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Ángel Tocino
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, Spain

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Review
Published: 18 August 2021 in Plants
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The Vitaceae Juss., in the basal lineages of Rosids, contains sixteen genera and 950 species, mainly of tropical lianas. The family has been divided in five tribes: Ampelopsideae, Cisseae, Cayratieae, Parthenocisseae and Viteae. Seed shape is variable in this family. Based on new models derived from equations representing heart and water drop curves, we describe seed shape in species of the Vitaceae. According to their similarity to geometric models, the seeds of the Vitaceae have been classified in ten groups. Three of them correspond to models before described and shared with the Arecaceae (lenses, superellipses and elongated water drops), while in the seven groups remaining, four correspond to general models (waterdrops, heart curves, elongated heart curves and other elongated models) and three adjust to the silhouettes of seeds in particular genera (heart curves of Cayratia and Pseudocayratia, heart curves of the Squared Heart Curve (SqHC) type of Ampelocissus and Ampelopsis and Elongated Superellipse-Heart Curves (ESHCs), frequent in Tetrastigma species and observed also in Cissus species and Rhoicissus rhomboidea). The utilities of the application of geometric models for seed description and shape quantification in this family are discussed.

ACS Style

Emilio Cervantes; José Javier Martín-Gómez; Diego Gutiérrez del Pozo; Ángel Tocino. Seed Geometry in the Vitaceae. Plants 2021, 10, 1695 .

AMA Style

Emilio Cervantes, José Javier Martín-Gómez, Diego Gutiérrez del Pozo, Ángel Tocino. Seed Geometry in the Vitaceae. Plants. 2021; 10 (8):1695.

Chicago/Turabian Style

Emilio Cervantes; José Javier Martín-Gómez; Diego Gutiérrez del Pozo; Ángel Tocino. 2021. "Seed Geometry in the Vitaceae." Plants 10, no. 8: 1695.

Journal article
Published: 11 July 2021 in Communications in Nonlinear Science and Numerical Simulation
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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 the technique, the stability study of the obtained ordinary systems reduces to calculate the spectrum of the governing matrix.

ACS Style

A. Tocino; A. Martín del Rey. Local stochastic stability of SIRS models without Lyapunov functions. Communications in Nonlinear Science and Numerical Simulation 2021, 103, 105956 .

AMA Style

A. Tocino, A. Martín del Rey. Local stochastic stability of SIRS models without Lyapunov functions. Communications in Nonlinear Science and Numerical Simulation. 2021; 103 ():105956.

Chicago/Turabian Style

A. Tocino; A. Martín del Rey. 2021. "Local stochastic stability of SIRS models without Lyapunov functions." Communications in Nonlinear Science and Numerical Simulation 103, no. : 105956.

Journal article
Published: 10 April 2021 in Agronomy
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Ampelography, the botanical discipline dedicated to the identification and classification of grapevine cultivars, was grounded on the description of morphological characters and more recently is based on the application of DNA polymorphisms. New methods of image analysis may help to optimize morphological approaches in ampelography. The objective of this study was the classification of representative cultivars of Vitis vinifera conserved in the Spanish collection of IMIDRA according to seed shape. Thirty eight cultivars representing the diversity of this collection were analyzed. A consensus seed silhouette was defined for each cultivar representing the geometric figure that better adjusted to their seed shape. All the cultivars tested were classified in ten morphological groups, each corresponding to a new model. The models are geometric figures defined by equations and similarity to each model is evaluated by quantification of percent of the area shared by the two figures, the seed and the model (J index). The comparison of seed images with geometric models is a rapid and convenient method to classify cultivars. A large proportion of the collection may be classified according to the new models described and the method permits to find new models according to seed shape in other cultivars.

ACS Style

Emilio Cervantes; José Martín-Gómez; Francisco Espinosa-Roldán; Gregorio Muñoz-Organero; Ángel Tocino; Félix Cabello-Sáenz de Santamaría. Seed Morphology in Key Spanish Grapevine Cultivars. Agronomy 2021, 11, 734 .

AMA Style

Emilio Cervantes, José Martín-Gómez, Francisco Espinosa-Roldán, Gregorio Muñoz-Organero, Ángel Tocino, Félix Cabello-Sáenz de Santamaría. Seed Morphology in Key Spanish Grapevine Cultivars. Agronomy. 2021; 11 (4):734.

Chicago/Turabian Style

Emilio Cervantes; José Martín-Gómez; Francisco Espinosa-Roldán; Gregorio Muñoz-Organero; Ángel Tocino; Félix Cabello-Sáenz de Santamaría. 2021. "Seed Morphology in Key Spanish Grapevine Cultivars." Agronomy 11, no. 4: 734.

