14,157 research outputs found
Dynamics of critical collapse
Critical collapse of a massless scalar field in spherical symmetry is
systematically studied. We combine numerical simulations and asymptotic
analysis, and synthesize critical collapse, spacetime singularities, and
complex science. First set of approximate analytic expressions near the center
are obtained. We observe that, near the center, the spacetime is nearly
conformally flat, the dynamics is not described by the Kasner solution, and the
Kreschmann scalar is proportional to r^(-5.30), where r is the areal radius.
These features are significantly different from those in black hole
singularities. It is speculated that the scalar field in critical collapse may
be a special standing wave.Comment: Title changed. 11 pages, 8 figures, 1 tabl
CapProNet: Deep Feature Learning via Orthogonal Projections onto Capsule Subspaces
In this paper, we formalize the idea behind capsule nets of using a capsule
vector rather than a neuron activation to predict the label of samples. To this
end, we propose to learn a group of capsule subspaces onto which an input
feature vector is projected. Then the lengths of resultant capsules are used to
score the probability of belonging to different classes. We train such a
Capsule Projection Network (CapProNet) by learning an orthogonal projection
matrix for each capsule subspace, and show that each capsule subspace is
updated until it contains input feature vectors corresponding to the associated
class. We will also show that the capsule projection can be viewed as
normalizing the multiple columns of the weight matrix simultaneously to form an
orthogonal basis, which makes it more effective in incorporating novel
components of input features to update capsule representations. In other words,
the capsule projection can be viewed as a multi-dimensional weight
normalization in capsule subspaces, where the conventional weight normalization
is simply a special case of the capsule projection onto 1D lines. Only a small
negligible computing overhead is incurred to train the network in
low-dimensional capsule subspaces or through an alternative hyper-power
iteration to estimate the normalization matrix. Experiment results on image
datasets show the presented model can greatly improve the performance of the
state-of-the-art ResNet backbones by and that of the Densenet by
respectively at the same level of computing and memory expenses. The
CapProNet establishes the competitive state-of-the-art performance for the
family of capsule nets by significantly reducing test errors on the benchmark
datasets.Comment: Liheng Zhang, Marzieh Edraki, Guo-Jun Qi. CapProNet: Deep Feature
Learning via Orthogonal Projections onto Capsule Subspaces, in Proccedings of
Thirty-second Conference on Neural Information Processing Systems (NIPS
2018), Palais des Congr\`es de Montr\'eal, Montr\'eal, Canda, December 3-8,
201
Revisit of directed flow in relativistic heavy-ion collisions from a multiphase transport model
We have revisited several interesting questions on how the rapidity-odd
directed flow is developed in relativistic Au+Au collisions at
= 200 and 39 GeV based on a multiphase transport model. As the
partonic phase evolves with time, the slope of the parton directed flow at
midrapidity region changes from negative to positive as a result of the later
dynamics at 200 GeV, while it remains negative at 39 GeV due to the shorter
life time of the partonic phase. The directed flow splitting for various quark
species due to their different initial eccentricities is observed at 39 GeV,
while the splitting is very small at 200 GeV. From a dynamical coalescence
algorithm with Wigner functions, we found that the directed flow of hadrons is
a result of competition between the coalescence in momentum and coordinate
space as well as further modifications by the hadronic rescatterings.Comment: 8 pages, 8 figures, version after major revisio
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