8,583 research outputs found
The fully connected N-dimensional skeleton: probing the evolution of the cosmic web
A method to compute the full hierarchy of the critical subsets of a density
field is presented. It is based on a watershed technique and uses a probability
propagation scheme to improve the quality of the segmentation by circumventing
the discreteness of the sampling. It can be applied within spaces of arbitrary
dimensions and geometry. This recursive segmentation of space yields, for a
-dimensional space, a succession of -dimensional subspaces that
fully characterize the topology of the density field. The final 1D manifold of
the hierarchy is the fully connected network of the primary critical lines of
the field : the skeleton. It corresponds to the subset of lines linking maxima
to saddle points, and provides a definition of the filaments that compose the
cosmic web as a precise physical object, which makes it possible to compute any
of its properties such as its length, curvature, connectivity etc... When the
skeleton extraction is applied to initial conditions of cosmological N-body
simulations and their present day non linear counterparts, it is shown that the
time evolution of the cosmic web, as traced by the skeleton, is well accounted
for by the Zel'dovich approximation. Comparing this skeleton to the initial
skeleton undergoing the Zel'dovich mapping shows that two effects are competing
during the formation of the cosmic web: a general dilation of the larger
filaments that is captured by a simple deformation of the skeleton of the
initial conditions on the one hand, and the shrinking, fusion and disappearance
of the more numerous smaller filaments on the other hand. Other applications of
the N dimensional skeleton and its peak patch hierarchy are discussed.Comment: Accepted for publication in MNRA
Geometry-Oblivious FMM for Compressing Dense SPD Matrices
We present GOFMM (geometry-oblivious FMM), a novel method that creates a
hierarchical low-rank approximation, "compression," of an arbitrary dense
symmetric positive definite (SPD) matrix. For many applications, GOFMM enables
an approximate matrix-vector multiplication in or even time,
where is the matrix size. Compression requires storage and work.
In general, our scheme belongs to the family of hierarchical matrix
approximation methods. In particular, it generalizes the fast multipole method
(FMM) to a purely algebraic setting by only requiring the ability to sample
matrix entries. Neither geometric information (i.e., point coordinates) nor
knowledge of how the matrix entries have been generated is required, thus the
term "geometry-oblivious." Also, we introduce a shared-memory parallel scheme
for hierarchical matrix computations that reduces synchronization barriers. We
present results on the Intel Knights Landing and Haswell architectures, and on
the NVIDIA Pascal architecture for a variety of matrices.Comment: 13 pages, accepted by SC'1
FullSWOF_Paral: Comparison of two parallelization strategies (MPI and SKELGIS) on a software designed for hydrology applications
In this paper, we perform a comparison of two approaches for the
parallelization of an existing, free software, FullSWOF 2D (http://www.
univ-orleans.fr/mapmo/soft/FullSWOF/ that solves shallow water equations for
applications in hydrology) based on a domain decomposition strategy. The first
approach is based on the classical MPI library while the second approach uses
Parallel Algorithmic Skeletons and more precisely a library named SkelGIS
(Skeletons for Geographical Information Systems). The first results presented
in this article show that the two approaches are similar in terms of
performance and scalability. The two implementation strategies are however very
different and we discuss the advantages of each one.Comment: 27 page
Richly Activated Graph Convolutional Network for Action Recognition with Incomplete Skeletons
Current methods for skeleton-based human action recognition usually work with
completely observed skeletons. However, in real scenarios, it is prone to
capture incomplete and noisy skeletons, which will deteriorate the performance
of traditional models. To enhance the robustness of action recognition models
to incomplete skeletons, we propose a multi-stream graph convolutional network
(GCN) for exploring sufficient discriminative features distributed over all
skeleton joints. Here, each stream of the network is only responsible for
learning features from currently unactivated joints, which are distinguished by
the class activation maps (CAM) obtained by preceding streams, so that the
activated joints of the proposed method are obviously more than traditional
methods. Thus, the proposed method is termed richly activated GCN (RA-GCN),
where the richly discovered features will improve the robustness of the model.
Compared to the state-of-the-art methods, the RA-GCN achieves comparable
performance on the NTU RGB+D dataset. Moreover, on a synthetic occlusion
dataset, the performance deterioration can be alleviated by the RA-GCN
significantly.Comment: Accepted by ICIP 2019, 5 pages, 3 figures, 3 table
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