Strictly and asymptotically scale-invariant probabilistic models of NN correlated binary random variables having {\em q}--Gaussians as N→∞N\to \infty limiting distributions

In order to physically enlighten the relationship between {\it $q$--independence} and {\it scale-invariance}, we introduce three types of asymptotically scale-invariant probabilistic models with binary random variables, namely (i) a family, characterized by an index $\nu=1,2,3,...$, unifying the Leibnitz triangle ($\nu=1$) and the case of independent variables ($\nu\to\infty$); (ii) two slightly different discretizations of $q$--Gaussians; (iii) a special family, characterized by the parameter $\chi$, which generalizes the usual case of independent variables (recovered for $\chi=1/2$). Models (i) and (iii) are in fact strictly scale-invariant. For models (i), we analytically show that the $N \to\infty$ probability distribution is a $q$--Gaussian with $q=(\nu -2)/(\nu-1)$. Models (ii) approach $q$--Gaussians by construction, and we numerically show that they do so with asymptotic scale-invariance. Models (iii), like two other strictly scale-invariant models recently discussed by Hilhorst and Schehr (2007), approach instead limiting distributions which are {\it not} $q$--Gaussians. The scenario which emerges is that asymptotic (or even strict) scale-invariance is not sufficient but it might be necessary for having strict (or asymptotic) $q$--independence, which, in turn, mandates $q$--Gaussian attractors.Comment: The present version is accepted for publication in JSTA

Functional-differential equations for FqF_q%-transforms of qq-Gaussians

In the paper the question - Is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor? - is studied for the whole range of $q\in (-\infty, 3)$. This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. We prove that the answer is affirmative if and only if q > 1, excluding two particular cases of q<1, namely, q = 1/2 and q = 2/3, which are also out of the theory valid for q \ge 1. We also discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.Comment: 14 pages A new section on a related solution of the porous medium equation in comparison with the previous version has been introduc

Note on a q-modified central limit theorem

A q-modified version of the central limit theorem due to Umarov et al. affirms that q-Gaussians are attractors under addition and rescaling of certain classes of strongly correlated random variables. The proof of this theorem rests on a nonlinear q-modified Fourier transform. By exhibiting an invariance property we show that this Fourier transform does not have an inverse. As a consequence, the theorem falls short of achieving its stated goal.Comment: 10 pages, no figure

Compacton existence and spin-orbit density dependence in Bose-Einstein condensates

We demonstrate the existence of compactons matter waves in binary mixtures of Bose-Einstein condensates (BEC) trapped in deep optical lattices (OL) subjected to equal contributions of intra-species Rashba and Dresselhaus spin-orbit coupling (SOC) under periodic time modulations of the intra-species scattering length. We show that these modulations lead to the rescaling of the SOC parameters that involve the density imbalance of the two components. This gives rise to a density-dependent SOC parameters strongly influence the existence and stability of compacton matter waves. The stability of SOC-compactons is investigated both by linear stability analysis and by time integrations of the coupled Gross-Pitaevskii equations. We find that SOC restricts the parameter ranges for stable stationary SOC-compacton existence but, on the other side, it gives a more stringent signature of their occurrence. In particular, SOC-compactons should appear when the intra-species interactions and the number of atoms in the two components are perfectly balanced (or close to being balanced for metastable cases). The possibility to use SOC-compactons as a tool for indirect measurements of the number of atoms and/or the intra-species interactions, is also suggested.Comment: 14 pages, 11 figure

THE STUDY OF MORPHO-PHYSIOLOGICAL PARAMETERS OF PATHOGENS OF CULTIVATED PLANTS FROM DIFFERENT AGROBIOCOENOSES

Collection the pathogens of fungal diseases of wheat and potatoes in agrobiocoenoses with different soil and climatic and agro-technical conditions the Republic of Bashkortostan was carried out. The strains of fun­gal pathogen Septoria nodorum, Septoria tritici, Bipolaris sorokiniana, Phy­tophthora infestans in pure culture were isolated and their morphological and physiological parameters were characterized.Работа выполнена при поддержке гранта Федеральной целевой программы ГК № 16.740.11.0061, РФФИ_поволжье_а № 11-04-97037

Deviation from Gaussianity in the cosmic microwave background temperature fluctuations

