All Seminars

Title: Point Allocations and Transport Algorithms
Seminar: Analysis and Differential Geometry
Speaker: Anastasia Svishcheva of Emory University
Contact: Vladimir Oliker, oliker@mathcs.emory.edu
Date: 2012-02-14 at 4:00PM
Venue: MSC W301
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Abstract: The work by Gershon Wolansky and Dmitry Meisler discussing surprising connections between the Monge-Kantorovich optimal transport and the problem of optimal partition of the state space will be presented.

Title: A geometric multigrid preconditioner for microFE analysis for bone structures based on a pointer-less octree
Colloquium: N/A
Speaker: Peter Arbenz of ETH Zurich, Switzerland
Contact: Michele Benzi, benzi@mathcs.emory.edu
Date: 2012-02-13 at 3:00PM
Venue: W306
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Abstract: The state of the art method to predict bone stiffness is micro finite element (microFE) analysis based on high-resolution computed tomography (CT). Modern parallel solvers enable simulations with billions of degrees of freedom. In this talk we present a solver that works directly on the CT-image and exploits the geometric properties given by the 3D-pixel. The data is stored in a pointer-less octree. The tree data structure provides different resolutions of the image that is used for the design of a geometric multigrid preconditioner. It makes possible the use of matrix-free implementations on all levels. This new solver reduces the memory footprint by more than a factor of 10 compared to a solver that uses an algebraic multigrid (AMG) preconditioner. It allows to solve much bigger problems and scales excellently on a Cray XT-5 Supercomputer.

Title: Motion and spatial regularization designs in motion-compensated image reconstruction (MCIR): application to simultaneous PET-MR
Colloquium: N/A
Speaker: Se Young Chun of University of Michigan
Contact: James Nagy, nagy@mathcs.emory.edu
Date: 2012-02-13 at 4:00PM
Venue: MSC W201
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Abstract: Often medical imaging systems cannot capture ideal quality images due to their innate acquisition speeds and patient motion. Gating methods have been investigated to reduce motion artifacts, but can suffer from insufficient measurements that result in low SNR images. Motion-compensated image reconstruction (MCIR) methods based on statistical iterative image reconstruction have been studied to improve image quality by using all collected data and motion information so that high SNR images are reconstructed without motion artifacts. This talk presents two different regularization designs for MCIR. First of all, we investigated methods for motion regularization. The usual choice for a motion regularizer in MCIR has been an elastic regularizer. Recently, there has been much research on regularizing nonrigid deformations with diffeomorphic motion priors. Conventional methods that enforce deformations to be locally invertible require high computational complexity and large memory. We developed a sufficient condition that guarantees the local invertibility of B-spline deformation and proposed a simple regularizer based on that sufficient condition. This motion regularizer was applied to the motion correction using prototype simultaneous PET-MR. We estimated deformable motion from simultaneously acquired tagged MR volumes and incorporated it into the system matrix of unregularized OSEM algorithm for list-mode PET. We demonstrated the improvement of image quality and detection task performance with deformable phantom, rabbit, and small non-human primate studies. Secondly, we studied the spatial resolution properties of MCIR methods and shows that nonrigid local motion can lead to non-uniform and anisotropic spatial resolution for conventional quadratic regularizers. This undesirable property is akin to the known effects of interactions between heteroscedastic loglikelihoods (e.g. Poisson likelihood) and quadratic regularizers, and can cause non-uniform bias in small or narrow structures such as small lesions or rings of reconstructed images and lead to quantification errors. We proposed novel spatial regularization design methods for three different MCIR methods that account for known nonrigid motion. We develop MCIR regularization designs that provide approximately uniform and isotropic spatial resolution and that match a user-specified target spatial resolution. 2D PET simulations demonstrate the performance and benefits of the proposed spatial regularization design methods.

