Nonlinear anomalous diffusion equation and fractal dimension: Exact generalized gaussian solution

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the $N$-dimensional nonlinear diffusion equation $\partial\rho /\partial{t}={\bf \nabla} \cdot (K{\bf \nabla} \rho^{\nu})-{\bf \nabla}\cdot(\mu{\bf F} \rho)-\alpha \rho ,$ where $K=D r^{-\theta}$, $\nu$, $\theta$, $\mu$ and $D$ are real parameters and $\alpha$ is a time-dependent source. This equation unifies the O'Shaugnessy-Procaccia anomalous diffusion equation on fractals ($\nu =1$) and the spherical anomalous diffusion for porous media ($\theta=0$). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.Comment: Latex, 6 pages. To appear in Phys. Rev.

Identification and characterisation of G-quadruplex DNA-forming sequences in the Pseudomonas aeruginosa genome

A number of Gram-negative bacteria such as Pseudomonas aeruginosa are becoming resistant to front-line antibiotics. Consequently, there is a pressing need to find alternative bio-molecular targets for the development of new drugs. Since non-canonical DNA structures such as guanine-quadruplexes (G4s) have been implicated in regulating transcription, we were interested in determining whether there are putative quadruplex-forming sequences (PQS) in the genome of Pseudomonas aeruginosa. Using bioinformatic tools, we screened 36 genes potentially relevant to drug resistance for the presence of PQS and 10 of these were selected for biophysical characterisation (i.e. circular dichroism and thermal difference UV/Vis spectroscopy). These studies showed that three of these G-rich sequences (linked to murE, ftsB and mexC genes) form stable guanine-quadruplexes which were studied by NMR spectroscopy; detailed analysis of one of the sequences (mexC) confirmed that it adopts a two-quartet antiparallel quadruplex structure in the presence of K+ ions. We also show by FRET melting assays that small molecules can stabilise these three new G4 DNA structures under physiological conditions. These initial results could be of future interest in the development of new antibiotics with alternative bio-molecular targets which in turn would help tackle antimicrobial resistance

Aging in Models of Non-linear Diffusion

We show that for a family of problems described by non-linear diffusion equations an exact calculation of the two time correlation function gives C(t,t')=f(t-t')g(t'), t>t', exhibiting normal and anomalous diffusions, as well as aging effects, depending on the degree of non-linearity. We discuss also the form in which FDT is violated in this class of systems. Finally we argue that in this type of models aging may be consequence of the non conservation of the "total mass".Comment: 4 pages, 1 figure, to appear in Phys.Rev.

Retarding Sub- and Accelerating Super-Diffusion Governed by Distributed Order Fractional Diffusion Equations

We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which, correspondingly, can not be viewed as self-affine random processes possessing a unique Hurst exponent. We prove the positivity of the solutions of the proposed equations and establish the relation to the Continuous Time Random Walk theory. We show that the distributed order time fractional diffusion equation describes the sub-diffusion random process which is subordinated to the Wiener process and whose diffusion exponent diminishes in time (retarding sub-diffusion) leading to superslow diffusion, for which the square displacement grows logarithmically in time. We also demonstrate that the distributed order space fractional diffusion equation describes super-diffusion phenomena when the diffusion exponent grows in time (accelerating super-diffusion).Comment: 11 pages, LaTe

Implications of Form Invariance to the Structure of Nonextensive Entropies

The form invariance of the statement of the maximum entropy principle and the metric structure in quantum density matrix theory, when generalized to nonextensive situations, is shown here to determine the structure of the nonextensive entropies. This limits the range of the nonextensivity parameter to so as to preserve the concavity of the entropies. The Tsallis entropy is thereby found to be appropriately renormalized.Comment: 8 page

Desynchronizing effect of high-frequency stimulation in a generic cortical network model

