Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces II: numerical stability

AbstractIn this paper, we concern ourselves with the determination and evaluation of polynomials that are orthogonal with respect to a general discrete Sobolev inner product, that is, an ordinary inner product on the real line plus a finite sum of atomic inner products involving a finite number of derivatives. In a previous paper we provided a complete set of formulas to compute the coefficients of this recurrence. Here, we study the numerical stability of these algorithms for the generation and evaluation of a finite series of Sobolev orthogonal polynomials. Besides, we propose several techniques for reducing and controlling the rounding errors via theoretical running error bounds and a carefully chosen recurrence

Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial

A new computational technique based on the symbolic description utilizing kneading invariants is proposed and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor. The technique allows for uncovering the stunning complexity and universality of bi-parametric structures and detect their organizing centers - codimension-two T-points and separating saddles in the kneading-based scans of the iconic Lorenz equation from hydrodynamics, a normal model from mathematics, and a laser model from nonlinear optics.Comment: Journal of Bifurcations and Chaos, 201

Incidencia de tuberculosis osteoarticular en el área sanitaria del Hospital de León. 1997-2001

Introducción y objetivos: Nos proponemos en este trabajo estudiar la incidencia de tuberculosis en su forma osteoarticular en el área sanitaria del Hospital de León durante los años 1997 a 2001, ambos inclusive. Material y método: Dieciséis casos de tuberculosis osteoarticular confirmados por cultivo microbiológico y/o análisis anatomopatológico fueron incluidos. De ellos, cinco afectaron a columna vertebral, cuatro a rodilla y el resto a otras localizaciones más inusuales. Resultados: De las cinco columnas vertebrales afectadas, tres requirieron tratamiento quirúrgico para descomprimir y estabilizar. En una rodilla se realizó sinovectomía abierta y en otra por artroscopia. Se drenaron abscesos fríos en diferentes localizaciones. Todos los casos recibieron tratamiento médico. Se reflejan los diferentes resultados, desde la restitución ad integrum hasta la anquilosis. Discusión y conclusiones: La incidencia de tuberculosis osteoarticular en nuestra área sanitaria en el periodo 1997-2001 fue del 2% al 4% de todos los cascos de tuberculosis. Hubo una alta incidencia de localizaciones inusuales (muñeca, codo, sacroilíaca).Introduction: Current issue is to study the incidence of osteoarticular tuberculosis, within the sanitary area of the Hospital of Leon. Material and Method: Sixteen cases of osteoarticular tuberculosis confirmed by culture and pathological analysis were included. Five of them involved the raquis and knee. Another cases in unusual local sites. Results: Three of five raquis were managed by decompression and stabilization. One knee was treated by open synovectomy and another one by arthroscopy synovectomy. Cold abscesses were drained in different sites. All cases were treated with drugs. Different results are showed since restitutio ad integrum to anquilosis. Discussion: Osteoarticular tuberculosis incidence in our sanitary area between 1997 to 2001 was 2% to 4%. There was a high incidence for unusual localizations (wrist, elbow and sacroiliaca joints)

Systematic search for gamma-ray periodicity in active galactic nuclei detected by the Fermi Large Area Telescope

We use nine years of gamma-ray data provided by the Fermi Large Area Telescope (LAT) to systematically study the light curves of more than two thousand active galactic nuclei (AGN) included in recent Fermi-LAT catalogs. Ten different techniques are used, which are organized in an automatic periodicity-search pipeline, in order to search for evidence of periodic emission in gamma rays. Understanding the processes behind this puzzling phenomenon will provide a better view about the astrophysical nature of these extragalactic sources. However, the observation of temporal patterns in gamma-ray light curves of AGN is still challenging. Despite the fact that there have been efforts on characterizing the temporal emission of some individual sources, a systematic search for periodicities by means of a full likelihood analysis applied to large samples of sources was missing. Our analysis finds 11 AGN, of which 9 are identified for the first time, showing periodicity at more than 4sigma in at least four algorithms. These findings will help in solving questions related to the astrophysical origin of this periodic behavior.Comment: 16 pages, 5 figures, 4 tables. Accepted by Ap

