There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

The Bioconductor project is an initiative for the collaborative creation of extensible software for computational biology and bioinformatics. The goals of the project include: fostering collaborative development and widespread use of innovative software, reducing barriers to entry into interdisciplinary scientific research, and promoting the achievement of remote reproducibility of research results. We describe details of our aims and methods, identify current challenges, compare Bioconductor to other open bioinformatics projects, and provide working examples.

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Bioconductor: open software development for computational biology and bioinformatics

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N \geq 3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

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Tensor Decompositions and Applications

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

A large number of MPI implementations are currently available, each of which emphasize different aspects of high-performance computing or are intended to solve a specific research problem. The result is a myriad of incompatible MPI implementations, all of which require separate installation, and the combination of which present significant logistical challenges for end users. Building upon prior research, and influenced by experience gained from the code bases of the LAM/MPI, LA-MPI, and FT-MPI projects, Open MPI is an all-new, production-quality MPI-2 implementation that is fundamentally centered around component concepts. Open MPI provides a unique combination of novel features previously unavailable in an open-source, production-quality implementation of MPI. Its component architecture provides both a stable platform for third-party research as well as enabling the run-time composition of independent software add-ons. This paper presents a high-level overview the goals, design, and implementation of Open MPI.

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Open MPI: Goals, Concept, and Design of a Next Generation MPI Implementation

Foreword. Preface. I User Guide. 1. Introduction. Some Graph Terminology. Graph Concepts. Vertex and Edge Descriptors. Property Maps. Graph Traversa. Graph Construction and Modification Algorithm Visitors. Graph Classes and Adaptors. Graph Classes. Graph Adaptors. Generic Graph Algorithms. The Topological Sort Generic Algorithm. The Depth-First Search Generic Algorithm. 2.Generic Programming in C++. Introduction. Polymorphism in Object-Oriented Programming. Polymorphism in Generic Programming. Comparison of GP and OOP. Generic Programming and the STL. Concepts and Models. Sets of Requirements. Example: InputIterator. Associated Types and Traits Classes. Associated Types Needed in Function Template. Typedefs Nested in Classes. Definition of a Traits Class. Partial Specialization. Tag Dispatching. Concept Checking. Concept-Checking Classes. Concept Archetypes. The Boost Namespace. Classes. Koenig Lookup. Named Function Parameters. 3. A BGL Tutorial. File Dependencies. Graph Setup. Compilation Order. Topological Sort via DFS. Marking Vertices Using External Properties. Accessing Adjacent Vertices. Traversing All the Vertices. Cyclic Dependencies. Toward a Generic DFS: Visitors. Graph Setup: Internal Properties. Compilation Time. A Generic Topological Sort and DFS. Parallel Compilation Time. Summary. 4. Basic Graph Algorithms. Breadth-First Search. Definitions. Six Degrees of Kevin Bacon. Depth-First Search. Definitions. Finding Loops in Program-Control-Flow Graphs. 5. Shortest-Paths Problems. Definitions. Internet Routing. Bellman-Ford and Distance Vector Routing. Dijkstra and Link-State Routing. 6. Minimum-Spanning-Tree Problem. Definitions. Telephone Network Planning. Kruskal's Algorithm. Prim's Algorithm. 7. Connected Components. Definitions. Connected Components and Internet Connectivity. Strongly Connected Components and Web Page Links. 8. Maximum Flow. Definitions. Edge Connectivity. 9. Implicit Graphs: A Knight's Tour. Knight's Jumps as a Graph. Backtracking Graph Search. Warnsdorff's Heuristic. 10. Interfacing with Other Graph Libraries. Using BGL Topological Sort with a LEDA Graph. Using BGL Topological Sort with a SGB Graph. Implementing Graph Adaptors. 11. Performance Guidelines. Graph Class Comparisons. The Results and Discussion. Conclusion. II Reference Manual. 12. BGL Concepts. Graph Traversal Concepts. Undirected Graphs. Graph. IncidenceGraph. BidirectionalGraph. AdjacencyGraph. VertexListGraph. EdgeListGraph. AdjacencyMatrix. Graph Modification Concepts. VertexMutableGraph. EdgeMutableGraph. MutableIncidenceGraph. MutableBidirectionalGraph. MutableEdgeListGraph. PropertyGraph. VertexMutablePropertyGraph. EdgeMutablePropertyGraph. Visitor Concepts. BFSVisitor. DFSVisitor. DijkstraVisitor. BellmanFordVisitor. 13. BGL Algorithms. Overview. Basic Algorithms. breadth_first_search. breadth_first_visit. depth_first_search. depth_first_visit. topological_sort. Shortest-Path Algorithms. dijkstra_shortest_paths. bellman_ford_shortest_paths. johnson_all_pairs_shortest_paths. Minimum-Spanning-Tree Algorithms. kruskal_minimum_spanning_tree. prim_minimum_spanning_tree. Static Connected Components. connected_components. strong_components. Incremental Connected Components. initialize_incremental_components. incremental_components. same_component. component_index. Maximum-Flow Algorithms. edmunds_karp_max_flow. push_relabel_max_flow. 14. BGL Classes. Graph Classes. adjacency_list. adjacency_matrix. Auxiliary Classes. graph_traits. adjacency_list_traits. adjacency_matrix_traits. property_map. property. Graph Adaptors. edge_list. reverse_graph. filtered_graph. SGB GraphPointer. LEDA GRAPH . std::vector . 15. Property Map Library. Property Map Concepts. ReadablePropertyMap. WritablePropertyMap. ReadWritePropertyMap. LvaluePropertyMap. Property Map Classes. property_traits. iterator_property_map. Property Tags. Creating Your Own Property Maps. Property Maps for Stanford GraphBase. A Property Map Implemented with std::map. 16 Auxiliary Concepts, Classes, and Functions. Buffer. ColorValue. MultiPassInputIterator. Monoid. mutable queue. Disjoint Sets. disjoint_sets. find_with_path_halving. find_with_full_path_compression. tie. graph_property_iter_range. Bibliography. Index. 0201729148T12172001

