ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation

Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincar\'e invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli (1993) generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a "warm" dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.Comment: Code and illustration movies available at: http://www.vlasix.org/index.php?n=Main.ColDICE - Article submitted to Journal of Computational Physic

Googling the brain: discovering hierarchical and asymmetric network structures, with applications in neuroscience

Hierarchical organisation is a common feature of many directed networks arising in nature and technology. For example, a well-defined message-passing framework based on managerial status typically exists in a business organisation. However, in many real-world networks such patterns of hierarchy are unlikely to be quite so transparent. Due to the nature in which empirical data is collated the nodes will often be ordered so as to obscure any underlying structure. In addition, the possibility of even a small number of links violating any overall “chain of command” makes the determination of such structures extremely challenging. Here we address the issue of how to reorder a directed network in order to reveal this type of hierarchy. In doing so we also look at the task of quantifying the level of hierarchy, given a particular node ordering. We look at a variety of approaches. Using ideas from the graph Laplacian literature, we show that a relevant discrete optimization problem leads to a natural hierarchical node ranking. We also show that this ranking arises via a maximum likelihood problem associated with a new range-dependent hierarchical random graph model. This random graph insight allows us to compute a likelihood ratio that quantifies the overall tendency for a given network to be hierarchical. We also develop a generalization of this node ordering algorithm based on the combinatorics of directed walks. In passing, we note that Google’s PageRank algorithm tackles a closely related problem, and may also be motivated from a combinatoric, walk-counting viewpoint. We illustrate the performance of the resulting algorithms on synthetic network data, and on a real-world network from neuroscience where results may be validated biologically

Pauses and the temporal structure of speech

Natural-sounding speech synthesis requires close control over the temporal structure of the speech flow. This includes a full predictive scheme for the durational structure and in particuliar the prolongation of final syllables of lexemes as well as for the pausal structure in the utterance. In this chapter, a description of the temporal structure and the summary of the numerous factors that modify it are presented. In the second part, predictive schemes for the temporal structure of speech ("performance structures") are introduced, and their potential for characterising the overall prosodic structure of speech is demonstrated

Hypergraph Partitioning in the Cloud

The thesis investigates the partitioning and load balancing problem which has many applications in High Performance Computing (HPC). The application to be partitioned is described with a graph or hypergraph. The latter is of greater interest as hypergraphs, compared to graphs, have a more general structure and can be used to model more complex relationships between groups of objects such as non-symmetric dependencies. Optimal graph and hypergraph partitioning is known to be NP-Hard but good polynomial time heuristic algorithms have been proposed. In this thesis, we propose two multi-level hypergraph partitioning algorithms. The algorithms are based on rough set clustering techniques. The first algorithm, which is a serial algorithm, obtains high quality partitionings and improves the partitioning cut by up to 71\% compared to the state-of-the-art serial hypergraph partitioning algorithms. Furthermore, the capacity of serial algorithms is limited due to the rapid growth of problem sizes of distributed applications. Consequently, we also propose a parallel hypergraph partitioning algorithm. Considering the generality of the hypergraph model, designing a parallel algorithm is difficult and the available parallel hypergraph algorithms offer less scalability compared to their graph counterparts. The issue is twofold: the parallel algorithm and the complexity of the hypergraph structure. Our parallel algorithm provides a trade-off between global and local vertex clustering decisions. By employing novel techniques and approaches, our algorithm achieves better scalability than the state-of-the-art parallel hypergraph partitioner in the Zoltan tool on a set of benchmarks, especially ones with irregular structure. Furthermore, recent advances in cloud computing and the services they provide have led to a trend in moving HPC and large scale distributed applications into the cloud. Despite its advantages, some aspects of the cloud, such as limited network resources, present a challenge to running communication-intensive applications and make them non-scalable in the cloud. While hypergraph partitioning is proposed as a solution for decreasing the communication overhead within parallel distributed applications, it can also offer advantages for running these applications in the cloud. The partitioning is usually done as a pre-processing step before running the parallel application. As parallel hypergraph partitioning itself is a communication-intensive operation, running it in the cloud is hard and suffers from poor scalability. The thesis also investigates the scalability of parallel hypergraph partitioning algorithms in the cloud, the challenges they present, and proposes solutions to improve the cost/performance ratio for running the partitioning problem in the cloud. Our algorithms are implemented as a new hypergraph partitioning package within Zoltan. It is an open source Linux-based toolkit for parallel partitioning, load balancing and data-management designed at Sandia National Labs. The algorithms are known as FEHG and PFEHG algorithms

The effect of an optical network on-chip on the performance of chip multiprocessors

Optical networks on-chip (ONoC) have been proposed to reduce power consumption and increase bandwidth density in high performance chip multiprocessors (CMP), compared to electrical NoCs. However, as buffering in an ONoC is not viable, the end-to-end message path needs to be acquired in advance during which the message is buffered at the network ingress. This waiting latency is therefore a combination of path setup latency and contention and forms a significant part of the total message latency. Many proposed ONoCs, such as Single Writer, Multiple Reader (SWMR), avoid path setup latency at the expense of increased optical components. In contrast, this thesis investigates a simple circuit-switched ONoC with lower component count where nodes need to request a channel before transmission. To hide the path setup latency, a coherence-based message predictor is proposed, to setup circuits before message arrival. Firstly, the effect of latency and bandwidth on application performance is thoroughly investigated using full-system simulations of shared memory CMPs. It is shown that the latency of an ideal NoC affects the CMP performance more than the NoC bandwidth. Increasing the number of wavelengths per channel decreases the serialisation latency and improves the performance of both ONoC types. With 2 or more wavelengths modulating at 25 Gbit=s , the ONoCs will outperform a conventional electrical mesh (maximal speedup of 20%). The SWMR ONoC outperforms the circuit-switched ONoC. Next coherence-based prediction techniques are proposed to reduce the waiting latency. The ideal coherence-based predictor reduces the waiting latency by 42%. A more streamlined predictor (smaller than a L1 cache) reduces the waiting latency by 31%. Without prediction, the message latency in the circuit-switched ONoC is 11% larger than in the SWMR ONoC. Applying the realistic predictor reverses this: the message latency in the SWMR ONoC is now 18% larger than the predictive circuitswitched ONoC

Parallel computation on sparse networks of processors

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