Frames of subspaces and operators

We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space $\mathcal{H}$. We get sufficient conditions on an orthonormal basis of subspaces $\mathcal{E} = \{E_i \}_{i\in I}$ of a Hilbert space $\mathcal{K}$ and a surjective $T\in L(\mathcal{K}, \mathcal{H})$ in order that $\{T(E_i)\}_{i\in I}$ is a frame of subspaces with respect to a computable sequence of weights. We also obtain generalizations of results in [J. A. Antezana, G. Corach, M. Ruiz and D. Stojanoff, Oblique projections and frames. Proc. Amer. Math. Soc. 134 (2006), 1031-1037], which related frames of subspaces (including the computation of their weights) and oblique projections. The notion of refinament of a fusion frame is defined and used to obtain results about the excess of such frames. We study the set of admissible weights for a generating sequence of subspaces. Several examples are given.Comment: 21 pages, LaTeX; added references and comments about fusion frame

Multiplicative Lidskii's inequalities and optimal perturbations of frames

In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame \cF for \hil\cong\C^d we compute those dual frames \cG of \cF that are optimal perturbations of the canonical dual frame for \cF under certain restrictions on the norms of the elements of \cG. On the other hand, for a fixed finite frame \cF=\{f_j\}_{j\in\In} for \hil we compute those invertible operators $V$ such that $V^*V$ is a perturbation of the identity and such that the frame V\cdot \cF=\{V\,f_j\}_{j\in\In} - which is equivalent to \cF - is optimal among such perturbations of \cF. In both cases, optimality is measured with respect to submajorization of the eigenvalues of the frame operators. Hence, our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error. The key tool for these results is a multiplicative analogue of Lidskii's inequality in terms of log-majorization and a characterization of the case of equality.Comment: 22 page

Optimal dual frames and frame completions for majorization

In this paper we consider two problems in frame theory. On the one hand, given a set of vectors $\mathcal F$ we describe the spectral and geometrical structure of optimal completions of $\mathcal F$ by a finite family of vectors with prescribed norms, where optimality is measured with respect to majorization. In particular, these optimal completions are the minimizers of a family of convex functionals that include the mean square error and the Bendetto-Fickus' frame potential. On the other hand, given a fixed frame $\mathcal F$ we describe explicitly the spectral and geometrical structure of optimal frames $\mathcal G$ that are in duality with $\mathcal F$ and such that the Frobenius norms of their analysis operators is bounded from below by a fixed constant. In this case, optimality is measured with respect to submajorization of the frames operators. Our approach relies on the description of the spectral and geometrical structure of matrices that minimize submajorization on sets that are naturally associated with the problems above.Comment: 29 pages, with modifications related with the exposition of the materia

Some properties of frames of subspaces obtained by operator theory methods

AbstractWe study the relationship among operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space H. We get sufficient conditions on an orthonormal basis of subspaces E={Ei}i∈I of a Hilbert space K and a surjective T∈L(K,H) in order that {T(Ei)}i∈I is a frame of subspaces with respect to a computable sequence of weights. We also obtain generalizations of results in [J.A. Antezana, G. Corach, M. Ruiz, D. Stojanoff, Oblique projections and frames, Proc. Amer. Math. Soc. 134 (2006) 1031–1037], which relate frames of subspaces (including the computation of their weights) and oblique projections. The notion of refinement of a fusion frame is defined and used to obtain results about the excess of such frames. We study the set of admissible weights for a generating sequence of subspaces. Several examples are given

Exploiting graphic processing units parallelism to improve intelligent data acquisition system performance in JET's correlation reflectometer

The performance of intelligent data acquisition systems relies heavily on their processing capabilities and local bus bandwidth, especially in applications with high sample rates or high number of channels. This is the case of the self adaptive sampling rate data acquisition system installed as a pilot experiment in KG8B correlation reflectometer at JET. The system, which is based on the ITMS platform, continuously adapts the sample rate during the acquisition depending on the signal bandwidth. In order to do so it must transfer acquired data to a memory buffer in the host processor and run heavy computational algorithms for each data block. The processing capabilities of the host CPU and the bandwidth of the PXI bus limit the maximum sample rate that can be achieved, therefore limiting the maximum bandwidth of the phenomena that can be studied. Graphic processing units (GPU) are becoming an alternative for speeding up compute intensive kernels of scientific, imaging and simulation applications. However, integrating this technology into data acquisition systems is not a straight forward step, not to mention exploiting their parallelism efficiently. This paper discusses the use of GPUs with new high speed data bus interfaces to improve the performance of the self adaptive sampling rate data acquisition system installed on JET. Integration issues are discussed and performance evaluations are presente

