3,703 research outputs found
Existence and uniqueness of the global conservative weak solutions for the integrable Novikov equation
The integrable Novikov equation can be regarded as one of the
Camassa-Holm-type equations with cubic nonlinearity. In this paper, we prove
the global existence and uniqueness of the H\"older continuous energy
conservative solutions for the Cauchy problem of the Novikov equation
Stability of solitary waves of a generalized two-component Camassa-Holm system
We study here the existence of solitary wave solutions of a generalized
two-component Camassa-Holm system. In addition to those smooth solitary-wave
solutions, we show that there are solitary waves with singularities: peaked and
cusped solitary waves. We also demonstrate that all smooth solitary waves are
orbitally stable in the energy space. We finally give a sufficient condition
for global strong solutions to the equation without certain parameters.Comment: 23 pages, 1 figur
Searching for axionlike particle at future colliders
We explore the possibility of searching for axionlike particle (ALP) by
collisions via the subprocess . Sensitivities to the effective ALP-photon coupling
for its mass in the range of 10 GeV TeV are
obtained for the LHeC and its high-energy upgrade, FCC-eh. Comparing to
existing bounds on the ALP free parameters, we find that the bounds given by
colliders are competitive and complementary to other colliders.Comment: 11 pages, 3 figure
On the well-posedness of a weakly dispersive Boussinesq system
We study the Cauchy problem for one-dimensional dispersive system of
Boussinesq type which models weakly nonlinear long wave surface waves. We
establish the local well-posedness and ill-posedness of solutions to the
system. We also provide criteria for the formation of singularities.Comment: 20 page
Finite Sample Analysis of the GTD Policy Evaluation Algorithms in Markov Setting
In reinforcement learning (RL) , one of the key components is policy
evaluation, which aims to estimate the value function (i.e., expected long-term
accumulated reward) of a policy. With a good policy evaluation method, the RL
algorithms will estimate the value function more accurately and find a better
policy. When the state space is large or continuous \emph{Gradient-based
Temporal Difference(GTD)} policy evaluation algorithms with linear function
approximation are widely used. Considering that the collection of the
evaluation data is both time and reward consuming, a clear understanding of the
finite sample performance of the policy evaluation algorithms is very important
to reinforcement learning. Under the assumption that data are i.i.d. generated,
previous work provided the finite sample analysis of the GTD algorithms with
constant step size by converting them into convex-concave saddle point
problems. However, it is well-known that, the data are generated from Markov
processes rather than i.i.d. in RL problems.. In this paper, in the realistic
Markov setting, we derive the finite sample bounds for the general
convex-concave saddle point problems, and hence for the GTD algorithms. We have
the following discussions based on our bounds. (1) With variants of step size,
GTD algorithms converge. (2) The convergence rate is determined by the step
size, with the mixing time of the Markov process as the coefficient. The faster
the Markov processes mix, the faster the convergence. (3) We explain that the
experience replay trick is effective by improving the mixing property of the
Markov process. To the best of our knowledge, our analysis is the first to
provide finite sample bounds for the GTD algorithms in Markov setting
The overshoot and phenotypic equilibrium in characterizing cancer dynamics of reversible phenotypic plasticity
The paradigm of phenotypic plasticity indicates reversible relations of
different cancer cell phenotypes, which extends the cellular hierarchy proposed
by the classical cancer stem cell (CSC) theory. Since it is still question able
if the phenotypic plasticity is a crucial improvement to the hierarchical model
or just a minor extension to it, it is worthwhile to explore the dynamic
behavior characterizing the reversible phenotypic plasticity. In this study we
compare the hierarchical model and the reversible model in predicting the
cell-state dynamics observed in biological experiments. Our results show that
the hierarchical model shows significant disadvantages over the reversible
model in describing both long-term stability (phenotypic equilibrium) and
short-term transient dynamics (overshoot) of cancer cells. In a very specific
case in which the total growth of population due to each cell type is
identical, the hierarchical model predicts neither phenotypic equilibrium nor
overshoot, whereas thereversible model succeeds in predicting both of them.
