1\documentclass{article}2\usepackage{url}3\usepackage{fullpage}4\title{Titles and Abstracts:\vspace{4ex}\mbox{}\\5\Large Interactive Parallel Computation in Support of Research in\\Algebra, Geometry6and Number Theory\vspace{4ex}\mbox{}\\7\large A Workshop at MSRI Jan 29-Feb 2 organized by\\Burhanuddin, Demmel, Goins, Kaltofen, Perez, Stein, Verrill, and Weening}8\begin{document}9\maketitle10\par\noindent11{\large \bf Bailey: {\em\sf Experimental Mathematics and High-Performance Computing}}\vspace{1ex}\newline12{\em David Bailey - Lawrence Berkeley Labs (LBL)}\vspace{1ex}\newline13\url{http://crd.lbl.gov/~dhbailey/}\vspace{1ex}\newline14{15Recent developments in ``experimental mathematics'' have underscored the value of high-performance computing in modern mathematical research. The most frequent computations that arise here are high-precision (typically several-hundred-digit accuracy) evaluations of integrals and series, together with integer relation detections using the ``PSLQ'' algorithm. Some recent highlights in this arena include: (2) the discovery of ``BBP'-type formulas for various mathematical constants, including pi and log(2); (3) the discovery of analytic evaluations for several classes of multivariate zeta sums; (4) the discovery of Apery-like formulas for the Riemann zeta function at integer arguments; and (5) the discovery of analytic evaluations and linear relations among certain classes of definite integrals that arise in mathematical physics. The talk will include a live demo of the ``experimental mathematician's toolkit''.16}\mbox{}\vspace{6ex}171819\par\noindent{\large \bf Bradshaw: {\em\sf Loosely Dependent Parallel Processes}}\vspace{1ex}\newline20{\em Robert Bradshaw - University of Washington}\vspace{1ex}\newline21\url{robertwb@math.washington.edu}\vspace{1ex}\newline22{23Many parallel computational algorithms involve dividing the problem into several smaller tasks and running each task in isolation in parallel. Often these tasks are the same procedure over a set of varying parameters. Inter-process communication might not be needed, but the results of one task may influence what subsequent tasks need to be performed. I will discuss the concept of job generators, or custom-written tasks that generate other tasks and process their feedback. I would discuss this specifically in the context of integer factorization.24}\mbox{}\vspace{6ex}252627\par\noindent{\large \bf Cohn: {\em\sf Parallel Computation Tools for Research: A Wishlist}}\vspace{1ex}\newline28{\em Henry Cohn - Microsoft Research}\vspace{1ex}\newline29\url{http://research.microsoft.com/~cohn/}\vspace{1ex}\newline30{}\mbox{}\vspace{6ex}313233\par\noindent{\large \bf Cooperman: {\em\sf Disk-Based Parallel Computing: A New Paradigm}}\vspace{1ex}\newline34{\em Gene Cooperman - Northeastern University}\vspace{1ex}\newline35\url{http://www.ccs.neu.edu/home/gene/}\vspace{1ex}\newline36{37One observes that 100 local commodity disks of an array have approximately the same streaming bandwidth as a single RAM subsystem. Hence, it is proposed to treat a cluster as if it were a single computer with tens of terabytes of data, and with RAM serving as cache for disk. This makes feasible the solution of truly large problems that are currently space-limited. We also briefly summarize other recent activities of our working group: lessons from supporting ParGAP and ParGCL; progress toward showing that 20 moves suffice to solve Rubik's cube; lessons about marshalling from support of ParGeant4 (parallelization of a million-line program at CERN); and experiences at the SCIEnce workshop (symbolic-computing.org), part of a 5-year, 3.2 million euro, European Union project. Our new distributed checkpointing package now provides a distributed analog of a SAVE-WORKSPACE command, for use in component-based symbolic software, such as SAGE.