https://ria.asturias.es/RIA/handle/123456789/7535 Sat, 07 Mar 2026 02:06:42 GMT 2026-03-07T02:06:42Z https://ria.asturias.es/RIA/handle/123456789/13926 Title: Spike-adding structure in fold/hom bursters Authors: Barrio Gil, Roberto; Ibáñez Mesa, Santiago; Pérez Pérez, Lucía; Serrano Pastor, Sergio Abstract: Square-wave or fold/hom bursting is typical of many excitable dynamical systems, such as pancreatic or other endocrine cells. Besides, it is also found in a great variety of fast-slow systems coming from other neural models, chemical reactions, laser dynamics, and so on. We focus on the spike-adding process and its connection with the homoclinic structure of the system. The creation of new fast spikes on a bursting neuron is an important phenomenon as it increases the duty cycle of the neuron. Here we mainly work with the Hindmarsh-Rose neuron model, a prototype of fold/hom bursting, but also with the pancreatic β-cell model, where, as already known from the literature, homoclinic bifurcations play an important role in bursting dynamics. Based on several numerical simulations, we present a theoretical scheme that provides a complete scenario of bifurcations involved in the spike-adding process and their connection with the homoclinic bifurcations on the parametric space. The global scheme explains the different phenomena of the spike-adding processes presented in literature (continuous and chaotic processes after Terman analysis) and moreover, it also indicates where each kind of spike-adding process occurs. Different elements are involved in the theoretical scheme, such as homoclinic isolas, canard orbits, inclination and orbit flip codimension-two bifurcation points and several pencils of period doubling and fold bifurcations, all of them illustrated with different numerical techniques. Some of these bifurcations needed in the process may be not visible on some numerical simulations because the organizing points are in different parametric planes due to the high dimension of the whole parameter space, but their effects are present. Therefore, we introduce a mechanism of the spike-adding process in fold/hom bursters in the whole space of parameters, even if apparently no role is played by the “far-away” homoclinic bifurcations. This fact is illustrated showing how the theoretical scheme provides a theoretical explanation to the different interspike-interval bifurcation diagrams (IBD) that have appeared in the literature for different models. Wed, 01 Jan 2020 00:00:00 GMT https://ria.asturias.es/RIA/handle/123456789/13926 2020-01-01T00:00:00Z https://ria.asturias.es/RIA/handle/123456789/14886 Title: Sets of Probability Measures and Convex Combination Spaces Authors: Alonso de la Fuente, Miriam; Terán, Pedro Abstract: The Wasserstein distances between probability distributions are an important tool in modern probability theory which has been generalized to sets of probability distributions. We will show that the (generalized) L1-Wasserstein metric, with the operations of convolution and rescaling, fits in the abstract framework of convex combination spaces: nonlinear metric spaces preserving some of the nice properties of a normed space but accomodating other unusual behaviours. For instance, unlike in a linear space, a singleton {𝑃} is typically not convex (it is so only if 𝑃 is degenerate). Also, some theorems for convex combination spaces are applied to this setting. Description: Enlace a la publicación original: https://proceedings.mlr.press/v215/fuente23a.html Sun, 01 Jan 2023 00:00:00 GMT https://ria.asturias.es/RIA/handle/123456789/14886 2023-01-01T00:00:00Z https://ria.asturias.es/RIA/handle/123456789/7545 Title: Proceedings of COMPSTAT 2016 Authors: Colubi, Ana; Blanco, Angela; Gatu, Cristian Abstract: The Proceedings of COMPSTAT 2016 are published in an electronic book comprising 34 papers. All the papers submitted have been evaluated through a rigorous peer review process. Those papers that have been accepted for publication in the Proceedings have been evaluated thoroughly by at least 2 referees. This ensures a high quality proceedings volume in the main areas of computational statistics. Description: Los proceeding de COMPSTAT 2016 contienen una selección de artículos completos en el área de la Estadística Computational que fueron presentados durante el congreso. Fri, 15 Jul 2016 00:00:00 GMT https://ria.asturias.es/RIA/handle/123456789/7545 2016-07-15T00:00:00Z https://ria.asturias.es/RIA/handle/123456789/14885 Title: On convergence in distribution of fuzzy random variables Authors: Alonso de la Fuente, Miriam; Terán, Pedro Abstract: We study whether convergence in distribution of fuzzy random variables, defined as the weak convergence of their probability distributions, is consistent with the additional structure of spaces of fuzzy sets. Positive results are obtained which reinforce the viability of that definition. Description: Enlace a la publicación original: http://dx.doi.org/10.1007/978-3-031-15509-3_2 Sun, 01 Jan 2023 00:00:00 GMT https://ria.asturias.es/RIA/handle/123456789/14885 2023-01-01T00:00:00Z