A seed-diffusion model for tropical tree diversity patterns

Diversity patterns of tree species in a tropical forest community are approached by a simple lattice model and investigated by Monte Carlo simulations using a backtracking method. Our spatially explicit neutral model is based on a simple statistical physics process, namely the diffusion of seeds. The model has three parameters: the speciation rate, the size of the meta-community in which the studied tree-community is embedded, and the average surviving time of the seeds. By extensive computer simulations we aim the reproduction of relevant statistical measures derived from the experimental data of the Barro Colorado Island tree census in year 1995. The first two parameters of the model are fixed to known values, characteristic of the studied community, thus obtaining a model with only one freely adjustable parameter. As a result of this, the average number of species in the considered territory, the relative species abundance distribution, the species-area relationship and the spatial auto-correlation function of the individuals in abundant species are simultaneously fitted with only one parameter which is the average surviving time of the seeds.Comment: 12 pages, 5 figure

An error analysis for polynomial optimization over the simplex based on the multivariate hypergeometric distribution

We study the minimization of fixed-degree polynomials over the simplex. This problem is well-known to be NP-hard, as it contains the maximum stable set problem in graph theory as a special case. In this paper, we consider a rational approximation by taking the minimum over the regular grid, which consists of rational points with denominator r (for given r). We show that the associated convergence rate is O(1/r^2 ) for quadratic polynomials. For general polynomials, if there exists a rational global minimizer over the simplex, we show that the convergence rate is also of the order O(1/r^2 ). Our results answer a question posed by De Klerk et al. [9] and improves on previously known O(1/r) bounds in the quadratic case

An alternative proof of a PTAS for fixed-degree polynomial optimization over the simplex

The problem of minimizing a polynomial over the standard simplex is one of the basic NP-hard nonlinear optimization problems --- it contains the maximum clique problem in graphs as a special case. It is known that the problem allows a polynomial-time approximation scheme (PTAS) for polynomials of fixed degree, which is based on polynomial evaluations at the points of a sequence of regular grids. In this paper, we provide an alternative proof of the PTAS property. The proof relies on the properties of Bernstein approximation on the simplex. We also refine a known error bound for the scheme for polynomials of degree three. The main contribution of the paper is to provide new insight into the PTAS by establishing precise links with Bernstein approximation and the multinomial distribution

Convergence analysis for Lasserre's measure-based hierarchy of upper bounds for polynomial optimization

We consider the problem of minimizing a continuous function f over a compact set K. We analyze a hierarchy of upper bounds proposed by Lasserre in [SIAM J. Optim. 21(3) (2011), pp. 864 − 885], obtained by searching for an optimal pr

Epistasis not needed to explain low dN/dS

An important question in molecular evolution is whether an amino acid that occurs at a given position makes an independent contribution to fitness, or whether its effect depends on the state of other loci in the organism's genome, a phenomenon known as epistasis. In a recent letter to Nature, Breen et al. (2012) argued that epistasis must be "pervasive throughout protein evolution" because the observed ratio between the per-site rates of non-synonymous and synonymous substitutions (dN/dS) is much lower than would be expected in the absence of epistasis. However, when calculating the expected dN/dS ratio in the absence of epistasis, Breen et al. assumed that all amino acids observed in a protein alignment at any particular position have equal fitness. Here, we relax this unrealistic assumption and show that any dN/dS value can in principle be achieved at a site, without epistasis. Furthermore, for all nuclear and chloroplast genes in the Breen et al. dataset, we show that the observed dN/dS values and the observed patterns of amino acid diversity at each site are jointly consistent with a non-epistatic model of protein evolution.Comment: This manuscript is in response to "Epistasis as the primary factor in molecular evolution" by Breen et al. Nature 490, 535-538 (2012

Initial Data and Eccentricity Reduction Toolkit for Binary Black Hole Numerical Relativity Waveforms

The production of numerical relativity waveforms that describe quasicircular binary black hole mergers requires high-quality initial data, and an algorithm to iteratively reduce residual eccentricity. To date, these tools remain closed source, or in commercial software that prevents their use in high performance computing platforms. To address these limitations, and to ensure that the broader numerical relativity community has access to these tools, herein we provide all the required elements to produce high-quality numerical relativity simulations in supercomputer platforms, namely: open source parameter files to numerical simulate spinning black hole binaries with asymmetric mass-ratios; open source $\texttt{Python}$ tools to produce high-quality initial data for numerical relativity simulations of spinning black hole binaries on quasi-circular orbits; open source $\texttt{Python}$ tools for eccentricity reduction, both as stand-alone software and deployed in the $\texttt{Einstein Toolkit}$'s software infrastructure. This open source toolkit fills in a critical void in the literature at a time when numerical relativity has an ever increasing role in the study and interpretation of gravitational wave sources. As part of our community building efforts, and to streamline and accelerate the use of these resources, we provide tutorials that describe, step by step, how to obtain and use these open source numerical relativity tools

Effets des Amendements Organiques sur la Gale Bactérienne et la Pourriture Apicale de la Tomate à Bobo-Dioulasso au Burkina Faso

L’étude a porté sur les effets des amendements organiques sur la gale bactérienne et la pourriture apicale de la tomate en milieu réel à l’Ouest du Burkina Faso. Un essai a été mis en place dans un dispositif en bloc de Fisher complètement randomisé. Il a comporté huit (08) traitements constitués des fertilisants organiques et minéraux tous répétés quatre (04) fois. L’incidence de la maladie et sa sévérité ont été évaluées ainsi que l’effet des traitements sur la qualité des fruits. La progression est relativement faible avec les déchets ménagers compostés associés aux engrais minéraux. La maladie est plus sévère avec les différents fertilisants pris individuellement. Dans l’ensemble, la maladie est évolutive avec tous les traitements.   The study focused on the effects of organic amendments on bacterial scab and apical rot of tomato in a real environment in western Burkina Faso. Indeed, a trial was set up in a completely randomized Fisher block design. It included eight (08) treatments consisting of organic and mineral fertilizers all repeated four (04) times. The incidence of the disease and its severity were evaluated as well as the effect of the treatments on the quality of the fruits. The disease is progressive with all treatments. However, the progression is relatively low with composted household waste associated with mineral fertilizers. The disease is more severe with the different fertilizers taken individually