Surgery of spline-type and molecular frames

We prove a result about producing new frames for general spline-type spaces by piecing together portions of known frames. Using spline-type spaces as models for the range of certain integral transforms, we obtain results for time-frequency decompositions and sampling.Comment: 34 pages. Corrected typo

Characterization of coorbit spaces with phase-space covers

We show that coorbit spaces can be characterized in terms of arbitrary phase-space covers, which are families of phase-space multipliers associated with partitions of unity. This generalizes previously known results for time-frequency analysis to include time-scale decompositions. As a by-product, we extend the existing results for time-frequency analysis to an irregular setting.Comment: 31 pages. Revised version (title slightly changed). Typos fixe

Multitaper estimation on arbitrary domains

Multitaper estimators have enjoyed significant success in estimating spectral densities from finite samples using as tapers Slepian functions defined on the acquisition domain. Unfortunately, the numerical calculation of these Slepian tapers is only tractable for certain symmetric domains, such as rectangles or disks. In addition, no performance bounds are currently available for the mean squared error of the spectral density estimate. This situation is inadequate for applications such as cryo-electron microscopy, where noise models must be estimated from irregular domains with small sample sizes. We show that the multitaper estimator only depends on the linear space spanned by the tapers. As a result, Slepian tapers may be replaced by proxy tapers spanning the same subspace (validating the common practice of using partially converged solutions to the Slepian eigenproblem as tapers). These proxies may consequently be calculated using standard numerical algorithms for block diagonalization. We also prove a set of performance bounds for multitaper estimators on arbitrary domains. The method is demonstrated on synthetic and experimental datasets from cryo-electron microscopy, where it reduces mean squared error by a factor of two or more compared to traditional methods.Comment: 28 pages, 11 figure

Alimentación de los pollos de Pico Menor (Dendrocopos minor) en un nido de la Val d'Aran (Lleida, NE de España)

Les dades sobre la dieta dels polls del picot garser petit es van obtenir mitjançant observacions directes en el primer niu descobert a la Vall d'Aran. Els adults van alimentar els polls amb insectes i aranyes entre les quals hi havia Coleoptera (44%), Lepidoptera (13%), Formicidae (10%), Arachnida (4%) i Diptera (2%). El 27% de les preses no van ser identificades (n=339). La femella va alimentar els polls més sovint que el mascle, especialment a principi del matí, encara que més avançat el dia el nombre de visites al niu fou similar. El menjar agafat pel picot garser petit en aquest estudi és bastant similar al trobat en altres estudis d'Europa, encara que amb lleugeres diferències en els percentatges dels diferents tipus de presa