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Past Seminars
Thu 02/01/2018 4:00pm	Colloquium: Computational Mathematics Computational mathematics meets medicine: Formulations, numerics, and parallel computing Andreas Mang, University of Houston Contact: James Nagy, jnagy@emory.edu Venue: Mathematics and Science Center, Room W301 Download printable flyer (PDF, 40.3 kB) Show abstract We will discuss computational methods that integrate imaging data with (bio)physics simulations and optimization in an attempt to aid decision-making in challenging clinical applications. In particular, we will focus on PDE-constrained formulations for diffeomorphic image registration, a classical inverse problem, which seeks to find pointwise correspondences between two or more images of the same scene. In its simplest form, the PDE constraints are the transport equations for the image intensities. We will augment these equations with a model of brain cancer progression to enable data assimilation in brain tumor imaging. We will see that our formulation yields strongly coupled, nonlinear, multiphysics systems that are challenging to solve in an efficient way. We will discuss the formulation, discretization, numerical solution, and the deployment of our methods in high-performance computing platforms. Our code is implemented in C/C++ and uses the message passing interface (MPI) library for parallelism.\\ \\We will showcase results for clinically relevant problems, study numerical accuracy, rate of convergence, time-to-solution, inversion quality, and scalability of our solver. We will see that we can solve clinically relevant problems (50 million unknowns) in less than two minutes on a standard workstation. If we use 512 MPI tasks we can reduce the runtime to under 2 seconds, paving the way to tackle real-time applications. We will also showcase results for the solution of registration problems of unprecedented scale, with up to 200 billion unknowns.
Tue 01/30/2018 4:00pm	Seminar: Algebra Irrational points on random hyperelliptic curves Jackson Morrow, Emory University Contact: David Zureick-Brown, dzb@mathcs.emory.edu Venue: Mathematics and Science Center, Room W304 Download printable flyer (PDF, 49 kB) Show abstract We consider genus $g$ hyperelliptic curves over $\mathbb{Q}$ with a rational Weierstrass point, ordered by height. If $d<g$ is odd, we prove there exists $B_d$ such that a positive proportion of these curves have at most $B_d$ points of degree $d$. If $d<g$ is even, we similarly bound degree $d$ points not pulled back from points of degree $d/2$ on the projective line. Furthermore, one may take $B_2 = 24$ and $B_3 = 114$. \\ Our proofs proceed by refining recent work of Park, which applied tropical geometry methods to symmetric power Chabauty, and then applying results of Bhargava and Gross on average ranks of Jacobians of hyperelliptic curves. This is joint work with Joseph Gunther.
Mon 01/29/2018 4:00pm	Seminar: Combinatorics On strong Sidon sets of integers Sang June Lee, Duksung Women's University Contact: Dwight Duffus, dwight@mathcs.emory.edu Venue: Mathematics and Science Center, Room W303 Download attached abstract (PDF, 120 kB) Download printable flyer (PDF, 120 kB) Show abstract FOR FULL ABSTRACT SEE PDF ATTACHMENT. The motivation of strong Sidon sets is that a strong Sidon set generates many Sidon sets by altering each element a bit. This implies that a dense strong Sidon set will guarantee a dense Sidon set contained in a sparse random subset of N. In this talk, we are interested in how dense a strong Sidon set can be. This is joint work with Yoshiharu Kohayakawa, Carlos Gustavo Moreira and Vojtech Rodl.
