Recurrence and Polya number of general one-dimensional random walks

The recurrence properties of random walks can be characterized by P\'{o}lya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we consider recurrence properties for a general 1D random walk on a line, in which at each time step the walker can move to the left or right with probabilities $l$ and $r$, or remain at the same position with probability $o$ ($l+r+o=1$). We calculate P\'{o}lya number $P$ of this model and find a simple expression for $P$ as, $P=1-\Delta$, where $\Delta$ is the absolute difference of $l$ and $r$ ($\Delta=|l-r|$). We prove this rigorous expression by the method of creative telescoping, and our result suggests that the walk is recurrent if and only if the left-moving probability $l$ equals to the right-moving probability $r$.Comment: 3 page short pape

Recent changes of water discharge and sediment load in the Yellow River basin, China

The Yellow River basin contributes approximately 6% of the sediment load from all river systems globally, and the annual runoff directly supports 12% of the Chinese population. As a result, describing and understanding recent variations of water discharge and sediment load under global change scenarios are of considerable importance. The present study considers the annual hydrologic series of the water discharge and sediment load of the Yellow River basin obtained from 15 gauging stations (10 mainstream, 5 tributaries). The Mann-Kendall test method was adopted to detect both gradual and abrupt change of hydrological series since the 1950s. With the exception of the area draining to the Upper Tangnaihai station, results indicate that both water discharge and sediment load have decreased significantly (p<0.05). The declining trend is greater with distance downstream, and drainage area has a significant positive effect on the rate of decline. It is suggested that the abrupt change of the water discharge from the late 1980s to the early 1990s arose from human extraction, and that the abrupt change in sediment load was linked to disturbance from reservoir construction.Geography, PhysicalGeosciences, MultidisciplinarySCI(E)43ARTICLE4541-5613

Estrogen metabolism and mammographic density in postmenopausal women : a cross-sectional study

Background: Prospective studies have consistently found that postmenopausal breast cancer risk increases with circulating estrogens; however, findings from studies of estrogens and mammographic density (MD), an intermediate marker of breast cancer risk, have been inconsistent. We investigated the cross-sectional associations of urinary estrogens, and their 2-, 4-, and 16-hydroxylated metabolites with MD. Methods: Postmenopausal women without breast cancer (n = 194), ages 48 to 82 years, and reporting no current menopausal hormone therapy use were enrolled at a clinic in Western NY in 2005. Urinary estrogens and estrogen metabolites were measured using mass spectrometry. Percent MD and dense area (cm2) were measured using computer-assisted analyses of digitized films. Linear regression models were used to estimate associations of log-transformed estrogen measures with MD while adjusting for age, body mass index (BMI), parity, and past hormone therapy use. Results: Urinary concentrations of most individual estrogens and metabolites were not associated with MD; however, across the interdecile range of the ratio of parent estrogens (estrone and estradiol) to their metabolites, MD increased by 6.8 percentage points (P = 0.02) and dense area increased by 10.3 cm2 (P = 0.03). Across the interdecile ranges of the ratios of 2-, 4-, and 16-hydroxylation pathways to the parent estrogens, MD declined by 6.2 (P = 0.03), 6.4 (P = 0.04), and 5.7 (P = 0.05) percentage points, respectively. All associations remained apparent in models without adjustment for BMI. Conclusion: In this study of postmenopausal women, less extensive hydroxylation of parent estrogens was associated with higher MD. Impact: Hydroxylation of estrogens may modulate postmenopausal breast cancer risk through a pathway involving MD

Studies of the electric dipole transitions of deformed rare-earth nuclei

Spectrum and electric dipole transition rates and relative intensities in $^{152-154}$Sm, $^{156-160}$Gd, $^{160-162}$Dy are studied in the framework of the interacting boson model with s,p,d,f bosons. It is found that E1 transition data among the low-lying levels are in good agreement with the SU(3) dynamical symmetry of the spdf interacting boson model proposed by Engel and Iachello to describe collective rotation with octupole vibration. These results show that these nuclei have SU(3) dynamic symmetry to a good approximation. Also in this work many algebraic expressions for electric dipole transitions in the SU(3) limit of the spdf-IBM have been obtained. These formulae together with the formulae given previously exhaust nearly all the E1 transitions for low-lying negative parity states. They are useful in analyzing experimental data.Comment: 26 pages, 1 figur

Modulation of mouse neural crest cell motility by N-cadherin and connexin 43 gap junctions

Connexin 43 (Cx43α1) gap junction has been shown to have an essential role in mediating functional coupling of neural crest cells and in modulating neural crest cell migration. Here, we showed that N-cadherin and wnt1 are required for efficient dye coupling but not for the expression of Cx43α1 gap junctions in neural crest cells. Cell motility was found to be altered in the N-cadherin–deficient neural crest cells, but the alterations were different from that elicited by Cx43α1 deficiency. In contrast, wnt1-deficient neural crest cells showed no discernible change in cell motility. These observations suggest that dye coupling may not be a good measure of gap junction communication relevant to motility. Alternatively, Cx43α1 may serve a novel function in motility. We observed that p120 catenin (p120ctn), an Armadillo protein known to modulate cell motility, is colocalized not only with N-cadherin but also with Cx43α1. Moreover, the subcellular distribution of p120ctn was altered with N-cadherin or Cx43α1 deficiency. Based on these findings, we propose a model in which Cx43α1 and N-cadherin may modulate neural crest cell motility by engaging in a dynamic cross-talk with the cell's locomotory apparatus through p120ctn signaling

Stability of 1+1 dimensional causal relativistic viscous hydrodynamics

The stability of the 1+1 dimensional solution of Israel-Stewart theory is investigated. Firstly, the evolution of the temperature and the ratio of the bulk pressure over the equilibrium pressure of the background is explored. Then the stability with linear perturbations is studied by using the Lyapunov direct method. It shows that the shear viscosity may weaken the instability induced by the large peak of bulk viscosity around the phase transition temperature $T_c$.Comment: 18 pages, 4 figures, 1 table; to be published in Nuclear Physics

Di-hadron azimuthal correlation and Mach-like cone structure in parton/hadron transport model

In the framework of a multi-phase transport model (AMPT) with both partonic and hadronic interactions, azimuthal correlations between trigger particles and associated scattering particles have been studied by the mixing-event technique. The momentum ranges of these particles are $3< p^{trig}_T< 6$ GeV/$c$ and $0.15< p_{T}^{assoc} < 3$ GeV/$c$ (soft), or $2.5<p^{trig}_T<$ 4 GeV/$c$ and $1< p_{T}^{assoc} < 2.5$ GeV/$c$ (hard) in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. A Mach-like structure has been observed in correlation functions for central collisions. By comparing scenarios with and without parton cascade and hadronic rescattering, we show that both partonic and hadronic dynamical mechanisms contribute to the Mach-like structure of the associated particle azimuthal correlations. The contribution of hadronic dynamical process can not be ignored in the emergence of Mach-like correlations of the soft scattered associated hadrons. However, hadronic rescattering alone cannot reproduce experimental amplitude of Mach-like cone on away-side, and the parton cascade process is essential to describe experimental amplitude of Mach-like cone on away-side. In addition, both the associated multiplicity and the sum of $p_{T}$ decrease, whileas the $$ increases, with the impact parameter in the AMPT model including partonic dynamics from string melting scenario.Comment: 9 pages, 5 figures; Physics Letters B 641, 362-367 (2006