Preprint
Published: 24 March 2021
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Ampelography, the botanical discipline dedicated to the identification and classification of grapevine cultivars, was grounded on the description of morphological characters and more recently is based on the application of DNA polymorphisms. New methods of image analysis may help to optimize morphological approaches in ampelography. The objective of this study was the classification of representative cultivars of Vitis vinifera conserved in the Spanish collection of IMIDRA according to seed shape. Thirty eight cultivars representing the diversity of this collection were analyzed. A consensus seed silhouette was defined for each cultivar representing the geometric figure that better adjusted to their seed shape. All the cultivars tested were classified in ten morphological groups, each corresponding to a new model. The models are geometric figures defined by equations and similarity to each model is evaluated by quantification of percent of the area shared by the two figures, the seed and the model (J index). The comparison of seed images with geometric models is a rapid and convenient method to classify cultivars. A large proportion of the collection may be classified according to the new models described and the method permits to find new models according to seed shape in other cultivars.

ACS Style

Emilio Cervantes; José Javier Martín-Gómez; Francisco Emmanuel Espinosa Roldán; Gregorio Muñoz Organero; Ángel Tocino; Félix Cabello Sáenz de Santamaría. Seed Morphology in Key Spanish Grapevine Cultivars. 2021, 1 .

AMA Style

Emilio Cervantes, José Javier Martín-Gómez, Francisco Emmanuel Espinosa Roldán, Gregorio Muñoz Organero, Ángel Tocino, Félix Cabello Sáenz de Santamaría. Seed Morphology in Key Spanish Grapevine Cultivars. . 2021; ():1.

Chicago/Turabian Style

Emilio Cervantes; José Javier Martín-Gómez; Francisco Emmanuel Espinosa Roldán; Gregorio Muñoz Organero; Ángel Tocino; Félix Cabello Sáenz de Santamaría. 2021. "Seed Morphology in Key Spanish Grapevine Cultivars." , no. : 1.

Review
Published: 07 October 2020 in Horticulturae
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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 of similarity of a seed image with a figure taken as a model. Models in shape quantification include geometrical figures (circle, ellipse, oval…) and their derivatives, as well as other figures obtained as geometric representations of algebraic equations. The analysis is based on three sources: Published work, images available on the Internet, and seeds collected or stored in our collections. Some of the models here described are applied for the first time in seed morphology, like the superellipses, a group of bidimensional figures that represent well seed shape in species of the Calamoideae and Phoenix canariensis Hort. ex Chabaud. Oval models are proposed for Chamaedorea pauciflora Mart. and cardioid-based models for Trachycarpus fortunei (Hook.) H. Wendl. Diversity of seed shape in the Arecaceae makes this family a good model system to study the application of geometric models in morphology.

ACS Style

Diego Gutiérrez del Pozo; José Martín-Gómez; Ángel Tocino; Emilio Cervantes. Seed Geometry in the Arecaceae. Horticulturae 2020, 6, 64 .

AMA Style

Diego Gutiérrez del Pozo, José Martín-Gómez, Ángel Tocino, Emilio Cervantes. Seed Geometry in the Arecaceae. Horticulturae. 2020; 6 (4):64.

Chicago/Turabian Style

Diego Gutiérrez del Pozo; José Martín-Gómez; Ángel Tocino; Emilio Cervantes. 2020. "Seed Geometry in the Arecaceae." Horticulturae 6, no. 4: 64.

Journal article
Published: 09 September 2020 in Mathematics and Computers in Simulation
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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 differential equations is given. The analyzed family is given in terms of two parameters that control the degree of implicitness of the method. For each selection of the parameters the stability region is obtained, letting its comparison. Particular cases of the counter-intuitive fact of losing numerical stability by reducing the step size, is confirmed and proved. Figures of the MS-stability regions and numerical examples that confirm the theoretical results are shown.

ACS Style

A. Tocino; R. Zeghdane; M.J. Senosiaín. On the MS-stability of predictor–corrector schemes for stochastic differential equations. Mathematics and Computers in Simulation 2020, 180, 289 -305.

AMA Style

A. Tocino, R. Zeghdane, M.J. Senosiaín. On the MS-stability of predictor–corrector schemes for stochastic differential equations. Mathematics and Computers in Simulation. 2020; 180 ():289-305.

Chicago/Turabian Style

A. Tocino; R. Zeghdane; M.J. Senosiaín. 2020. "On the MS-stability of predictor–corrector schemes for stochastic differential equations." Mathematics and Computers in Simulation 180, no. : 289-305.

