Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.

A critical analysis of Doppler velocimetry in the differential diagnosis of malignant and benign ovarian masses

Objectives: To evaluate the intratumoral reliability of color Doppler parameters and the contribution of Doppler sonography to the gray-scale differential diagnosis of ovarian masses. Methods: An observational study was performed including 67 patients, 15 (22.4%) with malignant ovarian neoplasm and 52 (77.6%) with benign ovarian diseases. We performed the Doppler evaluation in two distinct vessels selected after decreasing the Doppler gain to sample only vessels with higher velocity flow. Doppler measurements were obtained from each identified vessel, and resistive index (RI), pulsatility index (PI), peak systolic velocity (PSV), and end-diastolic velocity (EDV) were measured. Intraclass coefficient of correlation (ICC), sensitivity, specificity, and potential improvement in gray-scale ultrasound performance were calculated. Results: The general ICC were 0.60 (95% CI 0.42- 0.73) for RI, 0.65 (95% CI 0.49- 0.77) for PI, 0.07 (95% CI- 0.17-0.30) for PSV, and 0.19 (95% CI -0.05-0.41) for EDV. The sensitivity and specificity were respectively 84.6% and 86.7% for RI, 69.2% and 93.3% for PI, 80.0% and 65.4% for gray-scale sonography, and 93.3% and 65.4% for gray-scale plus RI (p = 0.013). Conclusions: Gynecologists must be careful in interpreting results from Doppler evaluation of ovarian masses because PSV and EDV present poor intratumoral reliability. The lower RI value, evaluated in at least two distinct sites of the tumor, was able to improve the performance of gray-scale ultrasound in differential diagnosis of ovarian masses.

Afferent Connections to the Rostrolateral Part of the Periaqueductal Gray: A Critical Region Influencing the Motivation Drive to Hunt and Forage

Previous studies have shown that a particular site in the periaqueductal gray (PAG), the rostrolateral PAG, influences the motivation drive to forage or hunt. To have a deeper understanding on the putative paths involved in the decision-making process between foraging, hunting, and other behavioral responses, in the present investigation, we carried out a systematic analysis of the neural inputs to the rostrolateral PAG (rlPAG), using Fluorogold as a retrograde tracer. According to the present findings, the rlPAG appears to be importantly driven by medial prefrontal cortical areas involved in controlling attention-related and decision-making processes. Moreover, the rlPAG also receives a wealth of information from different amygdalar, hypothalamic, and brainstem sites related to feeding, drinking, or hunting behavioral responses. Therefore, this unique combination of afferent connections puts the rlPAG in a privileged position to influence the motivation drive to choose whether hunting and foraging would be the most appropriate adaptive responses. Copyright (C) 2009 Sandra Regina Mota-Ortiz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Effect of Hormonal Supplementation Periods and In Vitro Maturation Media on Developmental Competence of Pig Oocytes

