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

Evaluation of the impact of functional foods on the course of Salmonella infection in piglets

With the aim to improve growth of weaning piglets and to minimize incidence of intestinal diseases, the effect of a combination of functional foods able to stimulate the development of systemic and mucosal immune system and to modulate bacterial populations in the gut was evaluated. In this study, we assessed the impact of functional foods on the course of Salmonella infection in piglets. Piglets from different litters were weaned at 21 days of age and assigned to 1 of the 4 feed additives (8 litters per treatment) as follow: 1-control (CTRL), 2-antibiotic (ATB), 3-cocktail of functional foods (CFF), 4-bovine colostrum + cocktail of functional foods (COL-CFF)

Dynamics of DNA Ejection From Bacteriophage

The ejection of DNA from a bacterial virus (``phage'') into its host cell is a biologically important example of the translocation of a macromolecular chain along its length through a membrane. The simplest mechanism for this motion is diffusion, but in the case of phage ejection a significant driving force derives from the high degree of stress to which the DNA is subjected in the viral capsid. The translocation is further sped up by the ratcheting and entropic forces associated with proteins that bind to the viral DNA in the host cell cytoplasm. We formulate a generalized diffusion equation that includes these various pushing and pulling effects and make estimates of the corresponding speed-ups in the overall translocation process. Stress in the capsid is the dominant factor throughout early ejection, with the pull due to binding particles taking over at later stages. Confinement effects are also investigated, in the case where the phage injects its DNA into a volume comparable to the capsid size. Our results suggest a series of in vitro experiments involving the ejection of DNA into vesicles filled with varying amounts of binding proteins from phage whose state of stress is controlled by ambient salt conditions or by tuning genome length.Comment: 17 pages, 5 figure

Reinnervation of late postnatal purkinje cells by climbing fibers: neosynaptogenesis without transient multi-innervation.

Synaptic partner selection and refinement of projections are important in the development of precise and functional neuronal connections. We investigated the formation of new synaptic connections in a relatively mature system to test whether developmental events can be recapitulated at later stages (i.e., after the mature synaptic organization has been established), using a model of postlesional reinnervation in the olivo-cerebellar pathway. During the development of this pathway, synaptic connections between climbing fibers (CFs) and Purkinje cells (PCs) are diffuse and redundant before synapse elimination refines the pattern. The regression of CFs during the first 2 postnatal weeks in the rat leads to mono-innervation of each PC. After unilateral transection of the rat olivo-cerebellar pathway and intracerebellar injection of BDNF 24 h after lesion, axons from the remaining inferior olive can sprout into the deafferented hemicerebellum and establish new contacts with denervated PCs at later developmental stages. We found that these contacts are first established on somatic thorns before the CFs translocate to the PC dendrites, recapitulating the morphological steps of normal CF-PC synaptogenesis, but on a relatively mature PC. However, electrophysiology of PC reinnervation by transcommissural CFs in these animals showed that each PC is reinnervated by only one CF. This mono-innervation contrasts with the reinnervation of grafted immature PCs in the same cerebellum. Our results provide evidence that relatively mature PCs do not receive several olivary afferents during late reinnervation, suggesting a critical role of the target cell state in the control of CF-PC synaptogenesis. Thus, synapse exuberance and subsequent elimination are not a prerequisite to reach a mature relationship between synaptic partners

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

Analyse de dynamiques spatio-temporelles d’un laser

La dynamique spatio-temporelle d’un système laser avec diffraction est étudiée. La correspondance entre la structure du portrait de phase et l’organisation relative desdéfauts topologiques dans les diagrammes spatio-temporels est clairement mise en évidence. Ainsi, une dynamique de type chaos toroïdal est associée à des défauts apparaissant périodiquement (dans l’espace et dans le temps). En revanche, il n’y a plus de périodicité des défauts sur les diagrammes spatio-temporels lorsque le régime est un chaos développé

Laser frequency stabilization by modulation transfer spectroscopy and balanced detection of molecular iodine for laser cooling of 174{}^{174}Yb

We report laser frequency stabilization by the combination of modulation transfer spectroscopy and balanced detection of a relatively weak hyperfine transition of the R(158)25-0 line of molecular iodine (${}^{127}$I$_{2}$), which is used as a new frequency reference for laser trapping and cooling of ${}^{174}$Yb on the $^{1}S_{0} - {}^{3}P_{1}$ transition. The atomic cloud is characterized by time-of-flight measurements, and an on-resonance optical depth of up to 47 is obtained. We show laser noise reduction and characterize the short-term laser frequency instability by the Allan deviation of the laser fractional frequency. The minimum measured value is 3.9 x $10^{-13}$ at 0.17 s of averaging time

Oral colistin sulfate in pigs: pharmacokinetics and effect on fecal Escherichia coli excretion of weaned pigs challenged with Escherichia coli F4 (K88)

Colistin sulfate (CS), a polymyxin antibiotic, is used in Canada for the treatment of post-weaning diarrhea in pigs as an alternative to neomycin. The aim of the present study was to evaluate some pharmcokinetics parameters of CS and its effect on the evolution of the intestinal Escherichia coli population in pigs challenged with enterotoxigenic E. coli (ETEC): F4