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.

On quantum integrability of the Landau-Lifshitz model

We investigate the quantum integrability of the Landau-Lifshitz (LL) model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization, which arises due to the ill-defined operator product, is dealt with by simultaneously regularizing the operator product and constructing the self-adjoint extensions of a very particular structure. The diagonalizibility difficulties of the Hamiltonian of the LL model, due to the highly singular nature of the quantum-mechanical Hamiltonian, are also resolved in our method for the arbitrary n-particle sector. We explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to Sklyanin [Lett. Math. Phys. 15, 357 (1988)] and give a prescription to systematically construct the general solution, which explains and generalizes the puzzling results of Sklyanin for the particular two-particle sector case. Moreover, we demonstrate the S-matrix factorization and show that it is a consequence of the discontinuity conditions on the functions involved in the construction of the self-adjoint extensions.

Gravitational wave recoil in Robinson-Trautman spacetimes

We consider the gravitational recoil due to nonreflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the nonlinear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the nonaxisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed.

Decoherence-free evolution of time-dependent superposition states of two-level systems and thermal effects

In this paper we detail some results advanced in a recent letter [Prado et al., Phys. Rev. Lett. 102, 073008 (2009).] showing how to engineer reservoirs for two-level systems at absolute zero by means of a time-dependent master equation leading to a nonstationary superposition equilibrium state. We also present a general recipe showing how to build nonadiabatic coherent evolutions of a fermionic system interacting with a bosonic mode and investigate the influence of thermal reservoirs at finite temperature on the fidelity of the protected superposition state. Our analytical results are supported by numerical analysis of the full Hamiltonian model.

Equivalence between Redfield- and master-equation approaches for a time-dependent quantum system and coherence control

We present a derivation of the Redfield formalism for treating the dissipative dynamics of a time-dependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a time-dependent spin-1/2 system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times T(1) and T(2) (associated with the longitudinal and transverse relaxations, respectively). These characteristic times are shown to be related to the operator-sum representation and the equivalent phenomenological-operator approach. Finally, we present a protocol to circumvent the decoherence processes due to the loss of energy (and thus, associated with T(1)). To this end, we simply associate the time dependence of the quantum system to an easily achieved modulated frequency. A possible implementation of the protocol is also proposed in the context of nuclear magnetic resonance.

Context tree selection: A unifying view

Context tree models have been introduced by Rissanen in [25] as a parsimonious generalization of Markov models. Since then, they have been widely used in applied probability and statistics. The present paper investigates non-asymptotic properties of two popular procedures of context tree estimation: Rissanen's algorithm Context and penalized maximum likelihood. First showing how they are related, we prove finite horizon bounds for the probability of over- and under-estimation. Concerning overestimation, no boundedness or loss-of-memory conditions are required: the proof relies on new deviation inequalities for empirical probabilities of independent interest. The under-estimation properties rely on classical hypotheses for processes of infinite memory. These results improve on and generalize the bounds obtained in Duarte et al. (2006) [12], Galves et al. (2008) [18], Galves and Leonardi (2008) [17], Leonardi (2010) [22], refining asymptotic results of Buhlmann and Wyner (1999) [4] and Csiszar and Talata (2006) [9]. (C) 2011 Elsevier B.V. All rights reserved.

Prevalence of fibromyalgia in a low socioeconomic status population

Background: The aim of this study was to estimate the prevalence of fibromyalgia, as well as to assess the major symptoms of this syndrome in an adult, low socioeconomic status population assisted by the primary health care system in a city in Brazil. Methods: We cross-sectionally sampled individuals assisted by the public primary health care system (n = 768, 35-60 years old). Participants were interviewed by phone and screened about pain. They were then invited to be clinically assessed (304 accepted). Pain was estimated using a Visual Analogue Scale (VAS). Fibromyalgia was assessed using the Fibromyalgia Impact Questionnaire (FIQ), as well as screening for tender points using dolorimetry. Statistical analyses included Bayesian Statistics and the Kruskal-Wallis Anova test (significance level = 5%). Results: From the phone-interview screening, we divided participants (n = 768) in three groups: No Pain (NP) (n = 185); Regional Pain (RP) (n = 388) and Widespread Pain (WP) (n = 106). Among those participating in the clinical assessments, (304 subjects), the prevalence of fibromyalgia was 4.4% (95% confidence interval [2.6%; 6.3%]). Symptoms of pain (VAS and FIQ), feeling well, job ability, fatigue, morning tiredness, stiffness, anxiety and depression were statically different among the groups. In multivariate analyses we found that individuals with FM and WP had significantly higher impairment than those with RP and NP. FM and WP were similarly disabling. Similarly, RP was no significantly different than NP. Conclusion: Fibromyalgia is prevalent in the low socioeconomic status population assisted by the public primary health care system. Prevalence was similar to other studies (4.4%) in a more diverse socioeconomic population. Individuals with FM and WP have significant impact in their well being.

