The Clumping Transition in Niche Competition: a Robust Critical Phenomenon

We show analytically and numerically that the appearance of lumps and gaps in the distribution of n competing species along a niche axis is a robust phenomenon whenever the finiteness of the niche space is taken into account. In this case depending if the niche width of the species $\sigma$ is above or below a threshold $\sigma_c$, which for large n coincides with 2/n, there are two different regimes. For $\sigma > sigma_c$ the lumpy pattern emerges directly from the dominant eigenvector of the competition matrix because its corresponding eigenvalue becomes negative. For $\sigma </- sigma_c$ the lumpy pattern disappears. Furthermore, this clumping transition exhibits critical slowing down as $\sigma$ is approached from above. We also find that the number of lumps of species vs. $\sigma$ displays a stair-step structure. The positions of these steps are distributed according to a power-law. It is thus straightforward to predict the number of groups that can be packed along a niche axis and it coincides with field measurements for a wide range of the model parameters.Comment: 16 pages, 7 figures; http://iopscience.iop.org/1742-5468/2010/05/P0500

On the eigenvalues of distance powers of circuits

Taking the d-th distance power of a graph, one adds edges between all pairs of vertices of that graph whose distance is at most d. It is shown that only the numbers -3, -2, -1, 0, 1, 2d can be integer eigenvalues of a circuit distance power. Moreover, their respective multiplicities are determined and explicit constructions for corresponding eigenspace bases containing only vectors with entries -1, 0, 1 are given.Comment: 14 page

Hierarchical Parallel Matrix Multiplication on Large-Scale Distributed Memory Platforms

Matrix multiplication is a very important computation kernel both in its own right as a building block of many scientific applications and as a popular representative for other scientific applications. Cannon algorithm which dates back to 1969 was the first efficient algorithm for parallel matrix multiplication providing theoretically optimal communication cost. However this algorithm requires a square number of processors. In the mid 1990s, the SUMMA algorithm was introduced. SUMMA overcomes the shortcomings of Cannon algorithm as it can be used on a non-square number of processors as well. Since then the number of processors in HPC platforms has increased by two orders of magnitude making the contribution of communication in the overall execution time more significant. Therefore, the state of the art parallel matrix multiplication algorithms should be revisited to reduce the communication cost further. This paper introduces a new parallel matrix multiplication algorithm, Hierarchical SUMMA (HSUMMA), which is a redesign of SUMMA. Our algorithm reduces the communication cost of SUMMA by introducing a two-level virtual hierarchy into the two-dimensional arrangement of processors. Experiments on an IBM BlueGene-P demonstrate the reduction of communication cost up to 2.08 times on 2048 cores and up to 5.89 times on 16384 cores.Comment: 9 page

Activity-conditioned continuous human pose estimation for performance analysis of athletes using the example of swimming

In this paper we consider the problem of human pose estimation in real-world videos of swimmers. Swimming channels allow filming swimmers simultaneously above and below the water surface with a single stationary camera. These recordings can be used to quantitatively assess the athletes' performance. The quantitative evaluation, so far, requires manual annotations of body parts in each video frame. We therefore apply the concept of CNNs in order to automatically infer the required pose information. Starting with an off-the-shelf architecture, we develop extensions to leverage activity information - in our case the swimming style of an athlete - and the continuous nature of the video recordings. Our main contributions are threefold: (a) We apply and evaluate a fine-tuned Convolutional Pose Machine architecture as a baseline in our very challenging aquatic environment and discuss its error modes, (b) we propose an extension to input swimming style information into the fully convolutional architecture and (c) modify the architecture for continuous pose estimation in videos. With these additions we achieve reliable pose estimates with up to +16% more correct body joint detections compared to the baseline architecture.Comment: 10 pages, 9 figures, accepted at WACV 201

Modeling 1D distributed-memory dense kernels for an asynchronous multifrontal sparse solver

To solve sparse systems of linear equations, multifrontal methods rely on dense partial LU decompositions of so-called frontal matrices; we consider a parallel asynchronous setting in which several frontal matrices can be factored simultaneously. In this context, to address performance and scalability issues of acyclic pipelined asynchronous factorization kernels, we study models to revisit properties of left and right-looking variants of partial $LU$ decompositions, study the use of several levels of blocking, before focusing on communication issues. The general purpose sparse solver MUMPS has been modified to implement the proposed algorithms and confirm the properties demonstrated by the models