Background: The oocyte ability to undergo successful fertilization, cleavage and embryonic development depends on meiotic maturation and developmental competence acquisition. In vitro maturation (IVM) protocols currently use eCG, hCG or a combination of both, the effect of these gonadotrophins during IVM and subsequent embryonic development is still controversial. Several media have been used for IVM of porcine oocytes: TCM199, Whitten's and NCSU23 have also been shown to support pig oocyte IVM. This study was designed to determine the effect of hormonal supplementation period and maturation media during in vitro maturation of pig oocytes (1) and subsequent embryonic development (2). Materials, Methods & Results: Oocytes with intact cumulus oophurus layers and homogeneous cytoplasm were collected from prebubertal gilts. IVM was subjected in NCSU23, TCM199 or Whitten's media supplemented with 10 IU/mL eCG and 10 IU/mL hCG for the first 24 or 48 h of IVM. In each replicate the oocytes were fixed every 4 h from 32 to 48 h IVM or the past 48 h after IVM, oocytes were fertilized in vitro in mTBM medium for six hours and cultured in NCSU23 medium for nine days. Cleavage, blastocyst and hatching rates were evaluated at 48 h (day 2), 168 h (day 7) and 216 h (day 9), respectively. The addition of eCG and hCG during the first 24 h IVM increased the proportion of oocytes that reached MII stage at 44 h of maturation in NCSU23 medium. This effect was also observed in Whitten medium at 44 and 48 h (P < 0.05). However, it was not observed in the TCM199 medium. No effect of maturation medium on oocyte nuclear maturation (P > 0.05) was observed in oocytes matured in the presence of eCG and hCG during the first 24 h IVM or during 48 h IVM. A progressive increase of maturation indexes was observed on oocytes matured with hormonal supplementation in Whitten media for 24 h. Higher indexes were obtained at 44 and 48 h. When NCSU23 media was used, no difference after 36 h of maturation was observed. The same result was observed in TCM199. A progressive increase of maturation indexes was observed on oocytes matured with hormonal supplementation for 48 h in Whitten media. Higher indexes were obtained in 36 and 40 h. When NCSU23 or TCM199 were used, no difference was observed. No effect of IVM media on the percentage of fertilized oocytes and polyspermic oocytes or number of spermatozoa per fertilized oocytes was observed. Also, no effect of IVM media on cleavage and blastocyst rates was seen. However, the proportion of hatched blastocysts was lower in NCSU23 compared to Whitten or TCM199. Discussion: Similar results were reported by Marques et al. [13], that it no differences between hormonal supplementation for 22 or 44 h were observed. Therefore, more studies are needed to elucidate the role of these hormones in nuclear in vitro maturation in pig oocytes. In conclusion, no effect of maturation media on meiotic progression was observed. However, the proportion of oocytes that reached metaphase II (MII) stage was higher when eCG + hCG were added for 24 h than 48 h mainly at the 44 h of maturation. In addition, no differences were observed in cleavage and blastocyst rates of the cultured embryos. However, embryos cultured in NCSU23 showed lower rates of hatching compared to other media. These results indicated no effect of maturation media on the fertilization and embryonic development even in the presence of cysteine, PFF and EGF, except for hatched embryos that these rates were lower in NCSU23.

Application of Low-Level Laser Irradiation (LLLI) and rhBMP-2 in Critical Bone Defect of Ovariectomized Rats: Histomorphometric Evaluation

Objectives: The aim of this study was to evaluate the osteogenic potential of recombinant human bone morphogenetic protein-2 (rhBMP-2) and low-level laser irradiation (LLLI), isolated or combined in critical bone defects (5mm) in parietal bone using ovariectomized female rats as an experimental animal model. Materials and Methods: Forty-nine female Wistar rats, bilaterally ovariectomized (OVX), were divided into seven treatment groups of seven animals each: (I) laser in a single application, (II) 7 mu g of pure rhBMP-2, (III) laser and 7 mu g of pure rhBMP-2, (IV) 7 mu g of rhBMP-2/monoolein gel, (V) laser and 7 mu g of rhBMP-2/monoolein gel, (VI) laser and pure monoolein gel, and (VII) critical bone defect controls. The low-level laser source used was a gallium aluminum arsenide semiconductor diode laser device (lambda = 780 nm, D = 120 J/cm(2)). Results: Groups II and III presented higher levels of newly formed bone than all other groups with levels of 40.57% and 40.39%, respectively (p < 0.05). The levels of newly formed bone of groups I, IV, V, and VI were similar with levels of 29.67%, 25.75%, 27.75%, and 30.64%, respectively (p > 0.05). The area of new bone formation in group VII was 20.96%, which is significantly lower than groups I, II, III, and VI. Conclusions: It was concluded that pure rhBMP-2 and a single dose of laser application stimulated new bone formation, but the new bone formation area was significantly increased when only rhBMP-2 was used. Additionally, the laser application in combination with other treatments did not influence the bone formation area.

