Angel Tocino

• University of Salamanca

Quantitative morphological methods have been applied here to seed morphology in species representative of the Cucurbitaceae: Curvature analysis, symmetry analysis and the comparison with geometric models. The three methods were applied to the comparison of three species and two varieties of Cucumis, and the results indicate that both symmetry analy...

Mean-square stability analysis of linear stochastic differential systems obtained perturbing ordinary systems by linear terms driven by independent Wiener processes is investigated. The so obtained stochastic regions are contractions of the asymptotic stability domain of the linear ordinary system. In this work, the mean-square stability regions ex...

In recent papers, a simple harmonic oscillator with additive noise has been studied by several researchers, and it has been shown that its mean total energy increases linearly as time goes to infinity. In contrast to them, we consider an underdamped harmonic oscillator with additive noise. Our analysis reveals that the mean total energy of the stoc...

Most of stability analysis for stochastic epidemiological models involve Lyapunov functions. This work shows how sufficient conditions for the local stochastic asymptotic stability of a nonlinear system can be derived from the stability analysis of an ordinary linear system. In the particular stochastic SIR/SIRS models proposed here to illustrate t...

Predictor–corrector schemes are designed to be a compromise to retain the stability properties of the implicit schemes and the computational efficiency of the explicit ones. In this paper a complete analytical study for the linear mean-square stability of the two-parameter family of Euler predictor–corrector schemes for scalar stochastic differenti...

Fruit and seed shape are important characteristics in taxonomy providing information on ecological, nutritional, and developmental aspects, but their application requires quantification. We propose a method for seed shape quantification based on the comparison of the bi-dimensional images of the seeds with geometric figures. J index is the percent...

Mean square stability of 2-dimensional stochastic differential systems with nonnormal drift coefficient is investigated. Using Routh–Hurwitz criterion, explicit necessary and sufficient conditions in terms of the parameters of the stochastic system as well as geometrical representation of the stability regions are given. In addition, using Jury’s t...

Particular criteria of linear MS-stability for two-dimensional stochastic differential systems given by the authors in previous works are here applied to investigate the stability behavior of systems driven by non-normal drift coefficients under the influence of different kind of noises.

Modern automated and semi-automated methods of shape analysis depart from the coordinates of the points in the outline of a figure and obtain, based on artificial vision algorithms, descriptive parameters (i.e., the length, width, area, and circularity index). These methods omit an important factor: the resemblance of the examined images to a geome...

The stochastic exponential method is applied to solve the undamped linear stochastic oscillator driven by a multidimensional Wiener process. The proposed additive noise model is new since the disturbances are introduced in the equivalent first order two dimensional system and can affect both space and velocity. It is shown that three important prop...

Deterministic predictor-corrector schemes are used mainly because of their numerical stability which they inherit from implicit counterparts of their corrector schemes. In principle these advantages carry over to the stochastic case. In this paper a complete study for the linear MS-stability of the oneparameter family of weak order 1.0 predictor-co...

A general class of linear two-step schemes for solving stochastic differential equations is presented. Necessary and sufficient conditions on its parameters to obtain mean square order 1.5 are derived. Then the linear stability of the schemes is investigated. In particular, among others, the stability regions of generalizations of the classical two...

A set of conditions on the parameters of stochastic linear two-step schemes for their order 1.0 mean-square convergence are established. Then two-step Milstein schemes are defined and necessary and sufficient conditions for their MS-stability are given. Regions of MS-stability are determined and plotted for Adams-Bashforth, Adams-Moulton and BDF Mi...

In recent years several numerical methods to solve a linear stochastic oscillator with one additive noise have been proposed. The usual aim of these approaches was to preserve different long time properties of the oscillator solution. In this work we collect these properties, namely, symplecticity, linear growth of its second moment and asymptotic...

In a previous work, the shape of Arabidopsis seed was described as a cardioid modified by a factor of Phi. In addition, J index was defined as the similarity of the seed (in an orthogonal, bi-dimensional image) to a cardioid, thus allowing the quantitative comparison of seed shape in seeds of varieties and mutants at different stages of development...

