Numerical evidence against a conjecture on the cover time of planar graphs

We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time tau (G(N)) of a planar graph G(N) of N vertices and maximal degree d is lower bounded by tau (G(N)) >= C(d)N(lnN)(2) with C(d) = (d/4 pi) tan(pi/d), with equality holding for some geometries. We tested this conjecture on the regular honeycomb (d = 3), regular square (d = 4), regular elongated triangular (d = 5), and regular triangular (d = 6) lattices, as well as on the nonregular Union Jack lattice (d(min) = 4, d(max) = 8). Indeed, the Monte Carlo data suggest that the rigorous lower bound may hold as an equality for most of these lattices, with an interesting issue in the case of the Union Jack lattice. The data for the honeycomb lattice, however, violate the bound with the conjectured constant. The empirical probability distribution function of the cover time for the square lattice is also briefly presented, since very little is known about cover time probability distribution functions in general.

Epidemics in networks of spatially correlated three-dimensional root-branching structures

Using digitized images of the three-dimensional, branching structures for root systems of bean seedlings, together with analytical and numerical methods that map a common susceptible-infected- recovered (`SIR`) epidemiological model onto the bond percolation problem, we show how the spatially correlated branching structures of plant roots affect transmission efficiencies, and hence the invasion criterion, for a soil-borne pathogen as it spreads through ensembles of morphologically complex hosts. We conclude that the inherent heterogeneities in transmissibilities arising from correlations in the degrees of overlap between neighbouring plants render a population of root systems less susceptible to epidemic invasion than a corresponding homogeneous system. Several components of morphological complexity are analysed that contribute to disorder and heterogeneities in the transmissibility of infection. Anisotropy in root shape is shown to increase resilience to epidemic invasion, while increasing the degree of branching enhances the spread of epidemics in the population of roots. Some extension of the methods for other epidemiological systems are discussed.

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.

Lepidopteran larva consumption of soybean foliage: basis for developing multiple-species economic thresholds for pest management decisions

BACKGROUND: Defoliation by Anticarsia gemmatalis (Hubner), Pseudoplusia includens (Walker), Spodoptera eridania (Cramer), S. cosmioides (Walker) and S. frugiperda (JE Smith) (Lepidoptera: Noctuidae) was evaluated in four soybean genotypes. A multiple-species economic threshold (ET), based upon the species` feeding capacity, is proposed with the aim of improving growers` management decisions on when to initiate control measures for the species complex. RESULTS: Consumption by A. gemmatalis, S. cosmioides or S. eridania on different genotypes was similar. The highest consumption of P. includens was 92.7 cm(2) on Codetec 219RR; that of S. frugiperda was 118 cm(2) on Codetec 219RR and 115.1 cm(2) on MSoy 8787RR. The insect injury equivalent for S. cosmoides, calculated on the basis of insect consumption, was double the standard consumption by A. gemmatalis, and statistically different from the other species tested, which were similar to each other. CONCLUSIONS: As S. cosmioides always defoliated nearly twice the leaf area of the other species, the injury equivalent would be 2 for this lepidopteran species and 1 for the other species. The recommended multiple-species ET to trigger the beginning of insect control would then be 20 insect equivalents per linear metre. (C) 2010 Society of Chemical Industry

The gaps-in-noise test: Gap detection thresholds in normal-hearing young adults

The aim of this study was to establish parameters for the gaps-in-noise test in normal-hearing young adults. One hundred subjects (50 males and 50 females) received an audiological evaluation to rule out hearing loss and auditory processing disorder. The gaps-in-noise test was then conducted on all subjects. The mean gap detection threshold was 4.19 ms. A psychometric function by gap duration was constructed, revealing that the percentage of correct responses was less than or equal to 5% for a gap duration of 2 ms, 10-30% for a gap duration of 3 ms, 60-70% for a gap duration of 4 ms, and over 96% for gap durations of 5 ms or longer. The results suggest that the data obtained can be applied as reference values for future testing. In the subjects evaluated, the gaps-in-noise test proved to be consistent with low variability.

Neural response thresholds in the Nucleus Contour cochlear implant before and after stylet removal

Conclusion. The study shows that there are differences in the measurement of the action potentials with and without the stylet in the Nucleus Freedom Contour Advance that are higher in the apex than in the base of the cochlea. Objectives. To determine if there are differences in the intraoperative impedances and in the neural response telemetry threshold values in the Nucleus Freedom Contour Advance before and after stylet removal. Subjects and methods. This was a prospective clinical study. Intraoperative impedances and neural response telemetry in users of the Freedom Contour Advance Cochlear Implant were measured before and after stylet removal. Results. There was a significant reduction in the impedance values of an average 1.5 k Omega +/- 2.3 in common ground mode and 1.3 k Omega +/- 2.3 for all monopolar modes after the stylet removal (p < 0.001). When analyzing the apical, medium, and basal electrodes, there was a statistically significant reduction in the neural response thresholds after stylet removal only in the apical electrodes (p = 0.001).