}\mbox{}\vspace{6ex}383940\par\noindent{\large \bf Edelman: {\em\sf Interactive Parallel Supercomputing: Today: MATLAB(r) and Python coming Cutting Edge: Symbolic Parallelism with Mathematica(r) and MAPLE(r)}}\vspace{1ex}\newline41{\em Alan Edelman - MIT}\vspace{1ex}\newline42\url{http://www-math.mit.edu/~edelman/}\vspace{1ex}\newline43{Star-P is a unique technology offered by Interactive Supercomputing after44nurturing at MIT. Star-P through its abstractions is solving the ease of use45problem that has plagued supercomputing. Some of the innovative features of46Star-P are the ability to program in MATLAB, hook in task parallel codes47written using a processor free abstraction, hook in existing parallel codes,48and obtain the performance that represents the HPC promise. All this is49through a client/server interface. Other clients such as Python or R could50be possible. The MATLAB, Python, or R becomes the "browser." Parallel51computing remains challenging, compared to serial coding but it is now that52much easier compared to solutions such as MPI. Users of MPI can plug in53their previously written codes and libraries and continue forward in Star-P.5455Numerical computing is challenging enough in a parallel environment,56symbolic computing will require even more research and more challenging57problems to be solved. In this talk we will demonstrate the possibilities58and the pitfalls.59}\mbox{}\vspace{6ex}606162\par\noindent{\large \bf Granger: {\em\sf Interactive Parallel Computing using Python and IPython}}\vspace{1ex}\newline63{\em Brian Granger - Tech X Corp.}\vspace{1ex}\newline64\url{http://txcorp.com}\vspace{1ex}\newline65{66Interactive computing environments, such as Matlab, IDL and67Mathematica are popular among researchers because their68interactive nature is well matched to the exploratory nature of69research. However, these systems have one critical weakness:70they are not designed to take advantage of parallel computing71hardware such as multi-core CPUs, clusters and supercomputers.72Thus, researchers usually turn to non-interactive compiled73languages, such as C/C++/Fortran when parallelism is needed.7475In this talk I will describe recent work on the IPython project76to implement a software architecture that allows parallel77applications to be developed, debugged, tested, executed and78monitored in a fully interactive manner using the Python79programming language. This system is fully functional and allows80many types of parallelism to be expressed, including message81passing (using MPI), task farming, shared memory, and custom user82defined approaches. I will describe the architecture, provide an83overview of its basic usage and then provide more sophisticated84examples of how it can be used in the development of new parallel85algorithms. Because IPython is one of the components of the SAGE86system, I will also discuss how IPython's parallel computing87capabilities can be used in that context.88}\mbox{}\vspace{6ex}899091\par\noindent{\large \bf Harrison: {\em\sf Science at the petascale: tools in the tool box}}\vspace{1ex}\newline92{\em Robert Harrison - Oak Ridge National Lab}\vspace{1ex}\newline93\url{http://www.csm.ornl.gov/ccsg/html/staff/harrison.html}\vspace{1ex}\newline94{95Petascale computing will require coordinating the actions of 100,000+96processors, and directing the flow of data between up to six levels97of memory hierarchy and along channels that differ by over a factor of98100 in bandwidth. Amdahl's law requires that petascale applications99have less than 0.001% sequential or replicated work in order to100be at least 50% efficient. These are profound challenges for all but101the most regular or embarrassingly parallel applications, yet we also102demand that not just bigger and better, but fundamentally new science.103In this presentation I will discuss how we are attempting to confront104simultaneously the complexities of petascale computation while105increasing our scientific productivity. I hope that I can convince you106that our development of MADNESS (multiresolution adaptive numerical107scientific simulation) is not as crazy as it sounds.108109This work is funded by the U.S. Department of Energy, the division of110Basic Energy Science, Office of Science, and was performed in part111using resources of the National Center for Computational Sciences, both112under contract DE-AC05-00OR22725 with Oak Ridge National Laboratory.113}\mbox{}\vspace{6ex}114115116\par\noindent{\large \bf Hart: {\em\sf Parallel Computation in Number Theory}}\vspace{1ex}\newline117{\em Bill Hart - Warwick}\vspace{1ex}\newline118\url{http://www.maths.warwick.ac.uk/~masfaw/}\vspace{1ex}\newline119{120This talk will have two sections. The first will121introduce a new library for number theory which is122under development, called FLINT. I will discuss the123various algorithms already available in FLINT, compare124them with similar implementations available elsewhere,125and speak about what the