Análisis del uso racional de antihipertensivos en la región de Murcia

ResumenObjetivoEl objetivo del presente estudio ha sido conocer el patrón de uso de los fármacos antihipertensivos en la Región de Murcia, contrastando los resultados con los datos nacionales (patrón de referencia), pudiendo de esta manera detectar posibles puntos de mejora o establecer hipótesis para posteriores estudios.DiseñoEstudio farmacoepidemiológico (2004 a 2008), conforme a las recomendaciones de la OMS.EmplazamientoRegión de Murcia.ParticipantesCenso poblacional anual.Mediciones principalesEl uso de antihipertensivos se ha medido mediante el cálculo de la dosis diaria definida por mil habitantes-día (DHD).ResultadosLa utilización de antihipertensivos se ha incrementado significativamente de 196,6 DHD a 235,8 DHD. Los antihipertensivos más usados en 2008 eran los ARA-II (38,6%), seguido de los IECA (21,8%). Se ha producido un cambio de tendencia en el uso de los bloqueantes del sistema renina angiotensina (BSRA), con un incremento del 77,5% en los ARA-II y una disminución del 9,5% en los IECA. La comparación con los datos nacionales muestran un menor uso de antihipertensivos y un diferente patrón en la Región de Murcia.ConclusionesSe constata un menor uso de antihipertensivos respecto a España, por lo que podría haber infratratamiento de esta u otras enfermedades cardiovasculares en las que se usan estos fármacos en la Región de Murcia. Se observa un mayor uso de ARA-II, así como un menor uso de IECA. Las diferencias encontradas ponen de manifiesto la necesidad de realizar estudios encaminados a esclarecer sus causas, para lograr un uso más racional y eficiente de los antihipertensivos.AbstractObjectiveThe objective of this study was to determine the pattern of use of antihypertensive drugs in the Murcia Region, comparing the results with the national data, and detecting problems in order to make improvements, or establish hypotheses and to plan new studies.DesignPharmacoepidemiological study (from 2004 to 2008) in accordance with the recommendations from World Heath Organization.Setting: Murcia Region.ParticipansAnnual census of each year.Main measurementsThe use of antihypertensive drugs was measured by the daily doses per 1000 inhabitans-day (DHD).ResultsThe use of antihypertensive drugs has significantly increased from 196.6 DHD to 235.8 DHD. The antihypertensives more used at the end of 2008 were: angiotensin II receptor blockers–ARB- (38.6%) and angiotensin converting enzyme inhibitors–ACEI- (21.8%). There has been a tendency to change the use of rennin-angiotensin system blockers–RASB-, with an increase in ARB of 77.5% and and a decrease in ACEI 9.5%. The comparison with the national data shows qualitative and quantitative differences in the pattern of antihypertensive drugs used during the studied period.ConclusionsThe use of antihypertensive drugs in Murcia is less than in the rest of Spain. Therefore, this may be due to a problem of under treatment of this illness or other cardiovascular illnesses in the region. A greater use of ARB in Murcia and a lower use of ACEI was observed in Murcia. The differences found suggest that further studies are required to clarify their origins and causes, with the objective of achieving a more rational and efficient use of these drugs

Calibration of semi-analytic models of galaxy formation using Particle Swarm Optimization

We present a fast and accurate method to select an optimal set of parameters in semi-analytic models of galaxy formation and evolution (SAMs). Our approach compares the results of a model against a set of observables applying a stochastic technique called Particle Swarm Optimization (PSO), a self-learning algorithm for localizing regions of maximum likelihood in multidimensional spaces that outperforms traditional sampling methods in terms of computational cost. We apply the PSO technique to the SAG semi-analytic model combined with merger trees extracted from a standard $\Lambda$CDM N-body simulation. The calibration is performed using a combination of observed galaxy properties as constraints, including the local stellar mass function and the black hole to bulge mass relation. We test the ability of the PSO algorithm to find the best set of free parameters of the model by comparing the results with those obtained using a MCMC exploration. Both methods find the same maximum likelihood region, however the PSO method requires one order of magnitude less evaluations. This new approach allows a fast estimation of the best-fitting parameter set in multidimensional spaces, providing a practical tool to test the consequences of including other astrophysical processes in SAMs.Comment: 11 pages, 4 figures, 1 table. Accepted for publication in ApJ. Comments are welcom

