All Seminars

Title: Algebraic Integral Geometry
Seminar: Analysis and Differential Geometry
Speaker: Professor Joseph Fu of University of Georgia
Contact: Vladimir Oliker, oliker@mathcs.emory.edu
Date: 2010-04-20 at 4:00PM
Venue: MSC W301
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Abstract:
A recently developed theoretical framework, due largely to S. Alesker, A. Bernig and the speaker, reduces many problems of classical integral geometry to algebra. In some cases the algebraic problems are then easy to solve, and in others they are not. I will describe the reduction in general terms and illustrate how it gives concrete information in a few examples. I will also state a mysterious conjecture that is completely algebraic in nature but represents the key to understanding the integral geometry of complex projective space and complex hyperbolic space.
Title: On generalized Folkman numbers
Seminar: Combinatorics
Speaker: Andrzej Dudek of Carnegie Mellon University
Contact: Vojtech Rodl, rodl@mathcs.emory.edu
Date: 2010-04-16 at 4:00PM
Venue: MSC W301
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Extending the previous results on Folkman numbers for cliques we are interested in the following generalization. For a given graph G and a number of colors r let F(G,r) be the order of the smallest graph H such that the clique number of H equals the clique number of G and any r-coloring of the vertices of H yields a monochromatic and induced copy of G. In this talk we give a relatively small upper bound on F(G,r) as a function of the order of G and its clique number.
Title: Experimental Design for Medical Applications
Seminar: Computational Mathematics
Speaker: Matthias Conrad of Emory University
Contact: Pascal Philipp, pphilipp@emory.edu
Date: 2010-04-14 at 4:00PM
Venue: MSC W201
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Abstract:
Many problems in medicine are governed by a models with unknown parameters. To have a meaningful representation of the model, these parameters need to be evaluated from observations. Experimentalists face the dilemma between accuracy of the parameters and costs of an experiment. The choice of the design of an experiment is important if we are to recover precise model parameters. It is important to know when and what kind of observations should be taken. Taking the wrong measurement can lead to inaccurate estimation of parameters, thus resulting in inaccurate representations of the dynamical system. Each experiment has its own specific challenges. However, optimization methods form the basic computational tool to address eminent questions of optimal experimental design. We present a methodology for the design of such experiments that can optimally recover parameters in a dynamical system, biomedical systems in particular. We show that the problem can be cast as a stochastic bilevel optimization problem. We then develop an effective algorithm that allows for the solution of the design problem. The advantages of our approach are demonstrated on a few basic biological models as well as a design problem for the energy metabolism to estimate insulin resistance.
Title: Understanding and Supporting People in Dynamic Information Environments
Seminar: Computer Science
Speaker: Sue Dumais of
Contact: Eugene Agichtein, eugene@mathcs.emory.edu
Date: 2010-04-14 at 4:00PM
Venue: 290 PAIS
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Abstract:
The Web is a dynamic, ever-changing collection of information, yet most of the tools that we have for interacting with Web content, such as browsers and search engines, focus on a single snapshot of the information. In this talk, I will present descriptive analyses of how web content changes over time, how people re-visit web pages over time, and how re-visitation patterns are influenced by user intent and changes in content. These results have implications for browser and site design, search algorithms, and crawling. I will describe a new prototype that supports people in understanding how information they interact with changes over time, by highlighting how a Web page has changed since your last visit. Finally, I will describe a new retrieval model that represents and use features about the temporal evolution of web pages to improve ranking and inform crawl policy. Susan Dumais is a Principal Researcher and manager of the Context, Learning and User Experience for Search (CLUES) Group at Microsoft Research. She has been at Microsoft Research since 1997 and has published widely in the areas of human-computer interaction and information retrieval. Her current research focuses on personal information management, user modeling and personalization, novel interfaces for interactive retrieval, and implicit measures of user interest and activity. She has worked closely with several Microsoft groups (Bing, Windows Desktop Search, Live Search, SharePoint Portal Server, and Office Online Help) on search-related innovations. Prior to joining Microsoft Research, she was at Bellcore and Bell Labs for many years, where she worked on Latent Semantic Indexing (a statistical method for concept-based retrieval), combining search and navigation, individual differences, and organizational impacts of new technology.
