1,601,602 research outputs found
Stability of singular jump-linear systems with a large state space : a two-time-scale approach
This paper considers singular systems that involve both continuous dynamics and discrete events with the coefficients being modulated by a continuous-time Markov chain. The underlying systems have two distinct characteristics. First, the systems are singular, that is, characterized by a singular coefficient matrix. Second, the Markov chain of the modulating force has a large state space. We focus on stability of such hybrid singular systems. To carry out the analysis, we use a two-time-scale formulation, which is based on the rationale that, in a large-scale system, not all components or subsystems change at the same speed. To highlight the different rates of variation, we introduce a small parameter ε>0. Under suitable conditions, the system has a limit. We then use a perturbed Lyapunov function argument to show that if the limit system is stable then so is the original system in a suitable sense for ε small enough. This result presents a perspective on reduction of complexity from a stability point of view
Cross-diffusion systems for image processing: II. The nonlinear case
In this paper the use of nonlinear cross-diffu\-sion systems to model image
restoration is investigated, theoretically and numerically. In the first case,
well-posedness, scale-space properties and long time behaviour are analyzed.
From a numerical point of view, a computational study of the performance of the
models is carried out, suggesting their diversity and potentialities to treat
image filtering problems. The present paper is a continuation of a previous
work of the same authors, devoted to linear cross-diffusion models.
\keywords{Cross-diffusion \and Complex diffusion \and Image restoration
Semiclassical Analysis of Constrained Quantum Systems
Exact procedures that follow Dirac's constraint quantization of gauge
theories are usually technically involved and often difficult to implement in
practice. We overview an "effective" scheme for obtaining the leading order
semiclassical corrections to the dynamics of constrained quantum systems
developed elsewhere. Motivated by the geometrical view of quantum mechanics,
our method mimics the classical Dirac-Bergmann algorithm and avoids direct
reference to a particular representation of the physical Hilbert space. We
illustrate the procedure through the example of a relativistic particle in
Minkowski spacetime.Comment: 8 pages, Proceedings of "The Planck Scale" (XXV Max Born Symposium,
Wroclaw
Dynamics of holographic thermalization
Dynamical evolution of thin shells composed by different kinds of degrees of
freedom collapsing within asymptotically AdS spaces is explored with the aim of
investigating models of holographic thermalization of strongly coupled systems.
From the quantum field theory point of view this corresponds to considering
different thermal quenches. We carry out a general study of the thermalization
time scale using different parameters and space-time dimensions, by calculating
renormalized space-like geodesic lengths and rectangular minimal area surfaces
as extended probes of thermalization, which are dual to two-point functions and
rectangular Wilson loops. Different kinds of degrees of freedom in the shell
are described by their corresponding equations of state. We consider a scalar
field, as well as relativistic matter, a pressureless massive fluid and
conformal matter, which can be compared with the collapse of an AdS-Vaidya thin
shell. Remarkably, for conformal matter, the thermalization time scale becomes
much larger than the others. Furthermore, in each case we also investigate
models where the cosmological constants of the inner and outer regions
separated by the shell are different. We found that in this case only a scalar
field shell collapses, and that the thermalization time scale is also much
larger than the AdS-Vaidya case.Comment: 25 pages, 4 figures. V2: published versio
Statistical Traffic State Analysis in Large-scale Transportation Networks Using Locality-Preserving Non-negative Matrix Factorization
Statistical traffic data analysis is a hot topic in traffic management and
control. In this field, current research progresses focus on analyzing traffic
flows of individual links or local regions in a transportation network. Less
attention are paid to the global view of traffic states over the entire
network, which is important for modeling large-scale traffic scenes. Our aim is
precisely to propose a new methodology for extracting spatio-temporal traffic
patterns, ultimately for modeling large-scale traffic dynamics, and long-term
traffic forecasting. We attack this issue by utilizing Locality-Preserving
Non-negative Matrix Factorization (LPNMF) to derive low-dimensional
representation of network-level traffic states. Clustering is performed on the
compact LPNMF projections to unveil typical spatial patterns and temporal
dynamics of network-level traffic states. We have tested the proposed method on
simulated traffic data generated for a large-scale road network, and reported
experimental results validate the ability of our approach for extracting
meaningful large-scale space-time traffic patterns. Furthermore, the derived
clustering results provide an intuitive understanding of spatial-temporal
characteristics of traffic flows in the large-scale network, and a basis for
potential long-term forecasting.Comment: IET Intelligent Transport Systems (2013
DART-MPI: An MPI-based Implementation of a PGAS Runtime System
A Partitioned Global Address Space (PGAS) approach treats a distributed
system as if the memory were shared on a global level. Given such a global view
on memory, the user may program applications very much like shared memory
systems. This greatly simplifies the tasks of developing parallel applications,
because no explicit communication has to be specified in the program for data
exchange between different computing nodes. In this paper we present DART, a
runtime environment, which implements the PGAS paradigm on large-scale
high-performance computing clusters. A specific feature of our implementation
is the use of one-sided communication of the Message Passing Interface (MPI)
version 3 (i.e. MPI-3) as the underlying communication substrate. We evaluated
the performance of the implementation with several low-level kernels in order
to determine overheads and limitations in comparison to the underlying MPI-3.Comment: 11 pages, International Conference on Partitioned Global Address
Space Programming Models (PGAS14
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