A class of quasi-sparse companion pencils

In this paper, we introduce a general class of quasi-sparse potential companion pencils for arbitrary square matrix polynomials over an arbitrary field, which extends the class introduced in [B. Eastman, I.-J. Kim, B. L. Shader, K.N. Vander Meulen, Companion matrix patterns. Linear Algebra Appl. 436 (2014) 255-272] for monic scalar polynomials. We provide a canonical form, up to permutation, for companion pencils in this class. We also relate these companion pencils with other relevant families of companion linearizations known so far. Finally, we determine the number of different sparse companion pencils in the class, up to permutation.This work has been partially supported by theMinisterio de Economía y Competitividad of Spain through grants MTM2015-68805-REDT and MTM2015-65798-P

The Polynomial Eigenvalue Problem is Well Conditioned for Random Inputs

We compute the exact expected value of the squared condition number for the polynomial eigenvalue problem, when the input matrices have entries coming from the standard complex Gaussian distribution, showing that in general this problem is quite well conditioned.The first author's work was partially supported by Agencia Nacional de Investigación e Innovación (ANII), Uruguay, and by CSIC group 618, Universidad de La República, Uruguay. The second author's work was partially supported by MTM2017-83816-P and MTM2017-90682-REDT from Spanish Ministry of Science MICINN and by 21.SI01.64658 from Universidad de Cantabria and Banco de Santander

When is a Hamiltonian matrix the commutator of two skew-Hamiltonian matrices?

The mapping (Formula presented.) , where the matrices (Formula presented.) are skew-Hamiltonian with respect to transposition, is studied. Let (Formula presented.) be the range of (Formula presented.) : we give an implicit characterization of (Formula presented.) , obtaining results that find an application in algebraic geometry. Namely, they are used in [R. Abuaf and A. Boralevi, Orthogonal bundles and skew-Hamiltonian matrices, Submitted] to study orthogonal vector bundles. We also give alternative and more explicit characterizations of (Formula presented.) for (Formula presented.). Moreover, we prove that for (Formula presented.) , the complement of (Formula presented.) is nowhere dense in the set of (Formula presented.) -dimensional Hamiltonian matrices, denoted by (Formula presented.) , implying that almost all matrices in (Formula presented.) are in (Formula presented.) for (Formula presented.). Finally, we show that (Formula presented.) is never surjective as a mapping from (Formula presented.) to (Formula presented.) , where (Formula presented.) is the set of (Formula presented.) -dimensional skew-Hamiltonian matrices. Along the way, we discuss the connections of this problem with several existing results in matrix theory

Análisis del fenómeno de sensibilización central y papel de la estimulación del nervio occipital en la cefalea en racimos

Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Medicina, Departamento de Medicina. Fecha de Lectura: 01-12-202

Comparison of two sample preparation methods for 1H-NMR wine profiling: Direct analysis and solid-phase extraction

This study compares two sample preparation methods: direct analysis (DA) and solid-phase extraction (SPE) for wine samples analysis by proton nuclear magnetic resonance (1H-NMR) spectroscopy. For this purpose, the profile of Mexican commercial wines was evaluated. The selected wines were produced with different grape varieties: ('Barbera', 'Nebbiolo', 'Zinfandel', 'Merlot', 'Petite Syrah', 'Cabernet Sauvignon', 'White Zinfandel' and mixture of 'Chenin blanc' and 'Colombard') coming from the principal wine-producing region of Mexico, Baja California State. DA provided faster data acquisition in comparison to SPE and preserved the original sample composition. Using DA-NMR thirty two metabolites were identified, including organic acids, amino acids, sugars, alcohols and phenolic compounds. Furthermore, SPE-NMR using a polymeric sorbent allowed to retain phenolic compounds giving a better picture on the aromatic region and eliminating major polar compounds like water, ethanol and sugars. Fourteen compounds were identified by SPE-NMR including higher alcohols, flavanols and hydroxybenzoates. A control chart for the first principal component allowed to confirm the precision of the SPE-NMR method, while a comparison of the concentration of two metabolites found in both methods was used to evaluate their recovery (20 % for isoamyl alcohol and 78 % for phenethyl alcohol). The information obtained with both methods about the main compounds and phenolic metabolites provides new insights into the metabolomic profile of wine, which could be useful in future targeted studies

