Subordination model of anomalous diffusion leading to the two-power-law relaxation responses

We derive a general pattern of the nonexponential, two-power-law relaxation from the compound subordination theory of random processes applied to anomalous diffusion. The subordination approach is based on a coupling between the very large jumps in physical and operational times. It allows one to govern a scaling for small and large times independently. Here we obtain explicitly the relaxation function, the kinetic equation and the susceptibility expression applicable to the range of experimentally observed power-law exponents which cannot be interpreted by means of the commonly known Havriliak-Negami fitting function. We present a novel two-power relaxation law for this range in a convenient frequency-domain form and show its relationship to the Havriliak-Negami one.Comment: 5 pages; 3 figures; corrected versio

Classification of Possible Finite-Time Singularities by Functional Renormalization

Starting from a representation of the early time evolution of a dynamical system in terms of the polynomial expression of some observable f (t) as a function of the time variable in some interval 0 < t < T, we investigate how to extrapolate/forecast in some optimal stability sense the future evolution of f(t) for time t>T. Using the functional renormalization of Yukalov and Gluzman, we offer a general classification of the possible regimes that can be defined based on the sole knowledge of the coefficients of a second-order polynomial representation of the dynamics. In particular, we investigate the conditions for the occurence of finite-time singularities from the structure of the time series, and quantify the critical time and the functional nature of the singularity when present. We also describe the regimes when a smooth extremum replaces the singularity and determine its position and amplitude. This extends previous works by (1) quantifying the stability of the functional renormalization method more accurately, (2) introducing new global constraints in terms of moments and (3) going beyond the ``mean-field'' approximation.Comment: Latex document of 18 pages + 7 ps figure

Diagnostic assessment of foetal brain malformations with intra-uterine MRI versus perinatal post-mortem MRI

PURPOSE: To evaluate differences in diagnostic yield of intra-uterine foetal (iuMR) and post-mortem MRI (PMMR) for complex brain malformations, using autopsy as the reference standard. METHODS: In this retrospective, multicentre study spanning 2 years, we reviewed 13 terminated singleton pregnancies with a prenatal ultrasound finding of complex foetal cerebral abnormalities, referred for both iuMR and PMMR. The iuMR and PMMR studies of the brain were reported independently by two groups of radiologists, blinded to each other's reports. Descriptive statistics were used to compare differences in intracranial abnormalities with autopsy (and genetic testing, where present) as reference standard. RESULTS: The median gestational age at termination was 24.6 weeks (IQR 22-29) with median time between delivery and PMMR of 133 h (IQR 101-165). There was full concordance between iuMR and PMMR findings and autopsy in 2/13 (15.3%) cases. Partial concordance between both imaging modalities was present in 6/13 (46.2%) and total discordance in the remainder (5/13, 38.5%). When compared to autopsy, PMMR missed important key findings specifically for neuronal migration and cerebellar anomalies, whereas iuMR appeared to overcall CSF space abnormalities which were less crucial to reaching the final overall diagnosis. CONCLUSIONS: iuMR should be performed to improve foetal phenotyping where there is a prenatal ultrasound for complex foetal brain abnormalities. Reliance on PMMR alone is likely to result in misdiagnosis in a majority of cases

Characterizations and simulations of a class of stochastic processes to model anomalous diffusion

In this paper we study a parametric class of stochastic processes to model both fast and slow anomalous diffusion. This class, called generalized grey Brownian motion (ggBm), is made up off self-similar with stationary increments processes (H-sssi) and depends on two real parameters alpha in (0,2) and beta in (0,1]. It includes fractional Brownian motion when alpha in (0,2) and beta=1, and time-fractional diffusion stochastic processes when alpha=beta in (0,1). The latters have marginal probability density function governed by time-fractional diffusion equations of order beta. The ggBm is defined through the explicit construction of the underline probability space. However, in this paper we show that it is possible to define it in an unspecified probability space. For this purpose, we write down explicitly all the finite dimensional probability density functions. Moreover, we provide different ggBm characterizations. The role of the M-Wright function, which is related to the fundamental solution of the time-fractional diffusion equation, emerges as a natural generalization of the Gaussian distribution. Furthermore, we show that ggBm can be represented in terms of the product of a random variable, which is related to the M-Wright function, and an independent fractional Brownian motion. This representation highlights the $H$-{\bf sssi} nature of the ggBm and provides a way to study and simulate the trajectories. For this purpose, we developed a random walk model based on a finite difference approximation of a partial integro-differenital equation of fractional type.Comment: 25 pages, 9 figure

A colanic acid operon deletion mutation enhances induction of early antibody responses by live attenuated salmonella vaccine strains

Colanic acid (CA) is a common exopolysaccharide produced by many genera in the Enterobacteriaceae. It is critical for biofilm formation on HEp-2 cells and on chicken intestinal tissue by Salmonella. In this study, we generated different CA synthesis gene mutants and evaluated the immune responses induced by these mutants. One of these mutations, Δ(wza-wcaM)8, which deleted the whole operon for CA synthesis, was introduced into two Salmonella vaccine strains attenuated by auxotrophic traits or by the regulated delayed attenuation strategy (RDAS). The mice immunized with the auxotrophic Salmonella vaccine strain with the deletion mutation Δ(wza-wcaM)8 developed higher vaginal IgA titers against the heterologous protective antigen and higher levels of antigen-specific IgA secretion cells in lungs. In Salmonella vaccine strains with RDAS, the strain with the Δ(wza-wcaM)8 mutation resulted in higher levels of protective antigen production during in vitro growth. Mice immunized with this strain developed higher serum IgG and mucosal IgA antibody responses at 2 weeks. This strain also resulted in better gamma interferon (IFN-γ) responses than the strain without this deletion at doses of 10(8) and 10(9) CFU. Thus, the mutation Δ(wza-wcaM)8 will be included in various recombinant attenuated Salmonella vaccine (RASV) strains with RDAS derived from Salmonella enterica serovar Paratyphi A and Salmonella enterica serovar Typhi to induce protective immunity against bacterial pathogens