Heat and Poisson semigroups for Fourier-Neumann expansions

Given $\alpha > -1$, consider the second order differential operator in $(0,\infty)$, $$L_\alpha f \equiv (x^2 \frac{d^2}{dx^2} + (2\alpha+3)x \frac{d}{dx} + x^2 + (\alpha+1)^2)(f),$$ which appears in the theory of Bessel functions. The purpose of this paper is to develop the corresponding harmonic analysis taking $L_\alpha$ as the analogue to the classical Laplacian. Namely we study the boundedness properties of the heat and Poisson semigroups. These boundedness properties allow us to obtain some convergence results that can be used to solve the Cauchy problem for the corresponding heat and Poisson equations.Comment: 16 page

Origin of coherent structures in a discrete chaotic medium

Using as an example a large lattice of locally interacting Hindmarsh-Rose chaotic neurons, we disclose the origin of ordered structures in a discrete nonequilibrium medium with fast and slow chaotic oscillations. The origin of the ordering mechanism is related to the appearance of a periodic average dynamics in the group of chaotic neurons whose individual slow activity is significantly synchronized by the group mean field. Introducing the concept of a "coarse grain" as a cluster of neuron elements with periodic averaged behavior allows consideration of the dynamics of a medium composed of these clusters. A study of this medium reveals spatially ordered patterns in the periodic and slow dynamics of the coarse grains that are controlled by the average intensity of the fast chaotic pulsation

Singular measures and convolution operators

We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type (1,1) inequalities. As an application, we prove that the best constants for the centered Hardy-Littlewood maximal operator associated to parallelotopes do not decrease with the dimension.Comment: 8 page

Genetic evaluation for subjective traits in the Pirenaica Breed

Ponencia publicada en ITEA, vol.104Los esquemas de selección en las especies ganaderas utilizan una amplia variedad de caracteres. En algunos casos, los registros fenotípicos se obtienen a partir de una valoración subjetiva por parte de evaluadores expertos. Esta valoración implica una clasificación en una escala arbitraria, y, por este motivo, puede diferir considerablemente de la distribución Normal. Por otra parte, cada evaluador puede utilizar criterios de clasificación específicos, y diferentes de los otros evaluadores. En este trabajo se propone un modelo multi-umbral para el análisis de datos procedentes de valoraciones subjetivas. El modelo asume una escala observable diferente para cada evaluador o grupo de evaluadores, y una escala subyacente común. El modelo propuesto se ha aplicado a datos de conformación de la canal de la Raza Bovina Pirenaica procedentes del sistema de valoración SEUROP en 12 mataderos del País Vasco y Navarra.Selection programs in livestock populations made use of a wide variety of traits. Among them, phenotypic records for some traits are obtained by a subjective evaluation from a set of experts, like sensory, type, carcass or fat score traits. Data from subjective evaluation usually involves a classification under an arbitrary predefined scale. The output of this process can lead to strong departures from the Gaussian distribution. Moreover, different criteria can be achieved for each expert. In this study, we propose a Slaughterhouse Specific Ordered Category Threshold Model, that assumes a specific observable scale for each specialist, and a common subjacent scale. The procedure is applied to SEUROP conformation score data from the Pirenaica Beef Cattle Breed evaluated at 12 different slaughterhouses from the Basque Country and Navarre

Interplay between subthreshold oscillations and depressing synapses in single neurons

Latorre R, Torres JJ, Varona P (2016) Interplay between Subthreshold Oscillations and Depressing Synapses in Single Neurons. PLoS ONE 11(1): e0145830. doi:10.1371/journal.pone.0145830In this paper we analyze the interplay between the subthreshold oscillations of a single neuron conductance-based model and the short-term plasticity of a dynamic synapse with a depressing mechanism. In previous research, the computational properties of subthreshold oscillations and dynamic synapses have been studied separately. Our results show that dynamic synapses can influence different aspects of the dynamics of neuronal subthreshold oscillations. Factors such as maximum hyperpolarization level, oscillation amplitude and frequency or the resulting firing threshold are modulated by synaptic depression, which can even make subthreshold oscillations disappear. This influence reshapes the postsynaptic neuron's resonant properties arising from subthreshold oscillations and leads to specific input/output relations. We also study the neuron's response to another simultaneous input in the context of this modulation, and show a distinct contextual processing as a function of the depression, in particular for detection of signals through weak synapses. Intrinsic oscillations dynamics can be combined with the characteristic time scale of the modulatory input received by a dynamic synapse to build cost-effective cell/channel-specific information discrimination mechanisms, beyond simple resonances. In this regard, we discuss the functional implications of synaptic depression modulation on intrinsic subthreshold dynamics.This work was supported by MINECO TIN2012-30883 (RL and PV) and FIS2013-43201-P (JJT). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Channel-specific input/output transformations arising from the interaction between dynamic synapses and subthreshold oscillations

Authors acknowledge support by MINECO TIN2012-30883 and FIS2013-43201-P

Consequences of paternally inherited effects on the genetic evaluation of maternal effects

Background: Mixed models are commonly used for the estimation of variance components and genetic evaluation of livestock populations. Some evaluation models include two types of additive genetic effects, direct and maternal. Estimates of variance components obtained with models that account for maternal effects have been the subject of a long-standing controversy about strong negative estimates of the covariance between direct and maternal effects. Genomic imprinting is known to be in some cases statistically confounded with maternal effects. In this study, we analysed the consequences of ignoring paternally inherited effects on the partitioning of genetic variance. Results: We showed that the existence of paternal parent-of-origin effects can bias the estimation of variance components when maternal effects are included in the evaluation model. Specifically, we demonstrated that adding a constraint on the genetic parameters of a maternal model resulted in correlations between relatives that were the same as those obtained with a model that fits only paternally inherited effects for most pairs of individuals, as in livestock pedigrees. The main consequence is an upward bias in the estimates of the direct and maternal additive genetic variances and a downward bias in the direct-maternal genetic covariance. This was confirmed by a simulation study that investigated five scenarios, with the trait affected by (1) only additive genetic effects, (2) only paternally inherited effects, (3) additive genetic and paternally inherited effects, (4) direct and maternal additive genetic effects and (5) direct and maternal additive genetic plus paternally inherited effects. For each scenario, the existence of a paternally inherited effect not accounted for by the estimation model resulted in a partitioning of the genetic variance according to the predicted pattern. In addition, a model comparison test confirmed that direct and maternal additive models and paternally inherited models provided an equivalent fit. Conclusions: Ignoring paternally inherited effects in the maternal models for genetic evaluation can lead to a specific pattern of bias in variance component estimates, which may account for the unexpectedly strong negative direct-maternal genetic correlations that are typically reported in the literature