49,818 research outputs found
Generalizations of Ekeland-Hofer and Hofer-Zehnder symplectic capacities and applications
This is the first installment in a series of papers aimed at generalizing
symplectic capacities and homologies. The main purposes of this paper are to
construct analogues of Ekeland-Hofer and Hofer-Zehnder symplectic capacities
based on a class of Hamiltonian boundary value problems motivated by Clarke's
and Ekeland's work, and to study generalizations of some important results
about the original these two capacities (for example, the famous Weinstein
conjecture, representation formula for and , a theorem
by Evgeni Neduv, Brunn-Minkowski type inequality and Minkowski billiard
trajectories proposed by Artstein-Avidan-Ostrover).Comment: Latex, 89 pages. Results in Section 1.6 are improved. Some typos are
corrected. arXiv admin note: text overlap with arXiv:1903.0067
On the Regularizing Property of Stochastic Gradient Descent
Stochastic gradient descent is one of the most successful approaches for
solving large-scale problems, especially in machine learning and statistics. At
each iteration, it employs an unbiased estimator of the full gradient computed
from one single randomly selected data point. Hence, it scales well with
problem size and is very attractive for truly massive dataset, and holds
significant potentials for solving large-scale inverse problems. In the recent
literature of machine learning, it was empirically observed that when equipped
with early stopping, it has regularizing property. In this work, we rigorously
establish its regularizing property (under \textit{a priori} early stopping
rule), and also prove convergence rates under the canonical sourcewise
condition, for minimizing the quadratic functional for linear inverse problems.
This is achieved by combining tools from classical regularization theory and
stochastic analysis. Further, we analyze the preasymptotic weak and strong
convergence behavior of the algorithm. The theoretical findings shed insights
into the performance of the algorithm, and are complemented with illustrative
numerical experiments.Comment: 22 pages, better presentatio
Improving the performance of SCTP Transport Protocol over wireless networks
[Abstract]: Stream Control Transmission Protocol(SCTP) is a reliable
transport protocol combining the advantages of
TCP and UDP. SCTP has many desirable features including
multihoming, multistreaming, and partial data
reliability. These features have made SCTP perform
much more effectively in multimedia networking applications.
They have also worked better in wireless environment
which traditional transport protocols are ineffective
and cumbersome.
Before the transmission, an application using
SCTP needs to establish an association between the
client and the server. The establishment of association
requires a number which will be used to create multiple
streams. However, SCTP has not specified a method or
suggested any ideas of determine the number.
In our paper, we focus on the performance of SCTP
protocol over the wireless networks. The ideas is to extend
the SCTP with a process of determining an optimal
number prior to the association establishing. We examine
the modified SCTP on a simulated wireless networks,
and the experiment results of simulation using
NS2 have shown the modified SCTP is feasible and also
demonstrated the modified SCTP’s superiority of performance
over TCP and UDP over the wireless networks
From data towards knowledge: Revealing the architecture of signaling systems by unifying knowledge mining and data mining of systematic perturbation data
Genetic and pharmacological perturbation experiments, such as deleting a gene
and monitoring gene expression responses, are powerful tools for studying
cellular signal transduction pathways. However, it remains a challenge to
automatically derive knowledge of a cellular signaling system at a conceptual
level from systematic perturbation-response data. In this study, we explored a
framework that unifies knowledge mining and data mining approaches towards the
goal. The framework consists of the following automated processes: 1) applying
an ontology-driven knowledge mining approach to identify functional modules
among the genes responding to a perturbation in order to reveal potential
signals affected by the perturbation; 2) applying a graph-based data mining
approach to search for perturbations that affect a common signal with respect
to a functional module, and 3) revealing the architecture of a signaling system
organize signaling units into a hierarchy based on their relationships.
Applying this framework to a compendium of yeast perturbation-response data, we
have successfully recovered many well-known signal transduction pathways; in
addition, our analysis have led to many hypotheses regarding the yeast signal
transduction system; finally, our analysis automatically organized perturbed
genes as a graph reflecting the architect of the yeast signaling system.
Importantly, this framework transformed molecular findings from a gene level to
a conceptual level, which readily can be translated into computable knowledge
in the form of rules regarding the yeast signaling system, such as "if genes
involved in MAPK signaling are perturbed, genes involved in pheromone responses
will be differentially expressed"
A High Order Stochastic Asymptotic Preserving Scheme for Chemotaxis Kinetic Models with Random Inputs
In this paper, we develop a stochastic Asymptotic-Preserving (sAP) scheme for
the kinetic chemotaxis system with random inputs, which will converge to the
modified Keller-Segel model with random inputs in the diffusive regime. Based
on the generalized Polynomial Chaos (gPC) approach, we design a high order
stochastic Galerkin method using implicit-explicit (IMEX) Runge-Kutta (RK) time
discretization with a macroscopic penalty term. The new schemes improve the
parabolic CFL condition to a hyperbolic type when the mean free path is small,
which shows significant efficiency especially in uncertainty quantification
(UQ) with multi-scale problems. The stochastic Asymptotic-Preserving property
will be shown asymptotically and verified numerically in several tests. Many
other numerical tests are conducted to explore the effect of the randomness in
the kinetic system, in the aim of providing more intuitions for the theoretic
study of the chemotaxis models
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