future holds for FLINT, with126the focus on parallel processing and integration into127Pari and the SAGE package.128129The second part of the talk will focus on low level130implementation details of parallel algorithms in131number theory. In particular I will discuss the design132decisions that we have made so far in the FLINT133library to facilitate multicore and multiprocessor134platforms.135136If time permits, there will be a live demonstration.137}\mbox{}\vspace{6ex}138139140\par\noindent{\large \bf Hida: {\em\sf Moving Lapack and ScaLapack to Higher Precision without Too Much Work}}\vspace{1ex}\newline141{\em Yozo Hida - UC Berkeley}\vspace{1ex}\newline142\url{http://www.cs.berkeley.edu/~yozo/}\vspace{1ex}\newline143{I will be discussing recent developments in Lapack and ScaLapack144libraries, along with some recent work on incorporating higher145precision into Lapack and ScaLapack.}\mbox{}\vspace{6ex}146147148\par\noindent{\large \bf Khan: {\em\sf Game Theoretical Solutions for Data Replication in Distributed Computing Systems}}\vspace{1ex}\newline149{\em Samee Khan - University of Texas, Arlington}\vspace{1ex}\newline150\url{sakhan@cse.uta.edu}\vspace{1ex}\newline151{152Data replication is an essential technique employed to reduce the user153perceived access time in distributed computing systems. One can find numerous154algorithms that address the data replication problem (DRP) each contributing in155its own way. These range from the traditional mathematical optimization156techniques, such as, linear programming, dynamic programming, etc. to the157biologically inspired meta-heuristics. We aim to introduce game theory as a new158oracle to tackle the data replication problem. The beauty of the game theory159lies in its flexibility and distributed architecture, which is well-suited to160address the DRP. We will specifically use action theory (a special branch of161game theory) to identify techniques that will effectively and efficiently solve162the DRP. Game theory and its necessary properties are briefly introduced,163followed by a through and detailed mapping of the possible game theoretical164techniques and DRP. As an example, we derive a game theoretical algorithm for165the DRP, and propose several extensions of it. An elaborate experimental setup166is also detailed, where the derived algorithm is comprehensively evaluated167against three conventional techniques, branch and bound, greedy and genetic168algorithms.169}\mbox{}\vspace{6ex}170171172\par\noindent{\large \bf Kotsireas: {\em\sf Combinatorial Designs: constructions, algorithms and new results}}\vspace{1ex}\newline173{\em Ilias Kotsireas - Laurier University, Canada}\vspace{1ex}\newline174\url{ikotsire@wlu.ca}\vspace{1ex}\newline175{176We plan to describe recent progress in the search for combinatorial designs of177high order. This progress has been achieved via some algorithmic concepts, such178as the periodic autocorrelation function, the discrete Fourier transform and179the power spectral density criterion, in conjunction with heuristic180observations on plausible patterns for the locations of zero elements. The181discovery of such patterns is done using meta-programming and automatic code182generation (and perhaps very soon data mining algorithms) and reveals the183remarkable phenomenon of crystalization, which does not yet possess a184satisfactory explanation. The resulting algorithms are amenable to parallelism185and we have implemented them on supercomputers, typically as implicit parallel186algorithms.187}\mbox{}\vspace{6ex}188189190\par\noindent{\large \bf Leykin: {\em\sf Parallel computation of Grobner bases in the Weyl algebra}}\vspace{1ex}\newline191{\em Anton Leykin - IMA (Minessota)}\vspace{1ex}\newline192\url{leykin@ima.umn.edu}\vspace{1ex}\newline193{194The usual machinery of Grobner bases can be applied to non-commutative algebras195of the so-called solvable type. One of them, the Weyl algebra, plays the196central role in the computations with $D$-modules. The practical complexity of197the Grobner bases computation in the Weyl algebra is much higher than in the198(commutative) polynomial rings, therefore, calling naturally for parallel199computation. We have developed an algorithm to perform such computation200employing the master-slave paradigm. Our implementation, which has been carried201out in C++ using MPI, draws ideas from both Buchberger algorithm