The QUIJOTE experiment: project overview and first results

QUIJOTE (Q-U-I JOint TEnerife) is a new polarimeter aimed to characterize the polarization of the Cosmic Microwave Background and other Galactic and extragalactic signals at medium and large angular scales in the frequency range 10-40 GHz. The multi-frequency (10-20~GHz) instrument, mounted on the first QUIJOTE telescope, saw first light on November 2012 from the Teide Observatory (2400~m a.s.l). During 2014 the second telescope has been installed at this observatory. A second instrument at 30~GHz will be ready for commissioning at this telescope during summer 2015, and a third additional instrument at 40~GHz is now being developed. These instruments will have nominal sensitivities to detect the B-mode polarization due to the primordial gravitational-wave component if the tensor-to-scalar ratio is larger than r=0.05.Comment: To appear in "Highlights of Spanish Astrophysics VIII", Proceedings of the XI Scientific Meeting of the Spanish Astronomical Society, Teruel, Spain (2014

QUIJOTE Experiment: status of telescopes and instrumentation

The QUIJOTE Experiment (Q-U-I JOint TEnerife) is a combined operation of two telescopes and three instruments working in the microwave band to measure the polarization of the Cosmic Microwave Background (CMB) from the northern hemisphere, at medium and large angular scales. The experiment is located at the Teide Observatory in Tenerife, one of the seven Canary Islands (Spain). The project is a consortium maintained by several institutions: the Instituto de Astrofísica de Canarias (IAC), the Instituto de Física de Cantabria (IFCA), the Communications Engineering Department (DICOM) at Universidad de Cantabria, and the Universities of Manchester and Cambridge. The consortium is led by the IAC

QUIJOTE-CMB experiment: a technical overview

The QUIJOTE-CMB experiment (Q-U-I JOint TEnerife CMB experiment) is an ambitious project to obtain polarization measurements of the sky microwave emission in the 10 to 47 GHz range. With this aim, a pair of 2,5m telescopes and three instruments are being sited at the Teide Observatory, in Tenerife (Canary Islands, Spain). The first telescope and the first instrument (the MFI: Multi Frequency Instrument) are both already operating in the band from 10 to 20 GHz, since November 2012. The second telescope and the second instrument (TGI: Thirty GHz instrument) is planned to be in commissioning by the end of summer 2014, covering the range of 26 to 36 GHz. After that, a third instrument named FGI (Forty GHz instrument) will be designed and manufactured to complete the sky survey in the frequency range from 37 to 47 GHz. In this paper we present an overview of the whole project current status, from the technical point of view

The QUIJOTE TGI

The QUIJOTE TGI instrument is currently being assembled and tested at the IAC in Spain. The TGI is a 31 pixel 26-36 GHz polarimeter array designed to be mounted at the focus of the second QUIJOTE telescope. This follows a first telescope and multi-frequency instrument that have now been observing almost 2 years. The polarimeter design is based on the QUIET polarimeter scheme but with the addition of an extra 90º phase switch which allows for quasiinstantaneous complete QUI measurements through each detector. The advantage of this is a reduction in the systematics associated with differencing two independent radiometer channels. The polarimeters are split into a cold front end and a warm back end. The back end is a highly integrated design by engineers at DICOM. It is also sufficiently modular for testing purposes. In this presentation the high quality wide band components used in the optical design (also designed in DICOM) are presented as well as the novel cryogenic modular design. Each polarimeter chain is accessible individually and can be removed from the cryostat and replaced without having to move the remaining pixels. The optical components work over the complete Ka band showing excellent performance. Results from the sub unit measurements are presented and also a description of the novel calibration technique that allows for bandpass measurement and polar alignment. Terrestrial Calibration for this instrument is very important and will be carried out at three points in the commissioning phase: in the laboratory, at the telescope site and finally a reduce set of calibrations will be carried out on the telescope before measurements of extraterrestrial sources begin. The telescope pointing model is known to be more precise than the expected calibration precision so no further significant error will be added through the telescope optics. The integrated back-end components are presented showing the overall arrangement for mounting on the cryostat. Many of the microwave circuits are in-house designs with performances that go beyond commercially available products. Individual component performance is be presented showing for each of the sub modules