Fri 01/26/2018 2:00pm	Seminar: Numerical Analysis and Scientific Computing New methods in EEG/MEG source analysis Johannes Vorwerk, Scientific Computing and Imaging (SCI) Institute, University of Utah Contact: Lars Ruthotto, lruthotto@emory.edu Venue: Mathematics and Science Center, Room W301 Download printable flyer (PDF, 41 kB) Show abstract Electro- and magnetoencephalography (EEG and MEG) have become important tools for non-invasive functional neuroimaging due to their unique time resolution. In many applications of EEG/MEG, the goal is to reconstruct the sources inside the brain volume that evoke the measured signal, which leads to a related ill-posed inverse problem (EEG/MEG inverse problem). To solve this inverse problem accurately, it is necessary to precisely simulate the electric/magnetic field caused by a point-like source inside the brain volume: the so-called forward problem of EEG/MEG. When aiming to take the individual head shape and conductivity distribution of the subject’s head into account, the EEG/MEG forward problem has to be solved numerically, e.g., using finite element methods (FEM). In this talk, we present examples showing how the use of novel mathematical methods can increase the accuracy of and help to better understand the uncertainties inherent to EEG/MEG forward solutions. We further analyze the influence of these uncertainties on EEG/MEG inverse solutions.
Tue 01/23/2018 4:00pm	Seminar: Algebra Cohomology of hyperkahler manifolds Nikon Kurnosov, University of Georgia Contact: David Zureick-Brown, dzb@mathcs.emory.edu Venue: Mathematics and Science Center, Room W304 Download printable flyer (PDF, 46.9 kB) Show abstract Hyperkahler manifolds are Riemannian manifolds with three complex structures satisfying quaternionic relations and kahler. There are known just few of them with maximal holonomy and being compact starting from K3. But existence of new examples and explicit structure of cohomology remain open. In this talk I will speak about cohomology of hyperkahler manifolds, Verbitsky, Loojenga and Lunts have proved that Lie algebra $so(4,b_2-2)$ acts on cohomology. Using it we can prove that the second Betti number is bounded and that all cohomology of hyperkahler manifold $X$ can be embedded into the cohomology of the product of several copies of abelian variety A, what generalize classical Kuga-Satake construction.
Fri 01/19/2018 2:00pm	Seminar: Numerical Analysis and Scientific Computing Building Energy - Modeling, Optimization and Optimal Control Raya Horesh, IBM Research AI, TJ Watson Research Center Contact: Lars Ruthotto, lruthotto@emory.edu Venue: Mathematics and Science Center, Room W301 Download printable flyer (PDF, 41.2 kB) Show abstract Buildings consume about 40\% of the total energy in most countries, contributing to a significant amount of greenhouse gas (GHG) emissions and global warming. Therefore, reducing energy consumption in buildings, making buildings more energy efficient and operating buildings in more energy efficient manner are important tasks. Analytics can play an important role in identifying energy saving opportunities in buildings by modeling and analyzing how energy is consumed in buildings and optimizing energy consuming operations of buildings. In this talk I will cover areas ranging from physics based (ODE/PDE models) and data driven modeling to inverse problem for parameter estimation and model predictive control (MPC) framework that optimally determines control profiles of HVAC system given dynamic demand response signal, on-site energy storage system and energy generation system while satisfying thermal comfort of building occupants within the physical limitation of HVAC and other equipment.
Fri 12/15/2017 2:00pm	Defense: Masters A Decision Support System For Heparin Dosing Romgmei Lin, Emory University Contact: Rongmei Lin, rongmei.lin@emory.edu Venue: Mathematics and Science Center, Room E408 Download printable flyer (PDF, 38.9 kB) Show abstract Medication dosing is a comprehensive problem with uncertainties. Every patient has unique condition, meanwhile some drugs have narrow therapeutic windows. Mis-dosing might result in preventable adverse event. Therefore, a robust decision support system would be helpful to clinicians by providing advisable dosing suggestions. Heparin is one of the sensitive drugs. In order to build up the decision support system for heparin patients, we present a clinician in the loop framework with deep reinforcement learning algorithm. There are two main objectives in this thesis, the first one is providing individualized dosing suggestion based on the multi-dimensional features of patients. The second one is evaluating the dosing predicted by our decision support system. We implemented several experiments to achieve these objectives. The data used in the experiments including simulated data, MIMIC-II intensive care unit data and Emory hospital intensive care unit data. There are two important processes with respect to our objectives. In the training process, the decision support system learned from the dosing executed by clinicians and the corresponding response of patients. In the evaluating process, we explored the results from several aspects and focused on the causality between variables and outcomes. The experimental results suggested that given the states of patients, our medication dosing support system is able to provide a reasonable recommendation
Tue 12/05/2017 4:00pm	Seminar: Algebra Patching for proper schemes Bastian Haase, Emory University Contact: John Duncan, john.duncan@emory.edu Venue: Mathematics and Science Center, Room W306 Download printable flyer (PDF, 37.4 kB) Show abstract We discuss an extension of field patching to proper schemes. Then, we will introduce Tannaka duality for stacks as first developed by Lurie and then refined by Hall and Rydh. Their work allows us to patch morphisms from proper schemes to nice stacks, in particular certain moduli stacks. As an application of this result, we prove that patching holds for relative torsors which allows us to give a characterization for local-global principles for torsors over proper schemes. This is joint work with Daniel Krashen and Max Lieblich.
