A characterization of Schauder frames which are near-Schauder bases

A basic problem of interest in connection with the study of Schauder frames in Banach spaces is that of characterizing those Schauder frames which can essentially be regarded as Schauder bases. In this paper, we give a solution to this problem using the notion of the minimal-associated sequence spaces and the minimal-associated reconstruction operators for Schauder frames. We prove that a Schauder frame is a near-Schauder basis if and only if the kernel of the minimal-associated reconstruction operator contains no copy of $c_0$. In particular, a Schauder frame of a Banach space with no copy of $c_0$ is a near-Schauder basis if and only if the minimal-associated sequence space contains no copy of $c_0$. In these cases, the minimal-associated reconstruction operator has a finite dimensional kernel and the dimension of the kernel is exactly the excess of the near-Schauder basis. Using these results, we make related applications on Besselian frames and near-Riesz bases.Comment: 12 page

Elevation modelling and palaeo-environmental interpretation in the Siwa area (Egypt): Application of SAR interferometry and radargrammetry to COSMO-SkyMed imagery

PublishedJournal Article© 2015 Elsevier B.V. Digital elevation models produced from COSMO-SkyMed imagery were used to delineate palaeo-drainage in a wide area surrounding the Siwa and Al-Jaghbub oases of the western Sahara Desert (Egypt and Libya).This new generation of synthetic aperture radar imagery is suitable for this purpose because of its high spatial resolution and capacity to penetrate dry surface sediments. Different techniques such as radar interferometry and radargrammetry were used to produce digital elevation models. These were assessed for accuracy and then combined to produce a single elevation model of the area. The resulting elevation model was used to support the geological study and palaeo-environmental interpretation of the area. It revealed buried features of the landscape, including inactive palaeo-drainage systems. Drainage features were extracted from the elevation model using geographical information systems; results were combined and assessed with respect to geological field data, as well as data from the literature. Previous studies in the area suggest that a wide river, probably the old Nile River, flowed into the Libyan palaeo-Sirte before the Late Messinian drawdown of the Mediterranean Sea. During the Late Messinian lowering of the sea the fluvial system changed shape and carved deep canyons throughout north-eastern Africa. The reported findings on the key Siwa area were used to precisely delineate the physiography of the modern drainage network and to confirm findings from our previous geological research in the area.We gratefully acknowledge Ruggero Matteucci and Johannes Pignatti (La Sapienza, University of Rome), Francesco Checchi (ENI S.p.A., IOEC), Filippo Bonciani and Debora Graziosi (University of Siena) for their collaboration. Research was supported by the ASI (Id 2262) in the framework of the COSMO-SkyMed Announcement of Opportunity project “Application of COSMO-SkyMed data for geological researches in Egypt and Libya”

The multiple vehicle balancing problem

This paper deals with the multiple vehicle balancing problem (MVBP). Given a fleet of vehicles of limited capacity, a set of vertices with initial and target inventory levels and a distribution network, the MVBP requires to design a set of routes along with pickup and delivery operations such that inventory is redistributed among the vertices without exceeding capacities, and routing costs are minimized. The MVBP is NP\u2010hard, generalizing several problems in transportation, and arising in bike\u2010sharing systems. Using theoretical properties of the problem, we propose an integer linear programming formulation and introduce strengthening valid inequalities. Lower bounds are computed by column generation embedding an ad\u2010hoc pricing algorithm, while upper bounds are obtained by a memetic algorithm that separate routing from pickup and delivery operations. We combine these bounding routines in both exact and matheuristic algorithms, obtaining proven optimal solutions for MVBP instances with up to 25 stations

On R-duals and the duality principle in Gabor analysis

The concept of R-duals of a frame was introduced by Casazza, Kutyniok and Lammers in 2004, with the motivation to obtain a general version of the duality principle in Gabor analysis. For tight Gabor frames and Gabor Riesz bases the three authors were actually able to show that the duality principle is a special case of general results for R-duals. In this paper we introduce various alternative R-duals, with focus on what we call R-duals of type II and III. We show how they are related and provide characterizations of the R-duals of type II and III. In particular, we prove that for tight frames these classes coincide with the R-duals by Casazza et el., which is desirable in the sense that the motivating case of tight Gabor frames already is well covered by these R-duals. On the other hand, all the introduced types of R-duals generalize the duality principle for larger classes of Gabor frames than just the tight frames and the Riesz bases; in particular, the R-duals of type III cover the duality principle for all Gabor frames

Recycling of Deuterium From Dideuterated Glucose During Moderate Exercise

A doubly labelled tracer molecule of glucose, [6,6-2HJglucose, has been used to measure the rate of glucose appearance in blood due to endogenous glucose production (by the liver and kidneysj.l,2 Considered \u27non-recirculating\u27, this tracer generally provides a realistic estimate of glucose kinetics.2,3 Used as a dual tracer in conjunction with [l-13C]glucose, the extent of glucose recycling can be quantitated.2-4 but the extent of possible recirculation of a single deuterium atom on newly formed glucose must then be considered