and202Faugere's $F_4$. It exhibits better speedups for the Weyl algebra in203comparison to polynomial problems of the similar size.204}\mbox{}\vspace{6ex}205206207\par\noindent{\large \bf Martin: {\em\sf MPMPLAPACK: The Massively Parallel Multi-Precision Linear Algebra Package}}\vspace{1ex}\newline208{\em Jason Martin - James Madison University}\vspace{1ex}\newline209\url{http://www.math.jmu.edu/~martin/}\vspace{1ex}\newline210{211For several decades, researchers in the applied fields have had access212to powerful linear algebra packages designed to run on massively213parallel systems. Libraries such as ScaLAPACK and PLAPACK provide a214rich set of functions (usually based on BLAS) for performing linear215algebra over single or double precision real or complex data.216However, such libraries are of limited use to researchers in discrete217mathematics who often need to compute with multi-precision data types.218219This talk will cover a massively parallel multi-precision linear220algebra package that I am attempting to write. The goal of this C/MPI221library is to provide drop-in parallel functionality to existing222number theory and algebraic geometry programs (such as Pari, Sage, and223Macaulay2) while preserving enough flexibility to eventually become a224full multi-precision version of PLAPACK. I will describe some225architectural assumptions, design descisions, and benchmarks made so226far and actively solicit input from the audience (I'll buy coffee for227the person who suggests the best alternative to the current name).228}\mbox{}\vspace{6ex}229230231\par\noindent{\large \bf Moreno Maza: {\em\sf Component-level Parallelization of Triangular Decompositions}}\vspace{1ex}\newline232{\em Marc Moreno Maza - Western Ontario}\vspace{1ex}\newline233\url{http://www.csd.uwo.ca/~moreno/}\vspace{1ex}\newline234{235We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decompositions. We introduce a component-level parallelism for which the number of processors in use depends on the geometry of the solution set of the input system. Our long term goal is to achieve an efficient multi-level parallelism: coarse grained (component) level for tasks computing geometric objects in the solution sets, and medium/fine grained level for polynomial arithmetic such as GCD/resultant computation within each task.236237Component-level parallelism belongs to the class of dynamic irregular parallel applications, which leads us to address the following questions: How to discover and use geometrical information, at an early stage of the solving process, that would be favorable to component-level parallel execution and load balancing? How to use this level of parallel execution to effectively eliminate unnecessary computations? What implementation mechanisms are feasible?238239We report on the effectiveness of the approaches that we have applied, including ``modular methods'', ``solving by decreasing order of dimension'', ``task cost estimation for guided scheduling''. We have realized a preliminary implementation on a SMP using multiprocessed parallelism in Aldor and shared memory segments for data communication. Our experimentation shows promising speedups for some well-know problems. We expect that this speedup would add a multiple factor to the speedup of medium/fine grained level parallelization as parallel GCD/resultant computations.240}\mbox{}\vspace{6ex}241242243\par\noindent{\large \bf Noel: {\em\sf Structure and Representations of Real Reductive Lie Groups: A Computational Approach}}\vspace{1ex}\newline244{\em Alfred Noel - UMass Boston / MIT}\vspace{1ex}\newline245\url{http://www.math.umb.edu/~anoel/}\vspace{1ex}\newline246{247I work with David Vogan (MIT) on the Atlas of Lie Groups and Representations. This is a project to make available information about representations of semi-simple Lie groups over real and p-adic fields. Of particular importance is the problem of the unitary dual: classifying all of the irreducible unitary representations of a given Lie group.248249I will present some of the main ideas behind the current and very preliminary version of the software. I will provide some examples also. Currently, we are developing sequential algorithms that are implemented in C++. However, because of time and space complexity we are slowly moving in the direction of parallel computation. For example, David Vogan is experimenting with multi-threads in the K-L polynomials