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Computational Science and Engineering Seminar Series
Computational Science and Engineering Seminar Series
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ItemSequences of Problems, Matrices, and Solutions(Georgia Institute of Technology, 2010-11-12) De Sturler, EricIn a wide range of applications, we deal with long sequences of slowly changing matrices or large collections of related matrices and corresponding linear algebra problems. Such applications range from the optimal design of structures to acoustics and other parameterized systems, to inverse and parameter estimation problems in tomography and systems biology, to parameterization problems in computer graphics, and to the electronic structure of condensed matter. In many cases, we can reduce the total runtime significantly by taking into account how the problem changes and recycling judiciously selected results from previous computations. In this presentation, I will focus on solving linear systems, which is often the basis of other algorithms. I will introduce the basics of linear solvers and discuss relevant theory for the fast solution of sequences or collections of linear systems. I will demonstrate the results on several applications and discuss future research directions.
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ItemMetanumerical computing for partial differential equations: the Sundance project(Georgia Institute of Technology, 2010-10-29) Kirby, Robert C.Metanumerical computing deals with computer programs that use abstract mathematical structure to manipulate, generate, and/or optimize compute-intensive numerical codes. This idea has gained popularity over the last decade in several areas of scientific computing, include numerical linear algebra, signal processing, and partial differential equations. The Sundance project is such an example, using high-level software-based differentiation of variational forms to automatically produce high-performance finite element implementations, all within a C++ library. In addition to automating the discretization of PDE by finite elements, recent work is demonstrating how to produce block-structured matrices and streamline the implementation of advanced numerical methods. I will conclude with some examples of this for some incompressible flow problems.
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ItemGravity's Strongest Grip: A Computational Challenge(Georgia Institute of Technology, 2010-10-22) Shoemaker, DeirdreGravitational physics is entering a new era driven by observation that will begin once gravitational-wave interferometers make their first detections. In the universe, gravitational waves are produced during violent events such as the merger of two black holes. The detection of these waves, sometimes called ripples in the fabric of spacetime, is a formidable undertaking, requiring innovative engineering, powerful data analysis tools and careful theoretical modeling. High performance computing plays a vital role in our ability to predict and interpret gravitational waves with theoretical modeling of the sources. I will provide an overview of the high performance and data analysis challenges we face in making the first and subsequent detection of gravitational waves.
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ItemNovel Applications of Graph Embedding Techniques(Georgia Institute of Technology, 2010-10-01) Bhowmick, SanjuktaForce-directed graph embedding algorithms, like the Fruchterman-Reingold method, are typically used to generate aesthetically pleasing graph layouts. At a fundamental level, these algorithms are based on manipulating the structural properties of the graph to match them to certain spatial requirements. This relation between structural and spatial properties is also present in other areas beyond graph visualization. In this talk, I will discuss how graph embedding can be used in diverse areas such as (i) improving the accuracy of unsupervised clustering, (ii) creating good quality elements in unstructured meshes and (iii) identifying perturbations in large-scale networks.
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ItemThe Joy of PCA(Georgia Institute of Technology, 2010-09-17) Vempala, Santosh S.Principal Component Analysis is the most widely used technique for high-dimensional or large data. For typical applications (nearest neighbor, clustering, learning), it is not hard to build examples on which PCA "fails." Yet, it is popular and successful across a variety of data-rich areas. In this talk, we focus on two algorithmic problems where the performance of PCA is provably near-optimal, and no other method is known to have similar guarantees. The problems we consider are (a) the classical statistical problem of unraveling a sample from a mixture of k unknown Gaussians and (b) the classic learning theory problem of learning an intersection of k halfspaces. During the talk, we will encounter recent extensions of PCA that are noise-resistant, affine-invariant and nonviolent.
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ItemComposite Objective Optimization and Learning for Massive Datasets(Georgia Institute of Technology, 2010-09-03) Singer, YoramComposite objective optimization is concerned with the problem of minimizing a two-term objective function which consists of an empirical loss function and a regularization function. Application with massive datasets often employ a regularization term which is non-differentiable or structured, such as L1 or mixed-norm regularization. Such regularizers promote sparse solutions and special structure of the parameters of the problem, which is a desirable goal for datasets of extremely high-dimensions. In this talk, we discuss several recently developed methods for performing composite objective minimization in the online learning and stochastic optimization settings. We start with a description of extensions of the well-known forward-backward splitting method to stochastic objectives. We then generalize this paradigm to the family of mirrordescent algorithms. Our work builds on recent work which connects proximal minimization to online and stochastic optimization. We focus in the algorithmic part on a new approach, called AdaGrad, in which the proximal function is adapted throughout the course of the algorithm in a data-dependent manner. This temporal adaptation metaphorically allows us to find needles in haystacks as the algorithm is able to single out very predictive yet rarely observed features. We conclude with several experiments on large-scale datasets that demonstrate the merits of composite objective optimization and underscore superior performance of various instantiations of AdaGrad.