Evaluation of somatic cell count thresholds to detect subclinical mastitis in Gyr cows

The objectives of this study were (1) to determine the sensitivity (Se) and specificity (Sp) of somatic cell count (SCC) thresholds to identify subclinical mastitis in Gyr cows caused by major and minor pathogens; (2) to study the effects of month of sampling, rear or front mammary quarters, herd, intramammary infection (IMI), and bacterial species on SCC at quarter level; and (3) to describe the prevalence of IMI in Gyr cows in commercial dairy herds. In total, 221 lactating Gyr cows from 3 commercial dairy farms were selected. Milk samples were collected from individual quarters once a month for 1 yr from all lactating cows for SCC and bacteriological analysis. Mammary quarters were considered the experimental units and the SCC results were log(10)-transformed. Four SCC thresholds (100, 200, 300 and 400 x 10(3) cells/mL) were used to determine Se and Sp to identify infected mammary quarters. The overall prevalence of IMI in quarter milk samples of Gyr cows was 49.8%, and the prevalence of minor pathogens was higher (31.9%) than that of major pathogens (17.8%). Quarter samples with microbial isolation presented higher SCC compared with negative samples. Sensitivity and Sp of selected SCC thresholds varied according to the group of pathogen (major and minor) involved in the IMI definition. Sensitivity increased and Sp decreased when mammary quarters with only major pathogens isolation were considered positive. The use of a single SCC analysis to classify quarters as uninfected or infected in Gyr cows may not be a useful test for this breed because Se and Sp of SCC at the studied thresholds were low. The occurrence of IMI and the bacterial species are the main factors responsible for SCC variation in mammary quarters of Gyr cows. Milk samples with major pathogens isolation elicited higher SCC than those with minor pathogens.

Oriented Percolation in One-dimensional 1/vertical bar x-y vertical bar(2) Percolation Models

We consider independent edge percolation models on Z, with edge occupation probabilities. We prove that oriented percolation occurs when beta > 1 provided p is chosen sufficiently close to 1, answering a question posed in Newman and Schulman (Commun. Math. Phys. 104: 547, 1986). The proof is based on multi-scale analysis.

Percolation in a network with long-range connections: Implications for cytoskeletal structure and function

Cell shape, signaling, and integrity depend on cytoskeletal organization. In this study we describe the cytoskeleton as a simple network of filamentary proteins (links) anchored by complex protein structures (nodes). The structure of this network is regulated by a distance-dependent probability of link formation as P = p/d(s), where p regulates the network density and s controls how fast the probability for link formation decays with node distance (d). It was previously shown that the regulation of the link lengths is crucial for the mechanical behavior of the cells. Here we examined the ability of the two-dimensional network to percolate (i.e. to have end-to-end connectivity), and found that the percolation threshold depends strongly on s. The system undergoes a transition around s = 2. The percolation threshold of networks with s < 2 decreases with increasing system size L, while the percolation threshold for networks with s > 2 converges to a finite value. We speculate that s < 2 may represent a condition in which cells can accommodate deformation while still preserving their mechanical integrity. Additionally, we measured the length distribution of F-actin filaments from publicly available images of a variety of cell types. In agreement with model predictions, cells originating from more deformable tissues show longer F-actin cytoskeletal filaments. (C) 2008 Elsevier B.V. All rights reserved.

The number of open paths in an oriented rho-percolation model

We study the asymptotic properties of the number of open paths of length n in an oriented rho-percolation model. We show that this number is e(n alpha(rho)(1+o(1))) as n ->infinity. The exponent alpha is deterministic, it can be expressed in terms of the free energy of a polymer model, and it can be explicitly computed in some range of the parameters. Moreover, in a restricted range of the parameters, we even show that the number of such paths is n(-1/2)We (n alpha(rho))(1+o(1)) for some nondegenerate random variable W. We build on connections with the model of directed polymers in random environment, and we use techniques and results developed in this context.

