Discrete Sturm–Liouville problems, Jacobi matrices and Lagrange interpolation series

AbstractThe close relationship between discrete Sturm–Liouville problems belonging to the so-called limit-circle case, the indeterminate Hamburger moment problem and the search of self-adjoint extensions of the associated semi-infinite Jacobi matrix is well known. In this paper, all these important topics are also related with associated sampling expansions involving analytic Lagrange-type interpolation series

The zero-removing property in some Hilbert spaces of entire functions arising in sampling theory

In the topic of sampling in reproducing kernel Hilbert spaces, sampling in Paley–Wiener spaces is the paradigmatic example. A natural generalization of Paley–Wiener spaces is obtained by substituting the Fourier kernel with an analytic Hilbert-space-valued kernel K. Thus we obtain a reproducing kernel Hilbert space HKHK of entire functions in which the Kramer property allows to prove a sampling theorem. A necessary and sufficient condition ensuring that this sampling formula can be written as a Lagrange-type interpolation series concerns the stability under removal of a finite number of zeros of the functions belonging to the space HKHK; this is the so-called zero-removing property. This work is devoted to the study of the zero-removing property in HKHK spaces, regardless of the Kramer property, revealing its connections with other mathematical fields

Efectos de distintos niveles de materia seca y tratamiento sobre la calidad de ensilado de alfalfa

Los autores analizan la calidad de 250 ensilados de alfalfa sometidos a cinco tratamientos (control, evacuación AIV, ácido fórmico y metabisulfito sódico), con forraje entero o picado. y cinco niveles de materia seca inicial (20. 23. 36, 38 y 42%).La elevación de la tasa de materia seca inicial, mejora la capacidad organoléptica hasta el 36-38% de materia seca. El efecto beneficioso del oreo se registra en todos los tratamientos ensayados, salvo en los silos con metabisulfito sódico, que presentan su máxima calidad en los más bajos niveles de materia seca

Generalized sampling: from shift-invariant to U-invariant spaces

The aim of this article is to derive a sampling theory in U-invariant subspaces of a separable Hilbert space ℋ where U denotes a unitary operator defined on ℋ. To this end, we use some special dual frames for L2(0, 1), and the fact that any U-invariant subspace with stable generator is the image of L2(0, 1) by means of a bounded invertible operator. The used mathematical technique mimics some previous sampling work for shift-invariant subspaces of L2(ℝ). Thus, sampling frame expansions in U-invariant spaces are obtained. In order to generalize convolution systems and deal with the time-jitter error in this new setting we consider a continuous group of unitary operators which includes the operator U

A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling

The aim of this work is to solve a question raised for average sampling in shift-invariant spaces by using the well-known matrix pencil theory. In many common situations in sampling theory, the available data are samples of some convolution operator acting on the function itself: this leads to the problem of average sampling, also known as generalized sampling. In this paper we deal with the existence of a sampling formula involving these samples and having reconstruction functions with compact support. Thus, low computational complexity is involved and truncation errors are avoided. In practice, it is accomplished by means of a FIR filter bank. An answer is given in the light of the generalized sampling theory by using the oversampling technique: more samples than strictly necessary are used. The original problem reduces to finding a polynomial left inverse of a polynomial matrix intimately related to the sampling problem which, for a suitable choice of the sampling period, becomes a matrix pencil. This matrix pencil approach allows us to obtain a practical method for computing the compactly supported reconstruction functions for the important case where the oversampling rate is minimum. Moreover, the optimality of the obtained solution is established

Effectiveness of integrated treatment for eating disorders in Spain: protocol for a multicentre, naturalistic, observational study

Introduction Eating disorders (EDs) are complex pathologies which require equally complex treatment strategies. These strategies should be multidisciplinary, personalised interventions, performed in appropriate settings along a healthcare continuum from inpatient to community care. Personalisation, and the complexity of levels of care and interventions make evaluation of treatments difficult. The present study aims to measure the effectiveness of a complex treatment programme for EDs which includes hospitalisation, day hospital and outpatient settings. Our purpose is to assess the complete therapeutic process of each patient through all these levels of care, capturing the multiplicity of trajectories that a programme of these characteristics involves. Methods and analysis This protocol describes a multicentre, naturalistic, observational study. All patients starting between November 2017 and October 2020 in a healthcare network for EDs in Spain are being invited to participate. The first phase of intensive change monitoring to November 2020 is followed by lower intensity follow-up until October 2025. In the first phase progress of all participants is assessed every 3 weeks using specific measures for ED and the Clinical Outcomes Routine Evaluation system, a family of instruments specifically designed to measure change in psychotherapy. In the second phase data collection will happen quarterly. Both cross-sectional and longitudinal analyses will be conducted, with a special focus on patterns and predictors of change studied through multilevel linear models. Ethics and dissemination The study has been approved by the Research Bioethics Committee of the University of Barcelona (no. IRB00003099) and the ethical committee of ITA Mental Health, the organisation to which all participating centres belong. Dissemination will be in papers for peer-reviewed research journals and to clinicians working with ED. Trial registration number NCT04127214

