All Seminars

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Title: Geometrically unfitted finite elements for PDEs posed on surfaces and in the bulk
Seminar: Numerical Analysis and Scientific Computing
Speaker: Maxim Olshanskii of University of Houston
Contact: Michele Benzi, benzi@mathcs.emory.edu
Date: 2016-04-28 at 4:00PM
Venue: W306
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Abstract:
Geometrically unfitted finite element methods are known in the literature under different names, e.g., XFEM, cut FEM, trace FEM, etc. These discretizations are mainly developed for efficient numerical treatment of differential equations posed in domains of complex geometry and/or having propagating interfaces. Unlike immersed boundary methods these discretizations typically treat interfaces in a `sharp' way, but avoid fitting the mesh. The talk will discuss some recent analysis and developments of unfitted FEM.
Title: The Kolchin Irreducibility Theorem
Seminar: Algebra
Speaker: Taylor Dupuy of University of Vermont
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2016-04-26 at 4:00PM
Venue: W304
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Abstract:
A jet bundle is a higher order version of a tangent bundle (one for each positive integer) and the points correspond to truncated power series on your original variety. It turns out that if you have a singular variety these spaces get all messed up---they have extra irreducible components above the singular locus (and encode interesting singularity invariants). Magically, if we take the limit of these spaces, where the points correspond to full power series, these spaces become irreducible again! This is Kolchin's Irreducibility theorem. We will talk about this theorem and what happens when power series are replaced by Witt vectors. This talk is based on joint work with Lance Edward Miller and James Freitag.
Title: Life is Better with Liberal Arts
Evans Hall Awards Ceremony and Lecture: N/A
Speaker: Chris Schoettle of Enservio
Contact: Vaidy Sunderam, vss@emory.edu
Date: 2016-04-25 at 4:00PM
Venue: MSC E208
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Abstract:
TBA
Title: A parallel solver for inverse tranport problems
Seminar: Numerical Analysis and Scientific Computing
Speaker: Dr. Andreas Mang of The University of Texas at Austin
Contact: Lars Ruthotto, lruthotto@emory.edu
Date: 2016-04-22 at 1:00PM
Venue: W306
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Abstract:
In this talk we will discuss fast algorithms for large-scale inverse transport problems. These type of problems appear in numerous areas like weather prediction, ocean physics, or the reconstruction of porous media flows. In this talk we will consider the problem of diffeomorphic image registration with applications in medical imaging. We use a PDE constrained optimization formulation, where the constraints are the transport equations for a given scalar field, which in our case is a grayscale image. We will compare semi-Lagrangian and spectral collocation schemes, discuss a two-level Hessian preconditioner, and showcase a parallel implementation on distributed memory architectures.. We invert for a velocity field that governs the transport equation for the image deformation. The objective functional consists of an L^2 mismatch term and a regularization functional that penalizes the H^k-norm of the velocity field and its divergence. We discretize the optimality conditions using a pseudospectral discretization in space with a Fourier basis. We use a globalized, preconditioned, inexact, matrix-free, reduced space Newton-Krylov method to solve for an optimal, diffeomorphic flow field. The reduced Hessian is an ill-conditioned, dense, and compact operator; efficiently solving this system represents a significant challenge. We introduce and analyze a semi-Lagrangian formulation that, together with a nested two-level Hessian preconditioner, yields a 20x speedup compared to the state of the art. We will showcase convergence results, and assess strong and weak scalability of our solver for problem sizes of up to 25 billion unknowns on up to 1024 compute nodes on the Texas Advanced Computing Center's systems. As a highlight: We can invert for half a billion unknowns in 140 seconds on one node with 16 MPI tasks. We can reduce the time to solution by 20x for 32 compute nodes with 512 MPI tasks. This is joint work with George Biros and Amir Gholami
Title: Computational Phenotyping using Tensor Factorization and Tensor Network
Seminar: Computer Science
Speaker: Dr. Jimeng Sun of Georgia Institute of Technology
Contact: Li Xiong, lxiong@emory.edu
Date: 2016-04-22 at 3:00PM
Venue: W301
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Abstract:
Computational phenotyping is the process of converting heterogeneous electronic health records (EHRs) into meaningful clinical concepts (phenotypes). Tensor factorization has been shown as a successful unsupervised approach for discovering phenotypes. However, tensor methods have some major limitations for phenotyping: 1) unable to incorporate existing medical knowledge; 2) fail to handle high-order tensors (e.g., order > 5) . We will talk about two of our recent developments in addressing these challenges: First, we proposed Rubik, a constrained non-negative tensor factorization and completion method for phenotyping. Rubik incorporates 1) guidance constraints to align with existing medical knowledge, and 2) pairwise constraints for obtaining distinct, non-overlapping phenotypes. Rubik also has built-in tensor completion that can significantly alleviate the impact of noisy and missing data. We evaluate Rubik on two large EHR datasets. Our results show that Rubik can discover more meaningful and distinct phenotypes than the baselines. Second, we extended a theoretical framework called tensor networks for analyzing high-order tensors. We developed an efficient sparse hierarchical Tucker model (Sparse H-Tucker) for finding interpretable tree-structured factorizations from sparse high-order tensor. Sparse H-Tucker scales nearly linearly in the number of non-zero tensor elements. We applied Sparse H-Tucker on a real EHR dataset for learning a disease hierarchy. The resulting tree structure provides an interpretable disease hierarchy, which is confirmed by a clinical expert. Bio Jimeng Sun is an Associate Professor of School of Computational Science and Engineering at College of Computing in Georgia Institute of Technology. Prior to joining Georgia Tech, he was a research staff member at IBM TJ Watson Research Center. His research focuses on health analytics using electronic health records and data mining, especially in designing novel tensor analysis and similarity learning methods and developing large-scale predictive modeling systems. He has published over 80 papers, filed over 20 patents (5 granted). He has received ICDM best research paper award in 2008, SDM best research paper award in 2007, and KDD Dissertation runner-up award in 2008. Dr. Sun received his B.S. and M.Phil. in Computer Science from Hong Kong University of Science and Technology in 2002 and 2003, and PhD in Computer Science from Carnegie Mellon University in 2007.
