The information capacity of hypercycles

Hypercycles are information integration systems which are thought to overcome the information crisis of prebiotic evolution by ensuring the coexistence of several short templates. For imperfect template replication, we derive a simple expression for the maximum number of distinct templates n(m). that can coexist in a hypercycle and show that it is a decreasing function of the length L of the templates. In the case of high replication accuracy we find that the product n(m)L tends to a constant value, limiting thus the information content of the hypercycle. Template coexistence is achieved either as a stationary equilibrium (stable fixed point) or a stable periodic orbit in which the total concentration of functional templates is nonzero. For the hypercycle system studied here we find numerical evidence that the existence of an unstable fixed point is a necessary condition for the presence of periodic orbits. (C) 2008 Elsevier Ltd. All rights reserved.

Package models and the information crisis of prebiotic evolution

The coexistence between different types of templates has been the choice solution to the information crisis of prebiotic evolution, triggered by the finding that a single RNA-like template cannot carry enough information to code for any useful replicase. In principle, confining d distinct templates of length L in a package or protocell, whose Survival depends on the coexistence of the templates it holds in, could resolve this crisis provided that d is made sufficiently large. Here we review the prototypical package model of Niesert et al. [1981. Origin of life between Scylla and Charybdis. J. Mol. Evol. 17, 348-353] which guarantees the greatest possible region of viability of the protocell population, and show that this model, and hence the entire package approach, does not resolve the information crisis. In particular, we show that the total information stored in a viable protocell (Ld) tends to a constant value that depends only on the spontaneous error rate per nucleotide of the template replication mechanism. As a result, an increase of d must be followed by a decrease of L, so that the net information gain is null. (C) 2008 Elsevier Ltd. All rights reserved.

A quasispecies approach to the evolution of sexual replication in unicellular organisms

This study develops a simplified model describing the evolutionary dynamics of a population composed of obligate sexually and asexually reproducing, unicellular organisms. The model assumes that the organisms have diploid genomes consisting of two chromosomes, and that the sexual organisms replicate by first dividing into haploid intermediates, which then combine with other haploids, followed by the normal mitotic division of the resulting diploid into two new daughter cells. We assume that the fitness landscape of the diploids is analogous to the single-fitness-peak approach often used in single-chromosome studies. That is, we assume a master chromosome that becomes defective with just one point mutation. The diploid fitness then depends on whether the genome has zero, one, or two copies of the master chromosome. We also assume that only pairs of haploids with a master chromosome are capable of combining so as to produce sexual diploid cells, and that this process is described by second-order kinetics. We find that, in a range of intermediate values of the replication fidelity, sexually reproducing cells can outcompete asexual ones, provided the initial abundance of sexual cells is above some threshold value. The range of values where sexual reproduction outcompetes asexual reproduction increases with decreasing replication rate and increasing population density. We critically evaluate a common approach, based on a group selection perspective, used to study the competition between populations and show its flaws in addressing the evolution of sex problem.

An improved estimate of leaf area index based on the histogram analysis of hemispherical photographs

Leaf area index (LAI) is a key parameter that affects the surface fluxes of energy, mass, and momentum over vegetated lands, but observational measurements are scarce, especially in remote areas with complex canopy structure. In this paper we present an indirect method to calculate the LAI based on the analyses of histograms of hemispherical photographs. The optimal threshold value (OTV), the gray-level required to separate the background (sky) and the foreground (leaves), was analytically calculated using the entropy crossover method (Sahoo, P.K., Slaaf, D.W., Albert, T.A., 1997. Threshold selection using a minimal histogram entropy difference. Optical Engineering 36(7) 1976-1981). The OTV was used to calculate the LAI using the well-known gap fraction method. This methodology was tested in two different ecosystems, including Amazon forest and pasturelands in Brazil. In general, the error between observed and calculated LAI was similar to 6%. The methodology presented is suitable for the calculation of LAI since it is responsive to sky conditions, automatic, easy to implement, faster than commercially available software, and requires less data storage. (C) 2008 Elsevier B.V. All rights reserved.

DETECTABILITY AND ERROR ESTIMATION IN ORBITAL FITS OF RESONANT EXTRASOLAR PLANETS

We estimate the conditions for detectability of two planets in a 2/1 mean-motion resonance from radial velocity data, as a function of their masses, number of observations and the signal-to-noise ratio. Even for a data set of the order of 100 observations and standard deviations of the order of a few meters per second, we find that Jovian-size resonant planets are difficult to detect if the masses of the planets differ by a factor larger than similar to 4. This is consistent with the present population of real exosystems in the 2/1 commensurability, most of which have resonant pairs with similar minimum masses, and could indicate that many other resonant systems exist, but are currently beyond the detectability limit. Furthermore, we analyze the error distribution in masses and orbital elements of orbital fits from synthetic data sets for resonant planets in the 2/1 commensurability. For various mass ratios and number of data points we find that the eccentricity of the outer planet is systematically overestimated, although the inner planet`s eccentricity suffers a much smaller effect. If the initial conditions correspond to small-amplitude oscillations around stable apsidal corotation resonances, the amplitudes estimated from the orbital fits are biased toward larger amplitudes, in accordance to results found in real resonant extrasolar systems.