computation module.250251This talk is in memory of Fokko du Cloux, the French mathematician who, until a few months ago, was the lead developer. He died this past November.252}\mbox{}\vspace{6ex}253254255\par\noindent{\large \bf Pernet: {\em\sf Parallelism perspectives for the LinBox library}}\vspace{1ex}\newline256{\em Clement Pernet - University of Waterloo}\vspace{1ex}\newline257\url{cpernet@uwaterloo.ca}\vspace{1ex}\newline258{259LinBox is a generic library for efficient linear algebra with blackbox260or dense matrices over a finite field or Z. We first present a few261notions of the sequential implementations of selected problems, such262as the system resolution or multiple triangular system resolution, or263the chinese remaindering algorithm. Then we expose perspectives for264incorporating parallelism in LinBox, including multi-prime lifting for265system resolution over Q, or parallel chinese remaindering. This last266problem raises the difficult problem of combining early termination267and work-stealing techniques.268}\mbox{}\vspace{6ex}269270271\par\noindent{\large \bf Qiang: {\em\sf Distributed Computing using SAGE}}\vspace{1ex}\newline272{\em Yi Qiang - University of Washington}\vspace{1ex}\newline273\url{http://www.yiqiang.net/}\vspace{1ex}\newline274{275Distributed SAGE (DSAGE) is a distributed computing framework for276SAGE which allows users to easily parallelize computations and277interact with them in a fluid and natural way. This talk will be278focused on the design and implementation of the distributed computing279framework in SAGE. I will describe the application of the280distributed computing framework to several problems, including the281problem of integer factorization and distributed ray tracing.282Demonstrations of using Distributed SAGE to tackle both problems will283be given plus information on how to parallelize your own problems. I284will also talk about design issues and considerations that have been285resolved or are yet unresolved in implementing Distributed SAGE.286}\mbox{}\vspace{6ex}287288289\par\noindent{\large \bf Roch: {\em\sf Processor oblivious parallel algorithms with provable performances: applications}}\vspace{1ex}\newline290{\em Jean-Louis Roch - ID-IMAG (France)}\vspace{1ex}\newline291\url{http://www-id.imag.fr/Laboratoire/Membres/Roch_Jean-Louis/perso.html}\vspace{1ex}\newline292{293Based on a work-stealing schedule, the on-line coupling of two algorithms294(one sequential; the other one recursive parallel and fine grain) enables295the design of programs that scale with provable performances on various296parallel architectures, from multi-core machines to heterogeneous grids,297including processors with changing speeds. After presenting a generic scheme298and framework, on top of the middleware KAAPI/Athapascan that efficiently299supports work-stealing, we present practical applications such as: prefix300computation, real time 3D-reconstruction, Chinese remainder modular lifting301with early termination, data compression.302}\mbox{}\vspace{6ex}303304305\par\noindent{\large \bf Tonchev: {\em\sf Combinatorial designs and code synchronization}}\vspace{1ex}\newline306{\em Vladimir Tonchev - Michigan Tech}\vspace{1ex}\newline307\url{tonchev@mtu.edu}\vspace{1ex}\newline308{309Difference systems of sets are combinatorial designs that arise in connection310with code synchronization. Algebraic constructions based on cyclic difference311sets and finite geometry and algorithms for finding optimal difference systems312of sets are discussed.313}\mbox{}\vspace{6ex}314315316\par\noindent{\large \bf Verschelde: {\em\sf Parallel Homotopy Algorithms to Solve Polynomial Systems}}\vspace{1ex}\newline317{\em Jan Verschelde - UIC}\vspace{1ex}\newline318\url{http://www.math.uic.edu/~jan/}\vspace{1ex}\newline319{320A homotopy is a family of polynomial systems which defines a deformation321from a system with known solutions to a system whose solutions are needed.322Via dynamic load balancing we may distribute the solution paths so that a323close to optimal speed up is achieved. Polynomial systems -- such as the3249-point problem in mechanical design leading to 286,720 paths -- whose325solving required real supercomputers twenty years ago can now be handled326by modest personal cluster computers, and soon by multicore multiprocessor327workstations. Larger polynomial systems however may lead to more328numerical difficulties