3,229 research outputs found
Moduli of Continuity for Viscosity Solutions
In this paper, we investigate the moduli of continuity for viscosity
solutions of a wide class of nonsingular quasilinear evolution equations and
also for the level set mean curvature flow, which is an example of singular
degenerate equations. We prove that the modulus of continuity is a viscosity
subsolution of some one dimensional equation. This work extends B. Andrews'
recent result on moduli of continuity for smooth spatially periodic solutions.Comment: 8 page
Jet magnetically accelerated from disk-corona around a rotating black hole
A jet acceleration model for extracting energy from disk-corona surrounding a
rotating black hole is proposed. In the disk-corona scenario, we obtain the
ratio of the power dissipated in the corona to the total for such disk-corona
system by solving the disk dynamics equations. The analytical expression of the
jet power is derived based on the electronic circuit theory of the
magnetosphere. It is shown that jet power increases with the increasing black
hole (BH) spin, and concentrates in the inner region of the disk-corona. In
addition, we use a sample consisting of 37 radio loud quasars to explore their
jet production mechanism, and show that our jet formation mechanism can
simulate almost all sources with high power jet, that fail to be explained by
the Blandford-Znajek (BZ) process
Sharp lower bound for the first eigenvalue of the Weighted -Laplacian II
Combined with our previous work \cite{LW19eigenvalue}, we prove sharp lower
bound estimates for the first nonzero eigenvalue of the weighted -Laplacian
with on a compact Bakry-\'Emery manifold , without
boundary or with a convex boundary and Neumann boundary condition, satisfying
for some .Comment: Final version, to appear Mathematical Research Letter
Moduli of Continuity for Viscosity Solutions on Manifolds
We establish the estimates of modulus of continuity for viscosity solutions
of nonlinear evolution equations on manifolds, extending previous work of B.
Andrews and J. Clutterbuck for regular solutions on manifolds \cite{AC3} and
the first author's recent work for viscosity solutions in Euclidean spaces
\cite{me1}.Comment: 16 page
Nonparametric hypersurfaces moving by powers of Gauss curvature
We study asymptotic behavior of nonparametric hypersurfaces moving by
powers of Gauss curvature . Our work generalizes the
results of V. Oliker [Oli91] for .Comment: 7 pages. Any comments are welcom
Parabolic frequency monotonicity on compact manifolds
This work is devoted to the study of parabolic frequency for solutions of the
heat equation on Riemannian manifolds. We show that the parabolic frequency
functional is almost increasing on compact manifolds with nonnegative sectional
curvature, which generalizes a monotonicity result proved by C. Poon and by L.
Ni. The proof is based on a generalization of R. Hamilton's matrix Harnack
inequality for small time. As applications, we obtain a unique continuation
result. Monotonicity of a new quantity under two-dimensional Ricci flow,
closely related to the parabolic frequency functional, is derived as well.Comment: 17 page
Oriented diameter and rainbow connection number of a graph
The oriented diameter of a bridgeless graph is $\min\{diam(H)\ | H\ is\
an orientation\ of\ G\}Grc(G)GkkGGrad(G)\eta(G)rad(G)G\eta(G)G\eta(G)GG$.Comment: 16 page
Four-dimentional Gradient Shrinking Solitons with Positive Isotropic Curvature
We show that a four-dimensional complete gradient shrinking Ricci soliton
with positive isotropic curvature is either a quotient of S^4 or a quotient of
S^3 cross R. This gives a clean classification result removing the earlier
additional assumptions in [13] by Wallach and the second author.Comment: 9 pages, Any comments are welcom
DeepRebirth: Accelerating Deep Neural Network Execution on Mobile Devices
Deploying deep neural networks on mobile devices is a challenging task.
Current model compression methods such as matrix decomposition effectively
reduce the deployed model size, but still cannot satisfy real-time processing
requirement. This paper first discovers that the major obstacle is the
excessive execution time of non-tensor layers such as pooling and normalization
without tensor-like trainable parameters. This motivates us to design a novel
acceleration framework: DeepRebirth through "slimming" existing consecutive and
parallel non-tensor and tensor layers. The layer slimming is executed at
different substructures: (a) streamline slimming by merging the consecutive
non-tensor and tensor layer vertically; (b) branch slimming by merging
non-tensor and tensor branches horizontally. The proposed optimization
operations significantly accelerate the model execution and also greatly reduce
the run-time memory cost since the slimmed model architecture contains less
hidden layers. To maximally avoid accuracy loss, the parameters in new
generated layers are learned with layer-wise fine-tuning based on both
theoretical analysis and empirical verification. As observed in the experiment,
DeepRebirth achieves more than 3x speed-up and 2.5x run-time memory saving on
GoogLeNet with only 0.4% drop of top-5 accuracy on ImageNet. Furthermore, by
combining with other model compression techniques, DeepRebirth offers an
average of 65ms inference time on the CPU of Samsung Galaxy S6 with 86.5% top-5
accuracy, 14% faster than SqueezeNet which only has a top-5 accuracy of 80.5%.Comment: AAAI 201
Two-Stream Multi-Task Network for Fashion Recognition
In this paper, we present a two-stream multi-task network for fashion
recognition. This task is challenging as fashion clothing always contain
multiple attributes, which need to be predicted simultaneously for real-time
industrial systems. To handle these challenges, we formulate fashion
recognition into a multi-task learning problem, including landmark detection,
category and attribute classifications, and solve it with the proposed deep
convolutional neural network. We design two knowledge sharing strategies which
enable information transfer between tasks and improve the overall performance.
The proposed model achieves state-of-the-art results on large-scale fashion
dataset comparing to the existing methods, which demonstrates its great
effectiveness and superiority for fashion recognition.Comment: Accepted by ICIP 201
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