A spectral-based numerical method for Kolmogorov equations in Hilbert spaces

We propose a numerical solution for the solution of the Fokker-Planck-Kolmogorov (FPK) equations associated with stochastic partial differential equations in Hilbert spaces. The method is based on the spectral decomposition of the Ornstein-Uhlenbeck semigroup associated to the Kolmogorov equation. This allows us to write the solution of the Kolmogorov equation as a deterministic version of the Wiener-Chaos Expansion. By using this expansion we reformulate the Kolmogorov equation as a infinite system of ordinary differential equations, and by truncation it we set a linear finite system of differential equations. The solution of such system allow us to build an approximation to the solution of the Kolmogorov equations. We test the numerical method with the Kolmogorov equations associated with a stochastic diffusion equation, a Fisher-KPP stochastic equation and a stochastic Burgers Eq. in dimension 1.Comment: 28 pages, 10 figure

Stability of real parametric polynomial discrete dynamical systems

We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameter $\lambda$, and generalize this characterization to cubic real polynomial maps, in a consistent theory that is further generalized to real $m$-th degree real polynomial maps. In essence, we give conditions for the stability of the fixed points of any real polynomial map with real fixed points. In order to do this, we have introduced the concept of Canonical Polynomial Maps which are topologically conjugate to any polynomial map of the same degree with real fixed points. The stability of the fixed points of canonical polynomial maps has been found to depend solely on a special function termed Product Position Function for a given fixed point. The values of this product position determine the stability of the fixed point in question, when it bifurcates, and even when chaos arises, as it passes through what we have termed stability bands. The exact boundary values of these stability bands are yet to be calculated for regions of type greater than one for polynomials of degree higher than three.Comment: 23 pages, 4 figures, now published in Discrete Dynamics in Nature and Societ

Geomorfología y paisaje en el ordenamiento territorial: valorizando el corredor inferior del río Mapocho

Considering the roles how biological corridor of the lower hydrological system of the Mapocho River, pointing to their integration in the urban planning of the respective communes from an ecologic, environmental and social perspective, is carried on a research about their geomorphological and landscape characteristics and the processes that are leading the evolution of the landscape. With this knowledge and from an ecosystemic perspective of the river territory, the limits of different homogeneous units were determined. Any geomorphological unit recognized, meaning also landscape systems, was characterized by its geology, sedimentology, soils and drainage, hydro-morphodynamic processes and human intervention, which allows through the determination of the quality and fragility of the geomorphic-landscape units, to establish land use proposals with their corresponding scopes on qualifications and restrictions. The resulting mapping contains implicit a proposal for land-use planning from the ecological planning point of view.    Considerando las funciones de corredor biológico del sistema hidrológico inferior del Río Mapocho, y apuntando a su integración a la planificación urbana de la intercomuna respectiva desde un punto de vista ecológico-ambiental y social, se reconocen sus características geomorfológicas y paisajísticas, y se establecen los procesos que lideran la evolución del modelado de las formas naturales. Con esta base se delimita el territorio fluvial desde una perspectiva ecosistémica y se determinan los límites de las diferentes unidades homogéneas resultantes. Cada unidad geomorfológica, en alta correspondencia con el sistema de paisajes, es caracterizada en función de su geología, sedimentología, suelos y drenaje, hidro-morfodinámica e intervención humana, lo cual permite mediante la determinación de la calidad y fragilidad de ellas, establecer propuestas de uso del suelo con sus correspondientes alcances sobre aptitudes y restricciones. La cartografía resultante contiene implícita una propuesta de ordenamiento del territorio desde el punto de vista de la planificación ecológica.  

Sensor Technologies for Caring People with Disabilities

Today, the population uses technology for every daily activity involving business, education, communication, entertainment, etc. Technologymay also help us to take care of peoplewho suffer some kind of disability. Complex technological ecosystems with pervasive and intelligent capabilities get along with us, facilitating the vigilance of those who need special attention or assisted living cares due to their health limitations. The advances in sensor research have enriched the powerful of these ecosystems to achieve more sophisticated monitoring and alarm systems, also taking into account the balance between the level of assistance and the people’s privacy. The Special Issue on “Sensor Technologies for Caring People with Disabilities” aims to present recent developments on sensor technologies for caring people with disabilities, focusing on the different configurations that can be used and novel applications in the field

Psychological elements explaining the consumer's adoption and use of a website recommendation system: A theoretical framework proposal