Even though the performance of the hierarchical model can be improved by
relaxing the specific assumption, its prediction to the phenotypic equilibrium
strongly depends on a precondition that may be unrealistic in biological
experiments, and it also fails to capture the overshoot of CSCs. By comparison,
it is more likely for the reversible model to correctly describe the stability
of the phenotypic mixture and various types of overshoot behavior.Comment: 24 pages, 6 figure
Convergence Analysis of Distributed Stochastic Gradient Descent with Shuffling
When using stochastic gradient descent to solve large-scale machine learning
problems, a common practice of data processing is to shuffle the training data,
partition the data across multiple machines if needed, and then perform several
epochs of training on the re-shuffled (either locally or globally) data. The
above procedure makes the instances used to compute the gradients no longer
independently sampled from the training data set. Then does the distributed SGD
method have desirable convergence properties in this practical situation? In
this paper, we give answers to this question. First, we give a mathematical
formulation for the practical data processing procedure in distributed machine
learning, which we call data partition with global/local shuffling. We observe
that global shuffling is equivalent to without-replacement sampling if the
shuffling operations are independent. We prove that SGD with global shuffling
has convergence guarantee in both convex and non-convex cases. An interesting
finding is that, the non-convex tasks like deep learning are more suitable to
apply shuffling comparing to the convex tasks. Second, we conduct the
convergence analysis for SGD with local shuffling. The convergence rate for
local shuffling is slower than that for global shuffling, since it will lose
some information if there's no communication between partitioned data. Finally,
we consider the situation when the permutation after shuffling is not uniformly
distributed (insufficient shuffling), and discuss the condition under which
this insufficiency will not influence the convergence rate. Our theoretical
results provide important insights to large-scale machine learning, especially
in the selection of data processing methods in order to achieve faster
convergence and good speedup. Our theoretical findings are verified by
extensive experiments on logistic regression and deep neural networks
On a shallow-water approximation to the Green-Naghdi equations with the Coriolis effect
We consider an asymptotic 1D (in space) rotation-Camassa-Holm (R-CH) model,
which could be used to describe the propagation of long-crested shallow-water
waves in the equatorial ocean regions with allowance for the weak Coriolis
effect due to the Earth's rotation. This model equation has similar
wave-breaking phenomena as the Camassa-Holm equation. It is analogous to the
rotation-Green-Naghdi (R-GN) equations with the weak Earth's rotation effect,
modeling the propagation of wave allowing large amplitude in shallow water. We
provide here a rigorous justification showing that solutions of the R-GN
equations tend to associated solution of the R-CH model equation in the
Camassa-Holm regime with the small amplitude and the larger wavelength.
Furthermore, we demonstrate that the R-GN model equations are locally
well-posed in a Sobolev space by the refined energy estimates
Symmetry Enforced Chiral Hinge States and Surface Quantum Anomalous Hall Effect in Magnetic Axion Insulator
A universal mechanism to generate chiral hinge states in the ferromagnetic
axion insulator phase is proposed, which leads to an exotic transport
phenomena, the quantum anomalous Hall effect (QAHE) on some particular surfaces
determined by both the crystalline symmetry and the magnetization direction. A
realistic material system Sm doped is then proposed to
realize such exotic hinge states by combing the first principle calculations
and the Green's function techniques. A physically accessible way to manipulate
the surface QAHE is also proposed, which makes it very different from the QAHE
in ordinary 2D systems.Comment: 8 pages, 5 figure
Asymmetrically interacting dynamics with mutual confirmation from multi-source on multiplex networks
In the early stage of epidemics, individuals' determination on adopting
protective measures, which can reduce their risk of infection and suppress
disease spreading, is likely to depend on multiple information sources and
their mutual confirmation due to inadequate exact information. Here we
introduce the inter-layer mutual confirmation mechanism into the
information-disease interacting dynamics on multiplex networks. In our model,
an individual increases the information transmission rate and willingness to
adopt protective measures once he confirms the authenticity of news and
severity of disease from neighbors status in multiple layers. By using the
microscopic Markov chain approach, we analytically calculate the epidemic
threshold and the awareness and infected density in the stationary state, which
agree well with simulation results. We find that the increment of epidemic
threshold when confirming the aware neighbors on communication layer is larger
than that of the contact layer. On the contrary, the confirmation of neighbors'
awareness and infection from the contact layer leads to a lower final infection
density and a higher awareness density than that of the communication layer.
The results imply that individuals' explicit exposure of their infection and
awareness status to neighbors, especially those with real contacts, is helpful
in suppressing epidemic spreading.Comment: 13 pages,8 figure
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