Publications

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The objectives of this presentation are: (1) Learn how to partition a problem using Zoltan; (2) Understand the following (a) Basic process of partitioning with Zoltan, (b) Setting Zoltan parameters, (c) Registering query functions, (d) Writing query functions, (e) Zoltan-LB-Partition and its input/output; and (3) Be able to integrate Zoltan into your own applications.

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We fabricated a split-gate defined point contact in a double gate enhancement mode Si-MOS device, and implanted Sb donor atoms using a self-aligned process. E-beam lithography in combination with a timed implant gives us excellent control over the placement of dopant atoms, and acts as a stepping stone to focused ion beam implantation of single donors. Our approach allows us considerable latitude in experimental design in-situ. We have identified two resonance conditions in the point contact conductance as a function of split gate voltage. Using tunneling spectroscopy, we probed their electronic structure as a function of temperature and magnetic field. We also determine the capacitive coupling between the resonant feature and several gates. Comparison between experimental values and extensive quasi-classical simulations constrain the location and energy of the resonant level. We discuss our results and how they may apply to resonant tunneling through a single donor.

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The cubed sphere geometry, obtained by inscribing a cube in a sphere and mapping points between the two surfaces using a gnomonic (central) projection, is commonly used in atmospheric models because it is free of polar singularities and is well-suited for parallel computing. Global meshes on the cubed-sphere typically project uniform (square) grids from each face of the cube onto the sphere, and if refinement is desired then it is done with non-conforming meshes - overlaying the area of interest with a finer uniform mesh, which introduces so-called hanging nodes on edges along the boundary of the fine resolution area. An alternate technique is to tile each face of the cube with quadrilaterals without requiring the quads to be rectangular. These meshes allow for refinement in areas of interest with a conforming mesh, providing a smoother transition between high and low resolution portions of the grid than non-conforming refinement. The conforming meshes are demonstrated in HOMME, NCAR's High Order Method Modeling Environment, where two modifications have been made: the dependence on uniform meshes has been removed, and the ability to read arbitrary quadrilateral meshes from a previously-generated file has been added. Numerical results come from a conservative spectral element method modeling a selection of the standard shallow water test cases.

Periodic, coordinated, checkpointing to disk is the most prevalent fault tolerance method used in modern large-scale, capability class, high-performance computing (HPC) systems. Previous work has shown that as the system grows in size, the inherent synchronization of coordinated checkpoint/restart (CR) limits application scalability; at large node counts the application spends most of its time checkpointing instead of executing useful work. Furthermore, a single component failure forces an application restart from the last correct checkpoint. Suggested alternatives to coordinated CR include uncoordinated CR with message logging, redundant computation, and RAID-inspired, in-memory distributed checkpointing schemes. Each of these alternatives have differing overheads that are dependent on both the scale and communication characteristics of the application. In this work, using the Structural Simulation Toolkit (SST) simulator, we compare the performance characteristics of each of these resilience methods for a number of HPC application patterns on a number of proposed exascale machines. The result of this work provides valuable guidance on the most efficient resilience methods for exascale systems.

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Trilinos is an object-oriented software framework to enabled the solution of large-scale, complex multiphysics engineering and scientific problems. Different Trilinos packages build on each other to create a stack providing the necessary capability: (1) Non-linear solver; (2) Linear solver/preconditioner; (3) Distributed linear algebra; and (4) Local linear algebra.

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Palacios is a new open-source VMM under development at Northwestern University and the University of New Mexico that enables applications executing in a virtualized environment to achieve scalable high performance on large machines. Palacios functions as a modularized extension to Kitten, a high performance operating system being developed at Sandia National Laboratories to support large-scale supercomputing applications. Together, Palacios and Kitten provide a thin layer over the hardware to support full-featured virtualized environments alongside Kitten's lightweight native environment. Palacios supports existing, unmodified applications and operating systems by using the hardware virtualization technologies in recent AMD and Intel processors. Additionally, Palacios leverages Kitten's simple memory management scheme to enable low-overhead pass-through of native devices to a virtualized environment. We describe the design, implementation, and integration of Palacios and Kitten. Our benchmarks show that Palacios provides near native (within 5%), scalable performance for virtualized environments running important parallel applications. This new architecture provides an incremental path for applications to use supercomputers, running specialized lightweight host operating systems, that is not significantly performance-compromised. © 2010 IEEE.

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Enumerating triangles (3-cycles) in graphs is a kernel operation for social network analysis. For example, many community detection methods depend upon finding common neighbors of two related entities. We consider Cohen's simple and elegant solution for listing triangles: give each node a 'bucket.' Place each edge into the bucket of its endpoint of lowest degree, breaking ties consistently. Each node then checks each pair of edges in its bucket, testing for the adjacency that would complete that triangle. Cohen presents an informal argument that his algorithm should run well on real graphs. We formalize this argument by providing an analysis for the expected running time on a class of random graphs, including power law graphs. We consider a rigorously defined method for generating a random simple graph, the erased configuration model (ECM). In the ECM each node draws a degree independently from a marginal degree distribution, endpoints pair randomly, and we erase self loops and multiedges. If the marginal degree distribution has a finite second moment, it follows immediately that Cohen's algorithm runs in expected linear time. Furthermore, it can still run in expected linear time even when the degree distribution has such a heavy tail that the second moment is not finite. We prove that Cohen's algorithm runs in expected linear time when the marginal degree distribution has finite 4/3 moment and no vertex has degree larger than {radical}n. In fact we give the precise asymptotic value of the expected number of edge pairs per bucket. A finite 4/3 moment is required; if it is unbounded, then so is the number of pairs. The marginal degree distribution of a power law graph has bounded 4/3 moment when its exponent {alpha} is more than 7/3. Thus for this class of power law graphs, with degree at most {radical}n, Cohen's algorithm runs in expected linear time. This is precisely the value of {alpha} for which the clustering coefficient tends to zero asymptotically, and it is in the range that is relevant for the degree distribution of the World-Wide Web.

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