Tue 12/05/2017 4:00pm	Seminar: Combinatorics The complexity of perfect matchings and packings in dense hypergraphs Jie Han, University of Sao Paulo Contact: Dwight Duffus, dwight@mathcs.emory.edu Venue: Mathematics and Science Center, Room W303 Download printable flyer (PDF, 42.6 kB) Show abstract Given two $k$-graphs $H$ and $F$, a perfect $F$-packing in $H$ is a collection of vertex-disjoint copies of $F$ in $H$ which together cover all the vertices in $H$. In the case when $F$ is a single edge, a perfect $F$-packing is simply a perfect matching. For a given fixed $F$, it is generally the case that the decision problem whether an $n$-vertex $k$-graph $H$ contains a perfect $F$-packing is NP-complete.\\ \\In this talk we describe a general tool which can be used to determine classes of (hyper)graphs for which the corresponding decision problem for perfect $F$-packings is polynomial time solvable. We then give applications of this tool. For example, we give a minimum $l$-degree condition for which it is polynomial time solvable to determine whether a $k$-graph satisfying this condition has a perfect matching (partially resolving a conjecture of Keevash, Knox and Mycroft). We also answer a question of Yuster concerning perfect $F$-packings in graphs.
Fri 12/01/2017 11:00am	Defense: Dissertation Recommender System and Information Fusion in Spatial Crowdsourcing Daniel Garcia Ulloa, Emory University Venue: Mathematics and Science Center, Room W301 Download printable flyer (PDF, 41.8 kB) Show abstract Spatial Crowdsourcing (SC) refers to a series of data collection mechanisms where a set of users with a sensing or computing device are asked to perform a set of tasks at different locations and times.\\ \\In this work, we explore some of the challenges that arise with SC and propose some solutions. These challenges concern a proper recommendation of tasks to users in such a away that they maximize their expected utility while at the same time maximizing the probability that all the tasks are performed. The utility for the users can be based on the tasks the expected reward they are planning to obtain, and the distance to the assignments. These aspects can be predicted through tensorfactorization techniques. To set an example, a high-paying assignment might be far from a user, while a low paying assignment is nearby. Depending on the users’ preference, we seek to recommend a set of tasks that maximize the user’s utility. On the other hand, we also want to maximize the sum of probabilities that the tasks are performed, considering the interdependencies between users. We define the system utility as a convex linear combination of the user and the task utility and suggest approximation methods to recommend the tasks that yield the highest system utility.\\ \\We also deal with the problem of truth inference, which focuses on integrating the responses from a mobile crowdsouring scenario and determining the true value. Many times, the answers from a mobile crowdsourcing scenario are noisy, contradicting or have missing values. We developed a recursive Bayesian system that updates the reputation model of the users, the probability that the users where in the correct time and location, and the probability that the reports are true or false. We further enhanced this algorithm using a Kalman filter that predicts the true state of the event at each time-stamp using a hidden event model and which is updated with the reports from the users. Our method was compared against the naive majority voting method as well as other state-of-the-art truth inference algorithms and our method shows a considerable improvement.