Nonlinear diffraction of light beams propagating in photorefractive media with embedded reflecting wire

The theory of nonlinear diffraction of intensive light beams propagating through photorefractive media is developed. Diffraction occurs on a reflecting wire embedded in the nonlinear medium at a relatively small angle with respect to the direction of the beam propagation. It is shown that this process is analogous to the generation of waves by a flow of a superfluid past an obstacle. The ""equation of state"" of such a superfluid is determined by the nonlinear properties of the medium. On the basis of this hydrodynamic analogy, the notion of the ""Mach number"" is introduced where the transverse component of the wave vector plays the role of the fluid velocity. It is found that the Mach cone separates two regions of the diffraction pattern: inside the Mach cone oblique dark solitons are generated and outside the Mach cone the region of ""optical ship waves"" (the wave pattern formed by a two-dimensional packet of linear waves) is situated. Analytical theory of the ""optical ship waves"" is developed and two-dimensional dark soliton solutions of the generalized two-dimensional nonlinear Schrodinger equation describing the light beam propagation are found. Stability of dark solitons with respect to their decay into vortices is studied and it is shown that they are stable for large enough values of the Mach number.

Thermodiffusion in a multicomponent lyotropic mixture in the vicinity of the critical micellar concentration by using the Z-scan technique

Thermodiffusion in a lyotropic mixture of water and potassium laurate is investigated by means of an optical technique (Z scan) distinguishing the index variations due to the temperature gradient and the mass gradients. A phenomenological framework allowing for coupled diffusion is developed in order to analyze thermodiffusion in multicomponent systems. An observable parameter relating to the mass gradients is found to exhibit a sharp change around the critical micellar concentration, and thus may be used to detect it. The change in the slope is due to the markedly different values of the Soret coefficients of the surfactant and the micelles. The difference in the Soret coefficients is due to the fact that the micellization process reduces the energy of interaction of the ball of amphiphilic molecules with the solvent.

Critical behavior of the susceptible-infected-recovered model on a square lattice

By means of numerical simulations and epidemic analysis, the transition point of the stochastic asynchronous susceptible-infected-recovered model on a square lattice is found to be c(0)=0.176 500 5(10), where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of lambda(c)=(1-c(0))/c(0)=4.665 71(3) and a net transmissibility of (1-c(0))/(1+3c(0))=0.538 410(2), which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the two-dimensional percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.

Critical behavior of the magnetization in the spin-gapped system NiCl(2)-4SC (NH(2))(2)

We report accurate magnetization measurements on the spin-gap compound NiCl(2)-4SC (NH(2))(2) around the low portion of the magnetic induced phase ordering. The critical density of the magnetization at the phase boundary is analyzed in terms of a Bose-Einstein condensation (BEC) of bosonic particles, and the boson interaction strength is obtained as upsilon(0)=0.61 meV. The detailed analysis of the magnetization data across the transition leads to the conclusion for the preservation of the U(1) symmetry, as required for BEC. (c) 2009 American Institute of Physics. [DOI: 10.1063/1.3055265]

Critical Properties at the Field-Induced Bose-Einstein Condensation in NiCl(2)-4SC(NH(2))(2)

We report new magnetization measurements on the spin-gap compound NiCl(2)-4SC(NH(2))(2) at the low-field boundary of the magnetic field-induced ordering. The critical density of the magnetization is analyzed in terms of a Bose-Einstein condensation of bosonic quasiparticles. The analysis of the magnetization at the transition leads to the conclusion for the preservation of the U(1) symmetry, as required for Bose-Einstein condensation. The experimental data are well described by quantum Monte Carlo simulations.

Character of magnetic excitations in a quasi-one-dimensional antiferromagnet near the quantum critical points: Impact on magnetoacoustic properties

We report results of magnetoacoustic studies in the quantum spin-chain magnet NiCl(2)-4SC(NH(2))(2) (DTN) having a field-induced ordered antiferromagnetic (AF) phase. In the vicinity of the quantum critical points (QCPs) the acoustic c(33) mode manifests a pronounced softening accompanied by energy dissipation of the sound wave. The acoustic anomalies are traced up to T > T(N), where the thermodynamic properties are determined by fermionic magnetic excitations, the ""hallmark"" of one-dimensional (1D) spin chains. On the other hand, as established in earlier studies, the AF phase in DTN is governed by bosonic magnetic excitations. Our results suggest the presence of a crossover from a 1D fermionic to a three-dimensional bosonic character of the magnetic excitations in DTN in the vicinity of the QCPs.

