All Seminars

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Title: A connection between coupled and penalty projection time-stepping schemes with FE spatial discretization for the Navier-Stokes equations
Seminar: Numerical Analysis and Scientific Computing
Speaker: Leo Rebholz of Clemson University
Contact: Michele Benzi, benzi@mathcs.emory.edu
Date: 2014-09-12 at 12:00AM
Venue: W301
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Abstract:
We prove that in finite element settings where the divergence-free subspace of the velocity space has optimal approximation properties, the solution of Chorin-Temam projection methods for Navier-Stokes equations equipped with grad-div stabilization with parameter $\gamma$, converge to the associated coupled method solution with rate $\gamma^{-1}$ as $\gamma\rightarrow \infty$. We prove this first for backward Euler schemes, and then extend the results to BDF2 schemes, and finally to schemes with outflow boundary conditions. Several numerical experiments are given which verify the convergence rate, and show how using projection methods in this setting with large grad-div stabilization parameters improves accuracy.
Title: Shifted convolution L-functions
Seminar: Algebra
Speaker: Ken Ono of Emory
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2014-09-09 at 4:00PM
Venue: W306
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Abstract:
Rankin-Selberg convolution L-functions are important functions in number theory. Their properties play a central role in many of deepest works on the Ramanujan-Petersson Conjecture. In a recent paper, Hoffstein and Hulse defined generalizations of these L-functions, the so-called ``shifted-convolution" L-functions. They obtained the meromorphic continuation of the functions in many cases. Here we consider symmetrizations of these L-functions, and we exactly evaluate their special values at diagonal weights for all shifts. This is joint work with Michael Mertens.
Title: Pursuit and Evasion
Colloquium: N/A
Speaker: Imre Leader of University of Cambridge
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2014-09-08 at 4:00PM
Venue: W303
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Abstract:
In Rado's famous "lion and man" problem, a man and a lion are in a circular arena. The lion wants to catch the man, and the man does not want to be caught by the lion. Each can run at the same speed. Who wins? We will start with some background on this kind of "continuous pursuit" problem, including the solution that was eventually given by Besicovitch. We will then move on to some surprising recent developments.
Title: What is the limit of a line bundle on a non normal variety?
Seminar: Algebra
Speaker: Jesse Kass of USC
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2014-09-02 at 4:00PM
Venue: W306
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Abstract:
On a nonnormal variety, the limit of a family of line bundles is not always a line bundle. What is the limit? I will present an answer to this question and give some applications. Time permitting, I will discuss connections with Néron models, autoduality, and recent work of R. Hartshorne and C. Polini.
Title: Applying Diploid Method to Improve Read-mapping and Analysis Based on NGS Data
Defense: Dissertation
Speaker: Shuai Yuan of Emory University
Contact: Shuai Yuan, shuaiyuan@emory.edu
Date: 2014-07-25 at 1:00PM
Venue: Grace Crum Rollins (GCR), Room 537
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Abstract:
Applying Diploid Method to Improve Read-mapping and Analysis Based on NGS Data Abstract: Next generation sequencing (NGS) technologies have been applied extensively in many areas of genetics and genomics research. A fundamental problem when comes to analyzing NGS data is mapping short sequencing reads back to the reference genome. Most of existing software packages rely on a single uniform reference genome and do not automatically take into the consideration of genetic variants. On the other hand, large proportions of incorrectly mapped reads affect the correct interpretation of the NGS experimental results. In this presentation, I will talk about a method that produces a personalized diploid reference genome based on all known genetic variants of that particular individual. Using such a reference genome can improve mapping accuracy and significantly reduce the bias toward reference allele in allele-specific expression analysis. By incorporating the imputation into the diploid method, genotype calling and SNP discovery results will also be improved.
Title: Modeling User Attention and Interaction on the Web
Defense: Dissertation
Speaker: Dmitry Lagun of Emory University
Contact: Dmitry Lagun, dlagun@emory.edu
Date: 2014-07-22 at 12:00AM
Venue: W301
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Abstract:
Analysis of user attention and Web page examination behavior, collected with specialized eye tracking equipment, has offered numerous insights about how online users examine content of the Web pages and remains a valuable tool for Web researchers and developers. Unfortunately, eye tracking technology is currently available for relatively small scale user studies, due to its high costs and the effort associated with participant recruitment. In this thesis we develop several alternatives to eye tracking for studying user attention and behavior. We start by introducing ViewSer - a method based on idea restricted focus viewing, that allows measuring attention for thousands of participants. Then, we develop a probabilistic model that infers most likely position of user’s gaze on the screen from user interactions and web page content. Our model outperforms current state of the art for gaze position prediction that only uses behavioral signals. In addition to the methodological contributions, this thesis develops several important applications in web search and medical domain. First, we describe a scalable approach for extracting frequent mouse cursor movement patterns from large scale cursor data. Second, we demonstrate how these patterns could be used to improve quality of search relevance estimation and search result ranking. Third, we show that attention measured with cursor and viewport position could be used to improve automatic summarization. Lastly, we show how restricted focus viewing could be adapted to develop an automated diagnostic of memory impairment that could be administered over the Web anywhere in the world. Together, the techniques developed and evaluated in this thesis substantially advance the state of the art and enable novel important practical applications.