Title: Scalable and Elastic Data Management in the Cloud
Colloquium: N/A
Speaker: Amr El Abbadi of University of California, Santa Barbara
Contact: Li Xiong, lxiong@emory.edu
Date: 2012-02-10 at 3:00PM
Venue: MSC W301
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Abstract: Over the past two decades, database and systems researchers have made significant advances in the development of algorithms and techniques to provide data management solutions that carefully balance the three major requirements when dealing with critical data: high availability, reliability, and data consistency. However, over the past few years the data requirements, in terms of data availability and system scalability, from Internet scale enterprises that provide services and cater to millions of users has been unprecedented. Cloud computing has emerged as an extremely successful paradigm for deploying Internet and Web-based applications. Scalability, elasticity, pay-per-use pricing, and autonomic control of large-scale operations are the major reasons for the successful widespread adoption of cloud infrastructures. In this talk, we analyze the design choices that allowed modern scalable data management systems to achieve orders of magnitude higher levels of scalability compared to traditional databases. With this understanding, we highlight some design principles for data management systems that can be used to augment existing databases with new cloud features such as scalability, elasticity, and autonomy. We then analyze several state of the art systems and discuss our proposed system, G-Store, which provides transactional guarantees on data granules formed on-demand while being efficient and scalable.\\ \\ Bio: Amr El Abbadi is currently a Professor in the Computer Science Department at the University of California, Santa Barbara. He received his B. Eng. in Computer Science from Alexandria University, Egypt, and received his Ph.D. in Computer Science from Cornell University in August 1987. Prof. El Abbadi is an ACM Fellow. He has served as a journal editor for several database journals, including, currently, The VLDB Journal. He has been Program Chair for multiple database and distributed systems conferences, most recently SIGSPATIAL GIS 2010 and ACM Symposium on Cloud Computing (SoCC) 2011. He has also served as a board member of the VLDB Endowment from 2002—2008. In 2007, Prof. El Abbadi received the UCSB Senate Outstanding Mentorship Award for his excellence in mentoring graduate students. He has published over 250 articles in databases and distributed systems.

Title: An Image-Based, Parallel Dynamic Meshing Framework for Patient-Specific Medical Interventions
Colloquium: N/A
Speaker: Suzanne M. Shontz of Department of Computer Science and Engineering, Pennsylvania State University
Contact: James Nagy, nagy@mathcs.emory.edu
Date: 2012-02-09 at 4:00PM
Venue: MSC W201
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Abstract: Patient-specific mesh generation is an important issue in computational simulations of the potential effectiveness of a medical device or the progression of a disease in a specific patient. Many radiology applications involve movement by the patient and medical device and require dynamic meshes for use in the associated imaged-based computational simulations. Two important examples include blood clot entrapment by inferior vena cava filters in pulmonary embolism (PE) patients and the evolution of the brain ventricles and cerebrospinal fluid (CSF) in hydrocephalus patients. There are several limitations of existing dynamic meshing algorithms that make them unsuitable for use in radiology applications. For example, the mesh warping algorithms upon which they are based often do not yield the desired volume meshes when applied to a noisy target surface mesh created from medical images of the patient. In addition, the mesh warping algorithms are often not designed to handle the large deformations that the patient's body and the medical device undergo. In particular, existing mesh warping algorithms sometimes yield tangled meshes with inverted elements which are invalid for use by the associated partial differential equation solver in the computational simulation. In this talk, I will describe the image-based, parallel dynamic meshing framework for patient-specific medical interventions, which we are designing. In particular, I will discuss two image-based meshing techninques we have developed for radiology applications. The first algorithm I will describe is a mesh warping technique for virtual implantation of an inferior vena cava (IVC) filter in the venous anatomy of a PE patient. The corresponding embedded geometric models are then used in generation of non-manifold topology meshes of the embedded device and venous anatomy for use in computational fluid dynamics simulations of the blood flow, and ultimately, for improved prevention of the disease. The second algorithm I will discuss is a combined level set/mesh warping technique for use in tracking, and, eventually, for predicting, the evolution of the deforming brain ventricles and CSF in hydrocephalus patients before and after shunt treatment. I will conclude by describing our plans for future research in these areas.

Title: Quadratic Forms Representing all Odd Positive Integers
Seminar: Number Theory
Speaker: Jeremy Rouse of Wake Forest University
Contact: Zachary A. Kent, kent@mathcs.emory.edu
Date: 2012-02-02 at 3:00PM
Venue: W306
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Abstract: We consider the problem of classifying all positive-de nite integer-valued quadratic forms that represent all positive odd integers. Kaplansky considered this problem for ternary forms, giving a list of 23 candidates, and proving that 19 of those represent all positive odds. (Jagy later dealt with a 20th candidate.) Assuming that the remaining three forms represent all positive odds, we prove that an arbitrary, positive-definite quadratic form represents all positive odds if and only if it represents the odd numbers from 1 up to 451. This result is analogous to Bhargava and Hanke's celebrated 290-theorem. In addition, we prove that these three remaining ternaries represent all positive odd integers, assuming the generalized Riemann hypothesis. This result is made possible by a new analytic method for bounding the cusp constants of integer-valued quaternary quadratic forms $Q$ with fundamental discriminant. This method is based on the analytic properties of Rankin-Selberg $L$-functions, and we use it to prove that if $Q$ is a quaternary form with fundamental discriminant, the largest locally represented integer $n$ for which $Q(\vec{x}) = n$ has no integer solutions is $O(D^{2+\epsilon})$.

