Abstract A novel parallel simulation algorithm on the GPU, implemented in CUDA and C++, is presented for the simulation of Brownian particles that display excluded volume repulsion and interact with long and short range forces. When an explicit Euler–Maruyama integration step is performed to take into account the pairwise forces and Brownian motion, particle overlaps can appear. The excluded volume property brings up the need for correcting these overlaps as they happen, since predicting them is not feasible due to the random displacement of Brownian particles. The proposed solution handles, at each time step, a Delaunay triangulation of the particle positions because it allows us to efficiently solve overlaps between particles by checking just their neighborhood. The algorithm starts by generating a periodic Delaunay triangulation of the particle initial positions on CPU, but after that the triangulation is always kept on GPU memory. We used a parallel edge-flip implementation to keep the triangulation updated during each time step, checking previously that the triangulation was not rendered invalid due to the particle displacements. We designed and implemented an exact long range force simulation with an all-pairs N -body simulation, tiling the particle interaction computations based on the warp size of the target device architecture. The resulting implementation was validated with two models of active colloidal particles, also showing a speedup of up to two orders of magnitude when compared to a sequential implementation. A short range forces simulation using Verlet lists for neighborhood handling was also developed and validated, showing similar performance improvements.
Finally, for overlap correction, Strating @cite_8 describes a brute-force sequential algorithm that checks all pairs of bodies for possible overlaps and corrects them following equation ). The algorithm may need to iterate an unbounded number of times at each time step because some corrections may generate new overlaps with neighboring particles.
@cite_8
2010676632 2962744241 2109323956 2950813619
We propose an algorithm which combines the discriminative information from depth images as well as from 3D joint positions to achieve high action recognition accuracy. To avoid the suppression of subtle discriminative information and also to handle local occlusions, we compute a vector of many independent local features. Each feature encodes spatiotemporal variations of depth and depth gradients at a specific space-time location in the action volume. Moreover, we encode the dominant skeleton movements by computing a local 3D joint position difference histogram. For each joint, we compute a 3D space-time motion volume which we use as an importance indicator and incorporate in the feature vector for improved action discrimination. To retain only the discriminant features, we train a random decision forest (RDF). The proposed algorithm is evaluated on three standard datasets and compared with nine state-of-the-art algorithms. Experimental results show that, on the average, the proposed algorithm outperform all other algorithms in accuracy and have a processing speed of over 112 frames second. We present a novel divide-and-conquer bijective graph matching algorithm.The algorithm is fully parallelizable, and scales to match "big data" graphs.We demonstrate the effectiveness of the algorithm by matching DTMRI human connectomes. We present a parallelized bijective graph matching algorithm that leverages seeds and is designed to match very large graphs. Our algorithm combines spectral graph embedding with existing state-of-the-art seeded graph matching procedures. We justify our approach by proving that modestly correlated, large stochastic block model random graphs are correctly matched utilizing very few seeds through our divide-and-conquer procedure. We also demonstrate the effectiveness of our approach in matching very large graphs in simulated and real data examples, showing up to a factor of 8 improvement in runtime with minimal sacrifice in accuracy. We propose a novel algorithm to register multiple 3D point sets within a common reference frame using a manifold optimization approach. The point sets are obtained with multiple laser scanners or a mobile scanner. Unlike most prior algorithms, our approach performs an explicit optimization on the manifold of rotations, allowing us to formulate the registration problem as an unconstrained minimization on a constrained manifold. This approach exploits the Lie group structure of SO 3 and the simple representation of its associated Lie algebra so 3 in terms of R3. Our contributions are threefold. We present a new analytic method based on singular value decompositions that yields a closed-form solution for simultaneous multiview registration in the noise-free scenario. Secondly, we use this method to derive a good initial estimate of a solution in the noise-free case. This initialization step may be of use in any general iterative scheme. Finally, we present an iterative scheme based on Newton's method on SO 3 that has locally quadratic convergence. We demonstrate the efficacy of our scheme on scan data taken both from the Digital Michelangelo project and from scans extracted from models, and compare it to some of the other well known schemes for multiview registration. In all cases, our algorithm converges much faster than the other approaches, (in some cases orders of magnitude faster), and generates consistently higher quality registrations. In this work, we use algebraic methods for studying distance computation and subgraph detection tasks in the congested clique model. Specifically, we adapt parallel matrix multiplication implementations to the congested clique, obtaining an @math round matrix multiplication algorithm, where @math is the exponent of matrix multiplication. In conjunction with known techniques from centralised algorithmics, this gives significant improvements over previous best upper bounds in the congested clique model. The highlight results include: -- triangle and 4-cycle counting in @math rounds, improving upon the @math triangle detection algorithm of [DISC 2012], -- a @math -approximation of all-pairs shortest paths in @math rounds, improving upon the @math -round @math -approximation algorithm of Nanongkai [STOC 2014], and -- computing the girth in @math rounds, which is the first non-trivial solution in this model. In addition, we present a novel constant-round combinatorial algorithm for detecting 4-cycles.