Title: Preserving Individual Privacy in Spatio-Temporal Data Analytics
Defense: Dissertation
Speaker: Liyue Fan of Emory University
Contact: Liyue Fan, liyue.fan@emory.edu
Date: 2014-06-27 at 2:00PM
Venue: W301
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Abstract:
We live in the age of big data. With an increasing number of people, devices, and sensors connected with digital networks, individual data now can be largely collected and analyzed by data mining applications for social good as well as for commercial interests. However, the data generated by individual users exhibit unique behavioral patterns and sensitive information, and therefore must be transformed prior to the release for analysis. The AOL search log release in 2006 is an example of privacy catastrophe, where the searches of an innocent citizen were quickly re-identified by a newspaper journalist. In this talk, I will present a novel framework to release continuous aggregation of private data for an important class of real-time data mining tasks, such as disease outbreak detection and web mining, to name a few. The key innovation is that the proposed framework captures the underlying dynamics of the continual aggregate statistics with time series state-space models, and simultaneously adopts filtering techniques to correct the observed, noisy data. I will show that the new framework provides a rigorous, provable privacy guarantee to individual data contributors without compromising the output analysis results. Extensive empirical studies confirm that it will enable privacy-preserving data analytical tasks in a broad range of application domains.
Title: Inverse Problems in Hyperspectral Imaging
Defense: Dissertation
Speaker: Sebastian Berisha of Emory University
Contact: Sebastian Berisha, sberish@emory.edu
Date: 2014-06-20 at 11:30AM
Venue: W304
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Abstract:
In hyperpsectral imaging, multiple images of the same scene are obtained over a contiguous range of wavelengths in the electromagnetic spectrum. Hyperspectral images represent observations of a scene at many different wavelengths and most importantly associate to each pixel in the imaged scene a full spectral vector or spectral signature. However, due to the presence of spectral mixtures (at different scales) in the scene and/or low spatial resolution of the hyperspectral sensor, the acquired spectral vectors of each pixel are actually a mixture of the spectra of the various materials present in the spatial coverage area of the corresponding pixel, and they also contain additional degradations caused by atmospheric blurring.We present a numerical approach for deblurring and sparse unmixing of space objects taken by ground based telescopes. A major challenge for deblurring hyperspectral images is that of estimating the overall blurring operator, taking into account the fact that the blurring operator point spread function (PSF) can be wavelength dependent and depend on the imaging system as well as the effects of atmospheric turbulence. We formulate the PSF estimation as a nonlinear least squares problem, which is solved using a variable projection Gauss-Newton method. Our analysis shows that the Jacobian can be potentially very ill-conditioned. To deal with this ill-conditioning, we use a combination of subset selection and regularization. We then incorporate the PSF estimation scheme with a preconditioned alternating direction method of multipliers to solve the deblurring and sparse unmixing problem. Experimental results illustrate the effectiveness of the resulting numerical schemes.
Title: Resonance asymptotics for asymptotically hyperbolic manifolds with warped-product ends
Defense: Dissertation
Speaker: Pascal Philipp of Emory University
Contact: Pascal Philipp, pphilip@emory.edu
Date: 2014-06-03 at 10:00AM
Venue: W301
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Abstract:
We study the spectral theory of asymptotically hyperbolic manifolds with ends of warped-product type. Our main result is an upper bound on the resonance counting function, with a geometric constant expressed in terms of the respective Weyl constants for the core of the manifold and the base manifold defining the ends. As part of this analysis, we derive asymptotic expansions of the modified Bessel functions of complex order.
Title: Secure and Privacy-Preserving Distributed Data Release
Defense: Dissertation
Speaker: Slawomir Goryczka of Emory University
Contact: Vaidy Sunderam, vss@emory.edu
Date: 2014-05-13 at 11:00AM
Venue: W301
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Abstract:
The rapidly increasing prevalence of distributed data-driven applications has highlighted security and privacy issues in storing and processing sensitive data. Although manipulating raw data may violate privacy of their owners, different techniques of preparing and using privacy-preserving data descriptions can be still used. It remains a challenge, however, to ensure that adapted and new solutions are efficient, secure, and preserve privacy of data owners without disclosing confidentiality of data providers.\\ \\ The dissertation proposes a new notion of $m$-privacy that addresses the challenges when data providers may act as adversaries. To verify if such adversaries are capable of breaching privacy, we introduce a few different strategies and an adaptive algorithm to select and run the most efficient approach. In addition, we designed an algorithm to anonymize data, such that its results are $m$-private, i.e., knowing the results would not help any $m$ colluding parties in their attacks. All verification and anonymization algorithms have been implemented to be run in distributed environments by a trusted third party.\\ \\ For settings without a trusted third party, we introduce new secure multiparty computation protocols that implement centralized $m$-privacy verification and anonymization algorithms. For each protocol, we provedits security, analyzed its communication complexity, and evaluated its overall performance for various settings.\\ \\ The dissertation also describes a new algorithm to build differentially private histograms for records with customized privacy levels. The algorithm has two data partitioning phases (privacy-driven and data-driven). In addition, we adapted a v-optimal partitioning algorithm to be used with differential privacy, and experimentally evaluated their performance. \\ \\ Finally, the dissertation presents a new differential privacy mechanism that achieves collusion resistance in distributed environments with small overhead. We also defined an enhanced fault tolerant secure scheme (EFT), which can be used to design a variety of secure multiparty aggregation operations, and we employed it to implement our differential privacy mechanism in distributed environments. Both, the privacy mechanism and the EFT scheme have been extensively analyzed and experimentally evaluated.