Microscopic dynamics underlying the anomalous diffusion

The time dependent Tsallis statistical distribution describing anomalous diffusion is usually obtained in the literature as the solution of a non-linear Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347 (1995)]. The scope of the present paper is twofold. Firstly we show that this distribution can be obtained also as solution of the non-linear porous media equation. Secondly we prove that the time dependent Tsallis distribution can be obtained also as solution of a linear FP equation [G. Kaniadakis and P. Quarati, Physica A, 237, 229 (1997)] with coefficients depending on the velocity, that describes a generalized Brownian motion. This linear FP equation is shown to arise from a microscopic dynamics governed by a standard Langevin equation in presence of multiplicative noise.Comment: 4 pag. - no figures. To appear on Phys. Rev. E 62, September 200

Ferromagnetic material in the eastern red-spotted newt notophthalmus viridescens

Behavioral results obtained from the eastern red-spotted newt (Notophthalmus viridescens) led to the suggestion of a hybrid homing system involving inputs from both a light-dependent and a non-light-dependent mechanism. To evaluate the possible role of a receptor based on biogenic magnetite in this animal, we performed magnetometry experiments on a set of newts previously used in behavioral assays. The natural remanent magnetization (NRM) carried by these newts was strong enough to be measured easily using a direct-current-biased superconducting quantum interference device functioning as a moment magnetometer. Isothermal remanent magnetizations were two orders of magnitude higher than the NRM, suggesting that ferromagnetic material consistent with magnetite is present in the body of the newt. The NRM has no preferential orientation among the animals when analyzed relative to their body axis, and the demagnetization data show that, overall, the magnetic material grains are not aligned parallel to each other within each newt. Although the precise localization of the particles was not possible, the data indicate that magnetite is not clustered in a limited area. A quantity of single-domain magnetic material is present which would be adequate for use in either a magnetic intensity or direction receptor. Our data, when combined with the functional properties of homing, suggest a link between this behavioral response and the presence of ferromagnetic material, raising the possibility that magnetite is involved at least in the map component of homing of the eastern red-spotted newt

Geometry of escort distributions

Given an original distribution, its statistical and probabilistic attributs may be scanned by the associated escort distribution introduced by Beck and Schlogl and employed in the formulation of nonextensive statistical mechanics. Here, the geometric structure of the one-parameter family of the escort distributions is studied based on the Kullback-Leibler divergence and the relevant Fisher metric. It is shown that the Fisher metric is given in terms of the generalized bit-variance, which measures fluctuations of the crowding index of a multifractal. The Cramer-Rao inequality leads to the fundamental limit for precision of statistical estimate of the order of the escort distribution. It is also quantitatively discussed how inappropriate it is to use the original distribution instead of the escort distribution for calculating the expectation values of physical quantities in nonextensive statistical mechanics.Comment: 12 pages, no figure

‘Fixed-axis’ magnetic orientation by an amphibian: non-shoreward-directed compass orientation, misdirected homing or positioning a magnetite-based map detector in a consistent alignment relative to the magnetic field?

Experiments were carried out to investigate the earlier prediction that prolonged exposure to long-wavelength (>500 nm) light would eliminate homing orientation by male Eastern red-spotted newts Notophthalmus viridescens. As in previous experiments, controls held in outdoor tanks under natural lighting conditions and tested in a visually uniform indoor arena under full-spectrum light were homeward oriented. As predicted, however, newts held under long-wavelength light and tested under either full-spectrum or long-wavelength light (>500 nm) failed to show consistent homeward orientation. The newts also did not orient with respect to the shore directions in the outdoor tanks in which they were held prior to testing. Unexpectedly, however, the newts exhibited bimodal orientation along a more-or-less `fixed' north-northeast—south-southwest magnetic axis. The orientation exhibited by newts tested under full-spectrum light was indistinguishable from that of newts tested under long-wavelength light, although these two wavelength conditions have previously been shown to differentially affect both shoreward compass orientation and homing orientation. To investigate the possibility that the `fixed-axis' response of the newts was mediated by a magnetoreception mechanism involving single-domain particles of magnetite, natural remanent magnetism (NRM) was measured from a subset of the newts. The distribution of NRM alignments with respect to the head—body axis of the newts was indistinguishable from random. Furthermore, there was no consistent relationship between the NRM of individual newts and their directional response in the overall sample. However, under full-spectrum, but not long-wavelength, light, the alignment of the NRM when the newts reached the 20 cm radius criterion circle in the indoor testing arena (estimated by adding the NRM alignment measured from each newt to its magnetic bearing) was non-randomly distributed. These findings are consistent with the earlier suggestion that homing newts use the light-dependent magnetic compass to align a magnetite-based `map detector' when obtaining the precise measurements necessary to derive map information from the magnetic field. However, aligning the putative map detector does not explain the fixed-axis response of newts tested under long-wavelength light. Preliminary evidence suggests that, in the absence of reliable directional information from the magnetic compass (caused by the 90° rotation of the response of the magnetic compass under long-wavelength light), newts may resort to a systematic sampling strategy to identify alignment(s) of the map detector that yields reliable magnetic field measurements