Recent measurements of the temperature fluctuations of the cosmic microwave background (CMB) radiation from the WMAP satellite provide indication of a non-Gaussian behavior. Although the observed feature is small, it is detectable and analyzable. Indeed, the temperature distribution P^{CMB}(Delta T) of these data can be quite well fitted by the anomalous probability distribution emerging within nonextensive statistical mechanics, based on the entropy S_q = k (1 - \int dx [P(x)]^q)/(q - 1) (where in the limit case q -> 1 we obtain the Boltzmann-Gibbs entropy S_1 = - k \int dx P(x) ln[P(x)]). For the CMB frequencies analysed, \nu= 40.7, 60.8, and 93.5 GHz, P^{CMB}(Delta T) is well described by P_q(Delta T) \propto 1/[1 + (q-1) B(\nu) (Delta T)^2]^{1/(q-1)}, with q = 1.04 \pm 0.01, the strongest non-Gaussian contribution coming from the South-East sector of the celestial sphere. Moreover, Monte Carlo simulations exclude, at the 99% confidence level, P_1(Delta T) \propto e^{- B(\nu) (Delta T)^2} to fit the three-year WMAP data.Comment: 6 pages, 1 figur

Black hole thermodynamical entropy

As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy $S_{BG}$ of a $(3+1)$ black hole is proportional to its area $L^2$ ($L$ being a characteristic linear length), and not to its volume $L^3$. Similarly it exists the \emph{area law}, so named because, for a wide class of strongly quantum-entangled $d$-dimensional systems, $S_{BG}$ is proportional to $\ln L$ if $d=1$, and to $L^{d-1}$ if $d>1$, instead of being proportional to $L^d$ ($d \ge 1$). These results violate the extensivity of the thermodynamical entropy of a $d$-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is \emph{not} to be identified with the BG {\it additive} entropy but with appropriately generalized {\it nonadditive} entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle.Comment: 7 pages, 2 figures. Accepted for publication in EPJ

In silico exploration of Red Sea Bacillus genomes for natural product biosynthetic gene clusters

Background: The increasing spectrum of multidrug-resistant bacteria is a major global public health concern, necessitating discovery of novel antimicrobial agents. Here, members of the genus Bacillus are investigated as a potentially attractive source of novel antibiotics due to their broad spectrum of antimicrobial activities. We specifically focus on a computational analysis of the distinctive biosynthetic potential of Bacillus paralicheniformis strains isolated from the Red Sea, an ecosystem exposed to adverse, highly saline and hot conditions. Results: We report the complete circular and annotated genomes of two Red Sea strains, B. paralicheniformis Bac48 isolated from mangrove mud and B. paralicheniformis Bac84 isolated from microbial mat collected from Rabigh Harbor Lagoon in Saudi Arabia. Comparing the genomes of B. paralicheniformis Bac48 and B. paralicheniformis Bac84 with nine publicly available complete genomes of B. licheniformis and three genomes of B. paralicheniformis, revealed that all of the B. paralicheniformis strains in this study are more enriched in nonribosomal peptides (NRPs). We further report the first computationally identified trans-acyltransferase (trans-AT) nonribosomal peptide synthetase/polyketide synthase (PKS/ NRPS) cluster in strains of this species. Conclusions:B. paralicheniformis species have more genes associated with biosynthesis of antimicrobial bioactive compounds than other previously characterized species of B. licheniformis, which suggests that these species are better potential sources for novel antibiotics. Moreover, the genome of the Red Sea strain B. paralicheniformis Bac48 is more enriched in modular PKS genes compared to B. licheniformis strains and other B. paralicheniformis strains. This may be linked to adaptations that strains surviving in the Red Sea underwent to survive in the relatively hot and saline ecosystems

Dynamics of Income Rank Volatility: Evidence from Germany and the US

This paper presents a methodology for comparing income rank volatility profiles over time and across distributions. While most of the existing measures are affected by changes in marginal distributions, this paper proposes a framework that is based on individuals’ relative positions in the distribution, and is neutral in relation to structural changes that occur in the economy. Applying this approach to investigate rank volatility in Germany and the US over three decades, we show that while poorer individuals within both countries are the most volatile, the volatility trend for the middle class in each of these countries differs