Transcranial Electrical Stimulation (TCES) and Deep Brain Stimulation (DBS) are two different applications of electrical current to the brain used in different areas of medicine. Both have a similar frequency dependence of their efficiency, with the most pronounced effects around 100Hz. We apply superthreshold electrical stimulation, specifically depolarizing DC current, interrupted at different frequencies, to a simple model of a population of cortical neurons which uses phenomenological descriptions of neurons by Izhikevich and synaptic connections on a similar level of sophistication. With this model, we are able to reproduce the optimal desynchronization around 100Hz, as well as to predict the full frequency dependence of the efficiency of desynchronization, and thereby to give a possible explanation for the action mechanism of TCES.Comment: 9 pages, figs included. Accepted for publication in Cognitive Neurodynamic

Anomalous diffusion, Localization, Aging and Sub-aging effects in trap models at very low temperature

We study in details the dynamics of the one dimensional symmetric trap model, via a real-space renormalization procedure which becomes exact in the limit of zero temperature. In this limit, the diffusion front in each sample consists in two delta peaks, which are completely out of equilibrium with each other. The statistics of the positions and weights of these delta peaks over the samples allows to obtain explicit results for all observables in the limit $T \to 0$. We first compute disorder averages of one-time observables, such as the diffusion front, the thermal width, the localization parameters, the two-particle correlation function, and the generating function of thermal cumulants of the position. We then study aging and sub-aging effects : our approach reproduces very simply the two different aging exponents and yields explicit forms for scaling functions of the various two-time correlations. We also extend the RSRG method to include systematic corrections to the previous zero temperature procedure via a series expansion in $T$. We then consider the generalized trap model with parameter $\alpha \in [0,1]$ and obtain that the large scale effective model at low temperature does not depend on $\alpha$ in any dimension, so that the only observables sensitive to $\alpha$ are those that measure the `local persistence', such as the probability to remain exactly in the same trap during a time interval. Finally, we extend our approach at a scaling level for the trap model in $d=2$ and obtain the two relevant time scales for aging properties.Comment: 33 pages, 3 eps figure

Young Muslim women's experiences of Islam and physical education in Greece and Britain: a comparative study

Previous research suggests that Muslim women can experience particular problems when taking physical education (PE) lessons, for example with dress codes, mixed-teaching and exercise during Ramadan; and they can face restrictions in extra-curricular activities for cultural and religious reasons. The area is under-researched and there is little evidence of comparative studies that explore similarities and differences in cross-national experiences, which is the aim of this paper. Two studies conducted in Greece and Britain that explored the views of Muslim women on school experiences of physical education are compared. Both studies focused on diaspora communities, Greek Turkish girls and British Asian women, living in predominantly non-Muslim countries. Growing concerns about global divisions between 'Muslims and the West' make this a particularly pertinent study. Qualitative data were collected by interviews with 24 Greek Muslim women, and 20 British Muslim women. \ud <P> \ud Physical education has national curriculum status and a similar rationale in both countries but with different cultures of formality and tradition, which impacted on pupils' experiences. Data suggested that Greek and British groups held positive views towards physical education but were restricted on their participation in extra-curricular activities. For the British women religious identity and consciousness of Islamic requirements were more evident than for the Greek women. Differences in stages of acculturation, historical and socio-cultural contexts contributed to less problematic encounters with physical education for Greek Muslims who appeared more closely assimilated into the dominant culture

Serial Dictatorship: The Unique Optimal Allocation Rule When Information is Endogenous

The study of matching problems typically assumes that agents precisely know their preferences over the goods to be assigned. Within applied contexts, this assumption stands out as particularly counterfactual. Parents typically do invest a large amount of time and resources to find out which school would be best for their children, doctors run costly tests to establish which kidney might be best for a given patient. In this paper I introduce the assumption of endogenous information acquisition into otherwise standard house allocation problems. I find that there is a unique ex ante Pareto-optimal, strategy-proof and non-bossy allocation mechanism: serial dictatorship. This stands in sharp contrast to the very large set of such mechanisms for house allocation problems without endogenous information acquisition