Skeletal maturation in relation to ethnic background in children of school age: The Generation R Study

Ethnicity is a well-established determinant of pediatric maturity, but the underlying genetic and environmental contributions to these ethnic differences are poorly comprehended. We aimed to evaluate the influence of ethnicity on skeletal age (SA), an assessment of pediatric maturation widely used in clinical settings. We included children from the Generation R Study, a multiethnic population-based pregnancy cohort, assessed at a mean age of 9.78 (±0.33) years. SA was evaluated by a trained observer on hand DXA scans using the Greulich and Pyle method. Ethnic background was defined as geographic ancestry (questionnaire-based assessment) (N = 5325) and genetic ancestry (based on admixture analysis) (N = 3413). Associations between the ethnic background and SA were investigated separately in boys and girls, using linear regression models adjusted for age, height and BMI. Based on geographic ancestry, 84% of the children were classified as European, 6% as Asian and 10% as African. Children of European background had on average younger SA than those of Asian or African descent. Asian boys had 0.46 (95% CI 0.26–0.66, p-value < 0.0001) and African boys 0.36 years (95% CI 0.20–0.53, p-value < 0.0001) older SA as compared to European boys. Similarly, Asian girls showed 0.64 (95% CI 0.51–0.77, p-value < 0.0001) and African girls 0.38 years (95% CI 0.27–0.48, p-value < 0.0001) older SA as compared to European girls. A similar pattern was observed in the analysis with genetically-defined ancestry. Furthermore, an increase in the proportion of Asian or African component was associated with older SA in both boys (log[Non-European/European]proportion = 0.10, 95% CI 0.06–0.13, p-value < 0.0001) and girls (log[Non-European/European]proportion = 0.06, 95% CI 0.04–0.08, p-value < 0.0001). In summary, children of Asian and African backgrounds have on average older SA as compared to children of European descent, partially explained by a genetic com

Genetic polymorphism of miR-196a-2 is associated with bone mineral density (BMD)

MicroRNAs (miRNAs) are small non-coding RNA molecules that post-transcriptionally regulate the translation of messenger RNAs. Given the crucial role of miRNAs in gene expression, genetic variants within miRNA-related sequences may affect miRNA function and contribute to disease risk. Osteoporosis is characterized by reduced bone mass, and bone mineral density (BMD) is a major diagnostic proxy to assess osteoporosis risk. Here, we aimed to identify miRNAs that are involved in BMD using data from recent genome-wide association studies (GWAS) on femoral neck, lumbar spine and forearm BMD. Of 242 miRNA-variants available in the GWAS data, we found rs11614913:C > T in the precursor miR-196a-2 to be significantly associated with femoral neck-BMD (p-value = 9.9 × 10-7, β = −0.038) and lumbar spine-BMD (p-value = 3.2 × 10-11, β = −0.061). Furthermore, our sensitivity analyses using the Rotterdam study data showed a sex-specific association of rs11614913 with BMD only in women. Subsequently, we highlighted a number of miR-196a-2 target genes, expressed in bone and associated with BMD, that may mediate the miRNA function in BMD. Collectively, our results suggest that miR-196a-2 may contribute to variations in BMD level. Further biological investigations will give more insights into the mechanisms by which miR-196a-2 control expression of BMD-related genes

Optimal Radio Window for the Detection of Ultra-High-Energy Cosmic Rays and Neutrinos off the Moon

When high-energy cosmic rays impinge on a dense dielectric medium, radio waves are produced through the Askaryan effect. We show that at wavelengths comparable to the length of the shower produced by an Ultra-High Energy cosmic ray or neutrino, radio signals are an extremely efficient way to detect these particles. Through an example it is shown that this new approach offers, for the first time, the realistic possibility of measuring UHE neutrino fluxes below the Waxman-Bahcall limit. It is shown that in only one month of observing with the upcoming LOFAR radio telescope, cosmic-ray events can be measured beyond the GZK-limit, at a sensitivity level of two orders of magnitude below the extrapolated values.Comment: Submitted to Astroparticle Physic