POLLING SYSTEMS WITH PARAMETER REGENERATION, THE GENERAL CASE

We consider a polling model with multiple stations, each with Poisson arrivals and a queue of infinite capacity. The service regime is exhaustive and there is Jacksonian feedback of served customers. What is new here is that when the server comes to a station it chooses the service rate and the feedback parameters at random; these remain valid during the whole stay of the server at that station. We give criteria for recurrence, transience and existence of the sth moment of the return time to the empty state for this model. This paper generalizes the model, when only two stations accept arriving jobs, which was considered in [Ann. Appl. Probab. 17 (2007) 1447-1473]. Our results are stated in terms of Lyapunov exponents for random matrices. From the recurrence criteria it can be seen that the polling model with parameter regeneration can exhibit the unusual phenomenon of null recurrence over a thick region of parameter space.

A note on the likelihood and moments of the skew-normal distribution

In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting.

The impact of measurement errors in the identification of regulatory networks

Background: There are several studies in the literature depicting measurement error in gene expression data and also, several others about regulatory network models. However, only a little fraction describes a combination of measurement error in mathematical regulatory networks and shows how to identify these networks under different rates of noise. Results: This article investigates the effects of measurement error on the estimation of the parameters in regulatory networks. Simulation studies indicate that, in both time series (dependent) and non-time series (independent) data, the measurement error strongly affects the estimated parameters of the regulatory network models, biasing them as predicted by the theory. Moreover, when testing the parameters of the regulatory network models, p-values computed by ignoring the measurement error are not reliable, since the rate of false positives are not controlled under the null hypothesis. In order to overcome these problems, we present an improved version of the Ordinary Least Square estimator in independent (regression models) and dependent (autoregressive models) data when the variables are subject to noises. Moreover, measurement error estimation procedures for microarrays are also described. Simulation results also show that both corrected methods perform better than the standard ones (i.e., ignoring measurement error). The proposed methodologies are illustrated using microarray data from lung cancer patients and mouse liver time series data. Conclusions: Measurement error dangerously affects the identification of regulatory network models, thus, they must be reduced or taken into account in order to avoid erroneous conclusions. This could be one of the reasons for high biological false positive rates identified in actual regulatory network models.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

Can we make a Bohmian electron reach the speed of light, at least for one instant?

In Bohmian mechanics, a version of quantum mechanics that ascribes world lines to electrons, we can meaningfully ask about an electron's instantaneous speed relative to a given inertial frame. Interestingly, according to the relativistic version of Bohmian mechanics using the Dirac equation, a massive particle's speed is less than or equal to the speed of light, but not necessarily less. That is, there are situations in which the particle actually reaches the speed of light-a very nonclassical behavior. That leads us to the question of whether such situations can be arranged experimentally. We prove a theorem, Theorem 5, implying that for generic initial wave functions the probability that the particle ever reaches the speed of light, even if at only one point in time, is zero. We conclude that the answer to the question is no. Since a trajectory reaches the speed of light whenever the quantum probability current (psi) over bar gamma(mu)psi is a lightlike 4-vector, our analysis concerns the current vector field of a generic wave function and may thus be of interest also independently of Bohmian mechanics. The fact that the current is never spacelike has been used to argue against the possibility of faster-than-light tunneling through a barrier, a somewhat similar question. Theorem 5, as well as a more general version provided by Theorem 6, are also interesting in their own right. They concern a certain property of a function psi : R(4) -> C(4) that is crucial to the question of reaching the speed of light, namely being transverse to a certain submanifold of C(4) along a given compact subset of space-time. While it follows from the known transversality theorem of differential topology that this property is generic among smooth functions psi : R(4) -> C(4), Theorem 5 asserts that it is also generic among smooth solutions of the Dirac equation. (C) 2010 American Institute of Physics. [doi:10.1063/1.3520529]