Robust inference in an heteroscedastic measurement error model

In this paper we deal with robust inference in heteroscedastic measurement error models Rather than the normal distribution we postulate a Student t distribution for the observed variables Maximum likelihood estimates are computed numerically Consistent estimation of the asymptotic covariance matrices of the maximum likelihood and generalized least squares estimators is also discussed Three test statistics are proposed for testing hypotheses of interest with the asymptotic chi-square distribution which guarantees correct asymptotic significance levels Results of simulations and an application to a real data set are also reported (C) 2009 The Korean Statistical Society Published by Elsevier B V All rights reserved

Bayesian analysis of skew-t multivariate null intercept measurement error model

The multivariate skew-t distribution (J Multivar Anal 79:93-113, 2001; J R Stat Soc, Ser B 65:367-389, 2003; Statistics 37:359-363, 2003) includes the Student t, skew-Cauchy and Cauchy distributions as special cases and the normal and skew-normal ones as limiting cases. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis of repeated measures, pretest/post-test data, under multivariate null intercept measurement error model (J Biopharm Stat 13(4):763-771, 2003) where the random errors and the unobserved value of the covariate (latent variable) follows a Student t and skew-t distribution, respectively. The results and methods are numerically illustrated with an example in the field of dentistry.

Bayesian analysis for a skew extension of the multivariate null intercept measurement error model

Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in a multivariate, null intercept, measurement error model [R. Aoki, H. Bolfarine, J.A. Achcar, and D. Leao Pinto Jr, Bayesian analysis of a multivariate null intercept error-in -variables regression model, J. Biopharm. Stat. 13(4) (2003b), pp. 763-771] where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. The results and methods are applied to a real dental clinical trial presented in [A. Hadgu and G. Koch, Application of generalized estimating equations to a dental randomized clinical trial, J. Biopharm. Stat. 9 (1999), pp. 161-178].

Critical discontinuous phase transition in the threshold contact process

We analyze a threshold contact process on a square lattice in which particles are created on empty sites with at least two neighboring particles and are annihilated spontaneously. We show by means of Monte Carlo simulations that the process undergoes a discontinuous phase transition at a definite value of the annihilation parameter, in accordance with the Gibbs phase rule, and that the discontinuous transition exhibits critical behavior. The simulations were performed by using boundary conditions in which the sites of the border of the lattice are permanently occupied by particles.

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR-PREY STOCHASTIC MODEL IN A 2D LATTICE

We investigate the critical behavior of a stochastic lattice model describing a predator-prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.

Disentangling static and dynamic effects of low breakup threshold in fusion reactions

A new technique to analyze fusion data is developed. From experimental cross sections and results of coupled-channel calculations a dimensionless function is constructed. In collisions of strongly bound nuclei this quantity is very close to a universal function of a variable related to the collision energy, whereas for weakly bound projectiles the effects of breakup coupling are measured by the deviations with respect to this universal function. This technique is applied to collisions of stable and unstable weakly bound isotopes.

Near threshold vibrational excitation of molecules by positron impact: A projection operator approach

We report vibrational excitation (v(i) = 0 -> v(f) = 1) cross-sections for positron scattering by H(2) and model calculations for the (v(i) = 0 -> v(f) = 1) excitation of the C-C symmetric stretch mode of C(2)H(2). The Feshbach projection operator formalism was employed to vibrationally resolve the fixed-nuclei phase shifts obtained with the Schwinger multichannel method. The near threshold behavior of H(2) and C(2)H(2) significantly differ in the sense that no low lying singularity (either virtual or bound state) was found for the former, while a e(+)-acetylene virtual state was found at the equilibrium geometry (this virtual state becomes a bound state upon stretching the molecule). For C(2)H(2), we also performed model calculations comparing excitation cross-sections arising from virtual (-i kappa(0)) and bound (+i kappa(0)) states symmetrically located around the origin of the complex momentum plane (i.e. having the same kappa(0)). The virtual state is seen to significantly couple to vibrations, and similar cross-sections were obtained for shallow bound and virtual states. (c) 2007 Elsevier B.V. All rights reserved.

Inference and local influence assessment in skew-normal null intercept measurement error model

In this article, we discuss inferential aspects of the measurement error regression models with null intercepts when the unknown quantity x (latent variable) follows a skew normal distribution. We examine first the maximum-likelihood approach to estimation via the EM algorithm by exploring statistical properties of the model considered. Then, the marginal likelihood, the score function and the observed information matrix of the observed quantities are presented allowing direct inference implementation. In order to discuss some diagnostics techniques in this type of models, we derive the appropriate matrices to assessing the local influence on the parameter estimates under different perturbation schemes. The results and methods developed in this paper are illustrated considering part of a real data set used by Hadgu and Koch [1999, Application of generalized estimating equations to a dental randomized clinical trial. Journal of Biopharmaceutical Statistics, 9, 161-178].

A multivariate ultrastructural errors-in-variables model with equation error

This paper deals with asymptotic results on a multivariate ultrastructural errors-in-variables regression model with equation errors Sufficient conditions for attaining consistent estimators for model parameters are presented Asymptotic distributions for the line regression estimators are derived Applications to the elliptical class of distributions with two error assumptions are presented The model generalizes previous results aimed at univariate scenarios (C) 2010 Elsevier Inc All rights reserved

Bayesian estimation of regression parameters in elliptical measurement error models

The main object of this paper is to discuss the Bayes estimation of the regression coefficients in the elliptically distributed simple regression model with measurement errors. The posterior distribution for the line parameters is obtained in a closed form, considering the following: the ratio of the error variances is known, informative prior distribution for the error variance, and non-informative prior distributions for the regression coefficients and for the incidental parameters. We proved that the posterior distribution of the regression coefficients has at most two real modes. Situations with a single mode are more likely than those with two modes, especially in large samples. The precision of the modal estimators is studied by deriving the Hessian matrix, which although complicated can be computed numerically. The posterior mean is estimated by using the Gibbs sampling algorithm and approximations by normal distributions. The results are applied to a real data set and connections with results in the literature are reported. (C) 2011 Elsevier B.V. All rights reserved.