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

Ill-posed inverse problems arise in a variety of scientific applications. Regularization methods exist for computing stable solution approximations, but many of these methods are inadequate or insufficient for solving large-scale problems. This work addresses these limitations by developing advanced numerical methods to solve ill-posed inverse problems and by implementing high-performance parallel code for large-scale applications. Three mathematical models that frequently arise in imaging applications are considered: linear least squares, nonlinear least squares, and nonlinear Poisson maximum likelihood. Hybrid methods are developed for regularization of linear least squares problems, variable projection algorithms are used for nonlinear least squares problems, and reconstruction algorithms are investigated for nonlinear Poisson based models. Furthermore, an efficient parallel implementation based on the Message Passing Interface (MPI) library is described for use on state-of-the-art computer architectures. Numerical experiments illustrate the effectiveness and efficiency of the proposed methods on problems from image reconstruction, super-resolution imaging, cryo-electron microscopy reconstruction, and digital tomosynthesis.

Solving Diophantine equations is a central question of number theory. In this talk we focus on several quite explicit examples of Diophantine equations having no nontrivial solutions, and explore various explanations of this phenomenon. In particular, we present some computational evidence that the Brauer-Manin obstruction is the only one for certain Del Pezzo surfaces, as well as an application of the Brauer-Manin obstruction to descent on genus-2 curves. (No prior knowledge of the definitions of the above terms will be assumed!)

I will describe a variational model combining energies in two different dimensions: surface tension, and 1-d elastic energy at the boundary. The model is motivated by findings in molecular dynamics simulations of HDL particle.

Do you currently run Magma, Maple, Mathematica, or Matlab? In this talk, I will take an in-depth look at Sage, which is a free open source mathematics software project that I started in 2005. Sage can be used to study general and advanced, pure and applied mathematics. This includes a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, exact linear algebra and much more. It combines various software packages and seamlessly integrates their functionality into a common experience. It is well suited for education, studying and research.

Data integration technology aims to transform data from the providers’ form to a form consumers can use, and also to merge data from multiple providers. Relevant theory and algorithms appeared as early as the 1980s, but until very recently the transition to products was highly disappointing After an introduction to the challenges of data integration, we examine research areas whose results were difficult to transfer. From these, we identify two generic tactics for formulating good research problems whose theoretical results will also be exploitable by product planners and by development teams. First, if you have a theoretical results that applies to constrained, simplified problems, extend it to be /somewhat /useful on systems that violate the constraint. Second, work “downstream” first – tackle the last challenge that blocks creating runnable code with large user bases – otherwise your results may stay on the shelf for decades (e.g., schema matching circa 1985-2008). Finally, we will examine how well research has aligned with needs (i.e., areas desperately needing models and technique to clarify them. While there has been some terrific (and terrifically useful) recent research on data integration (e.g., {IBM, Microsoft, Google} Research), we will describe our pain points – terrifically important challenges for tractable research problems have not yet been formulated (let alone solved).

By exploiting the commuting actions of the general linear and symmetric groups, Schur was able to prove combinatorial results about such things as symmetric functions and invariants. These methods work in a variety of settings and reveal beautiful connections with diagram algebras and walks on Dynkin diagrams.

By choosing a suitable basis of the Lie algebra sl(2) of 2 x 2 matrices of trace 0, connections with the modular group, the braid group on 3 strands, Tits buildings, and hyperbolic space become readily apparent. This talk will be a trip through these topics.

In typical extremal problem one wants to determine maximum cardinality of discrete structure with certain prescribed properties. Probably the earliest such result was obtain 100 years ago by Mantel who computed the maximum number of edges in a triangle free graph on n vertices. This was generalized by Turan for all complete graphs and became a starting point of Extremal Graph Theory. In this talk we survey several classical problems and results in this area and present some interesting applications of Extremal Graph Theory to other areas of mathematics. We also describe a recent surprising generalization of Turan's theorem which was motivated by question in Computational Complexity.

Abstract: While factoring large polynomials over finite fields is (apparently) far easier than factoring large integers, it is still an open problem to give an algorithm that does it ``as fast as possible'' (roughly speaking, in time proportional to the length of the input data). We will explain a recent improvement in the complexity of factoring polynomials over finite fields, based on an asymptotically optimal solution of a related problem (the modular composition problem). Joint work with Chris Umans (Caltech).

Lean body mass (LBM) is one of the three major components of body composition, which includes also body fat (FBM) and bone mass (BBM). As the other two components it is highly important for normal physiology and metabolism, and deviations from normal values are often associated with various pathological conditions. Of these the major one is probably sarcopenia ? the age related loss of muscle mass. However, while for each of FBM and BBM, many dozens of publications concerning candidate genes, whole genome linkage and association studies were published during the last two decades, there are virtually no publications on LBM in this respect. Huge effort is now invested in creation of a large international consortium which will tackle this problem. The main aim of this talk will be twofold. One, it will be focused on the results of our genetic epidemiological study of LBM and sarcopenia in a normal human population. We present estimates of the putative genetic factors contribution and results of the whole genome linkage and association analyses. The second aim is to attract the mathematicians? attention to a number of difficult problems in which modern biology became engaged with unprecedented development of biotechnology and bioinformatics. This includes such ?classical? problems, inherited from whole genome linkage studies, as multiple testing adjustments and multiple signal combination, and relatively new problems as e.g. multiple low effect signals and their interactions and several others.