LIMIT THEOREMS FOR A GENERAL STOCHASTIC RUMOUR MODEL

We study a general stochastic rumour model in which an ignorant individual has a certain probability of becoming a stifler immediately upon hearing the rumour. We refer to this special kind of stifler as an uninterested individual. Our model also includes distinct rates for meetings between two spreaders in which both become stiflers or only one does, so that particular cases are the classical Daley-Kendall and Maki-Thompson models. We prove a Law of Large Numbers and a Central Limit Theorem for the proportions of those who ultimately remain ignorant and those who have heard the rumour but become uninterested in it.

The impact of the subtropical South Atlantic SST on South American precipitation

The Community Climate Model (CCM3) from the National Center for Atmospheric Research (NCAR) is used to investigate the effect of the South Atlantic sea surface temperature (SST) anomalies on interannual to decadal variability of South American precipitation. Two ensembles composed of multidecadal simulations forced with monthly SST data from the Hadley Centre for the period 1949 to 2001 are analysed. A statistical treatment based on signal-to-noise ratio and Empirical Orthogonal Functions (EOF) is applied to the ensembles in order to reduce the internal variability among the integrations. The ensemble treatment shows a spatial and temporal dependence of reproducibility. High degree of reproducibility is found in the tropics while the extratropics is apparently less reproducible. Austral autumn (MAM) and spring (SON) precipitation appears to be more reproducible over the South America-South Atlantic region than the summer (DJF) and winter (JJA) rainfall. While the Inter-tropical Convergence Zone (ITCZ) region is dominated by external variance, the South Atlantic Convergence Zone (SACZ) over South America is predominantly determined by internal variance, which makes it a difficult phenomenon to predict. Alternatively, the SACZ over western South Atlantic appears to be more sensitive to the subtropical SST anomalies than over the continent. An attempt is made to separate the atmospheric response forced by the South Atlantic SST anomalies from that associated with the El Nino - Southern Oscillation (ENSO). Results show that both the South Atlantic and Pacific SSTs modulate the intensity and position of the SACZ during DJF. Particularly, the subtropical South Atlantic SSTs are more important than ENSO in determining the position of the SACZ over the southeast Brazilian coast during DJF. On the other hand, the ENSO signal seems to influence the intensity of the SACZ not only in DJF but especially its oceanic branch during MAM. Both local and remote influences, however, are confounded by the large internal variance in the region. During MAM and JJA, the South Atlantic SST anomalies affect the magnitude and the meridional displacement of the ITCZ. In JJA, the ENSO has relatively little influence on the interannual variability of the simulated rainfall. During SON, however, the ENSO seems to counteract the effect of the subtropical South Atlantic SST variations on convection over South America.

Haplotype distribution of five nuclear genes based on network genealogies and Bayesian inference indicates that Trypanosoma cruzi hybrid strains are polyphyletic

Chagas disease is still a major public health problem in Latin America. Its causative agent, Trypanosoma cruzi, can be typed into three major groups, T. cruzi I, T. cruzi II and hybrids. These groups each have specific genetic characteristics and epidemiological distributions. Several highly virulent strains are found in the hybrid group; their origin is still a matter of debate. The null hypothesis is that the hybrids are of polyphyletic origin, evolving independently from various hybridization events. The alternative hypothesis is that all extant hybrid strains originated from a single hybridization event. We sequenced both alleles of genes encoding EF-1 alpha, actin and SSU rDNA of 26 T. cruzi strains and DHFR-TS and TR of 12 strains. This information was used for network genealogy analysis and Bayesian phylogenies. We found T. cruzi I and T. cruzi II to be monophyletic and that all hybrids had different combinations of T. cruzi I and T. cruzi II haplotypes plus hybrid-specific haplotypes. Bootstrap values (networks) and posterior probabilities (Bayesian phylogenies) of clades supporting the monophyly of hybrids were far below the 95% confidence interval, indicating that the hybrid group is polyphyletic. We hypothesize that T. cruzi I and T. cruzi II are two different species and that the hybrids are extant representatives of independent events of genome hybridization, which sporadically have sufficient fitness to impact on the epidemiology of Chagas disease.