Monte Carlo investigation of the critical behavior of Stavskaya's probabilistic cellular automaton

Stavskaya's model is a one-dimensional probabilistic cellular automaton (PCA) introduced in the end of the 1960s as an example of a model displaying a nonequilibrium phase transition. Although its absorbing state phase transition is well understood nowadays, the model never received a full numerical treatment to investigate its critical behavior. In this Brief Report we characterize the critical behavior of Stavskaya's PCA by means of Monte Carlo simulations and finite-size scaling analysis. The critical exponents of the model are calculated and indicate that its phase transition belongs to the directed percolation universality class of critical behavior, as would be expected on the basis of the directed percolation conjecture. We also explicitly establish the relationship of the model with the Domany-Kinzel PCA on its directed site percolation line, a connection that seems to have gone unnoticed in the literature so far.

Precise determination of quantum critical points by the violation of the entropic area law

Finite-size scaling analysis turns out to be a powerful tool to calculate the phase diagram as well as the critical properties of two-dimensional classical statistical mechanics models and quantum Hamiltonians in one dimension. The most used method to locate quantum critical points is the so-called crossing method, where the estimates are obtained by comparing the mass gaps of two distinct lattice sizes. The success of this method is due to its simplicity and the ability to provide accurate results even considering relatively small lattice sizes. In this paper, we introduce an estimator that locates quantum critical points by exploring the known distinct behavior of the entanglement entropy in critical and noncritical systems. As a benchmark test, we use this new estimator to locate the critical point of the quantum Ising chain and the critical line of the spin-1 Blume-Capel quantum chain. The tricritical point of this last model is also obtained. Comparison with the standard crossing method is also presented. The method we propose is simple to implement in practice, particularly in density matrix renormalization group calculations, and provides us, like the crossing method, amazingly accurate results for quite small lattice sizes. Our applications show that the proposed method has several advantages, as compared with the standard crossing method, and we believe it will become popular in future numerical studies.

Finite-size corrections to entanglement in quantum critical systems

We analyze the finite-size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite-size contributions to a general measure of ground state entanglement, which are ruled by the central charge of the underlying conformal field theory. More generally, we show that all conformal towers formed by an infinite number of excited states (as the size of the system L -> infinity) exhibit a unique pattern of entanglement, which differ only at leading order (1/L)(2). In this case, entanglement is also shown to obey a universal structure, given by the anomalous dimensions of the primary operators of the theory. As an illustration, we discuss the behavior of pairwise entanglement for the eigenspectrum of the spin-1/2 XXZ chain with an arbitrary length L for both periodic and twisted boundary conditions.

Catalytic oxidation of ethanol on gold electrode in alkaline media

This work presents a study of the catalytic oxidation of ethanol on polycrystalline gold electrode in alkaline media. The investigation was carried out by means of chronoamperometry, cyclic voltammetry, and in situ FTIR spectroscopy. The main goal was to investigate the early stages of ethanol electrooxidation, namely at fairly low potentials (E = 600 mV vs. RHE) and for moderate reaction times (t < 300 s). Chronoamperometric experiments show a current increase accompanying the increasing in the ethanol concentration up to about 2 M and then a slight decrease at 3 M. Adsorbed CO has been observed as early as about 200 mV vs. RHE and indicates that the cleavage of the C-C bond might occur, probably to a small extent, at very low overpotentials during ethanol adsorption on gold surface. The amount of dissolved acetate ions produced during the chronoamperomentry was followed by the asymmetric stretching band at 1558 cm(-1) as a function of time, and found to increase linearly with time up to 300 s. This allowed estimating the reaction order of acetate formation with respect to ethanol concentration.