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 $\lambda_i$ that satisfy $\lambda_1+ \lambda_2+\lambda_3<0$, so the Lyapunov dimension is $D_L=2+|\lambda_3|/\lambda_1 < 3$ 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 $R^3$ to determine which can be used as embeddings to reconstruct the dynamics. We find dramatically different behavior in the two simplest mappings: projections from $R^4$ to $R^3$. 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

A semantic web approach for built heritage representation

In a built heritage process, meant as a structured system of activities aimed at the investigation, preservation, and management of architectural heritage, any task accomplished by the several actors involved in it is deeply influenced by the way the knowledge is represented and shared. In the current heritage practice, knowledge representation and management have shown several limitations due to the difficulty of dealing with large amount of extremely heterogeneous data. On this basis, this research aims at extending semantic web approaches and technologies to architectural heritage knowledge management in order to provide an integrated and multidisciplinary representation of the artifact and of the knowledge necessary to support any decision or any intervention and management activity. To this purpose, an ontology-based system, representing the knowledge related to the artifact and its contexts, has been developed through the formalization of domain-specific entities and relationships between them

Peeling Bifurcations of Toroidal Chaotic Attractors

Chaotic attractors with toroidal topology (van der Pol attractor) have counterparts with symmetry that exhibit unfamiliar phenomena. We investigate double covers of toroidal attractors, discuss changes in their morphology under correlated peeling bifurcations, describe their topological structures and the changes undergone as a symmetry axis crosses the original attractor, and indicate how the symbol name of a trajectory in the original lifts to one in the cover. Covering orbits are described using a powerful synthesis of kneading theory with refinements of the circle map. These methods are applied to a simple version of the van der Pol oscillator.Comment: 7 pages, 14 figures, accepted to Physical Review

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 $d$-dimensional node dynamics ($d>1$). 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

Protection of pigs against experimental Salmonella Typhimurium infection by use of a single dose subunit slow delivery vaccine

Infections caused by septicemic strains of Salmonella are significant animal health as well as food safety concerns for the North American swine industry. Among the various strategies to control these infections at the herd level, development of vaccines are attractive alternatives. In this study, based on previous studies of immune response to various protems following natural and experimental infections of pigs by Salmonella, we designed a subunit slow delivery vaccine and tested it in an experimental model of infection. The selected immunogenic protein was cloned and purified by chromatography. The purified protein was then incorporated m PLGA (a polymer that is slowly degraded within the animal\u27s gastro-intestinal system) microspheres and given orally once to groups of pigs (n=8) while control animals (n=8) received only PBS. Animals were challenged orally 4 weeks after the vaccmation with 108 cells of a virulent strains of Salmonella Typhimurium. Animals were examined twice a day and climcal signs evaluated using a predetermined scoring grid. Pigs were sacrificed 12 days later and bacterial cultures of vanous organs, electron microscopy and evaluation of lgA response by ELISA were performed. No significant difference was found at bacteriology and ELISA but marked differences in clinical signs were observed between vaccinated and non vaccinated animals. None of vaccmated animals showed fever exceeding 40°C while it was observed in 5 out of 8 non vaccinated Only one of vaccmated pigs showed mild diarrhea while severe diarrhea was observed in all control animals different sizes of microspheres were observed in intestinal crypts of vaccinated animals at electron microscopy. We concluded that this vaccine can protect pigs against clinical signs associated with experimental infection by Salmonella Typhimunum

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

Environmental and geographical factors structure soil microbial diversity in New Caledonian ultramafic substrates: A metagenomic approach

Soil microorganisms play key roles in ecosystem functioning and are known to be influenced by biotic and abiotic factors, such as plant cover or edaphic parameters. New Caledonia, a biodiversity hotspot located in the southwest Pacific, is one-third covered by ultramafic substrates. These types of soils are notably characterised by low nutrient content and high heavy metal concentrations. Ultramafic outcrops harbour diverse vegetation types and remarkable plant diversity. In this study, we aimed to assess soil bacterial and fungal diversity in New Caledonian ultramafic substrates and to determine whether floristic composition, edaphic parameters and geographical factors affect this microbial diversity. Therefore, four plant formation types at two distinct sites were studied. These formations represent different stages in a potential chronosequence. Soil cores, according to a given sampling procedure, were collected to assess microbial diversity using a metagenomic approach, and to characterise the physico-chemical parameters. A botanical inventory was also performed. Our results indicated that microbial richness, composition and abundance were linked to the plant cover type and the dominant plant species. Furthermore, a large proportion of Ascomycota phylum (fungi), mostly in non-rainforest formations, and Planctomycetes phylum (bacteria) in all formations were observed. Interestingly, such patterns could be indicators of past disturbances that occurred on different time scales. Furthermore, the bacteria and fungi were influenced by diverse edaphic parameters as well as by the interplay between these two soil communities. Another striking finding was the existence of a site effect. Differences in microbial communities between geographical locations may be explained by dispersal limitation in the context of the biogeographical island theory. In conclusion, each plant formation at each site possesses is own microbial community resulting from multiple interactions between abiotic and biotic factors. (Résumé d'auteur