Title: Totaro's Question for Tori of Low Rank
Seminar: Algebra
Speaker: Reed Sarney of Emory University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2016-04-19 at 4:00PM
Venue: W304
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Abstract:
Let k be a field, let G/k be a smooth connected linear algebraic group, and let X be a G-torsor over k. Generalizing a question of Serre, Totaro asked if the existence of a zero-cycle on X of degree d greater than or equal to 1 implies the existence of closed etale point on X of degree dividing d. This question is entirely unexplored in the literature for algebraic tori. We settle Totaro's question affirmatively for algebraic tori of rank less than or equal to 2.
Title: An upper bound on the size of a $k$-uniform family with covering number $k$
Seminar: Combinatorics
Speaker: John Retter of Emory University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2016-04-18 at 4:00PM
Venue: W301
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Abstract:
See downloadable flyer.
Title: Topics in Decision Analysis for Cloud Computing
Seminar: Computer Science
Speaker: Radhika Garg of University of Zurich, Zurich, Switzerland
Contact: Avani Wildani, avani@mathcs.emory.edu
Date: 2016-04-15 at 3:00PM
Venue: W301
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Abstract:
Adopting a new technology in an organization is a crucial decision as its impact can be at technical, economical, and organizational level. One of such decisions is related to adoption of Cloud-based services in an organization. Cloud Computing is changing the way IT infrastructure is used today primarily due to high cost savings associated to it. However, if the solution adopted by an organization is not fulfilling its requirements, it can have tremendous negative consequences at technical, economical, and organizational level. Therefore, the decision to adopt Cloud-based services should be based on a methodology that supports a wide array of criteria for evaluating any available alternative. Also, as these criteria or factors can be mutually interdependent and conflicting, a trade-offs- based methodology is needed to make such decisions. In addition, inclusion and modeling of qualitative factors (e.g., legal and regulative constraints) that influence such a decision forms a crucial part of this methodology. This talk, therefore, discusses the design and implementation of Trade-offs based Methodology for Adoption of Cloud-based Services (TrAdeCIS). This methodology is based on Multi-attribute Decision Algorithms (MADA), which selects the best alternative, based on the priorities given to different criteria by decision maker. Furthermore, the talk will be concluded with the extendibility and applicability of this methodology to other domains.
Title: Athens-Atlanta Joint Number Theory Seminar
Type: Number Theory
Speaker: Hosted by Georgia Tech of
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2016-04-14 at 4:00PM
Venue: Skiles 006
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Abstract:
The speakers are Melanie Matchett-Wood (UW-Madison) Zhiwei Yun (Stanford)
Title: Zeta polynomials for modular form periods
Seminar: Algebra
Speaker: Ken Ono of Emory University
Contact: David Zurieck-Brown, dzb@mathcs.emory.edu
Date: 2016-04-12 at 4:00PM
Venue: W304
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Abstract:
Yuri Manin has been developing a theory of zeta-polynomials, polynomials which are arithmetic geometric in origin which also satisfy a functional equation and the Riemann Hypothesis. He conjectured the existence of such functions for all newforms which arise from critical values of L-functions. We confirm his conjecture by constructing a Bloch-Kato complex using weighted moments of orders of Tate-Shafarevich groups. Surprisngly, for fixed weights, as levels tend to infinity we find these zeta-polynomials converge to Earhart polynomials for classical polytopes. This is joint work with Larry Rolen and Florian Sprung.