Assessment of methods for estimating wild rabbit population abundance in agricultural landscapes

Various methods have been used to estimate rabbit abundance, but comparisons of standard methods are still lacking, and thus, results remain roughly comparable across studies. Ideally, a method should be applicable over a wide range of situations, such as differing abundances or habitat types. Comparisons of methods are required to evaluate the benefits of each of them, and survey methods should be validated for the conditions in which they will be used. In this study, we compare the performance of direct methods (kilometric abundance index and distance sampling) in two seasons and at two times of day (dusk and night) for estimating wild rabbit abundances in agricultural landscapes. Estimates based on direct methods were highly correlated and detected similar seasonal population changes. Night counts provided better estimates than did dusk counts and exhibited more precision. Results are discussed within the context of rabbit behaviour and their implications for rabbit population surveys.Funding was provided by FEDENCA. ICB was supported by a PhD fellowship from the Spanish Ministry of Science and Innovation. PA is currently enjoying a Juan de la Cierva research contract awarded by the Spanish Ministry of Science and Innovation and is supported by the project CGL2006-09567/BOS.Peer Reviewe

Using the Sound Card as a Timer

Experiments in mechanics can often be timed by the sounds they produce. In such cases, digital audio recordings provide a simple way of measuring time intervals with an accuracy comparable to that of photogate timers. We illustrate this with an experiment in the physics of sports: to measure the speed of a hard-kicked soccer ball.Comment: 3 pages, 4 figures, Late

Symbolic dynamical unfolding of spike-adding bifurcations in chaotic neuron models

We characterize the systematic changes in the topological structure of chaotic attractors that occur as spike-adding and homoclinic bifurcations are encountered in the slow-fast dynamics of neuron models. This phenomenon is detailed in the simple Hindmarsh-Rose neuron model, where we show that the unstable periodic orbits appearing after each spike-adding bifurcation are associated with specific symbolic sequences in the canonical symbolic encoding of the dynamics of the system. This allows us to understand how these bifurcations modify the internal structure of the chaotic attractors

Evaluation of the energy consumption and overheating of homes in Miami, Guayaquil and Tenerife

Year after year, global warming is elevating temperatures all over the world, causing indoor overheating environments that are inhabitable, and increasing energy demand in housing. Given this global concern, the aim of the study was to evaluate the thermal behavior of the house in the cities of Miami, Guayaquil and Tenerife, by a comparison assisted with a simulation for their indoor overheating hours and cooling demand, considering their climates, energy efficiency codes, and construction systems. These were: Miami, with two models (M1 with timber frame as the thermal envelope and M2 with a concrete block system), Guayaquil, with two models (G1 with the limitations for a dwelling with cooling system and G2 without it), and Tenerife with only one model. As a result, was found that Miami is the case with the higher consumption, which has a higher energy demand in a house of timber wall system than in a house of concrete block system, due to the thermal inertia. Despite that both models have the same usage time for the cooling system, meaning that more power was needed to reach the thermal comfort. Then, Guayaquil and Tenerife, are the cases that follows, with less consumption. While, according to the UNE EN 16798 methodology, in the indoor overheating hour evaluation in a year, Miami has the higher cases with a 31.43% of its hours in overheating for the timber frame system and a 22.88% for the concrete block system, followed by two cases in Guayaquil, with 4.2%, other with none, and also Tenerife with 2.43%. Nevertheless, the study showed that energy consumption is not necessarily related to the indoor overheating hours that a house could have. Given that, in the case of Guayaquil, where it doesn’t have any indoor overheating hour in all year, while Tenerife, with a similar energy consumption, has 2.43% of its hours in overheating. Due to the different parameters that the UNE follows in comparison with the cooling setpoints given by the CTE-DB-HE all over the year for the respective cases, because of their long warm seasons. Therefore, the study analyses the limits establish by the Spanish normative in relation to overheating, showing an overestimation assessment if the results with the UNE methodology are compared