Weighted random--geometric and random--rectangular graphs: Spectral and eigenfunction properties of the adjacency matrix

Within a random-matrix-theory approach, we use the nearest-neighbor energy level spacing distribution $P(s)$ and the entropic eigenfunction localization length $\ell$ to study spectral and eigenfunction properties (of adjacency matrices) of weighted random--geometric and random--rectangular graphs. A random--geometric graph (RGG) considers a set of vertices uniformly and independently distributed on the unit square, while for a random--rectangular graph (RRG) the embedding geometry is a rectangle. The RRG model depends on three parameters: The rectangle side lengths $a$ and $1/a$, the connection radius $r$, and the number of vertices $N$. We then study in detail the case $a=1$ which corresponds to weighted RGGs and explore weighted RRGs characterized by $a\sim 1$, i.e.~two-dimensional geometries, but also approach the limit of quasi-one-dimensional wires when $a\gg1$. In general we look for the scaling properties of $P(s)$ and $\ell$ as a function of $a$, $r$ and $N$. We find that the ratio $r/N^\gamma$, with $\gamma(a)\approx -1/2$, fixes the properties of both RGGs and RRGs. Moreover, when $a\ge 10$ we show that spectral and eigenfunction properties of weighted RRGs are universal for the fixed ratio $r/{\cal C}N^\gamma$, with ${\cal C}\approx a$.Comment: 8 pages, 6 figure

In vitro Study of the Survival, Reproduction and Morphology of Daphnia pulicaria irradiated with a Low Energy Laser

Daphnia is a genus of crustaceans that is representative of freshwater communities. The species exhibit a high sensitivity to a wide range of toxic compounds so that they have been used internationally as biomonitors in toxicity tests to evaluate ecosystem conditions such as water quality. It is also a model genus in genetics, epigenetics and reproductive ecology. In this work, we used Daphnia pulicaria as a model to measure the effects of low-energy laser irradiation on survival, reproduction, and morphology variables of parental organisms and their offspring. We used (1) a single clone line of organisms to eliminate interindividual genetic variability; (2) individuals from more than 50 generations after the clone line was established, and offspring from the third brood onwards to dissipate maternal and epigenetic effects, and (3) neonates, those individuals of the species that have less than 48 hours of life, because they are the most sensitive stage to optical stimuli. We analyzed number of deaths, longevity, age at first reproduction, number of offspring per week, number of total offspring during all their life cycle, body size, size of the antennules, and length of the apical spine of the 4th and 5th brood of the irradiated individuals, who were exposed to a blue laser stimulus of 405 nm for 25 minutes with a power of 40 mW at a distance of 50 cm, compared to those of the control (non-irradiated) group

Theoretical Model to Estimate the Distribution of Radon in Alveolar Membrane Neighborhood

Radon is a naturally occurring radioactive gas which tends to concentrate indoors, easily emanates from the ground into the air, where it disintegrates and emits radioactive particles. It can enter the human body through breathing or ingesting mostly water. When radon inhaled, travels through the respiratory tract to alveoli where the majority is expelled into the environment. Moreover, when ingested in water, it passes into the intestine where it is absorbed and driven from the bloodstream to the lungs; in these organs, due to differences in partial pressures, it is transported to alveoli by simple diffusion process. When radon is not removed, it decays in short-lived solid disintegration products (218Po and 214Po) with high probability of being deposited in biological tissues, causing DNA damage because of the densely ionizing alpha radiation emitted. We propose a semi-empirical, smooth, and continuous pair potential function in order to model the molecular interactions between radon and lung alveolar walls; we use Molecular Dynamics (MD) to determine the gas distribution in an alveolar neighborhood wall, and estimate the quantity thereof it diffuses through the alveolar membrane as a concentration function

Revan-degree indices on random graphs

Given a simple connected non-directed graph $G=(V(G),E(G))$, we consider two families of graph invariants: $RX_\Sigma(G) = \sum_{uv \in E(G)} F(r_u,r_v)$ (which has gained interest recently) and $RX_\Pi(G) = \prod_{uv \in E(G)} F(r_u,r_v)$ (that we introduce in this work); where $uv$ denotes the edge of $G$ connecting the vertices $u$ and $v$, $r_u$ is the Revan degree of the vertex $u$, and $F$ is a function of the Revan vertex degrees. Here, $r_u = \Delta + \delta - d_u$ with $\Delta$ and $\delta$ the maximum and minimum degrees among the vertices of $G$ and $d_u$ is the degree of the vertex $u$. Particularly, we apply both $RX_\Sigma(G)$ and R$X_\Pi(G)$ on two models of random graphs: Erd\"os-R\'enyi graphs and random geometric graphs. By a thorough computational study we show that \left and \left, normalized to the order of the graph, scale with the average Revan degree \left; here \left denotes the average over an ensemble of random graphs. Moreover, we provide analytical expressions for several graph invariants of both families in the dense graph limit.Comment: 16 pages, 10 figure

An Examination of Cesarean and Vaginal Birth Histories Among Hispanic Women Entering Prenatal Care in Two California Counties with Large Immigrant Populations

Repeat cesarean delivery (CD) rates among US Hispanic women are the highest of all racial/ethnic groups (90%). Vaginal birth after cesarean (VBAC) is an alternative delivery method, but requires medical records documentation of a non-vertical incision and favorable conditions in the current pregnancy. VBAC rates for Hispanic women are extremely low. This study explores the birth histories and medical records access among Hispanic women in California, taking into account the potential role of immigration on access to VBAC. Study aims are to describe for a sample of Hispanic women: (1) CD and VBAC histories as well as history of vaginal delivery preceding CD; and (2) medical records access, among women who had previous births in Mexico. Chart review was conducted for prenatal patients from three safety net clinics in two California counties with large Mexican migrant populations between August, 2003 and February 2004—during which VBAC was widely available in these two counties to determine: obstetric histories, CD details, birthplace and whether or not medical records had been requested/obtained for CD. 355 multiparous Hispanic women were included. Thirty-three percent had a previous CD, almost two-thirds (64%) had only one CD. Over half of the women (55%) with 2+ births and CD history also reported a vaginal birth history. Medical records for CD were infrequently requested (29%). Of those requested, records were received for 77% of women with a US CD, compared with 13% of women with Mexican CD histories. Policies to address: (1) VBAC opportunities for low risk women, such as those with prior vaginal births and one CD, and (2) overcoming limited medical records access, could mitigate against unnecessary CD and associated medical expenditures and risks for future complications

Effects of Low-Energy Laser Irradiation on Sperm Cells Dynamics of Rabbit (Oryctolagus Cuniculus)

Infertility is a world disease in which a couple is unable to achieve pregnancy. There are numerous parameters to determinate fertility; nevertheless, sperm motility is by consensus one of the most important attributes to evaluate male fertility. Contributions to a better understanding of this crucial parameter are imperative; hence, the aim of this investigation was to assess the effect of low-energy laser irradiation on sperm cell dynamics in thawed samples that were cryopreserved. We used a 405 nm blue laser beam to irradiate spermatic cells from rabbit inside a temperature-controlled dispersion chamber at 37 °C; then, we applied an image recognizing system to calculate individual sperm trajectories and velocities. We found that sperms raise its motility after irradiation suggesting that λ=405 nm is an optimal wavelength for spermatic photo-stimulation