62731399
NAS parallel benchmark results
The NAS (Numerical Aerodynamic Simulation) parallel benchmarks have been developed at NASA Ames Research Center to study the performance of parallel supercomputer. The eight benchmark problems are specified in a 'pencil and paper' fashion. The performance results of various systems using the NAS parallel benchmarks are presented. These results represent the best results that have been reported to the authors for the specific systems listed. They represent implementation efforts performed by personnel in both the NAS Applied Research Branch of NASA Ames Research Center and in other organizations.<<ETX>>
6270234
Spectral Relaxation for K-means Clustering
The popular K-means clustering partitions a data set by minimizing a sum-of-squares cost function. A coordinate descend method is then used to find local minima. In this paper we show that the minimization can be reformulated as a trace maximization problem associated with the Gram matrix of the data vectors. Furthermore, we show that a relaxed version of the trace maximization problem possesses global optimal solutions which can be obtained by computing a partial eigendecomposition of the Gram matrix, and the cluster assignment for each data vectors can be found by computing a pivoted QR decomposition of the eigenvector matrix. As a by-product we also derive a lower bound for the minimum of the sum-of-squares cost function.
17421545
Recent trends in the marketplace of high performance computing
In this paper we analyze major recent trends and changes in the High Performance Computing (HPC) market place. The introduction of vector computers started the area of 'Supercomputing'. The initial success of vector computers in the seventies was driven by raw performance. Massive parallel systems (MPP) became successful in the early nineties due to their better price/performance ratios, which was enabled by the attack of the 'killer-micros'. The success of microprocessor based on the shared memory concept (referred to as symmetric multiprocessors (SMP)) even for the very high-end systems, was the basis for the emerging cluster concepts in the early 2000s. Within the first half of this decade clusters of PC's and workstations have become the prevalent architecture for many HPC application areas on all ranges of performance. However, the Earth Simulator vector system demonstrated that many scientific applications could benefit greatly from other computer architectures. At the same time there is renewed broad interest in the scientific HPC community for new hardware architectures and new programming paradigms. The IBM BlueGene/L system is one early example of a shifting design focus for large-scale system. The DARPA HPCS program has the declared goal of building a Petaflops computer system by the end of the decade using novel computer architectures.
35264400
Parallel Efficiency of the Lanczos Method for Eigenvalue Problems
LBNL-42828 Parallel Efficiency of the Lanczos Method for Eigenvalue Problems ^ Kesheng Wu+and Horst Simon* Abstract Two of the commonly used versions of the Lanczos method for eigenvalues problems are the shift-and-invert Lanczos method and the restarted Lanczos method. In this talk, we will address two questions, is the shift-and-invert Lanczos method a viable option on massively parallel machines and which one is more appropriate for a given eigenvalue problem? Introduction T h i s talk is o n how to compute eigenvalues a n d eigenvectors of large sparse s y m m e t r i c matrices o n massively parallel machines. One of the the most c o m m o n l y used algorithms for this task is the Lanczos m e t h o d w h i c h projects the large eigenvalue p r o b l e m onto a low dimensional K r y l o v subspace [7, 10]. I n most cases, the K r y l o v subspace basis is built t h r o u g h a series of matrix-vector m u l t i p l i c a t i o n s , the whole Lanczos m e t h o d c a n be implemented w i t h a matrix-vector m u l t i p l i c a t i o n routine a n d a few simple vector operations. T h i s a l g o r i t h m is highly efficient on parallel machines a n d it is effective for c o m p u t i n g extreme a n d well separated eigenvalues. To compute the interior or not well-separated eigenvalues, the shift-and-invert Lanczos m e t h o d is one of the most effective methods. Since the eigenvalues of a m a t r i x A are related to the eigenvalues of (A — c r l ) by a simple relation X(A) = a + 1/X((A — c r l ) ) a n d the corresponding eigenvectors of A a n d (A — c r l ) are identical, the shift-and-invert scheme computes the extreme eigenvalues of (A — c r l ) a n d deduce the corresponding eigenvalues of A. W i t h appropriate choice of a, the extreme eigenvalues of (A — al)^ are well separated and can be easily computed. T h e shift-and-invert Lanczos m e t h o d needs to b u i l d a K r y l o v subspace basis of (A — c r l ) w h i c h is done by solving a series of linear systems involving the coefficient m a t r i x (A — a I). T h e linear systems need to be solved accurately a n d the only reliable means to accomplish this is by using a direct m e t h o d [5]. Because it is difficult to implement direct methods o n d i s t r i b u t e d parallel computers, efficient parallel i m p l e m e n t a t i o n has not been widely available u n t i l recently [1, 8]. T h i s talk w i l l present our s t u d y of the parallel efficiency of the shift-and-invert Lanczos m e t h o d using these newly available direct solvers. T h e study w i l l show that the shift-and-invert Lanczos m e t h o d is ' T h i s w o r k was s u p p o r t e d b y t h e D i r e c t o r , Office o f E n e r g y R e s e a r c h , Office o f L a b o r a t o r y P o l i c y a n d Infrastructure M a n a g e m e n t , of the U . S . D e p a r t m e n t of E n e r g y under C o n t r a c t N o . D E - A C 0 3 - 7 6 S F 0 0 0 9 8 . T h i s r e s e a r c h u s e d r e s o u r c e s o f t h e N a t i o n a l E n e r g y R e s e a r c h S c i e n t i f i c C o m p u t i n g C e n t e r , w h i c h is s u p p o r t e d b y t h e Office o f E n e r g y R e s e a r c h o f t h e U . S . D e p a r t m e n t o f E n e r g y . 'Lawrence Berkeley National Laboratory/NERSC, Berkeley, CA Email: {ksni, hdsimon}81bl.gov.
26191709
The Implementation of the U.S. High Performance Computing and Communications Program
This paper gives an overview of the federal High Performance Computing and Communication (HPCC) Program. This initiative involves the Defense Advanced Projects Agency (DARPA), the Department of Energy (DOE), the National Aeronautics and Space Administration (NASA), and the National Science Foundation (NSF). Its goal is to advance U.S. science and industrial competitiveness by supporting the development of teraops high performance systems, the software and algorithms required to render those massively parallel systems efficiently usable, and the Gigabit networks to make those machines accessible, as well as to broaden the base of computationally literate scientists. We outline the HPCC effort and the rationale underlying it, and give an overview of some of the “Grand Challenge” work under way at Argonne’s Mathematics and Computer Science Division, as well as the Grand Challenges addressed by NASA’s Computational Aerosciences program.
6041481
Parallel preconditioning and approximation inverses on the Connection Machine
The authors present a new approach to preconditioning for very large, sparse, non-symmetric, linear systems. It explicitly computes an approximate inverse to the original matrix that can be applied most efficiently for iterative methods on massively parallel machines. The algorithm and its implementation on the Connection Machine CM-2 are discussed in detail and supported by timings obtained from real problem data.<<ETX>>
34207468
Scientific Discovery and Simplicity of Method
3-Benzoyl-3-thiocyanatopropionic acid, alkyl esters are prepared by the reaction of a 3-benzoyl-3-halopropionic acid alkyl ester with an alkali metal thiocyanate. The products so produced exhibit antitubercular activity.
31930258
How Many Missing Answers Can Be Tolerated by Query Learners?
We consider the model of exact learning using an equivalence oracle and an incomplete membership oracle. In this model, a random subset of the learners membership queries is left unanswered. Our results are as follows. First, we analyze the obvious method for coping with missing answers: search exhaustively through all possible "answer patterns" associated with the unanswered queries. Thereafter, we present two specific concept classes that are efficiently learnable using an equivalence oracle and a (completely reliable) membership oracle, but are provably not polynomially learnable if the membership oracle becomes slightly incomplete. The first class will demonstrate that the aforementioned method of exhaustively searching through all possible answer patterns cannot be substantially improved in general (despite its apparent simplicity). The second class will demonstrate that the incomplete membership oracle can be rendered useless even if it leaves only a fraction 1/poly(n) of all queries unanswered. Finally, we present a learning algorithm for monotone DNF formulas that can cope with a relatively large fraction of missing answers (more than sixty percent), but is as efficient (in terms of run-time and number of queries) as the classical algorithm whose questions are always answered reliably.