Journal article
Published: 20 May 2020 in Agronomy
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Morphometric methods based on artificial vision algorithms provide measurements for magnitudes descriptive of seed images (i.e., the length, width, area, and surface circularity index). Nevertheless, their results frequently omit the resemblance of the images to geometric figures that may be used as models. A complementary method based on the comparison of seed images with geometric models is applied to seeds of Vitis spp. The J index gives the percentage of similarity between a seed image and the model. Seven new geometric models are described based on the heart-shaped and piriform curves. Seeds of different species, subspecies and cultivars of Vitis adjust to different models. Models 1 and 3, the heart curve and the water drop, adjust better to seeds of V. amurensis, V. labrusca and V. rupestris than to V. vinifera. Model 6, the Fibonacci’s pear, adjusts well to seeds of V. vinifera, in general, and better to V. vinifera ssp. vinifera than to V. vinifera ssp. sylvestris. Seed morphology in species of Cissus and Parthenocissus, two relatives of Vitis in the Vitaceae, is also analysed. Geometric models are a tool for the description and identification of species and lower taxonomic levels complementing the results of morphometric analysis.

ACS Style

José Javier Martín-Gómez; Diego Gutiérrez Del Pozo; Mariano Ucchesu; Gianluigi Bacchetta; Félix Cabello Sáenz De Santamaría; Ángel Tocino; Emilio Cervantes. Seed Morphology in the Vitaceae Based on Geometric Models. Agronomy 2020, 10, 739 .

AMA Style

José Javier Martín-Gómez, Diego Gutiérrez Del Pozo, Mariano Ucchesu, Gianluigi Bacchetta, Félix Cabello Sáenz De Santamaría, Ángel Tocino, Emilio Cervantes. Seed Morphology in the Vitaceae Based on Geometric Models. Agronomy. 2020; 10 (5):739.

Chicago/Turabian Style

José Javier Martín-Gómez; Diego Gutiérrez Del Pozo; Mariano Ucchesu; Gianluigi Bacchetta; Félix Cabello Sáenz De Santamaría; Ángel Tocino; Emilio Cervantes. 2020. "Seed Morphology in the Vitaceae Based on Geometric Models." Agronomy 10, no. 5: 739.

Journal article
Published: 25 April 2020 in Journal of Computational and Applied Mathematics
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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 test, a similar MS-stability analysis is carried out for the numerical recurrence obtained applying a stochastic θ-method to solve the system. Analytical comparison of the stability regions (stochastic differential system vs. stochastic θ-numerical difference system) is done, concluding that stochastic θ-methods are A-stable in mean-square for θ≥1∕2.

ACS Style

A. Tocino; M.J. Senosiain. MS-Stability of nonnormal stochastic differential systems. Journal of Computational and Applied Mathematics 2020, 379, 112950 .

AMA Style

A. Tocino, M.J. Senosiain. MS-Stability of nonnormal stochastic differential systems. Journal of Computational and Applied Mathematics. 2020; 379 ():112950.

Chicago/Turabian Style

A. Tocino; M.J. Senosiain. 2020. "MS-Stability of nonnormal stochastic differential systems." Journal of Computational and Applied Mathematics 379, no. : 112950.

Journal article
Published: 18 July 2019 in Agronomy
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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 geometric figure. We have described a method based on the comparison of the outline of seed images with geometric figures. The J index is the percentage of similarity between a seed image and a geometric figure used as a model. This allows the description and classification of wheat kernels based on their similarity to geometric models. The figures used are the ellipse and the lens of different major/minor axis ratios. Kernels of different species, subspecies and varieties of wheat adjust to different figures. A relationship is found between their ploidy levels and morphological type. Kernels of diploid einkorn and ancient tetraploid emmer varieties adjust to the lens and have curvature values in their poles superior to modern “bread” varieties. Kernels of modern varieties (hexaploid common wheat) adjust to an ellipse of aspect ratio = 1.6, while varieties of tetraploid durum and Polish wheat and hexaploid spelt adjust to an ellipse of aspect ratio = 2.4.

ACS Style

José Javier Martín-Gómez; Agnieszka Rewicz; Klaudia Goriewa-Duba; Marian Wiwart; Ángel Tocino; Emilio Cervantes; Martín- Gómez; Goriewa- Duba. Morphological Description and Classification of Wheat Kernels Based on Geometric Models. Agronomy 2019, 9, 399 .

AMA Style

José Javier Martín-Gómez, Agnieszka Rewicz, Klaudia Goriewa-Duba, Marian Wiwart, Ángel Tocino, Emilio Cervantes, Martín- Gómez, Goriewa- Duba. Morphological Description and Classification of Wheat Kernels Based on Geometric Models. Agronomy. 2019; 9 (7):399.

Chicago/Turabian Style

José Javier Martín-Gómez; Agnieszka Rewicz; Klaudia Goriewa-Duba; Marian Wiwart; Ángel Tocino; Emilio Cervantes; Martín- Gómez; Goriewa- Duba. 2019. "Morphological Description and Classification of Wheat Kernels Based on Geometric Models." Agronomy 9, no. 7: 399.

