We show how modern Bayesian Machine Learning tools can be effectively used in order to develop efficient methods for filtering Earth Observation signals. Bayesian statistical methods can be thought of as a generalization of the classical least-squares adjustment methods where both the unknown signals and the parameters are endowed with probability distributions, the priors. Statistical inference under this scheme is the derivation of posterior distributions, that is, distributions of the unknowns after the model has seen the data. Least squares can then be thought of as a special case that uses Gaussian likelihoods, or error statistics. In principle, for most non-trivial models, this framework requires performing integration in high-dimensional spaces. Variational methods are effective tools for approximate inference in Statistical Machine Learning and Computational Statistics. In this paper, after introducing the general variational Bayesian learning method, we apply it to the modelling and implementation of sparse mixtures of Gaussians (SMoG) models, intended to be used as adaptive priors for the efficient representation of sparse signals in applications such as wavelet-type analysis. Wavelet decomposition methods have been very successful in denoising real-world, non-stationary signals that may also contain discontinuities. For this purpose we construct a constrained hierarchical Bayesian model capturing the salient characteristics of such sets of decomposition coefficients. We express our model as a Dirichlet mixture model. We then show how variational ideas can be used to derive efficient methods for bypassing the need for integration: the task of integration becomes one of optimization. We apply our SMoG implementation to the problem of denoising of Synthetic Aperture Radar images, inherently affected by speckle noise, and show that it achieves improved performance compared to established methods, both in terms of speckle reduction and image feature preservation. Full article

This paper presents a discrete compartmental Susceptible–Exposed–Infected–Recovered/Dead (SEIR/D) model to address the expansion of Covid-19. This model is based on a grid. As time passes, the status of the cells updates by means of binary rules following a neighborhood and a delay pattern. This model has already been analyzed in previous works and successfully compared with the corresponding continuous models solved by ordinary differential equations (ODE), with the intention of finding the homologous parameters between both approaches. Thus, it has been possible to prove that the combination neighborhood-update rule is responsible for the rate of expansion and recovering/death of the disease. The delays (between Susceptible and Asymptomatic, Asymptomatic and Infected, Infected and Recovered/Dead) may have a crucial impact on both height and timing of the peak of Infected and the Recovery/Death rate. This theoretical model has been successfully tested in the case of the dissemination of information through mobile social networks and in the case of plant pests. Full article

Marital relations depend on many factors which can increase the amount of satisfaction or unhappiness in the relation. A large percentage of marriages end up in divorce. While there are many studies about the causes of divorce and how to prevent it, there are very few mathematical models dealing with marital relations. In this paper, we present a continuous model based on the ideas presented by Gottman and coauthors. We show that the type of influence functions that describe the interaction between husband and wife is critical in determining the outcome of a marriage. We also introduce stochasticity into the model to account for the many factors that affect the marriage and that are not easily quantified, such as economic climate, work stress, and family relations. We show that these factors are able to change the equilibrium state of the couple. Full article

Kernel density estimation is a non-parametric method to estimate the probability density function of a random quantity from a finite data sample. The estimator consists of a kernel function and a smoothing parameter called the bandwidth. Despite its undeniable usefulness, the convergence rate may be slow with the number of realizations and the discontinuity and peaked points of the target density may not be correctly captured. In this work, we analyze the applicability of a parametric method based on Monte Carlo simulation for the density estimation of certain random variable transformations. This approach has important applications in the setting of differential equations with input random parameters. Full article

Currently, one of the challenges of universities is attracting talent in students, researchers, and teachers. The transition from high school to college requires a student to take a succession of decisions that will shape their future. For this reason, knowledge of the motivations of the students, their family, and their personal environment, to choose a particular degree and/or university to pursue their higher studies, would allow universities to efficiently adjust their recruitment strategies. In this article, a study was developed based on a structural equation model of the access to the Spanish Public University System (SUPE), which can help with supply and demand problems, recruitment actions and policies, and other strategic decisions. This was done through an extensive survey of first-year students of Spanish universities. The results allowed us to obtain the parameters of the model, which showed that the fit between the model and the data obtained were excellent at a global level and acceptable as well in all knowledge areas. The objective of the structural model was to provide a general view of the behavior of the students when deciding the degree and university in which they are going to study, and can help in the decision making of university leaders and to understand some behaviors of the Spanish Public University System. Full article

We perturbed a family of exponential polynomial maps in order to show both analytically and numerically their unpredictable orbit behavior. Due to the analytical form of the iteration functions the family has numerically different behavior than its correspondent analytical one, which is a topic of paramount importance in computer mathematics. We discover an unexpected oscillatory parametrical behavior of the perturbed family. Full article