which may skew the timing results, so that329attention must be given to ``quality up'' as well. Modern homotopy methods330consist of sequences of different families of polynomial systems so that331not only the solution paths but also parametric polynomial systems must be332exchanged frequently.333}\mbox{}\vspace{6ex}334335336\par\noindent{\large \bf Wolf: {\em\sf Parallel sparsening and simplification of systems of equations}}\vspace{1ex}\newline337{\em Thomas Wolf and Winfried Neun }\vspace{1ex}\newline338\url{twolf@brocku.ca neun@zib.de}\vspace{1ex}\newline339{340In a Groebner Basis computation the guiding principle for pairing and341`reducing' equations is a total ordering of monomials or of derivatives for342differential Groebner Bases. If reduction based on an ordering is replaced by343reduction to minimize the number of terms of an equation through another344equation then on the downside the resulting (shorter) system does depend on the345order of pairing of equations for shortening but on the upside there are number346of advantages that makes this procedure a perfect addition/companion to the347Groebner Basis computation. Such features are:348349\begin{itemize}\item In contrast to Groebner Basis computations, this algorithm is safe in the sense that it does not need any significant amount of memory, even not temporarily.350\item It is self-enforcing, i.e. the shorter equations become, the more useful for shortening other equations they potentially get.351\item Equations in a sparse system are less coupled and a cost effective elimination strategy (ordering) is much easier to spot (for humans and computers) than for a dense system.352\item Statistical tests show that the probability of random polynomials to factorize increases drastically the fewer terms a polynomial has.353\item By experience the shortening of partial differential equations increases their chance to become ordinary differential equations which are usually easier to solve explicitly.354\item The likelihood of shortenings to be possible is especially high for large overdetermined systems. This is because the number of pairings goes quadratically with the number of equations but for overdetermined systems, more equations does not automatically mean more unknowns to occur which potentially obstruct shortening by introducing terms that can not cancel.355\item The algorithm offers a fine grain parallelization in the computation to shorten one equation with another one and a coarse grain parallelization in that any pair of two equations of a larger system can be processed in parallel. In the talk we will present the algorithm, show examples supporting the above statements and give a short demo.356\end{itemize}}\mbox{}\vspace{6ex}357358359\par\noindent{\large \bf Yelick: {\em\sf Programming Models for Parallel Computing}}\vspace{1ex}\newline360{\em Kathy Yelick - UC Berkeley}\vspace{1ex}\newline361\url{http://www.cs.berkeley.edu/~yelick/}\vspace{1ex}\newline362{363The introduction of multicore processors into mainstream computing is364creating a revolution in software development. While Moore's365Law continues to hold, most of the increases in transistor density will be366used for explicit, software-visible parallelism, rather than increasing367clock rate. The major open question is how these machines will be368programmed.369In this talk I will give an overview of some of the hardware trends, and370describe programming techniques using Partitioned Global Address Space371(PGAS)372languages. PGAS languages have emerged as a viable alternative to message373passing programming models for large-scale parallel machines and clusters.374They also offer an alternative to shared memory programming models (such as375threads and OpenMP) and the possibility of a single programming model that376will work well across a wide range of shared and distributed memory377platforms.378PGAS languages provide a shared memory abstraction with support for locality379through the user of distributed data types. The three most mature PGAS380languages (UPC, CAF and Titanium) offer a statically partitioned global381address space with a static SPMD control model, while languages emerging382from the DARPA HPCS program are more dynamic. I will describe these383languages as well as our experience using them in both numeric and384symbolic applications.}\mbox{}\vspace{6ex}385386387\par\noindent\end{document}388