Journal article
Published: 04 December 2018 in Applied Numerical Mathematics
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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 properties related to long time behavior of its analytical solution are preserved. In addition, the mean-square error of the numerical solution is analyzed. Numerical experiments confirming the theoretical results are presented.

ACS Style

M.J. Senosiain; A. Tocino. On the numerical integration of the undamped harmonic oscillator driven by independent additive gaussian white noises. Applied Numerical Mathematics 2018, 137, 49 -61.

AMA Style

M.J. Senosiain, A. Tocino. On the numerical integration of the undamped harmonic oscillator driven by independent additive gaussian white noises. Applied Numerical Mathematics. 2018; 137 ():49-61.

Chicago/Turabian Style

M.J. Senosiain; A. Tocino. 2018. "On the numerical integration of the undamped harmonic oscillator driven by independent additive gaussian white noises." Applied Numerical Mathematics 137, no. : 49-61.

Review
Published: 18 July 2014 in BIT Numerical Mathematics
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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 oscillation around zero. We show that these features can be studied in terms of the coefficients of the matrices that appear in the linear recurrence obtained when the schemes are applied to the oscillator. We use this study to compare the numerical schemes as well as to propose new schemes improving some properties of classical methods.

ACS Style

M. J. Senosiaín; A. Tocino. A review on numerical schemes for solving a linear stochastic oscillator. BIT Numerical Mathematics 2014, 55, 515 -529.

AMA Style

M. J. Senosiaín, A. Tocino. A review on numerical schemes for solving a linear stochastic oscillator. BIT Numerical Mathematics. 2014; 55 (2):515-529.

Chicago/Turabian Style

M. J. Senosiaín; A. Tocino. 2014. "A review on numerical schemes for solving a linear stochastic oscillator." BIT Numerical Mathematics 55, no. 2: 515-529.

Journal article
Published: 15 October 2011 in Journal of Computational and Applied Mathematics
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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 particular cases the 3.0 and 4.0 weak order explicit Taylor schemes. Since the implementation of the multiple integrals that appear in these theoretical schemes is difficult, for the applications they are replaced by simpler random variables, obtaining simplified schemes. In this way, for the multidimensional case with one-dimensional noise, we present an infinite family of semi-implicit simplified schemes of weak order 3.0 and for the multidimensional case with additive one-dimensional noise, we give an infinite family of semi-implicit simplified schemes of weak order 4.0. The mean-square stability of the 3.0 family is analyzed, concluding that, as in the deterministic case, the stability behavior improves when the degree of implicitness grows. Numerical experiments confirming the theoretical results are shown.

ACS Style

R. Zeghdane; L. Abbaoui; A. Tocino. Higher-order semi-implicit Taylor schemes for Itô stochastic differential equations. Journal of Computational and Applied Mathematics 2011, 236, 1009 -1023.

AMA Style

R. Zeghdane, L. Abbaoui, A. Tocino. Higher-order semi-implicit Taylor schemes for Itô stochastic differential equations. Journal of Computational and Applied Mathematics. 2011; 236 (6):1009-1023.

Chicago/Turabian Style

R. Zeghdane; L. Abbaoui; A. Tocino. 2011. "Higher-order semi-implicit Taylor schemes for Itô stochastic differential equations." Journal of Computational and Applied Mathematics 236, no. 6: 1009-1023.

Journal article
Published: 09 February 2007 in BIT Numerical Mathematics
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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 oscillator: It reproduces exactly the growth rate of the second moment and the oscillation property of the solution.

ACS Style

A. Tocino. On preserving long-time features of a linear stochastic oscillator. BIT Numerical Mathematics 2007, 47, 189 -196.

AMA Style

A. Tocino. On preserving long-time features of a linear stochastic oscillator. BIT Numerical Mathematics. 2007; 47 (1):189-196.

Chicago/Turabian Style

A. Tocino. 2007. "On preserving long-time features of a linear stochastic oscillator." BIT Numerical Mathematics 47, no. 1: 189-196.

Journal article
Published: 28 July 2004 in Journal of Computational and Applied Mathematics
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ACS Style

A. Tocino. Mean-square stability of second-order Runge–Kutta methods for stochastic differential equations. Journal of Computational and Applied Mathematics 2004, 175, 355 -367.

AMA Style

A. Tocino. Mean-square stability of second-order Runge–Kutta methods for stochastic differential equations. Journal of Computational and Applied Mathematics. 2004; 175 (2):355-367.

Chicago/Turabian Style

A. Tocino. 2004. "Mean-square stability of second-order Runge–Kutta methods for stochastic differential equations." Journal of Computational and Applied Mathematics 175, no. 2: 355-367.