Algebro-geometric analysis of bisectors of two algebraic plane curves

In this paper, a general theoretical study, from the perspective of the algebraic geometry, of the untrimmed bisector of two real algebraic plane curves is presented. The curves are considered in C2, and the real bisector is obtained by restriction to R2. If the implicit equations of the curves are given, the equation of the bisector is obtained by projection from a variety contained in C7, called the incidence variety, into C2. It is proved that all the components of the bisector have dimension 1. A similar method is used when the curves are given by parametrizations, but in this case, the incidence variety is in C5. In addition, a parametric representation of the bisector is introduced, as well as a method for its computation. Our parametric representation extends the representation in Farouki and Johnstone (1994b) to the case of rational curves

Fibromatosis extraabdominal agresiva: descripción de un caso y revisión de la literatura

El tumor desmoide es un raro tumor benigno de partes blandas, con gran capacidad invasiva local y sin potencial metastático. Se han descrito diversas variedades según su localización; siendo la variedad extraabdominal ó fibromatosis extraabdominal agresiva, en la que centramos nuestra revisión, más frecuente en las cinturas escapular y pélvica. Presentamos el caso de un varón de 35 años con un tumor localizado en cadera izquierda, que provocaba una cadera en resorte sintomática. Se valora la bibliografía existente sobre esta patología haciendo hincapié en las características biológicas del tumor, su histología, historia natural y tratamiento.Desmoid tumour is a rare benign neoplasm of soft tissues, with local aggressivity and without metastatic possibility. There are different types depending on its location, the one we are going to review being the extraabdominal one or aggressive extra-abdominal fibromatosis, the one we are going to review, more frequent in scapular and pelvic waists. We report a case of a 35 years old man with a tumour in his left hip, with clinical findings of snapping hip. A review of the existing literature on this pathology is also carried out, with special emphasis on the biological characteristics of the tumour, as well as its histology, natural history and treatment

The effect of the Spanish Law of Political Parties (LPP) on the attitude of the Basque Country population towards ETA: A dynamic modelling approach

In June 2002, the Spanish Government passed the ¿Law of Political Parties¿ (LPP) with the aim, among others, of preventing parties giving political support to terrorist organizations. This law affected the Basque nationalist party ¿Batasuna¿, due to its proved relation with ETA. In this paper, taking data from the Euskobarometro (Basque Country survey) related to the attitude of the Basque population towards ETA, we propose a dynamic model for the pre-LPP scenario. This model will be extrapolated to the future in order to predict what would have happened to the attitude of the Basque population if the law had not been passed. These model predictions will be compared to post-LPP data from the Euskobarometro using a bootstrapping approach in order to quantify the effect of the LPP on the attitude of Basque Country population towards ETA.Peco Yeste, M.; Santonja, F.; Tarazona Tornero, AC.; Villanueva Micó, RJ.; Villanueva Oller, FJ. (2013). The effect of the Spanish Law of Political Parties (LPP) on the attitude of the Basque Country population towards ETA: A dynamic modelling approach. Mathematical and Computer Modelling. 1-7. doi:10.1016/j.mcm.2011.11.007S1

Calibration of an agent-based simulation model to the data of women infected by Human Papillomavirus with uncertainty

[EN] Recently, the transmission dynamics of the Human Papillomavirus (HPV) has been studied. In previous works, we have designed and implemented a computational model (agent-based simulation model) where the contagion of the HPV is described on a network of lifetime sexual partners. The run of a single simulation of this computational model, composed of a network with 500 000 nodes, takes about one hour and a half. In addition to set an adequate model, finding out the model parameters that best fit the proposed model to the available data of prevalence is a crucial goal. Taking into account that the necessary number of simulations to perform the calibration of the model may be very high, the aforementioned goal may become unaffordable. In this paper, we present a procedure to fit the proposed HPV model to the available data and the design of an asynchronous version of the Particle Swarm Optimization (PSO) algorithm adapted to the distributed computing environment. In the process, the number of particles used in PSO should be set carefully looking for a compromise between quality of the solutions and computation time. Another feature of the procedure presented here is that we want to capture the intrinsic uncertainty in the data (data come from a survey) when calibrating the model. To do so, we also propose the design of an algorithm to select the model parameter sets obtained during the calibration that best capture the data uncertainty.This work has been supported by the Spanish Ministerio de Economia y Competitividad grants MTM2017-89664-P, TIN2014-54806-R and RTI2018-095180-B-I00, Grants Y2018/NMT-4668 (Micro-Stres-MAP-CM) and GenObIA-CM (S2017/BMD-3773) financed by the Community of Madrid, Spain and co-financed with EU Structural Funds, Spain, and by GLENO project financed by Fundacion Eugenio Rodriguez Pascual, Spain.Villanueva Micó, RJ.; Hidalgo, J.; Cervigon, C.; Villanueva-Oller, J.; Cortés, J. (2019). Calibration of an agent-based simulation model to the data of women infected by Human Papillomavirus with uncertainty. Applied Soft Computing. 80:546-556. https://doi.org/10.1016/j.asoc.2019.04.015S5465568