Bootstrap percolation on homogeneous trees has 2 phase transitions

We study the threshold theta bootstrap percolation model on the homogeneous tree with degree b + 1, 2 <= theta <= b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call p(f), such that a) for p > p(f), the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p < p(f) , then for almost every initial configuration, the final bootstrapped configuration has density of occupied vertices less than 1. In this paper, we establish the existence of a distinct critical value for p, p(c), such that 0 < p(c) < p(f), with the following properties: 1) if p <= p(c), then for almost every initial configuration there is no infinite cluster of occupied vertices in the final bootstrapped configuration; 2) if p > p(c), then for almost every initial configuration there are infinite clusters of occupied vertices in the final bootstrapped configuration. Moreover, we show that 3) for p < p(c), the distribution of the occupied cluster size in the final bootstrapped configuration has an exponential tail; 4) at p = p(c), the expected occupied cluster size in the final bootstrapped configuration is infinite; 5) the probability of percolation of occupied vertices in the final bootstrapped configuration is continuous on [0, p(f)] and analytic on (p(c), p(f) ), admitting an analytic continuation from the right at p (c) and, only in the case theta = b, also from the left at p(f).

The disk-percolation model on graphs

We study a long-range percolation model whose dynamics describe the spreading of an infection on an infinite graph. We obtain a sufficient condition for phase transition and prove all upper bound for the critical parameter of spherically symmetric trees. (C) 2008 Elsevier B.V. All rights reserved.

Validity and reliability of methods for the detection of secondary caries around amalgam restorations in primary teeth

Secondary caries has been reported as the main reason for restoration replacement. The aim of this in vitro study was to evaluate the performance of different methods - visual inspection, laser fluorescence (DIAGNOdent), radiography and tactile examination - for secondary caries detection in primary molars restored with amalgam. Fifty-four primary molars were photographed and 73 suspect sites adjacent to amalgam restorations were selected. Two examiners evaluated independently these sites using all methods. Agreement between examiners was assessed by the Kappa test. To validate the methods, a caries-detector dye was used after restoration removal. The best cut-off points for the sample were found by a Receiver Operator Characteristic (ROC) analysis, and the area under the ROC curve (Az), and the sensitivity, specificity and accuracy of the methods were calculated for enamel (D2) and dentine (D3) thresholds. These parameters were found for each method and then compared by the McNemar test. The tactile examination and visual inspection presented the highest inter-examiner agreement for the D2 and D3 thresholds, respectively. The visual inspection also showed better performance than the other methods for both thresholds (Az = 0.861 and Az = 0.841, respectively). In conclusion, the visual inspection presented the best performance for detecting enamel and dentin secondary caries in primary teeth restored with amalgam.

Operant measurement of auditory threshold in prelingually deaf users of cochlear implants: II

Two experiments evaluated an operant procedure for establishing stimulus control using auditory and electrical stimuli as a baseline for measuring the electrical current threshold of electrodes implanted in the cochlea. Twenty-one prelingually deaf children, users of cochlear implants, learned a Go/No Go auditory discrimination task (i.e., pressing a button in the presence of the stimulus but not in its absence). When the simple discrimination baseline became stable, the electrical current was manipulated in descending and ascending series according to an adapted staircase method. Thresholds were determined for three electrodes, one in each location in the cochlea (basal, medial, and apical). Stimulus control was maintained within a certain range of decreasing electrical current but was eventually disrupted. Increasing the current recovered stimulus control, thus allowing the determination of a range of electrical currents that could be defined as the threshold. The present study demonstrated the feasibility of the operant procedure combined with a psychophysical method for threshold assessment, thus contributing to the routine fitting and maintenance of cochlear implants within the limitations of a hospital setting.

Medidas operantes de limiar auditivo em crianças com surdez pré-lingual, usuárias de implante coclear

Limiares auditivos de crianças surdas pré-linguais usuárias de implante coclear foram avaliados com estimulação elétrica em um dos eletrodos mediais. A avaliação empregou um procedimento operante do tipo go/no go para ensinar uma discriminação simples, evidenciada por uma resposta motora, entre presença e ausência do estímulo auditivo. Estabelecida a linha de base, a manipulação na intensidade do estímulo foi implementada de acordo com o método psicofísico de escada modificado, começando por uma seqüência descendente. Os sete participantes do estudo mostraram perda da precisão no responder sob controle do estímulo quando a intensidade diminuía além de um certo valor e a precisão era recuperada quando a intensidade era novamente aumentada, o que permitiu a identificação de limiares individuais. Os resultados sugerem que o método psicofísico combinado com o procedimento operante pode ser uma alternativa viável para avaliar limiar auditivo de pessoas sem linguagem em situação clínica de regulagem do implante coclear.