Integrated phased array transducer for on-board structural health monitoring

Permanently bonded onto a structure, an integrated Phased Array (PhA II) transducer that can provide reliable electromechanical connection with corresponding sophisticated miniaturized ?all in one? SHM electronic device installed directly above it, without need for any interface cabling, during all aerospace structure lifecycle phases and for a huge variety of real harsh service environments of structures to be monitored is presented. This integrated PhA II transducer [1], as a key component of the PAMELA SHM? (Phased Array Monitoring for Enhanced Life Assessment) system, has two principal tasks at the same time, reliably transceive elastic waves in real aerospace service environments and serves as a reliable sole carrier or support for associated integrated on-board SHM electronic device attached above. The PhA II transducer successfully accomplished both required task throughout extensive test campaigns which included low to high temperature tests, temperature cycling, mechanical loading, combined thermo- mechanical loading and vibration resistance, etc. both with and without SHM device attached above due to RTCA DO-160F

Structural health monitoring network system with wireless communications inside closed aerospace structures

Structural Health Monitoring (SHM) requires integrated "all in one" electronic devices capable of performing analysis of structural integrity and on-board damage detection in aircraft?s structures. PAMELA III (Phased Array Monitoring for Enhanced Life Assessment, version III) SHM embedded system is an example of this device type. This equipment is capable of generating excitation signals to be applied to an array of integrated piezoelectric Phased Array (PhA) transducers stuck to aircraft structure, acquiring the response signals, and carrying out the advanced signal processing to obtain SHM maps. PAMELA III is connected with a host computer in order to receive the configuration parameters and sending the obtained SHM maps, alarms and so on. This host can communicate with PAMELA III through an Ethernet interface. To avoid the use of wires where necessary, it is possible to add Wi-Fi capabilities to PAMELA III, connecting a Wi-Fi node working as a bridge, and to establish a wireless communication between PAMELA III and the host. However, in a real aircraft scenario, several PAMELA III devices must work together inside closed structures. In this situation, it is not possible for all PAMELA III devices to establish a wireless communication directly with the host, due to the signal attenuation caused by the different obstacles of the aircraft structure. To provide communication among all PAMELA III devices and the host, a wireless mesh network (WMN) system has been implemented inside a closed aluminum wingbox. In a WMN, as long as a node is connected to at least one other node, it will have full connectivity to the entire network because each mesh node forwards packets to other nodes in the network as required. Mesh protocols automatically determine the best route through the network and can dynamically reconfigure the network if a link drops out. The advantages and disadvantages on the use of a wireless mesh network system inside closed aerospace structures are discussed

Effect of serum phosphate on parathyroid hormone secretion during hemodialysis

Effect of serum phosphate on parathyroid hormone secretion during hemodialysis.BackgroundRecent studies have demonstrated that a high concentration of phosphate directly stimulates parathyroid hormone (PTH) secretion. High serum levels of phosphate are usually observed in patients with end-stage renal disease. The aim of the present study was to evaluate whether serum phosphate concentration had an acute effect on PTH secretion in hemodialysis patients. The levels of serum phosphate were manipulated during the hemodialysis session by using a phosphate free dialysate or a dialysate with a high content of phosphate.MethodsTen stable hemodialysis patients with PTH values above 300 pg/ml were included in the study. A PTH-calcium curve was obtained during both high phosphate and phosphate free hemodialysis.ResultsThe serum phosphate concentration remained high (2.17 ± 0.18mM) throughout the high phosphate hemodialysis and decreased progressively to normal levels (1.02 ± 0.06mM) during the phosphate free hemodialysis. The serum PTH levels at maximal inhibition by hypercalcemia (minimal PTH) were greater during the high phosphate than the phosphate free hemodialysis (413 ± 79 vs. 318 ± 76 pg/ml, P < 0.003). In all patients the values of minimum PTH were greater during the high phosphorus than the phosphorus free hemodialysis. The values of maximally stimulated PTH during hypocalcemia and the set point of the PTH-calcium curve were similar during the high phosphate and the phosphate free hemodialysis.ConclusionThe maintenance of high serum phosphorus levels during hemodialysis prevented, in part, the inhibition of PTH secretion by calcium, which strongly suggests that in hemodialysis patients high serum phosphate contributes directly to the elevation of PTH levels despite normal or high serum calcium concentration