A record-driven growth process

We introduce a novel stochastic growth process, the record-driven growth process, which originates from the analysis of a class of growing networks in a universal limiting regime. Nodes are added one by one to a network, each node possessing a quality. The new incoming node connects to the preexisting node with best quality, that is, with record value for the quality. The emergent structure is that of a growing network, where groups are formed around record nodes (nodes endowed with the best intrinsic qualities). Special emphasis is put on the statistics of leaders (nodes whose degrees are the largest). The asymptotic probability for a node to be a leader is equal to the Golomb-Dickman constant omega=0.624329... which arises in problems of combinatorical nature. This outcome solves the problem of the determination of the record breaking rate for the sequence of correlated inter-record intervals. The process exhibits temporal self-similarity in the late-time regime. Connections with the statistics of the cycles of random permutations, the statistical properties of randomly broken intervals, and the Kesten variable are given.Comment: 30 pages,5 figures. Minor update

Tomographic entropy and cosmology

The probability representation of quantum mechanics including propagators and tomograms of quantum states of the universe and its application to quantum gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator, free pointlike particle and repulsive oscillator are considered. The notion of tomographic entropy and its properties are used to find some inequalities for the tomographic probability determining the quantum state of the universe. The sense of the inequality as a lower bound for the entropy is clarified.Comment: 19 page

Improvement of the Heisenberg and Fisher-information-based uncertainty relations for D-dimensional central potentials

The Heisenberg and Fisher-information-based uncertainty relations are improved for stationary states of single-particle systems in a D-dimensional central potential. The improvement increases with the squared orbital hyperangular quantum number. The new uncertainty relations saturate for the isotropic harmonic oscillator wavefunction.We are very grateful for partial support to Junta de Andalucía (under the grants FQM- 0207 and FQM-481), Ministerio de Educaci´on y Ciencia (under the project FIS2005-00973), and the European Research Network NeCCA (under the project INTAS-03-51-6637). RGF acknowledges the support of Junta de Andalucía under the program of Retorno de Investigadores a Centros de Investigación Andaluces

Multifractal Spatial Patterns and Diversity in an Ecological Succession

We analyzed the relationship between biodiversity and spatial biomass heterogeneity along an ecological succession developed in the laboratory. Periphyton (attached microalgae) biomass spatial patterns at several successional stages were obtained using digital image analysis and at the same time we estimated the species composition and abundance. We show that the spatial pattern was self-similar and as the community developed in an homogeneous environment the pattern is self-organized. To characterize it we estimated the multifractal spectrum of generalized dimensions Dq. Using Dq we analyze the existence of cycles of heterogeneity during succession and the use of the information dimension D1 as an index of successional stage. We did not find cycles but the values of D1 showed an increasing trend as the succession developed and the biomass was higher. D1 was also negatively correlated with Shannon's diversity. Several studies have found this relationship in different ecosystems but here we prove that the community self-organizes and generates its own spatial heterogeneity influencing diversity. If this is confirmed with more experimental and theoretical evidence D1 could be used as an index, easily calculated from remote sensing data, to detect high or low diversity areas

A four-surface schematic eye of macaque monkey obtained by an optical method

AbstractSchematic eyes for four Macaca fascicularis monkeys were constructed from measurements of the positions and curvatures of the anterior and posterior surfaces of the cornea and lens. All of these measurements were obtained from Scheimpflug photography through the use of a ray-tracing analysis. Some of these measurements were also checked (and confirmed) by keratometry and ultrasound. Gaussian lens equations were applied to the measured dimensions of each individual eye in order to construct schematic eyes. The mean total power predicted by the schematic eyes agreed closely with independent measurements based on retinoscopy and ultrasound results, 74.2 ± 1.3 (SEM) vs 74.7 ± 0.3 (SEM) diopters. The predicted magnification of 202 μm/deg in one eye was confirmed by direct measurement of 205 μm/deg for a foveal laser lesion. The mean foveal retinal magnification calculated for our eight schematic eyes was 211 ± (SEM) μm/deg, slightly less than the value obtained by application of the method of Rolls and Cowey [Experimental Brain Research, 10, 298–310 (1970)] to our eight eyes but just 4% more than the value obtained by application of the method of Perry and Cowey [Vision Research, 12, 1795–1810 (1985)]

Role of retinoic receptors in lung carcinogenesis

Several in vitro and in vivo studies have examined the positive and negative effects of retinoids (vitamin A analogs) in premalignant and malignant lesions. Retinoids have been used as chemopreventive and anticancer agents because of their pleiotropic regulator function in cell differentiation, growth, proliferation and apoptosis through interaction with two types of nuclear receptors: retinoic acid receptors and retinoid X receptors. Recent investigations have gradually elucidated the function of retinoids and their signaling pathways and may explain the failure of earlier chemopreventive studies