The Boost graph library : user guide and reference manual

L. SUSAN BLACKFORD Myricom, Inc. JAMES DEMMEL University of California, Berkeley JACK DONGARRA The University of Tennessee IAIN DUFF Rutherford Appleton Laboratory and CERFACS SVEN HAMMARLING Numerical Algorithms Group, Ltd. GREG HENRY Intel Corporation MICHAEL HEROUX Sandia National Laboratories LINDA KAUFMAN William Patterson University ANDREW LUMSDAINE Indiana University ANTOINE PETITET Sun Microsystems ROLDAN POZO National Institute of Standards and Technology KARIN REMINGTON The Center for Advancement of Genomics and R. CLINT WHALEY Florida State University

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An Updated Set of Basic Linear Algebra Subprograms (BLAS)

Plenoptic cameras, constructed with internal microlens arrays, focus those microlenses at infinity in order to sample the 4D radiance directly at the microlenses. The consequent assumption is that each microlens image is completely defocused with respect to to the image created by the main camera lens and the outside object. As a result, only a single pixel in the final image can be rendered from it, resulting in disappointingly low resolution. In this paper, we present a new approach to lightfield capture and image rendering that interprets the microlens array as an imaging system focused on the focal plane of the main camera lens. This approach captures a lightfield with significantly higher spatial resolution than the traditional approach, allowing us to render high resolution images that meet the expectations of modern photographers. Although the new approach samples the lightfield with reduced angular density, analysis and experimental results demonstrate that there is sufficient parallax to completely support lightfield manipulation algorithms such as refocusing and novel views

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The focused plenoptic camera

Graph algorithms are becoming increasingly important for solving many problems in scientific computing, data mining and other domains. As these problems grow in scale, parallel computing resources are required to meet their computational and memory requirements. Unfortunately, the algorithms, software, and hardware that have worked well for developing mainstream parallel scientific applications are not necessarily effective for large-scale graph problems. In this paper we present the inter-relationships between graph problems, software, and parallel hardware in the current state of the art and discuss how those issues present inherent challenges in solving large-scale graph problems. The range of these challenges suggests a research agenda for the development of scalable high-performance software for graph problems.

https://cfwebprod.sandia.gov/cfdocs/CompResearch/docs/graphs-and-machines.pdf

Andrew Lumsdaine

Papers

Open MPI: Goals, Concept, and Design of a Next Generation MPI Implementation

The Boost graph library : user guide and reference manual

An Updated Set of Basic Linear Algebra Subprograms (BLAS)

The focused plenoptic camera

Challenges in parallel graph processing