20188177
Simulation of human verbal learning behavior
the eoinposition is or in not an ins:atl{'e of Arnohl 8el]oel/}}el,g>s so-ealhM "twelve-tone" system of l]ltb-:ieal eompositiol]. Wrilten ill a notation which modifies a notation for finite sequentia{ proces. ses developed /)y Kenneth It. lverso~:, che Mgori:hm in easily tra::slatatfle into most machine languages which allow processing of nlphanumerh: data. The decision process involved will be fully autolnatic when vharacter-recognitio~: maehiiws :hat "read" nlusi{'a/signs ape { mployed. A limited s::pply {}[ copies of lhe t)<~qter listed t>e]ow in available for distribution : The paper contains !he algorithm and a lengthy diseussi(m of issues r(lated to the synt'~c~i(~ properties of Schoenberg's system. A s s o c i a t i o n a l (' h a r a e t e r i s t i (: s o f ~I/()i'ds in T e x t S y s l (, m I)(~volopm(u~) (' o r p. , S a n t a M()l:i<l, (lalif. [i'cp(rl('d tilt; l,auPen B. I)oyle (t"et)iuiat'y 19(i2) An iuvestigation of the ten(teney {tf' words to eo..o(!e/iP in tl[li{,s of text (articles, Imragr,aphs, sentences) is continuing, with em-l)hasis on the eharaeteristies of strongly (o-oe(~urritlg op ":.tsso-elated" words. The ultimate chief.live of lho study i8 to eonfronl, litePalure searchers with usal}le representations (if text-derived associations which earl serve at least as automatically generated thesauri and at best as a.~sociative indexes. 'I'he most eonvelfient form for representing Such associations has been fotnid to lie di:> granmmtie or map-like {1!. Tile study is currently entering a new phase, in which the effect {m associations of varying the size and compost{ion of libraries is io be observed. For ihis purpose a PhiJco 2(}00 prograui is being written by which one ean flexibly deal with an unlimited number of libraries wifi0i: arc subsets of a given ~qiiastei" l i b r a r y " ; this avoids the necessity (if preparilig itew input for each rull on It different library. Library subsets to be processed can be specified either by control card or by programmed computation [2]. Further examples of the sort of study this program wil! facilitate are : (1) Automatic separation of homographs (e.g. in internatiolnal affairs "force" has a different meaning from "force" in physics; if a physics corptts can be automatically separated from one in international affairs, then homograph separation will oeetir in this ease). (2) Promotion of suppressed associations (i.e, two words wtiieh eo-oeeur …
5520100
The Theory of Problem Solving
It is now about fifteen years since the first computer programs were written and tested that used the method of heuristic search to solve problems. Dozens of such programs, some designed for specific task domains, others claiming various degrees of generality, have now been described in the literature, and many experiments with their performance have been reported and analysed. It is an appropriate time to ask what has been learned from these experiments about the general theory of problem solving, and to try to summarize the present state of that theory.
10043574
Scientific Model-Building as Search in Matrix Spaces
Many reported discovery systems build discrete models of hidden structure, properties, or processes in the diverse fields of biology, chemistry, and physics. We show that the search spaces underlying many well-known systems are remarkably similar when re-interpreted as search in matrix spaces. A small number of matrix types are used to represent the input data and output models. Most of the constraints can be represented as matrix constraints; most notably, conservation laws and their analogues can be represented as matrix equations. Typically, one or more matrix dimensions grow as these systems consider more complex models after simpler models fail, and we introduce a notation to express this. The novel framework of matrix-space search serves to unify previous systems and suggests how at least two of them can be integrated. Our analysis constitutes an advance toward a generalized account of model-building in science.