The mean-square stability for two-step schemes applied to scalar stochastic differential equations is studied. Necessary and sufficient conditions in terms of the parameters of the schemes guaranteeing their MS-stability are derived. Particular members of the studied family are considered, their stability regions are plotted and compared with the s...

As in the deterministic case, the introduction of implicitness in stochastic schemes improves the stability behavior. In this paper a complete study for the linear MS-stability of the two-parameter family of semi-implicit weak order 2.0 Taylor schemes for scalar stochastic differential equations is given. Figures of the MS-stability regions and num...

Seed shape in the model legumes Lotus japonicus and Medicago truncatula is described. Based in previous work with Arabidopsis, the outline of the longitudinal sections of seeds is compared with a cardioid curve. L. japonicus seeds adjust well to an unmodified cardioid, whereas accurate adjustment in M. truncatula is obtained by the simple transform...

For ordinary differential systems, the study of A-stability for a numerical method reduces to the scalar case by means of a transformation that uncouples the linear test system as well as the difference system provided by the method. For stochastic differential equations (SDEs), mean-square stability (MS-stability) has been successfully proposed as...

In this paper, a new procedure for deriving efficient symplectic integrators for Hamiltonian problems is introduced. This procedure is based on the combination of the trigonometric fitting technique and symplecticness conditions. Based on this procedure, a simple modified Runge–Kutta–Nyström second algebraic order trigonometrically fitted method is...

The paper considers the derivation of families of semi-implicit schemes of weak order N=3.0 (general case) and N=4.0 (additive noise case) for the numerical solution of Itô stochastic differential equations. The degree of implicitness of the schemes depends on the selection of N parameters which vary between 0 and 1 and the families contain as part...

A new model for the description of Arabidopsis seed shape based on the comparison of the outline of its longitudinal section with a transformed cardioid is presented. The transformation consists of scaling the horizontal axis by a factor equal to the Golden Ratio. The elongated cardioid approximates the shape of the Arabidopsis seed with more accur...

Following Kloeden and Platen [P.E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Berlin, 1992] Taylor schemes are considered here as the starting point to obtain simplified Taylor schemes replacing the multiple integrals by simpler variables. The conditions that a group of variables has to fulfill...

In the construction of numerical methods for solving stochastic differential equations it becomes necessary to calculate the expectations of products of multiple stochastic integrals. In the Ito case, explicit formulae for the expectation of a multiple integral with integrand identically equal to 1 and for the product of two such integrals are know...

Treatment with hydrogen peroxide has notable effects in the morphology of the root apex in Arabidopsis seedlings. The result was described as consisting in two aspects: first, a reduction in curvature values in the root profile. Second, alterations in size and shape of the cells in the root cap. Cells of the root cap were smaller and had higher cir...

In the construction of numerical methods for solving stochastic differential equations it becomes necessary to calculate the expectation of products of multiple stochastic integrals. Well-known recursive relationships between these multiple integrals make it possible to express any product of them as a linear combination of integrals of the same ty...

Curvature of a plane curve is a measurement related to its shape. A Mathematica code was developed [Cervantes E, Tocino A. J Plant Physiol 2005;162:1038-1045] to obtain parametric equations from microscopic images of the Arabidopsis thaliana root apex. In addition, curvature values for these curves were given. It was shown that ethylene-insensitive...

In the recent papers [A. H. Strømmen Melbø and D. J. Higham, Appl. Numer. Math. 51, No. 1, 89–99 (2004; Zbl 1060.65007), J. Hong, R. Scherer and L. Wang, Neural Parallel Sci. Comput. 14, No. 1, 1–12 (2006; Zbl 1105.65008), and A. Tocino, BIT 47, No. 1, 189–196 (2007; Zbl 1119.65006)], three numerical methods preserving some properties of the analyt...

