All Seminars
| Title: Large-Scale Inverse Problems in Imaging: Two Case Studies |
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| Defense: Computer Science |
| Speaker: Sarah Knepper of Emory University |
| Contact: Sarah Knepper, smknepp@emory.edu |
| Date: 2011-06-06 at 11:00AM |
| Venue: W302 |
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| Abstract: Solving inverse problems is an important part of scientific computing. As computers become more powerful, solutions to increasingly larger problems are sought, allowing for more accurate representations of real-world applications. We consider solving large-scale inverse problems, ranging from linear to fully nonlinear. We look at aspects common to inverse problems, such as their ill-posedness, and see how regularization can help produce meaningful results. We discuss a number of different methods for solving while providing regularization. One such technique is to solve using an iterative method but stop the iterations early, before convergence is fully achieved. Iterative solvers are particularly useful for large-scale inverse problems as computations can be done in parallel. Trilinos is a mathematical software library for solving problems coming from many fields of scientific computing. One particular package, Belos, provides both an abstract framework and concrete implementations of various iterative solvers. We have implemented two additional solvers within the Belos framework, LSQR and MRNSD, which can be used to solve linear inverse problems.\\ \\ We then consider two different case studies, where we wish to solve a large-scale linear inverse problem. In the first study, we want to remove patient motion blur from positron emission tomography (PET) images when motion information is tracked and recorded during the scan. We describe how this problem can be formulated as a linear equation, then we solve it using the solvers we implemented. We also look at a number of results, seeing how the reconstruction improves as more motion information is included in our model. The second case study comes from the field of adaptive optics. Here we wish to determine the distortion caused by the atmosphere when imaging using ground-based telescopes. Sensors are able to obtain noisy estimates of the gradients of the distortion, resulting in a Kronecker product-structured linear least squares problem. We describe a solving method that employs Tikhonov-type regularization by exploiting properties of the Kronecker product and utilizing the generalized singular value decomposition (GSVD). Our approach includes constructing a preconditioner off-line and then applying a few iterations of preconditioned LSQR. |
| Title: Enabling Relational Databases for Effective CSP Solving |
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| Defense: Dissertation |
| Speaker: Sebastien Siva of Emory University |
| Contact: Sebastein Siva, siva@mathcs.emory.edu |
| Date: 2011-06-06 at 1:00PM |
| Venue: W304 |
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| Abstract: Constraint satisfaction problems (CSP) are frequently solved over data residing in relational database systems. In such scenarios, the database is typically just used as a data storage back end. However, there exist important advantages, such as the wide availability of database practices and tools for modeling, to having database systems that are capable of natively modeling and solving CSPs. This research introduces general concepts and techniques to extend a database system with constraint processing capabilities. Topics include relational constraint satisfaction problems (RCSP) and their specification in SQL, compiling RCSP into SAT, supporting multiple solving algorithms, and automated problem decomposition. |
| Title: Augmented Lagrangian-based Preconditioners for the Incompressible Navier-Stokes Equations |
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| Defense: Dissertation |
| Speaker: Zhen Wang of Emory University |
| Contact: Zhen Wang, zhen.wang@emory.edu |
| Date: 2011-06-03 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: We analyze different variants of the augmented Lagrangian-based block triangular preconditioners for the incompressible Navier--Stokes equations in two and three space dimensions. Both steady and unsteady problems are considered. The preconditioners are used to accelerate the convergence of the Generalized Minimal Residual (GMRES) method applied to both stable and stabilized finite element and MAC discretizations of the linearized problem. We study the eigenvalues of the preconditioned matrices obtained from Picard linearization, and we devise a simple and effective method for the choice of the augmentation parameter based on Fourier analysis. Numerical experiments on a wide range of model problems demonstrate the robustness of these preconditioners, yielding fast convergence independent of mesh size and only mildly dependent on viscosity on both uniform and stretched grids. Good results are also obtained on linear systems arising from Newton linearization. We also show that performing inexact preconditioner solves with an algebraic multigrid algorithm results in excellent scalability. Comparisons of the modified augmented Lagrangian preconditioners with other state-of-the-art techniques show the competitiveness of our approach. Implementation on parallel architectures is also considered. |
| Title: Leveraging User Interaction to Improve Search Experience with Difficult and Exploratory Queries |
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| Seminar: Computer Science |
| Speaker: Alexander Kotov of UIUC |
| Contact: Eugene Agichtein, eugene@mathcs.emory.edu |
| Date: 2011-04-29 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: While modern search engines perform well on easy navigational queries, every search engine user knows that there exist queries for which few or none of the top-ranked results are relevant. Such queries are commonly referred to as difficult. There are several major reasons for poor search results. In some cases, users do not have a clear information need and would simply like to explore a particular topic. In other cases, users may have a clear and specific information need, but either cannot accurately formulate it as a keyword query (the query is too short) or their formulation is ambiguous. Such queries are known as exploratory. Although many users are aware that the quality of search results can be improved by reformulating queries, finding a good reformulation is often non-trivial and takes time. Depending on a particular reason for poor initial retrieval results, search systems can try to engage the users into the feedback loop by generating the candidate query reformulations. In this talk, I provide an overview of three interactive feedback methods that I developed as part of my PhD thesis in order to address the specific challenges presented by difficult and exploratory queries: question feedback, sense feedback and concept feedback. Question feedback is aimed at interactive refinement of short, exploratory keyword-based queries by automatically generating and presenting to the users a list of natural language clarification questions. Sense feedback enables the users to interactively improve the quality of retrieval results by selecting the intended sense from a list of automatically generated collection-specific senses of an ambiguous query term. Concept feedback leverages the possibility of multi-step inference on the semantic network of ConceptNet to select and present to the users a small number of concepts, which are related to the original query and can be used for its expansion.\\ |
