804 research outputs found
When are projections also embeddings?
We study an autonomous four-dimensional dynamical system used to model certain geophysical processes.This system generates a chaotic attractor that is strongly contracting, with four Lyapunov exponents that satisfy , so the Lyapunov dimension is in the range of coupling parameter values studied. As a result, it should be possible to find three-dimensional spaces in which the attractors can be embedded so that topological analyses can be carried out to determine which stretching and squeezing mechanisms generate chaotic behavior. We study mappings into to determine which can be used as embeddings to reconstruct the dynamics. We find dramatically different behavior in the two simplest mappings: projections from to . In one case the one-parameter family of attractors studied remains topologically unchanged for all coupling parameter values. In the other case, during an intermediate range of parameter values the projection undergoes self-intersections, while the embedded attractors at the two ends of this range are topologically mirror images of each other
A Comparison of Tests for Embeddings
It is possible to compare results for the classical tests for embeddings of chaotic data with the results of a recently proposed test. The classical tests, which depend on real numbers (fractal dimensions, Lyapunov exponents) averaged over an attractor, are compared with a topological test that depends on integers. The comparison can only be done for mappings into three dimensions. We find that the classical tests fail to predict when a mapping is an embedding and when it is not. We point out the reasons for this failure, which are not restricted to three dimensions
Observability of dynamical networks from graphic and symbolic approaches
A dynamical network, a graph whose nodes are dynamical systems, is usually
characterized by a large dimensional space which is not always accesible due to
the impossibility of measuring all the variables spanning the state space.
Therefore, it is of the utmost importance to determine a reduced set of
variables providing all the required information for non-ambiguously
distinguish its different states. Inherited from control theory, one possible
approach is based on the use of the observability matrix defined as the
Jacobian matrix of the change of coordinates between the original state space
and the space reconstructed from the measured variables. The observability of a
given system can be accurately assessed by symbolically computing the
complexity of the determinant of the observability matrix and quantified by
symbolic observability coefficients. In this work, we extend the symbolic
observability, previously developed for dynamical systems, to networks made of
coupled -dimensional node dynamics (). From the observability of the
node dynamics, the coupling function between the nodes, and the adjacency
matrix, it is indeed possible to construct the observability of a large network
with an arbitrary topology.Comment: 12 pages, 4 figures made from 12 eps file
An outbreak of sheep-associated malignant catarrhal fever in sows
his paper describes a case of malignant catarrhal fever in a sow herd in Belgium caused by infection with ovine herpesvirus-2 (OHV-2). The 11 affected sows had high fever and 10 of them died within 3 days after the onset of clinical disease. The most prominent macroscopic lesion was a hemorrhagic to pseudo-membranous gastritis. Histopathology revealed severe infiltration and necrosis of the gastric mucosa. Neither antimicrobial treatment nor injection with anti-inflammatory drugs ameliorated the severity of the disease. As the sows and sheep were housed in the same building with the possibility of having direct nose-to-nose contact, and as PCR testing showed that the virus found in the sows was identical to that found in the sheep, it is very likely that the infection was transmitted from the subclinically infected sheep to the sows. The present case showed that OHV-2 infection should be included in the differential diagnosis when facing problems of fever followed by death, especially when pigs are housed in close contact with sheep
Detection of hepatitis e virus (HEV) antibiodies in swine herds in Québec, Canada
Hepatitis E virus (HEV) has a zoonotic potential and pork products have been identified as possible human infection sources. Swine HEV infection in pigs have now been reported in pigs in many countries and generally occurs at about 2-3 months of age. Data from USA indicated that about 80-100% of pigs in commercial farms are infected. The objective of this study was to estimate prevalence of HEV in selected Canadian herds by serology using the PrioCHECK HEV Ab porcine-ELISA kit
Nonlinear Analysis of Irregular Variables
The Fourier spectral techniques that are common in Astronomy for analyzing
periodic or multi-periodic light-curves lose their usefulness when they are
applied to unsteady light-curves. We review some of the novel techniques that
have been developed for analyzing irregular stellar light or radial velocity
variations, and we describe what useful physical and astronomical information
can be gained from their use.Comment: 31 pages, to appear as a chapter in `Nonlinear Stellar Pulsation' in
the Astrophysics and Space Science Library (ASSL), Editors: M. Takeuti & D.
Sasselo
Stabilization of space–time laser instability through the finite transverse extension of pumping
We investigate the space–time dynamics of a homogeneously broadened single-mode laser when diffraction is taken into account. It is well known that such a laser displays instability when pumping reaches the second laser threshold. We show that the laser dynamics can be stabilized by pumping in a domain of finite width. The analysis of stationary solutions to the Maxwell–Bloch equations (evanescent waves, travelling waves, localized solutions) allows the stabilization mechanism to be explained
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