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ItemAutomating Topology Aware Task Mapping on Large Supercomputers(Georgia Institute of Technology, 2010-03-30) Bhatele, Abhinav S.Parallel computing is entering the era of petascale machines. This era brings enormous computing power to us and new challenges to harness this power efficiently. Machines with hundreds of thousands of processors already exist, connected by complex interconnect topologies. Network contention is becoming an increasingly important factor affecting overall performance. The farther different messages travel on the network, greater is the chance of resource sharing between messages and hence, of contention. Recent studies on IBM Blue Gene and Cray XT machines have shown that under contention, message latencies can be severely affected. Mapping of communicating tasks on nearby processors can minimize contention and lead to better application performance. In this talk, I will propose algorithms and techniques for automatic mapping of parallel applications to relieve the application developers of this burden. I will first demonstrate the effect of contention on message latencies and use these studies to guide the design of mapping algorithms. I will introduce the hop-bytes metric for the evaluation of mapping algorithms and suggest that it is a better metric than the previously used maximum dilation metric. I will then discuss in some detail, the mapping framework which comprises of topology aware mapping algorithms for parallel applications with regular and irregular communication patterns.
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ItemFast Algorithms for Querying and Mining Large Graphs(Georgia Institute of Technology, 2010-03-16) Tong, HanghangGraphs appear in a wide range of settings and have posed a wealth of fascinating problems. In this talk, I will present our recent work on (1) querying (e.g., given a social network, how to measure the closeness between two persons? how to track it over time?); and (2) mining (e.g., how to identify abnormal behaviors of computer networks? In the case of virus attacks, which nodes are the best to immunize?) large graphs. For the task of querying, our main finding is that many complex user-specific patterns on large graphs can be answered by means of proximity measurement. In other words, proximity allows us to query large graphs on the atomic levels. Then, I will talk about how to adapt querying tasks to the time evolving graphs. For fast computation of proximity, we developed a family of fast solutions to compute the proximity in several different scenarios. By carefully leveraging some important properties shared by many real graphs (e.g., the block-wise structure, the linear correlation, the skewness of real bipartite graphs, etc), we can often achieve orders of magnitude of speedup with little or no quality loss. For the task of mining, I will talk about immunization and anomaly detection. For immunization, we proposed a near-optimal, fast and scalable algorithm. For anomaly detection, we proposed a family of example-based low-rank matrix approximation methods. The proposed algorithms are provably equal to or better than best known methods in both space and time, with the same accuracy. On real data sets, it is up to 112x faster than the best competitors, for the same accuracy.
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ItemLoad-Balanced Bonded Force Calculations on Anton(Georgia Institute of Technology, 2010-03-15) Franchetti, FranzSpiral (www.spiral.net) is a program and hardware design generation system for linear transforms such as the discrete Fourier transform, discrete cosine transforms, filters, and others. We are currently extending Spiral beyond its original problem domain, using coding algorithms (Viterbi decoding and JPEG 2000 encoding) and image formation synthetic aperture radar, SAR) as examples. For a user-selected problem specification, Spiral autonomously generates different algorithms, represented in a declarative form as mathematical formulas, and their implementations to find the best match to the given target platform. Besides the search, Spiral performs deterministic optimizations on the formula level, effectively restructuringthe code in ways unpractical at the code or design level. Spiral generates specialized single-size implementations or adaptive general-size autotuning libraries, and utilizes special instructions and multiple processor cores. The implementation generated by Spiral rival the performance of expertly hand-tuned libraries. In this talk, we give a short overview on Spiral. We explain how Spiral generates efficient programs for parallel platforms including vector architectures, shared and distributed memory platforms, and GPUs; as well as hardware designs (Verilog) and automatically partitioned software/hardware implementations. We overview how Spiral targets the Cell BE and PowerXCell 8i, the BlueGene/P PPC450d processors, as well as Intel's upcoming Larrabee GPU and AVX vector instruction set. As all optimizations in Spiral, parallelization and partitioning are performed on a high abstraction level of algorithm representation, using rewriting systems.
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ItemAccurate Inference of Phylogenetic Relationships from Multi-locus Data(Georgia Institute of Technology, 2010-03-09) Nakhleh, LuayAccurate inference of phylogenetic relationships of species, and understanding their relationships with gene trees are two central themes in molecular and evolutionary biology. Traditionally, a species tree is inferred by (1) sequencing a genomic region of interest from the group of species under study, (2) reconstructing its evolutionary history, and (3) declaring it to be the estimate of the species tree. However, recent analyses of increasingly available multi-locus data from various groups of organisms have demonstrated that different genomic regions may have evolutionary histories (called "oegene trees") that may disagree with each other, as well as with that of the species. This observation has called into question the suitability of the traditional approach to species tree inference. Further, when some, or all, of these disagreements are caused by reticulate evolutionary events, such as hybridization, then the phylogenetic relationship of the species is more appropriately modeled by a phylogenetic network than a tree. As a result, a new, post-genomic paradigm has emerged, in which multiple genomic regions are analyzed simultaneously, and their evolutionary histories are reconciled in order to infer the evolutionary history of the species, which may not necessarily be treelike. In this talk, I will describe our recent work on developing mathematical criteria and algorithmic techniques for analyzing incongruence among gene trees, and inferring phylogenetic relationships among species despite such incongruence. This includes work on lineage sorting, reticulate evolution, as well as simultaneous treatment of both. If time permits, I will describe our recent work on population genomic analysis of bacterial data, and the implications on the evolutionary forces shaping the genomic diversity in these populations.