| Title: P-adic Properties of Modular Forms of Half-integral Weight |
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| Seminar: Algebra and Number Theory |
| Speaker: Nick Ramsey of DePaul University |
| Contact: Zachary A. Kent, kent@mathcs.emory.edu |
| Date: 2011-04-28 at 3:00PM |
| Venue: MSC E406 |
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| Abstract: Motivating with some classical examples, I will explain why congruences are germane to the theory of modular forms and how this "p-adic" point of view has borne fruit in the integral weight setting. As many quantities of arithmetic significance occur in half-integral weight, it is natural to inquire about analogues of the p-adic theory in that world. I will explain a number of aspects of my work on p-adic modular forms of half-integral weight and some of their consequences for congruences. |
| Title: EUMMA Kickball |
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| Seminar: N/A |
| Speaker: Faculty of Emory |
| Contact: Alex Carstairs, acarsta@emory.edu |
| Date: 2011-04-27 at 11:30AM |
| Venue: W306 |
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| Abstract: |
| Title: The Mathematical Foundations of Finance |
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| Lecture: Annual Evans/Hall Lecture Series |
| Speaker: Joshua M. Pollet of Broad College of Business, Michigan State University |
| Contact: Steve Batterson, sb@mathcs.emory.edu |
| Date: 2011-04-26 at 4:00PM |
| Venue: E208 |
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| Abstract: Even though finance is a relatively modern area of academic interest, the key innovations in finance are based on straightforward mathematical models. These models are often designed to mimic the decision making process of individuals in the context of saving behavior and portfolio choice. Of course, the process of building useful models reflects a trade-off between tractability and applicability, that is, simple models are less difficult to analyze, but they may not reflect reality with sufficient accuracy. In spite of the dangers posed by oversimplification, the importance of building useful models cannot be emphasized enough. Such models will have interesting secondary implications that may or may not have been anticipated, but are nevertheless testable. The specific models to be outlined include the basic intertemporal saving decision, static portfolio choice, the Capital Asset Pricing Model (CAPM), and asset pricing with irrational investors. |
| Title: Inference of gene regulatory networks by feature selection |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: David Correa Martins of Universidade Federal de ABC |
| Contact: Alexis Aposporidis, aapospo@emory.edu |
| Date: 2011-04-25 at 4:00PM |
| Venue: W302 |
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| Abstract: Gene Regulatory Networks (GRN) can be viewed as a gene interaction network where the level of expression of each gene is related to how vigorously that gene will be transcribed into RNA. The cell control is the result of a multivariate activity of genes, and the understanding of such activity is crucial for therapeutic purposes and development of new drugs. In this context, since the available data is usually noisy and scarce (only dozens of samples with thousands of gene expression values), the inference of GRNs is one of the big challenges in bioinformatics. GRNs can be modeled as graphs where the vertices represent genes and the edges represent dependencies between genes. There are many categories of GRN modeling, such as Bayesian Networks, Boolean Networks (and its stochastic version: Probabilistic Boolean Networks), differential equations and others. This presentation will give an overview of GRNs and some problems about inference by feature selection approaches. Works in progress on this topic will be briefly discussed. |
| Title: Lifting the j-invariant |
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| Seminar: Algebra and Number Theory |
| Speaker: Luis R. Finotti of University of Tennessee, Knoxville |
| Contact: Zachary A. Kent, kent@mathcs.emory.edu |
| Date: 2011-04-19 at 3:00PM |
| Venue: W306 |
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| Abstract: The coordinates of the j-invariant of the canonical lifting of an ordinary elliptic curve are functions on the j invariant of the latter curve. Mazur asked about the nature of these functions and Tate asked about the possibility to extend them to supersingular values. After describing methods to deal with Witt vectors in an efficient way, we will show that only the first three coordinates can be extend to supersingular values and give precise descriptions for the first four coordinates. |
| Title: Decoding Network Structure by Matrix Functions |
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| Colloquium: N/A |
| Speaker: Ernesto Estrada of University of Strathclyde |
| Contact: Michelle Benzi, benzi@mathcs.emory.edu |
| Date: 2011-04-19 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: The aim of this talk is to illustrate the necessity of introducing concepts and invariants beyond those of 'small-worldness' (SW) and 'scale-freeness' (SF) that pervade current network analysis. I will present three challenging examples from the real-world analysis of networks. The first is related to the identification of essential proteins in a protein-protein interaction map. The second deals with the identification of communities in rather homogeneous networks like an international trade network. The third one focuses on the discrimination of human brains after suffering strokes from healthy ones. The solution to these three problems are presented on the basis of matrix functions, such as the exponential adjacency matrix. Other extensions are also mentioned. They are presented by introducing the concepts of subgraph centrality and communicability in networks and are compared with the use of simple measures based of SW and SF concepts, such as the use of degree, average path length or betweenness centrality. |