Nonextensive Entropies derived from Form Invariance of Pseudoadditivity

The form invariance of pseudoadditivity is shown to determine the structure of nonextensive entropies. Nonextensive entropy is defined as the appropriate expectation value of nonextensive information content, similar to the definition of Shannon entropy. Information content in a nonextensive system is obtained uniquely from generalized axioms by replacing the usual additivity with pseudoadditivity. The satisfaction of the form invariance of the pseudoadditivity of nonextensive entropy and its information content is found to require the normalization of nonextensive entropies. The proposed principle requires the same normalization as that derived in [A.K. Rajagopal and S. Abe, Phys. Rev. Lett. {\bf 83}, 1711 (1999)], but is simpler and establishes a basis for the systematic definition of various entropies in nonextensive systems.Comment: 16 pages, accepted for publication in Physical Review

Liver transplantation for arteriohepatic dysplasia (Alagille's syndrome)

Thirteen out of 268 children (<18 years old) underwent hepatic transplantation (OLT) for end-stage liver disease (ESLD) associated with arteriohepatic dysplasia (AHD). Seven children are alive and well with normal liver function. Six children died, four within 11 days of the operation and the other two at 4 and 10 months after the OLT. Vascular complications with associated septicemia were responsible for the deaths of three children. Two died of heart failure and circulatory collapse, secondary to pulmonary hypertension and congenital heart disease. The remaining patient died of overwhelming sepsis not associated with technical complications. Seven patients had a portoenterostomy or portocholecystostomy early in life; five of these died after the OLT. Severe cardiovascular abnormalities in some of our patients suggest that complete hemodynamic monitoring with invasive studies should be performed in all patients with AHD, especially in cases of documented hypertrophy of the right ventricle. The improved quality of life in our surviving patients confirms the validity of OLT as a treatment of choice in cases of ESLD due to AHD. © 1992 Springer-Verlag

Individual and collective stock dynamics: intra-day seasonalities

We establish several new stylised facts concerning the intra-day seasonalities of stock dynamics. Beyond the well known U-shaped pattern of the volatility, we find that the average correlation between stocks increases throughout the day, leading to a smaller relative dispersion between stocks. Somewhat paradoxically, the kurtosis (a measure of volatility surprises) reaches a minimum at the open of the market, when the volatility is at its peak. We confirm that the dispersion kurtosis is a markedly decreasing function of the index return. This means that during large market swings, the idiosyncratic component of the stock dynamics becomes sub-dominant. In a nutshell, early hours of trading are dominated by idiosyncratic or sector specific effects with little surprises, whereas the influence of the market factor increases throughout the day, and surprises become more frequent.Comment: 9 pages, 7 figure

Information Theory based on Non-additive Information Content

We generalize the Shannon's information theory in a nonadditive way by focusing on the source coding theorem. The nonadditive information content we adopted is consistent with the concept of the form invariance structure of the nonextensive entropy. Some general properties of the nonadditive information entropy are studied, in addition, the relation between the nonadditivity $q$ and the codeword length is pointed out.Comment: 9 pages, no figures, RevTex, accepted for publication in Phys. Rev. E(an error in proof of theorem 1 was corrected, typos corrected

Multiplicative noise: A mechanism leading to nonextensive statistical mechanics

A large variety of microscopic or mesoscopic models lead to generic results that accommodate naturally within Boltzmann-Gibbs statistical mechanics (based on $S_1\equiv -k \int du p(u) \ln p(u)$). Similarly, other classes of models point toward nonextensive statistical mechanics (based on $S_q \equiv k [1-\int du [p(u)]^q]/[q-1]$, where the value of the entropic index $q\in\Re$ depends on the specific model). We show here a family of models, with multiplicative noise, which belongs to the nonextensive class. More specifically, we consider Langevin equations of the type $\dot{u}=f(u)+g(u)\xi(t)+\eta(t)$, where $\xi(t)$ and $\eta(t)$ are independent zero-mean Gaussian white noises with respective amplitudes $M$ and $A$. This leads to the Fokker-Planck equation $\partial_t P(u,t) = -\partial_u[f(u) P(u,t)] + M\partial_u\{g(u)\partial_u[g(u)P(u,t)]\} + A\partial_{uu}P(u,t)$. Whenever the deterministic drift is proportional to the noise induced one, i.e., $f(u) =-\tau g(u) g'(u)$, the stationary solution is shown to be $P(u, \infty) \propto \bigl\{1-(1-q) \beta [g(u)]^2 \bigr\}^{\frac{1}{1-q}}$ (with $q \equiv \frac{\tau + 3M}{\tau+M}$ and $\beta=\frac{\tau+M}{2A}$). This distribution is precisely the one optimizing $S_q$ with the constraint $_q \equiv \{\int du [g(u)]^2[P(u)]^q \}/ \{\int du [P(u)]^q \}=$constant. We also introduce and discuss various characterizations of the width of the distributions.Comment: 3 PS figure

Nonlinear equation for anomalous diffusion: unified power-law and stretched exponential exact solution

The nonlinear diffusion equation $\frac{\partial \rho}{\partial t}=D \tilde{\Delta} \rho^\nu$ is analyzed here, where $\tilde{\Delta}\equiv \frac{1}{r^{d-1}}\frac{\partial}{\partial r} r^{d-1-\theta} \frac{\partial}{\partial r}$, and $d$, $\theta$ and $\nu$ are real parameters. This equation unifies the anomalous diffusion equation on fractals ($\nu =1$) and the spherical anomalous diffusion for porous media ($\theta=0$). Exact point-source solution is obtained, enabling us to describe a large class of subdiffusion ($\theta > (1-\nu)d$), normal diffusion ($\theta= (1-\nu)d$) and superdiffusion ($\theta < (1-\nu)d$). Furthermore, a thermostatistical basis for this solution is given from the maximum entropic principle applied to the Tsallis entropy.Comment: 3 pages, 2 eps figure