LCA of hospital solid waste treatment alternatives in a developing country: The case of District Swat, Pakistan

Improper management of hospital waste leads to serious health and environmental issues, particularly in the case of developing countries, where, often, applied technologies are obsolete and there is a lack of compliance with respect to international best practices. The present study is designed to assess the environmental impacts of hospital waste management practices in Swath District, Pakistan. For this purpose, a life-cycle assessment (LCA) is applied for the estimation of different impacts of current and alternative hospital solid waste (HSW) treatment practices. Two scenarios are used to describe the current alternative practices (Scenario A and Scenario B), referring either to incineration or to direct landfilling of HSW without any sorting of collected materials. Conversely, Scenario C, which includes the use of pyrolysis and chemical disinfection, are considered as an up-to-date alternative, based on current international recommendations in this field. Prior to the analysis of impacts, due to the lack of available information, data were directly collected from both government and private hospitals in District Swat, involving measurements and a characterization of collected waste. In parallel, interviews were conducted, involving the hospitals' personnel. With respect to waste generation, government hospitals produce a larger amount of waste (74%) compared to private hospitals (24%). Poor regulatory indications and the absence of clear obligations for collection, disposal and management still represent a first obstacle to implement good practices. After defining the boundary of the system and the functional unit, according to standardized LCA practices, a life-cycle impact assessment (LCIA) was conducted, considering eight impact categories: human toxicity, freshwater eco-toxicity, marine aquatic eco-toxicity, terrestrial eco-toxicity, acidification potential, climate change, eutrophication and photochemical oxidation. The current practices (Scenario A and Scenario B) turned out to be the worst for all categories. In particular, the largest impact of all is recorded for human toxicity generated by incineration. In parallel, it must be considered that, currently, no recycling or reusing practices are implemented. Conversely, Scenario C (alternative up-to-date practices) would generate lower impacts. In detail, the highest value was recorded for marine aquatic ecotoxicity in relation to pyrolysis. Applying Scenario C, it would be possible to recover some materials, such as plastics, paper and sharps. In detail, considering the observed compositional characteristics, it would be possible to recover up to 78% of sharps and recycle 41% of plastic and paper from the general waste stream. Moreover, energy could be recovered from the pyrolysis process, generating a further benefit for the surrounding area. A lack of awareness, knowledge and infrastructures prevents the application of correct management practices, further degrading life and environmental conditions of this remote region of Pakistan. The huge difference in impacts between current practices and alternatives is demonstrated, showing a clear alternative for future management plans in this remote region and supporting future actions for local policymakers and hospital managers

Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements

We introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then such designs can be interpreted as generalizations of complete sets of mutually unbiased bases, being equivalent whenever the design is composed of d+1 bases in dimension d. We show that, for the purpose of quantum state determination, these designs specify an optimal collection of orthogonal measurements. Using highly nonlinear functions on abelian groups, we construct explicit examples from d+2 orthonormal bases whenever d+1 is a prime power, covering dimensions d=6, 10, and 12, for example, where no complete sets of mutually unbiased bases have thus far been found.Comment: 28 pages, to appear in J. Math. Phy

Prime tight frames

We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of prime tight frames. We then characterize all prime harmonic tight frames and use this characterization to suggest effective analysis and synthesis computation strategies for such frames. Finally, we describe all prime frames constructed from the spectral tetris method, and, as a byproduct, we obtain a characterization of when the spectral tetris construction works for redundancies below two

The molecular signature of therapeutic mesenchymal stem cells exposes the architecture of the hematopoietic stem cell niche synapse

BACKGROUND: The hematopoietic stem cells (HSCs) niche of the bone marrow is comprised of HSCs, osteoblasts, endothelial cells and a stromal component of non-hematopoietic multipotent cells of mesenchymal origin named "mesenchymal stem cells" (MSCs). RESULTS: Here we studied the global transcriptional profile of murine MSCs with immuno-therapeutic potential and compared it with that of 486 publicly available microarray datasets from 12 other mouse tissues or cell types. Principal component analysis and hierarchical clustering identified a unique pattern of gene expression capable of distinctively classifying MSCs from other tissues and cells. We then performed an analysis aimed to identify absolute and relative abundance of transcripts in all cell types. We found that the set of transcripts uniquely expressed by MSCs is enriched in transcription factors and components of the Wnt signaling pathway. The analysis of differentially expressed genes also identified a set of genes specifically involved in the HSC niche and is complemented by functional studies that confirm the findings. Interestingly, some of these genes play a role in the maintenance of HSCs in a quiescent state supporting their survival and preventing them from proliferating and differentiating. We also show that MSCs modulate T cell functions in vitro and, upon in vivo administration, ameliorate experimental autoimmune encephalomyelitis (EAE). CONCLUSION: Altogether, these findings provide novel and important insights on the mechanisms of T cell function regulation by MSCs and help to cement the rationale for their application in the treatment of autoimmune diseases