Title: Applications and Theory of a Continuum-Mechanics-Based Immersed Boundary Method
Seminar: Numerical Analysis and Scientific Computing
Speaker: Dharshi Devendran of New York University
Contact: Michele Benzi, benzi@mathcs.emrory.edu
Date: 2012-01-30 at 4:00PM
Venue: MSC W201
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Abstract: Fluid-structure interaction problems, in which the dynamics of a deformable structure is coupled to the dynamics of a fluid, are prevalent in biology. For example, the heart can be modeled as an elastic boundary that interacts with the blood circulating through it. The immersed boundary method is a popular method for simulating fluid-structure problems. The traditional immersed boundary method discretizes the elastic structure using a network of springs. This makes it difficult to use material models from continuum mechanics within the framework of the immersed boundary method. In this talk, I present a new immersed boundary method that uses continuum mechanics to discretize the elastic structure, with a finite-element-like discretization. This method is first applied to a warm-up problem, in which a viscoelastic incompressible material fills a two-dimensional periodic domain. Next, we apply the method to a three-dimensional fluid-structure interaction problem. Finally, I will present theory for this new immersed boundary method.

Title: Crowd-Powered Systems
Seminar: Computer Science
Speaker: Michael Bernstein of MIT CSAIL
Contact: Eugene Agichtein, eugene@mathcs.emory.edu
Date: 2012-01-27 at 3:00PM
Venue: MSC W301
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Abstract: By combining machine and crowd intelligence, we can open up a broad new class of software systems that solve problems neither approach could solve alone. However, while crowds are increasingly adept at straightforward parallel tasks, they struggle with complex work because participants vary in quality, well-intentioned contributions can introduce errors, and future participants amplify and propagate those errors. I introduce techniques that decompose complex tasks into simpler, verifiable steps, and return crowd results in realtime. I use these techniques to create crowd-powered systems: interactive applications that react with a combination of human and algorithmic intelligence. These systems support goals like rewriting and shortening text, polling opinions within seconds, and taking better photographs.

Title: 5-Coloring Graphs on Surfaces
Seminar: Combinatorics
Speaker: Luke Postle of Georgia Institute of Technology
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2012-01-25 at 3:00PM
Venue: W306
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Abstract: Graph coloring is a much studied subfield of graph theory. Theorems concerning coloring graphs on topological surfaces, such as the Four Color Theorem or the Heawood Bound, are a useful avenue to understanding graph coloring in general. A deep theorem of Thomassen from the 1990's shows that for any surface that there are only finitely many 6-critical graphs that embed on that surface. We discuss the history of this modern approach and its realisation for small surfaces. We also give a shorter self-contained proof of Thomassen's result by showing that for any 6-critical graph G that embeds on a surface of genus $g$, that the number of vertices is at most linear in $g$. Finally, we discuss generalizations to 5-list coloring,such as a recent solution to Albertson's conjecture that a planar graph with distant precolored vertices has a 5-list-coloring.

Title: Degeneration and the Determinant of the Laplacian
Seminar: Analysis and Differential Geometry
Speaker: David Sher of Stanford University
Contact: David Borthwick, davidb@mathcs.emory.edu
Date: 2012-01-24 at 4:00PM
Venue: MSC W301
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Abstract: When doing analysis on singular spaces, it is often useful to approximate them by smooth manifolds. In this spirit, we consider a family of smooth manifolds which degenerate to a manifold with a conical singularity, and analyze the behavior of various spectral-theoretic quantities under this degeneration. In particular, when we consider the behavior of the eigenvalues of the Laplacian and of the heat kernel, interesting structure becomes apparent. In this talk, I'll discuss this structure, and then discuss how it can be used to give an asymptotic expansion for the determinant of the Laplacian under conic degeneration. I'll also discuss applications and directions for further research.