Constructive updating/downdating of oblique projectors: a generalization of the Gram-Schmidt process

A generalization of the Gram-Schmidt procedure is achieved by providing equations for updating and downdating oblique projectors. The work is motivated by the problem of adaptive signal representation outside the orthogonal basis setting. The proposed techniques are shown to be relevant to the problem of discriminating signals produced by different phenomena when the order of the signal model needs to be adjusted.Comment: As it will appear in Journal of Physics A: Mathematical and Theoretical (2007

Measurements design and phenomena discrimination

The construction of measurements suitable for discriminating signal components produced by phenomena of different types is considered. The required measurements should be capable of cancelling out those signal components which are to be ignored when focusing on a phenomenon of interest. Under the hypothesis that the subspaces hosting the signal components produced by each phenomenon are complementary, their discrimination is accomplished by measurements giving rise to the appropriate oblique projector operator. The subspace onto which the operator should project is selected by nonlinear techniques in line with adaptive pursuit strategies

On the truncation of the harmonic oscillator wavepacket

We present an interesting result regarding the implication of truncating the wavepacket of the harmonic oscillator. We show that disregarding the non-significant tails of a function which is the superposition of eigenfunctions of the harmonic oscillator has a remarkable consequence: namely, there exist infinitely many different superpositions giving rise to the same function on the interval. Uniqueness, in the case of a wavepacket, is restored by a postulate of quantum mechanics

On the existence and asymptotic stability of solutions for unsteady mixing-layer models

We introduce in this paper some elements for the mathematical analysis of turbulence models for oceanic surface mixing layers. We consider Richardson-number based vertical eddy diffusion models. We prove the existence of unsteady solutions if the initial condition is close to an equilibrium, via the inverse function theorem in Banach spaces. We use this result to prove the non-linear asymptotic stability of equilibrium solutions

Metodología para seleccionar tecnologías Web 2.0 para la docencia

Actualmente existe un gran auge en el uso y difusión de las herramientas Web 2.0 tanto en el contexto profesional como en el personal. Su aplicación al ámbito de la docencia, tal y como sugieren algunos estudios, puede tener numerosas ventajas. Sin embargo, el abanico de herramientas Web 2.0 es muy amplio y por tanto sería de utilidad disponer de una metodología que pudiera guiar al docente a la hora de elegir la tecnología más adecuada a su proceso de enseñanza-aprendizaje según los objetivos perseguidos, así como en su implantación y posterior evaluación de los resultados alcanzados. En este artículo, se presenta una metodología de ayuda a los docentes de cualquier área de conocimiento para la selección e implantación de la tecnología Web 2.0 que más se adapte a un determinado proceso de enseñanza-aprendizaje en base a criterios docentes y técnicos. Esta metodología es el resultado de un proyecto de mejora e innovación educativa en el cual se han llevado a cabo diversas experiencias docentes sobre la aplicación de herramientas Web 2.0 en asignaturas de distintas titulaciones universitarias.SUMMARY -- The use and dissemination of Web 2.0 tools in professional and personal context is becoming more popular every day. Its application to teaching, as it is suggested by some studies, may have numerous advantages. However, the range of Web 2.0 tools is very broad and it would therefore be useful to have a methodology that guide the teacher in choosing the most appropriate technology to their teaching-learning process, taking into account some final objectives, as well as implementing and evaluating the achieved results. This paper presents a methodology to assist teachers from any area of knowledge in the selection of the Web 2.0 technology that best suits a particular teaching-learning process. This selection is based on some educational and technical criteria. The presented methodology is the result of an educational innovation and improvement project in which various teaching experiences based on the use of Web 2.0 tools have been carried out in different subjects of science degrees.Peer Reviewe

Safety Profile and Tolerability of Topical Phosphodiesterase 4 Inhibitors for the Treatment of Atopic Dermatitis: A Systematic Review and Meta-Analysis

Evaluate the safety profile and tolerability of topical phosphodiesterase 4 (PDE4) inhibitors versus vehicle as treatment for atopic dermatitis in published studies.A search was performed in Medline/PubMed, Web of Science, and Cochrane Library databases on September 27, 2021, by 1 evaluator, without restrictions on publication dates or languages. Terms such as atopic dermatitis, phosphodiesterase 4 inhibitors, calcineurin inhibitors, and randomized controlled trials were included. The database searches were carried out by 1 evaluator. The titles and abstracts were reviewed for the identification and evaluation of potentially eligible studies. Study selection was made by two reviewers, so there was no intra-examiner statistic at the study selection step. The full-text articles were reviewed to determine whether or not they would be included in the systematic review. Global analyses, which included studies with both unclear and low risk of bias and subanalyses of studies with a low risk of bias were performed.Out of 237 identified articles, 14 clinical trials were included in the meta-analysis. In global analyses of studies with low and unclear risk of bias, topical treatment with PDE4 inhibitors did not differ from vehicle treatment in global treatment emergent adverse events (relative risk?=?0.99; 95% CI, 0.87-1.14; P?=?0.94) or in serious emergent adverse events appearance (relative risk?=?0.92; 95% CI, 0.39-2.20; P?=?0.86). In subanalyses of studies with a low risk of bias, a reduced rate of atopic dermatitis exacerbation was observed in PDE4 inhibitors compared with the vehicle (relative risk?=?0.62; 95% CI, 0.39-0.98; P?=?0.04) and risk of pain at the application site was confirmed (relative risk?=?2.59; 95% CI, 1.27-5.28; P?=?0.01).PDE4 inhibitors did not show differences from vehicle treatment in treatment emergent adverse events or serious emergent adverse events incidence. In studies with low risk of bias, PDE4 inhibitors had a statistically significant risk of producing pain and reduced occurrence of atopic dermatitis exacerbation.© 2022 The Author(s)

From cardinal spline wavelet bases to highly coherent dictionaries

Wavelet families arise by scaling and translations of a prototype function, called the mother wavelet. The construction of wavelet bases for cardinal spline spaces is generally carried out within the multi-resolution analysis scheme. Thus, the usual way of increasing the dimension of the multi-resolution subspaces is by augmenting the scaling factor. We show here that, when working on a compact interval, the identical effect can be achieved without changing the wavelet scale but reducing the translation parameter. By such a procedure we generate a redundant frame, called a dictionary, spanning the same spaces as a wavelet basis but with wavelets of broader support. We characterize the correlation of the dictionary elements by measuring their 'coherence' and produce examples illustrating the relevance of highly coherent dictionaries to problems of sparse signal representation