The purpose of this paper is to understand, with an emphasis on the psychological perspective of the research problem, the consumer's adoption and use of a certain web site recommendation system as well as the main psychological outcomes involved. The approach takes the form of theoretical modelling. Findings: A conceptual model is proposed and discussed. A total of 20 research propositions are theoretically analyzed and justified. Research limitations/implications: The theoretical discussion developed here is not empirically validated. This represents an opportunity for future research. Practical implications: The ideas extracted from the discussion of the conceptual model should be a help for recommendation systems designers and web site managers, so that they may be more aware, when working with such systems, of the psychological process consumers undergo when interacting with them. In this regard, numerous practical reflections and suggestions are presented

Complexity and anisotropy in host morphology make populations safer against epidemic outbreaks

One of the challenges in epidemiology is to account for the complex morphological structure of hosts such as plant roots, crop fields, farms, cells, animal habitats and social networks, when the transmission of infection occurs between contiguous hosts. Morphological complexity brings an inherent heterogeneity in populations and affects the dynamics of pathogen spread in such systems. We have analysed the influence of realistically complex host morphology on the threshold for invasion and epidemic outbreak in an SIR (susceptible-infected-recovered) epidemiological model. We show that disorder expressed in the host morphology and anisotropy reduces the probability of epidemic outbreak and thus makes the system more resistant to epidemic outbreaks. We obtain general analytical estimates for minimally safe bounds for an invasion threshold and then illustrate their validity by considering an example of host data for branching hosts (salamander retinal ganglion cells). Several spatial arrangements of hosts with different degrees of heterogeneity have been considered in order to analyse separately the role of shape complexity and anisotropy in the host population. The estimates for invasion threshold are linked to morphological characteristics of the hosts that can be used for determining the threshold for invasion in practical applications.Comment: 21 pages, 8 figure

The effect of heterogeneity on invasion in spatial epidemics: from theory to experimental evidence in a model system

Heterogeneity in host populations is an important factor affecting the ability of a pathogen to invade, yet the quantitative investigation of its effects on epidemic spread is still an open problem. In this paper, we test recent theoretical results, which extend the established “percolation paradigm” to the spread of a pathogen in discrete heterogeneous host populations. In particular, we test the hypothesis that the probability of epidemic invasion decreases when host heterogeneity is increased. We use replicated experimental microcosms, in which the ubiquitous pathogenic fungus Rhizoctonia solani grows through a population of discrete nutrient sites on a lattice, with nutrient sites representing hosts. The degree of host heterogeneity within different populations is adjusted by changing the proportion and the nutrient concentration of nutrient sites. The experimental data are analysed via Bayesian inference methods, estimating pathogen transmission parameters for each individual population. We find a significant, negative correlation between heterogeneity and the probability of pathogen invasion, thereby validating the theory. The value of the correlation is also in remarkably good agreement with the theoretical predictions. We briefly discuss how our results can be exploited in the design and implementation of disease control strategies

Accessory soleus muscle in an athlete. Presentation of a case and a literature review

The incidence of an accessory soleus muscle, according to autopsy studies, ranged from 0.5 to 6.0% of the population. The typical presentation is a soft mass in the posteromedial distal third of the leg, which increases in size with physical activity, especially plantar flexion. It is accompanied by pain with exercise in 67% of reported cases. The treatment of choice is conservative, but when it causes compartment syndrome, fasciotomy should be performed. If a patient has symptoms of claudication or nerve compression, a complete excision of the muscle is required. We report the case of an athlete who had a symptomatic accessory soleus muscle, which was studied by standard X-ray, ultrasound and magnetic resonance imaging (MRI)

Músculo sóleo accesorio de una deportista. A propósito de un caso y revisión de la bibliografía

Según los estudios necrópsicos, la incidencia del músculo sóleo accesorio fluctúa entre el 0,5 y el 6,0% de la población. La presentación típica es una tumoración blanda del tercio distal posteromedial de la pierna que aumenta de tamaño con la actividad física, especialmente con la flexión plantar. Se acompaña de dolor con el ejercicio en el 67% de los casos publicados. El tratamiento de elección es conservador, pero cuando provoca un síndrome compartimental se debe realizar la fasciotomía y, en el caso de tener síntomas de claudicación o compresión nerviosa, se necesitará una escisión completa del músculo. Presentamos el caso clínico de una deportista que presenta un músculo sóleo accesorio sintomático que fue estudiado mediante radiología, ecografía y resonancia magnética nuclear (RMN)