Continued Fraction Representation of Temporal Multi Scaling in Turbulence

It was shown recently that the anomalous scaling of simultaneous correlation functions in turbulence is intimately related to the breaking of temporal scale invariance, which is equivalent to the appearance of infinitely many times scales in the time dependence of time-correlation functions. In this paper we derive a continued fraction representation of turbulent time correlation functions which is exact and in which the multiplicity of time scales is explicit. We demonstrate that this form yields precisely the same scaling laws for time derivatives and time integrals as the "multi-fractal" representation that was used before. Truncating the continued fraction representation yields the "best" estimates of time correlation functions if the given information is limited to the scaling exponents of the simultaneous correlation functions up to a certain, finite order. It is worth noting that the derivation of a continued fraction representation obtained here for an operator which is not Hermitian or anti-Hermitian may be of independent interest.Comment: 7 pages, no figur

Capacity of a bosonic memory channel with Gauss-Markov noise

We address the classical capacity of a quantum bosonic memory channel with additive noise, subject to an input energy constraint. The memory is modeled by correlated noise emerging from a Gauss-Markov process. Under reasonable assumptions, we show that the optimal modulation results from a "quantum water-filling" solution above a certain input energy threshold, similar to the optimal modulation for parallel classical Gaussian channels. We also derive analytically the optimal multimode input state above this threshold, which enables us to compute the capacity of this memory channel in the limit of an infinite number of modes. The method can also be applied to a more general noise environment which is constructed by a stationary Gauss process. The extension of our results to the case of broadband bosonic channels with colored Gaussian noise should also be straightforward.Comment: 11 pages, 4 figures, final corrections mad

A feasibility study on the use of equine chondrogenic induced mesenchymal stem cells as a treatment for natural occurring osteoarthritis in dogs

Conventional treatments of osteoarthritis (OA) reduce pain and the inflammatory response but do not repair the damaged cartilage. Xenogeneic peripheral blood-derived equine chondrogenically induced mesenchymal stem cells (ciMSC) could thus provide an interesting alternative. Six client-owned dogs with confirmed elbow OA were subjected to a baseline orthopedic examination, pressure plate analysis, general clinical examination, hematological analysis, synovial fluid sampling, and radiographic examination, and their owners completed two surveys. After all examinations, a 0.9% saline solution (placebo control product=CP) was administered intra-articularly. After 6 weeks, all examinations were repeated, owners again completed two surveys, and equine ciMSCs were administered in the same joint. After another 6 weeks, dogs were returned for a final follow-up. No serious adverse events or suspected adverse drug reactions were present during this study. No significant differences in blood analysis were noted between the CP and ciMSC treatment. Two adverse events were observed, both in the same dog, one after CP treatment and one after ciMSC treatment. The owner surveys revealed significantly less pain and lameness after ciMSC treatment compared to after CP treatment. There was no significant difference in the orthopedic examination parameters, the radiographic examination, synovial fluid sampling, and pressure plate analysis between CP treatment and ciMSC treatment. A single intra-articular administration of equine ciMSCs proved to be a well-tolerated treatment, which reduced lameness and pain according to the owner's evaluations compared to a placebo treatment

Non-diagonalizability of the Frobenius-Perron operator and transition between decay modes of the time autocorrelation function

We show that for one-dimensional piecewise linear Markov maps the Frobenius-Perron operator evolving probability densities may admit Jordan blocks. Its spectral decomposition is obtained in that case using the formalism of the generalized master equation developed by MacKernan and Nicolis. For mixing piecewise linear Markov maps with two branches and a corresponding two-cell partition, it is shown that the particular situation occurring when the Frobenius-Perron operator restricted to piecewise linear functions is not diagonalizable is a transition between two different decay modes of the time autocorrelation function. The general case of an M-cell partition is also addressed. Copyright © 1996 Elsevier Science Ltd.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Transitions in the communication capacity of dissipative qubit channels

info:eu-repo/semantics/publishe

Probabilistic and thermodynamic aspects of dynamical systems

Doctorat en Sciencesinfo:eu-repo/semantics/nonPublishe

Probabilistic and thermodynamic aspects of dynamical systems

Doctorat en Sciencesinfo:eu-repo/semantics/nonPublishe

Daems replies

A Reply to the Comment by Michael Nathanson and Mary Beth Ruskai. © 2010 The American Physical Society.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Probabilistic and thermodynamic aspects of dynamical systems

The probabilistic approach to dynamical systems giving rise to irreversible behavior at the macroscopic, mesoscopic, and microscopic levels of description is outlined. Signatures of the complexity of the underlying dynamics on the spectral properties of the Liouville, Frobenius-Perron, and Fokker-Planck operators are identified. Entropy and entropy production-like quantities are introduced and the connection between their properties in nonequilibrium steady states and the characteristics of the dynamics in phase space are explored.info:eu-repo/semantics/publishe

Probabilistic approach to homoclinic chaos

Three-dimensional systems possessing a homoclinic orbit associated to a saddle focus with eigenvalues ρ{variant}±iω, -λ and giving rise to homoclinic chaos when the Shil'nikov condition ρ{variant}<λ is satisfied are studied. The 2D Poincaré map and its 1D contractions capturing the essential features of the flow are given. At homoclinicity, these 1D maps are found to be piecewise linear. This property allows one to reduce the Frobenius-Perron equation to a master equation whose solution is analytically known. The probabilistic properties such as the time autocorrelation function of the state variable x are explicitly derived. © 1994 Plenum Publishing Corporation.SCOPUS: ar.jinfo:eu-repo/semantics/publishe