- a theme that pervades the computing lectures, assignments, and examples which relates the content to a concrete application domain. Contextualized computing education has even allowed us to be successful with challenging audiences, such as the non-technical major. In this talk, we review why Georgia Tech has chosen to teach serious computer science to every student on campus, and then discuss research findings from several schools on the benefits and costs of contextualized computing education. |
| Title: Groups have Shape |
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| Graduate Student Seminar: Algebra |
| Speaker: Dr. Aaron Abrams of Emory University |
| Contact: Praphat Fernandes, praphat.fernandes@emory.du |
| Date: 2008-11-19 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: Discrete groups come in all shapes and sizes. I'll show you some. Then I'll explain what I think a quasi-isometry is. |
| Title: Morse theory and conjugacy classes of finite subgroups |
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| Seminar: Topology |
| Speaker: Dani Pallavi of Emory University |
| Contact: Aaron Abrams, abrams@mathcs.emory.edu |
| Date: 2008-11-18 at 4:00PM |
| Venue: W304 |
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| Abstract: Many groups have the property of having only finitely many conjugacy classes of finite subgroups. Examples include hyperbolic groups, CAT(0) groups, mapping class groups, and automorphism groups of free groups. Do subgroups of these groups inherit this property? The answer turns out to be no. I will describe how combinatorial Morse theory can be used to produce couterexamples. This is joint work with Noel Brady and Matt Clay. |
| Title: An Investigation into Managing SQL-Cardinality Constraints |
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| Defense: Master's Thesis |
| Speaker: Lesi Wang of Emory University |
| Contact: Lesi Wang, lwang31@emory.edu |
| Date: 2008-11-17 at 2:00PM |
| Venue: MSC E408 |
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| Abstract: Constraint Satisfaction Problems (CSP) are commonly found in practice and finding effective representation language and efficient constraint solving techniques are important research areas. A recent development is the integration of CSP (specifically SAT) solvers with relational database systems to enable CSPs to be modelled using SQL, and solved within the database system. A key challenge in this integration is to keep the SAT encoding of SQL constraints small. In this work, we describe a divide-and- conquer technique for reducing the encoding of cardinality constraints. We present a number of experiments to show the improvements on performance. |
| Title: Pattern Discovery Under Saturation Constraints |
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| Seminar: Computer Science |
| Speaker: Dr. Alberto Apostolico of Georgia Institute of Technology |
| Contact: James Lu, jlu@mathcs.emory.edu |
| Date: 2008-11-14 at 3:00PM |
| Venue: MSC W201 |
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| Abstract: The problem of characterizing and detecting surprisingly recurrent sequence patterns such as substrings or motifs and related associations or rules is pursued ubiquitously in order to compress data, unveil structure, infer succinct descriptions, extract and classify features, etc. In Molecular Biology, some such patterns are variously implicated in facets of biological structure and function. Because of that, Pattern Discovery constitutes one of the most battered, flourishing and arguably useful applications of Computational Molecular Biology. The very notion of a pattern still embodies subtleties and ambiguities, as do related concepts such as class and structure. And the discovery, particularly on a massive scale, of surprising patterns and correlations thereof poses interesting methodological and algorithmic problems, some of which appear to be hardly surmountable. This talk proposes a brief account of algorithmic pattern discovery under constraints of saturation, displays some of its applications, and highlights issues, products and challenges emerged in recent and current work. |
| Title: Cohomology and support varieties for Cartan Lie superalgebras |
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| Seminar: Algebra |
| Speaker: Irfan Bagci of University of Georgia |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2008-11-11 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: V.~Kac classified finite dimensional simple Lie superalgebras over the field of complex numbers in 1970s. They constitute several series and are divided into two types based on their even part: classical type and Cartan type. Lie superalgebras of Cartan type consists of four series $W(n)$, $S(n)$, $S^{~}(n)$, and $H(n)$. In this talk I will briefly introduce Cartan type Lie superalgebras and then I will show how explicitly one can compute cohomology and support varieties for $W(n)$ and $S(n)$. I will also mention what we have for $H(n)$ and present a new theorem on realizability of support varieties that holds both for classical and Cartan type Lie superalgebras. If I have time I am planning to present some open problems at the end of my talk. The results about $W(n)$ represents joint work with Jonathan Kujawa and Daniel Nakano. |