Seminars archive

With the trend of cloud computing, data and computing are moved away from desktop and are instead provided as a service from the cloud. Data-as-a-service enables access to a wealth of data across distributed and heterogeneous data sources in the cloud. It remains a challenge, however, to ensure the privacy, interoperability, and scalability for such services.\\ \\ We designed and developed DObjects, a general-purpose P2P-based query and data operations infrastructure that can be deployed in the cloud and provides access to heterogeneous data sources. The system builds on top of a distributed mediator-wrapper architecture where individual system nodes serve as mediators and/or wrappers and interact with each other in a P2P fashion what guarantees good scalability. As an analogy, the system nodes can be considered as droplets, small elements that provide similar functionality in the cloud. Just as thousands or millions of droplets form a single drop in nature, in cloud computing, groups of droplets that provide similar functionality can form a micro-cloud. Micro-clouds are an integral part of the whole cloud computing system and can provide specific services to users.\\ \\ The dissertation also discusses the novel dynamic query execution engine within the data query infrastructure that dynamically adapts to network and node (or droplet) conditions. The query processing is capable of fully benefiting from all the distributed resources to minimize the query response time and maximize system throughput. In addition to leveraging the traditional distributed query optimization techniques, the (sub)queries are deployed and executed on droplets in a dynamic and iterative manner in order to guarantee the best reaction to network and resource dynamics.\\ \\ Finally, the dissertation presents an extension to the basic DObjects model that enables access to private data that is distributed and needs anonymization. The extension enables droplets to form virtual groups in order to addresses two important privacy issues for the sensitive data: privacy of data subjects and confidentiality of data providers. The dissertation discusses decentralized protocols that enable data sharing for horizontally partitioned databases given these constraints. These protocols can be run by the groups of droplets. Concretely, given a query spanning multiple databases, the query results do not contain individually identifiable information. In addition, institutions do not reveal their databases to each other apart from the query results.

TBA

This talk will describe some recent results using exact mass formulas to determine all definite quadratic forms of small class number in at least 3 variables, particularly those of class number one. The mass of a quadratic form connects the class number (i.e. number of classes in the genus) of a quadratic form with the volume of its adelic stabilizer, and is explicitly computable in terms of special values of zeta functions. Comparing this with known results about the sizes of automorphism groups, one can make precise statements about the growth of the class number, and in principle determine those quadratic forms of small class number. We will describe some known results about masses and class numbers (over number fields), then present some new computational work over the rational numbers, and perhaps over some totally real number fields.

There are now several constructions of elliptic curves of high rank over function fields, most involving high-tech things like $L$-functions, cohomology, and the Tate or BSD conjectures. I'll review some of this and then give a very down-to-earth, low-tech construction of elliptic curves of high ranks over the rational function field $\mathbf{F}_p(t)$.

Dyson's rank and crank statistics have long been important in the combinatorial study of integer partitions. Both statistics were introduced in efforts to better understand the famous Ramanujan congruences for the partition function $p(n)$, and there is no apparent relation between their simple combinatorial definitions. The main results of this talk (essentially) prove a remarkable conjecture of Garvan that the moments of the crank are always larger than the moments of the rank. More generally, these inequalities are an important example of relations for the asymptotics of hypergeometric $q$-series that are governed by modularity properties. In this case, the crank is associated to a modular form, while the rank is associated to a mock theta function/harmonic Maass form. If time permits, I will also briefly discuss some ideas of Zagier for deriving asymptotic expansions in these settings.

Fix integers n and k with n at least k, and n, k > 2. With Bill Sands, we proved that if P is a finite partially ordered set and every maximal chain C of P has between n and n + (n - k)/k - 2) elements, then P must contain k pairwise disjoint maximal antichains. We also constructed a family of examples to show that these inequalities are tight. We raised and made observations about the dual problem, which Dave Howard and Tom Trotter [Georgia Tech] have recently solved.

There are some objects in number theory that are particularly fundamental -- examples include "number fields", "class groups", and "elliptic curves" -- yet very little is known about how many such objects there are having given invariants, or how these objects are distributed with respect to these invariants. In this talk, I will try to describe why number theorists are so interested in these questions, and will discuss a few recent results that give some answers.

In the talk we discuss a variational multiscale approach for the pressure subgrid modeling in the Galerkin method for incompressible Navier-Stokes equations. We relate the approach with a stabilization procedure of least-square type known as grad-div stabilization and consider the search of optimal stabilization parameters as a trade-off between mass and energy balance in the discrete system. Application to numerical simulation of laminar and turbulent flows is studied

An increasing volume of patient data in clinical data warehouses makes possible the identification and analysis of populations with therapeutic responses, outcomes and clinical care processes that are reflected by multivariate trends and patterns over time. This presentation will describe a grid-based software system that is under development at Emory, the Analytic Information Warehouse (AIW), that aims to facilitate discovery and query of those patterns. The AIW will provide controlled terminology support in queries. It will also provide analytic services for extracting concepts from unstructured text, de-identification, discovering features of a patient population and predicting responses and outcomes. Schema adaptors will support connecting to Emory Healthcare's existing clinical data warehouse and other research and clinical databases with appropriate levels of security. These capabilities ultimately will provide broad support to Emory Healthcare and researchers in risk factor identification, prediction, and evaluation of interventions to improve patient care quality and outcomes.\\ \\ Bio:\\ \\ Andrew Post, MD, PhD is a Clinical Informatics Architect at Emory University's Center for Comprehensive Informatics, and Assistant Professor in the Department of Biomedical Engineering. Dr. Post completed an MD at the University of Pennsylvania, and a fellowship and PhD in Biomedical Informatics at the University of Pittsburgh. He is faculty lead of an Analytic Information Warehouse supporting informatics-based quality improvement and research at Emory. He has conducted research in temporal pattern detection, clinical decision support, clinical user interfaces and the promotion of cross-disciplinary collaborations in clinical and translational research environments. His roles have included hospital and research information systems planning.

The art and science of secure communication is called cryptography. To send someone a secret message, you need two things: (1) a message scrambler ("the cryptosystem"), and (2) a piece of information that tells the sender and the receiver just how the scrambling is done ("the key"). Keeping the key in the right hands and out of the wrong hands is a major problem for cryptographers, and public key cryptography is a solution to this problem that is at work on every computer and in every network in the world. This talk is about Chocolate Key Cryptography, which is a way to describe a certain public key cryptosystem that is easy to learn, fun, interactive, and delicious. Biographical Sketch: Ezra (Bud) Brown grew up in New Orleans, has degrees from Rice and LSU, and has been at Virginia Tech since 1969, where he is currently Alumni Distinguished Professor of Mathematics. Although most of his research has been in number theory and combinatorics, he once wrote a paper with a sociologist. During the summers, he works on problems of cryptography with an unnamed government agency. He has been honored with some teaching and writing awards. He enjoys singing in operas, playing jazz piano, and gardening, and he occasionally bakes biscuits for his students.

I will speak about the characterization of the polar reflectors (duality transformations of the set of reflectors), i.e. the sufficient conditions for the transformation to be polarity.

A weighting of the edges of a graph with integer weights gives rise to a weighting of the vertices, the weight of a vertex being the sum of the weights of its incident edges. It is natural to consider edge weighting where we require that adjacent vertices have different weights, that is, that the vertex weighting induce a proper coloring of the graph.\\ \\ Conjecture [Karonski, Luczak and Thomason, 2001]. Edges of every graph that does not contain a component isomorphic to an edge can be weighted with the integers {1,2,3} such that the resultant vertex weighting is a proper coloring.\\ \\ In my talk I will discuss some recent developments regarding the above conjecture.