Title: Reality-Based Interaction and Next Generation User Interfaces
Seminar: Computer Science
Speaker: Robert J.K. Jacob of Department of Computer Science, Tufts University
Contact: Eugene Agichtein, eugene@mathcs.emory.edu
Date: 2010-04-12 at 3:30PM
Venue: MSC W201
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Abstract:
I will describe the notion of Reality-Based Interaction (RBI) as a unifying concept that ties together a large subset of the emerging generation of new, non-WIMP user interfaces.  It attempts to connect current paths of research in HCI and to provide a framework that can be used to understand, compare, and relate these new developments. Viewing them through the lens of RBI can provide insights for designers and allow us to find gaps or opportunities for future development.  I will then discuss work in my research group on a variety of next generation interfaces, such as brain-computer interfaces, tangible interfaces, and eye movement-based interaction techniques, along with some of the software issues they raise and our work on developing new software models and abstractions for non-WIMP interfaces.   Robert Jacob is a Professor of Computer Science at Tufts University, where his research interests are new interaction media and techniques and user interface software.  He was also a visiting professor at the Universite Paris-Sud and at the MIT Media Laboratory, in the Tangible Media Group.  Before coming to Tufts, he was in the Human-Computer Interaction Lab at the Naval Research Laboratory.  He received his Ph.D. from Johns Hopkins University, and he is a member of the editorial board of Human-Computer Interaction and the ACM Transactions on Computer-Human Interaction. He was Papers Co-Chair of the CHI 2001 conference, Co-Chair of UIST 2007, and Vice-President of ACM SIGCHI. He was elected to the ACM CHI Academy in 2007, an honorary group of people who have made extensive contributions to the study of HCI and have shaped the field.
Title: Some Quotients of the Boolean Lattice are Symmetric Chain Orders
Undergraduate Honors Thesis Defense: N/A
Speaker: Jeremy McKibben-Sanders of Emory University
Contact: Dwight Duffus,
Date: 2010-04-12 at 4:00PM
Venue: W302
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Title: Harmonics Echoing Across Time and Space: A Summary of Research on the Topology of the Universe
Undergraduate Honors Thesis Defense: N/A
Speaker: Sara Lykken of Emory University
Contact: Emily Hamilton,
Date: 2010-04-09 at 1:30PM
Venue: MSC E406
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Title: Centroidal Voronoi tessellations: algorithms and applications
SIAM Student Chapter: Numerical Analysis and Scientific Computing
Speaker: Max Gunzburger of Florida State University
Contact: Alessandro Veneziani, ale@mathcs.emory.edu
Date: 2010-04-09 at 4:00PM
Venue: MSC W301
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Abstract:
One of the beauties of mathematics is that it can uncover connections between seemingly disparate applications. One of the most fertile grounds for unearthing connections is computational algorithms where one often discovers that an algorithm developed for one application is equally useful in several others. One such algorithm is centroidal Voronoi tessellations (CVTs) which are special Voronoi diagrams for which the generators of the diagrams are also the centers of mass (with respect to a given density function) of the Voronoi cells. CVTs have many uses and applications, a non-exhaustive list of which includes data compression, image segmentation and edge detection, clustering, cell biology, territorial behavior of animals, resource allocation, stippling, grid generation in volumes and on surfaces, meshless computing, hypercube sampling, and reduced-order modeling. We discuss mathematical features of CVTs (that give an indication of why they are so effective) as well as deterministic and probabilistic methods for their construction. Our main focus, however, is on considering as many applications of CVTs as time permits.
Title: Relationships between areas in a triangulation of a square
Undergraduate Honors Thesis Defense: N/A
Speaker: Phillip Andreae of Emory University
Contact: Aaron Abrams,
Date: 2010-04-09 at 4:00PM
Venue: MSC E406
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Abstract:
For a triangulation of the unit square---that is, a tiling of the square by triangles---we consider the general problem of studying the relationships between the areas of these triangles. For a particular combinatorial arrangement of vertices and edges, by a dimension argument we expect that there must be a relation among the areas of the triangles. By generalizing the notion of triangulating a square and applying some facts from algebraic geometry, we can prove that this relation is in fact a homogeneous polynomial equation that is an invariant of the combinatorial triangulation. Our focus is on calculating the degree of this polynomial for any arbitrary triangulation. We develop an algorithm to compute this degree by inductively relating a triangulation to simpler ``factor" triangulations and studying the relationship between the associated polynomials.
Title: Numerical Simulations of Aortic Blood Flow with a Bicuspid Aortic Valve
Undergraduate Honors Thesis Defense: N/A
Speaker: Ruth Blum of Emory University
Contact: Alessandro Veneziani,
Date: 2010-04-08 at 3:00PM
Venue: MSC W301
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Abstract: