A geometric approach to phase response curves and its numerical computation through the parameterization method

The final publication is available at link.springer.comThe phase response curve (PRC) is a tool used in neuroscience that measures the phase shift experienced by an oscillator due to a perturbation applied at different phases of the limit cycle. In this paper, we present a new approach to PRCs based on the parameterization method. The underlying idea relies on the construction of a periodic system whose corresponding stroboscopic map has an invariant curve. We demonstrate the relationship between the internal dynamics of this invariant curve and the PRC, which yields a method to numerically compute the PRCs. Moreover, we link the existence properties of this invariant curve as the amplitude of the perturbation is increased with changes in the PRC waveform and with the geometry of isochrons. The invariant curve and its dynamics will be computed by means of the parameterization method consisting of solving an invariance equation. We show that the method to compute the PRC can be extended beyond the breakdown of the curve by means of introducing a modified invariance equation. The method also computes the amplitude response functions (ARCs) which provide information on the displacement away from the oscillator due to the effects of the perturbation. Finally, we apply the method to several classical models in neuroscience to illustrate how the results herein extend the framework of computation and interpretation of the PRC and ARC for perturbations of large amplitude and not necessarily pulsatile.Peer ReviewedPostprint (author's final draft

Can optical spectroscopy directly elucidate the ground state of C20?

The optical response of the lowest energy members of the C20 family is calculated using time-dependent density functional theory within a real-space, real-time scheme. Significant differences are found among the spectra of the different isomers, and thus we propose optical spectroscopy as a tool for experimental investigation of the structure of these important clusters.Comment: 11 pages, 2 figures. To be published in J. Chem. Phy

Multimode: An R Package for Mode Assessment

In several applied fields, multimodality assessment is a crucial task as a previous exploratory tool or for determining the suitability of certain distributions. The goal of this paper is to present the utilities of the R package multimode, which collects different exploratory and testing nonparametric approaches for determining the number of modes and their estimated location. Specifically, some graphical tools, allowing for the identification of mode patterns, based on the kernel density estimation are provided (SiZer map, mode tree or mode forest). Several formal testing procedures for determining the number of modes are described in this paper and implemented in the multimode package, including methods based on the ideas of the critical bandwidth, the excess mass or using a combination of both. This package also includes a function for estimating the modes locations and different classical data examples that have been considered in mode testing literature

multimode: An R Package for Mode Assessment

In several applied fields, multimodality assessment is a crucial task as a previous exploratory tool or for determining the suitability of certain distributions. The goal of this paper is to present the utilities of the R package multimode, which collects different exploratory and testing non-parametric approaches for determining the number of modes and their estimated location. Specifically, some graphical tools (SiZer map, mode tree or mode forest) are provided, allowing for the identification of mode patterns, based on the kernel density estimation. Several formal testing procedures for determining the number of modes are described in this paper and implemented in the multimode package, including methods based on the ideas of the critical bandwidth, the excess mass or using a combination of both. This package also includes a function for estimating the modes locations and different classical data examples that have been considered in mode testing literature

Two new power indices based on winning coalitions

Deegan and Packel (1979) and Holler (1982) proposed two power indices for simple games: the Deegan–Packel index and the Public Good Index. In the definition of these indices, only minimal winning coalitions are taken into account. Using similar arguments, we define two new power indices. These new indices are defined taking into account only those winning coalitions that do not contain null players. The results obtained with the different power indices are compared by means of two real-world examples taken from the political field

Effects of litter mixing on litter decomposition and soilproperties along simulated invasion gradients of non-nativetrees

Aims Plant invasions generally lead to mixtures betweennative and non-native litter. We assess the interactionsbetween leaf litters from two invasive non-native trees(Robinia pseudoacia or Ailanthus altissima) and the nativePopulus alba on litter decomposition, nutrient releaseand soil properties along two gradients of invasion.Methods Microcosms with field-collected soil coveredby varying proportions of native and non-native littersimulated the two invasion gradients. We assessed theproportion of remaining litter mass and nutrient mass(N, P, C), and soil C, N-NO3−, total N, and pH, fivetimes throughout a period of 11 months. Observedvalues were compared to the expected values on theassumption of no interactions.Results Litter mass and C mass decayed slower inRobinia and faster in Ailanthus than in Populus. Thethree species immobilized N and P. Soil properties didnot differ across pure litters. Both litter mixture gradientsshowed additive or antagonistic interactions onlitter decomposition, whereas N and P mass were equalor higher than expected. The proportion of non-nativelitter in the mixture had non-linear effects on mostvariables, suggesting that the impact of these nonnativetrees on litter decay levels off or even declinesas they become more abundant.Conclusion The impacts of Ailanthus and Robinia litteron soil processes should not be derived from singlespecies experiments, both due to non-additive effectsand to non-linear responses to litter abundance.Ministerio de Ciencia, Innovación y UniversidadesComunidad de Madri

Estudio de fatiga térmica de cermets base hierro

Ponencia presentada en: XI Congreso Nacional de Materiales Compuestos, celebrado los días 6, 7 y 8 de julio de 2015, en Móstoles (España).En el presente trabajo se analiza el comportamiento a fatiga térmica de materiales compuestos de matriz férrea y refuerzo de TiCN desde dos puntos de vista: la influencia de la temperatura máxima alcanzada durante la fatiga térmica y la influencia del número de ciclos de calentamiento y enfriamiento. Además, se compara el comportamiento de estos materiales con el de un acero de herramientas de uso convencional. Este estudio del comportamiento frente a cambios cíclicos de temperatura para ambos materiales se realiza en base a su resistencia a la oxidación y se compara con la oxidación estática que se produce a temperatura elevada constante. Para ello las probetas se han sometido a diferentes ciclos de fatiga térmica, alcanzando temperaturas máximas de 1000 ºC durante un máximo de 100 ciclos; posteriormente se ha caracterizado tanto su superficie como su sección transversal utilizando diferentes técnicas: medida de cambio de masa, DRX, SEM, EDX y microdureza.Los autores agradecen la financiación recibida para la realización de este trabajo al MINECO (proyecto MAT2012-38650-C02-01) y a la Comunidad de Madrid por el programa MULTIMAT-CHALLENGE, ref. S2013/MIT-2862Publicad