Evaluation of accurate eye corner detection methods for gaze estimation

Accurate detection of iris center and eye corners appears to be a promising approach for low cost gaze estimation. In this paper we propose novel eye inner corner detection methods. Appearance and feature based segmentation approaches are suggested. All these methods are exhaustively tested on a realistic dataset containing images of subjects gazing at different points on a screen. We have demonstrated that a method based on a neural network presents the best performance even in light changing scenarios. In addition to this method, algorithms based on AAM and Harris corner detector present better accuracies than recent high performance face points tracking methods such as Intraface

Extending the deterministic Riemann-Liouville and Caputo operators to the random framework: A mean square approach with applications to solve random fractional differential equations

[EN] This paper extends both the deterministic fractional Riemann¿Liouville integral and the Caputo fractional derivative to the random framework using the mean square random calculus. Characterizations and sufficient conditions to guarantee the existence of both fractional random operators are given. Assuming mild conditions on the random input parameters (initial condition, forcing term and diffusion coefficient), the solution of the general random fractional linear differential equation, whose fractional order of the derivative is ¿ ¿ [0, 1], is constructed. The approach is based on a mean square chain rule, recently established, together with the random Fröbenius method. Closed formulae to construct reliable approximations for the mean and the covariance of the solution stochastic process are also given. Several examples illustrating the theoretical results are included.This work has been partially supported by the Ministerio de Economia y Competitividad grant MTM2013-41765-P. The co-author Prof. L. Villafuerte acknowledges the support by Mexican Conacyt.Burgos, C.; Cortés, J.; Villafuerte, L.; Villanueva Micó, RJ. (2017). Extending the deterministic Riemann-Liouville and Caputo operators to the random framework: A mean square approach with applications to solve random fractional differential equations. Chaos, Solitons and Fractals. 102:305-318. https://doi.org/10.1016/j.chaos.2017.02.008S30531810

A nonlinear dynamic age-structured model of e-commerce in Spain: Stability analysis of the equilibrium by delay and stochastic perturbations

[EN] First, we propose a deterministic age-structured epidemiological model to study the diffusion of e-commerce in Spain. Afterwards, we determine the parameters (death, birth and growth rates) of the underlying demographic model as well as the parameters (transmission of the use of e-commerce rates) of the proposed epidemiological model that best fit real data retrieved from the Spanish National Statistical Institute. Motivated by the two following facts: first the dynamics of acquiring the use of a new technology as e-commerce is mainly driven by the feedback after interacting with our peers (family, friends, mates, mass media, etc.), hence having a certain delay, and second the inherent uncertainty of sampled real data and the social complexity of the phenomena under analysis, we introduce aftereffect and stochastic perturbations in the initial deterministic model. This leads to a delayed stochastic model for e-commerce. We then investigate sufficient conditions in order to guarantee the stability in probability of the equilibrium point of the dynamic e-commerce delayed stochastic model. Our theoretical findings are numerically illustrated using real data. (C) 2018 Elsevier B.V. All rights reserved.This work has been partially supported by the Ministerio de Economia y Competitividad grant MTM2017-89664-P.Burgos-Simon, C.; Cortés, J.; Shaikhet, L.; Villanueva Micó, RJ. (2018). A nonlinear dynamic age-structured model of e-commerce in Spain: Stability analysis of the equilibrium by delay and stochastic perturbations. Communications in Nonlinear Science and Numerical Simulation. 64:149-158. https://doi.org/10.1016/j.cnsns.2018.04.022S1491586