Integro-difference equations for interacting species and the Neolithic transition

We introduce a set of sequential integro-difference equations to analyze the dynamics of two interacting species. Firstly, we derive the speed of the fronts when a species invades a space previously occupied by a second species, and check its validity by means of numerical random-walk simulations. As an example, we consider the Neolithic transition: the predictions of the model are consistent with the archaeological data for the front speed, provided that the interaction parameter is low enough. Secondly, an equation for the coexistence time between the invasive and the invaded populations is obtained for the first time. It agrees well with the simulations, is consistent with observations of the Neolithic transition, and makes it possible to estimate the value of the interaction parameter between the incoming and the indigenous populations

Fronts from integrodifference equations and persistence effects on the Neolithic transition

We extend a previous model of the Neolithic transition in Europe [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)] by taking two effects into account: (i) we do not use the diffusion approximation (which corresponds to second-order Taylor expansions), and (ii) we take proper care of the fact that parents do not migrate away from their children (we refer to this as a time-order effect, in the sense that it implies that children grow up with their parents, before they become adults and can survive and migrate). We also derive a time-ordered, second-order equation, which we call the sequential reaction-diffusion equation, and use it to show that effect (ii) is the most important one, and that both of them should in general be taken into account to derive accurate results. As an example, we consider the Neolithic transition: the model predictions agree with the observed front speed, and the corrections relative to previous models are important (up to 70%)

Tamanho de amostra para estimação do coeficiente de correlação linear de Pearson entre caracteres de milho

O objetivo deste trabalho foi determinar o tamanho de amostra para a estimação do coeficiente de correlação linear de Pearson entre caracteres de três híbridos de milho. Para as análises, foram tomadas aleatoriamente 361, 373 e 416 plantas, respectivamente, de híbridos simples, triplo e duplo. Para cada planta, os seguintes caracteres foram mensurados: diâmetro maior e menor do colmo, altura da planta e altura, peso, comprimento e diâmetro da espiga, número de fileiras por espiga, peso e diâmetro de sabugo, massa de cem grãos, número de grãos por espiga, comprimento e produtividade de grãos. Para cada um dos 91 pares de caracteres e híbridos, foi determinado o tamanho de amostra a partir de "bootstrap", com reposição de 1.000 amostras, de cada tamanho de amostra simulado. Na estimação do coeficiente de correlação linear de Pearson com a mesma precisão, o tamanho de amostra (número de plantas) aumenta na direção de pares de caracteres com menor intensidade de relação linear, independentemente do tipo de híbrido. Para os 91 pares de caracteres estudados, 252 plantas são suficientes para a estimação do coeficiente de correlação linear de Pearson, no intervalo de confiança de "bootstrap" de 95%, igual a 0,30

Biomass equations for European trees : addendum

Abstract

Estimating parameters for generalized mass action models using constraint propagation.

As modern molecular biology moves towards the analysis of biological systems as opposed to their individual components, the need for appropriate mathematical and computational techniques for understanding the dynamics and structure of such systems is becoming more pressing. For example, the modeling of biochemical systems using ordinary differential equations (ODEs) based on high-throughput, time-dense profiles is becoming more common-place, which is necessitating the development of improved techniques to estimate model parameters from such data. Due to the high dimensionality of this estimation problem, straight-forward optimization strategies rarely produce correct parameter values, and hence current methods tend to utilize genetic/evolutionary algorithms to perform non-linear parameter fitting. Here, we describe a completely deterministic approach, which is based on interval analysis. This allows us to examine entire sets of parameters, and thus to exhaust the global search within a finite number of steps. In particular, we show how our method may be applied to a generic class of ODEs used for modeling biochemical systems called Generalized Mass Action Models (GMAs). In addition, we show that for GMAs our method is amenable to the technique in interval arithmetic called constraint propagation, which allows great improvement of its efficiency. To illustrate the applicability of our method we apply it to some networks of biochemical reactions appearing in the literature, showing in particular that, in addition to estimating system parameters in the absence of noise, our method may also be used to recover the topology of these networks.

Smooth height/age curves from stem analysis with linear programming

[Abstract]

Degree of multicollinearity and variables involved in linear dependence in additive-dominant models

The objective of this work was to assess the degree of multicollinearity and to identify the variables involved in linear dependence relations in additive-dominant models. Data of birth weight (n=141,567), yearling weight (n=58,124), and scrotal circumference (n=20,371) of Montana Tropical composite cattle were used. Diagnosis of multicollinearity was based on the variance inflation factor (VIF) and on the evaluation of the condition indexes and eigenvalues from the correlation matrix among explanatory variables. The first model studied (RM) included the fixed effect of dam age class at calving and the covariates associated to the direct and maternal additive and non-additive effects. The second model (R) included all the effects of the RM model except the maternal additive effects. Multicollinearity was detected in both models for all traits considered, with VIF values of 1.03 - 70.20 for RM and 1.03 - 60.70 for R. Collinearity increased with the increase of variables in the model and the decrease in the number of observations, and it was classified as weak, with condition index values between 10.00 and 26.77. In general, the variables associated with additive and non-additive effects were involved in multicollinearity, partially due to the natural connection between these covariables as fractions of the biological types in breed composition.

A random linear functional approach to efficiency bounds

This paper suggests a method for obtaining efficiency bounds in models containing either only infinite-dimensional parameters or both finite- and infinite-dimensional parameters (semiparametric models). The method is based on a theory of random linear functionals applied to the gradient of the log-likelihood functional and is illustrated by computing the lower bound for Cox's regression model

High capacity robust audio watermarking scheme based on FFT and linear regression

Peer-reviewed

Linear prediction application for modelling the relationships between a large number of stand characteristics of Norway spruce stands

Abstract

Comments on "On resistor-induced thermal noise in linear circuits"

Correspondència referida a l'article de R. Giannetti, publicat ibid. vol.49 p.87-88