On the Diagnostic Role of Morphological Signs of Wild Rose (Rosa L.)

Identification and systematics of species of wild rose (Rosa L.) are often associated with difficulties due to the diversity and variability of morphological features used in this process. They also arise in establishing genetic links between taxa of different ranks. Clarity in the diagnostic role of specific or group of characters is not only theoretical but also of practical importance. Such an attempt is made on the example of species of the genus Rosa from different sections and subsections (R. canina. R. danaiorum, R. ruprechtii, R. marschalliana, R. obtusifolia, R. svanetica, Rosa mollis, R. buschiana, R. pulverulenta, R pomifera, R. iberica, R. pimpinnefolia, etc.) of Chechnya and adjacent territories. The set of signs of the vegetative and generative sphere used in identifying species, subsections, sections has been considered. There was a lack of representativeness for the intraspecific diagnostics of such signs as: “free, immersed columns”, or “sessile stigmas in the hemispherical head above the fetal throat”, “occasionally solid sepals, with downward directed fruits” and others used in sectional diagnoses, because they are characteristic of species of different sections. The authors noted the heterogeneity of the authors’ approach to the characterization of section rank taxa, the inadmissibility of the universal, and the need for a differentiated approach in using the same characteristics when identifying taxa of different levels

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

An Integro-Differential Equation of the Fractional Form: Cauchy Problem and Solution

Producción CientíficaWe solve the Cauchy problem defined by the fractional partial differential equation [∂tt − κD]u = 0, with D the pseudo-differential Riesz operator of first order, and certain initial conditions. The solution of the Cauchy problem resulting from the substitution of the Gaussian pulse u(x, 0) by the Dirac delta distribution ϕ(x) = μδ(x) is obtained as corollary.MINECO grant MTM2014-57129-C2-1-P

Probability densities for the sums of iterates of the sine-circle map in the vicinity of the quasi-periodic edge of chaos

We investigate the probability density of rescaled sum of iterates of sine-circle map within quasi-periodic route to chaos. When the dynamical system is strongly mixing (i.e., ergodic), standard Central Limit Theorem (CLT) is expected to be valid, but at the edge of chaos where iterates have strong correlations, the standard CLT is not necessarily to be valid anymore. We discuss here the main characteristics of the central limit behavior of deterministic dynamical systems which exhibit quasi-periodic route to chaos. At the golden-mean onset of chaos for the sine-circle map, we numerically verify that the probability density appears to converge to a q-Gaussian with q<1 as the golden mean value is approached.Comment: 7 pages, 7 figures, 1 tabl

Distributed Order Derivatives and Relaxation Patterns

We consider equations of the form $(D_{(\rho)}u)(t)=-\lambda u(t)$, $t>0$, where $\lambda >0$, $D_{(\rho)}$ is a distributed order derivative, that is the Caputo-Dzhrbashyan fractional derivative of order $\alpha$, integrated in $\alpha\in (0,1)$ with respect to a positive measure $\rho$. Such equations are used for modeling anomalous, non-exponential relaxation processes. In this work we study asymptotic behavior of solutions of the above equation, depending on properties of the measure $\rho$

Floristic Research of the Biological Reserve “Bragunsky”

Flora of the biological reserve “Bragunsky” of republican significance, located on the territory of three districts of the Chechen Republic (area of 17,000 hectares, forest land – 10.2 thousand hectares) is studied. Its boundaries are indicated. Preliminary studies in the summer-autumn flora of the reserve have revealed 237 species from 175 genera and 53 families, among which more than 15 endemics are of different statuses, 25 relict species are of different geological eras. Dominant by the number of family species are indicated (Asteraceae, Lamiaceae, Rosaceae, Poaceae, Fabaceae, Caryophyllaceae, Apiaceae, Brassicaceae, Cyperaceae, Scrophyliaceae, Orchidaceae), Geographic elements are considered. The general-holarctic and boreal nature of the flora is noted with a significant participation of ancient Mediterranean and binding elements. The prevalence of hemicryptophytes in the reserve flora has been noted – 115 (49.78 %) species, 48 therophytes (20.25 %) and 40 phanerophytes (10 %) and a slight presence of cryptophytes – 4.21 %. The economically and scientifically valuable, as well as rare, red book and protected species are listed

Generation of Three-Qubit Entangled W-State by Nonlinear Optical State Truncation

We propose an alternative scheme to generate W state via optical state truncation using quantum scissors. In particular, these states may be generated through three-mode optical state truncation in a Kerr nonlinear coupler. The more general three-qubit state may be also produced if the system is driven by external classical fields.Comment: 7 pages, 2 figur

Use of the q-Gaussian mutation in evolutionary algorithms

Copyright @ Springer-Verlag 2010.This paper proposes the use of the q-Gaussian mutation with self-adaptation of the shape of the mutation distribution in evolutionary algorithms. The shape of the q-Gaussian mutation distribution is controlled by a real parameter q. In the proposed method, the real parameter q of the q-Gaussian mutation is encoded in the chromosome of individuals and hence is allowed to evolve during the evolutionary process. In order to test the new mutation operator, evolution strategy and evolutionary programming algorithms with self-adapted q-Gaussian mutation generated from anisotropic and isotropic distributions are presented. The theoretical analysis of the q-Gaussian mutation is also provided. In the experimental study, the q-Gaussian mutation is compared to Gaussian and Cauchy mutations in the optimization of a set of test functions. Experimental results show the efficiency of the proposed method of self-adapting the mutation distribution in evolutionary algorithms.This work was supported in part by FAPESP and CNPq in Brazil and in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant EP/E060722/1 and Grant EP/E060722/2

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