IN MATHEMATICS, CURVATURE IS AN IMPORTANT MAGNITUDE IN THE DESCRIPTION OF PLANE CURVES: it represents the rate of change of direction of a curve with respect to distance along the curve. By looking at root tips of Arabidopsis, we observed that their shape is altered in ethylene insensitive mutants. Here we describe the mathematical meaning of the c...

The shape of Arabidopsis thaliana dry seed is described here as a prolate spheroid. The accuracy of this approximation is discussed. Considering its limitations, it allows a geometric approximation to the analysis of changes occurring in seed shape during imbibition prior to seed germination as well as the differences in shape between genotypes and...

Recently, curvature was described as a new trait useful in the analysis of root apex shape. Treating the root profile as a geometric curve revealed that root apex curvature values are lower in ethylene-insensitive mutants (Cervantes E, Tocino A. Geometric analysis of Arabidopsis root apex reveals a new aspect of the ethylene signal transduction pat...

A method for the numerical solution of stochastic differential equations is presented. The method has mean-square order equal to 1/2 when it is applied to a general stochastic differential equation and equal to 1 if the equation has additive noise. In addition, it is shown that the method captures some long-time properties of a linear stochastic os...

In this note, simplecticity conditions easy to handle for constructing symplectic Runge-Kutta-Nyström methods fitted to trigonometric functions are given. These conditions generalize that of [1] when the frequencies tends to zero.

Structurally, ethylene is the simplest phytohormone and regulates multiple aspects of plant growth and development. Its effects are mediated by a signal transduction cascade involving receptors, MAP kinases and transcription factors. Many morphological effects of ethylene in plant development, including root size, have been previously described. In...

In a previous paper, we proposed the stochastic Generalization of classical second-order two-stage explicit Runge-Kutta (RK) methods. The obtained stochastic schemes have second order in the weak sense. In this paper, the numerical stability of these RK schemes is studied. The study focuses on stability with respect to the second moment (MS-stabili...

A new expression for weak truncated Itô–Taylor expansions of functionals of Itô processes is proposed. The new truncated expansion is expressed, as in the ordinary case, in terms of powers of the increments of the variables. A systematic procedure to obtain such expansions and general results in order to avoid some parts of the calculation are pres...

A general procedure to construct weak methods for the numerical solution of stochastic differential systems is presented. As in the deterministic case, the procedure consists of comparing the stochastic expansion of the approximation with the corresponding Taylor scheme. In this way the authors obtain the order conditions that a stochastic Runge-Ku...

We propose, as a generalization of truncated deterministic Taylor expansions, truncated expansions about a point for sufficiently smooth functions of a solution of a stochastic differential equation. The first order expansion will be the natural one according to Itô's formula. The second order one has been obtained in the multi-dimensional case and...

The way to obtain deterministic Runge–Kutta methods from Taylor approximations is generalized for stochastic differential equations, now by means of stochastic truncated expansions about a point for sufficiently smooth functions of an Itô process. A class of explicit Runge–Kutta schemes of second order in the weak sense for systems of stochastic di...

A quick overview of the fundamental concepts for the construction of weak methods for the numerical solution of stochastic differential equations and a new way to construct these methods are presented. As in the deterministic case, the presented procedure to obtain these methods consists of the comparison of their stochastic expansions with the cor...

Concurso Nacional de Proyectos de Investigación Educativa CIDE 1995 Bibliografía a pie de página Elaborar un modelo matemático que permita cuantificar las distancias que existen entre tipos ideales puros y tipos ideales híbridos de directores y directores reales. Definir tipos ideales puros y tipos ideales híbridos de directores. Se plantean 4 hipó...

En: Bordón Madrid 2003, v. 55, n. 4 ; p. 513-526 Se justifica la utilidad de reemplazar el índice de discriminación, como indicador de la capacidad que tienen los ítems de test de instrucción para diferenciar a quienes los cumplimentan en función de su nivel instructivo real, con un nuevo índice, el de efectividad, en el que los ítems alcanzan valo...