Geometric Hermite interpolation by rational curves of constant width

A constructive characterization of the support function for a rationally parameterized curve of constant width is given. In addition, a Hermite interpolation problem for such kind of curves is solved, which yields a method to determine a rational curve of constant width that passes through a set of free points with the corresponding tangent directions. Finally, the case of piecewise rational support functions is considered, which increases the design freedom. The procedure is presented in the general case of hedgehogs of constant width taking the advantage of projective hedgehogs, so that some constraints must be taken to ensure convexity of the desired curve.Funding for the other authors not affiliated with BCAM: Grant PID2021-124577NBI00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”. Project PID2019-104927GB-C21 funded by MCIN/AEI/10.13039/501100011033. Project UJI-B2022-19 funded by Universitat Jaume I. Project CIAICO/2021/180 funded by Generalitat Valenciana

Ultrarobust calibration of an optical lattice depth based on a phase shift

We report on a new method to calibrate the depth of an optical lattice. It consists in triggering the intrasite dipole mode of the cloud by a sudden phase shift. The corresponding oscillatory motion is directly related to the intraband frequencies on a large range of lattice depths. Remarkably, for a moderate displacement, a single frequency dominates this oscillation for the zeroth and first order interference pattern observed after a sufficiently long time-of-flight. The method is robust against atom-atom interactions and the exact value of the extra external confinement of the initial trapping potential.Comment: 7 pages, 6 figure

Closedness of star products and cohomologies

We first review the introduction of star products in connection with deformations of Poisson brackets and the various cohomologies that are related to them. Then we concentrate on what we have called ``closed star products" and their relations with cyclic cohomology and index theorems. Finally we shall explain how quantum groups, especially in their recent topological form, are in essence examples of star products.Comment: 16 page

Lower Cretaceous (Hauterivian-Albian) ammonite biostratigraphy in the Maestrat Basin (E Spain)

Peer reviewedPublisher PD

Acid/base flow battery environmental and economic performance based on its potential service to renewables support

An innovative technology, called Acid Base Flow Battery (AB-FB), has been developed to overcome the intermittent supply of wind and solar electricity generation. It stores electrical energy using pH and salinity differences in the water and compared with other battery technologies, such as Vanadium Redox Flow Battery (VRFB), the new system is expected to be safer, more sustainable and to become a cost competitive option. To provide a deeper knowledge of the new system potentials, in this research, Life Cycle studies under cradle to grave approach have been carried out to assess the environmental and economic performance of 1 MW/6 MWh AB-FB system. Furthermore, 1 MW/6 MWh VRFB has been considered as the reference case. According to the comparative analysis, the AB-FB system exhibited the best environmental and economic performance, placing the AB-FB system as the most sustainable technology. In terms of environmental impacts related to the three process stages, the AB-FB system operation stage yielded the most relevant environmental burden, mostly attributed to energy losses due to the system efficiency. Manufacturing of the AB-FB system was the second stage with the more significant quote to the total environmental burden. Particularly, impacts were related to the power subsystem components being steel, copper, polyethylene and polyvinylchloride identified as the key materials responsible of this tendency. In contrast, the VRFB manufacturing was the most relevant process stage in terms of environmental implications. The energy subsystem was responsible for this tendency due to the vanadium-based electrolyte production related impacts. This component of the VRFB system was also its main constrains in terms of costs. The VRFB investment cost (339 €/kWh) was almost twice the AB-FB one (184 €/kWh), mostly affected by the VRFB electrolyte cost production

Biomaterials for Cardiac Tissue Engineering

Semiotics / semiolog

Refining and mining the phylogeny of Glycoside Hydrolase Family 74 via structure-function analysis

Sustained interest in the use of carbohydrates from plant cell walls, coupled with the advancement of high-throughput (meta)genomic sequencing, has led to the discovery of an overwhelming number of predicted carbohydrate-active enzymes (CAZymes) in the last decade. The CAZy database provides a powerful framework for the study of CAZymes, including Glycoside Hydrolases (GHs), by enabling the prediction of key enzyme features such as 3-D fold, catalytic residues, catalytic mechanism, and – with certain limitations – substrate specificity. Refined phylogenetic analyses contribute to increasing the accuracy of predictions by further clustering proteins into sub-families (1, 2). However, reliable prediction of substrate specificity for newly discovered GHs remains a challenge due to a general lack of in-depth biochemical and structural characterization across the existing phylogenetic diversity. Glycoside Hydrolase family 74 (GH74) comprises endo-glucanases, many of which have predominant activity toward xyloglucan, a highly branched plant cell wall matrix glycan. To better delineate overall substrate specificity, backbone cleavage position, and endo-dissociative vs. endo-processive hydrolytic modes, a broad-based structure-function analysis of GH74 guided by molecular phylogeny was performed. Seven sub-families were discerned, which grouped nearly 40% of the current \u3e300 GH74 sequences in the public CAZy database. Thirty one GH74 members were targeted for further investigation based on their phylogenetic position and unique primary structural features identified during manual curation. The biochemical characterization of 18 recombinant GH74s revealed key sequence features governing xyloglucan backbone cleavage sites and highlighted clear phylogenetic differences between endo-dissociative and endo-processive enzymes. Commensurate with previous studies (3), site-directed mutagenesis of key active-site tryptophan residues defined their essential contributions to processivity on the soluble polysaccharide substrate. Six new GH74 tertiary structures (apo and/or in complex with xylogluco-oligosaccharides) were determined that further resolved the contribution of active-site loops in modulating the size of oligosaccharide products released by individual subfamily members. Refining the correlation between phylogeny and enzyme structure-function properties in GH74 significantly enhances the prediction of catalytic ability, highlights key steps in the evolution of function in the family, and ultimately informs applications in biomass conversion. 1. Stam MR, Danchin EGJ, Rancurel C, Coutinho PM, Henrissat B. 2006. Dividing the large glycoside hydrolase family 13 into subfamilies: towards improved functional annotations of alpha-amylase-related proteins. Protein Engineering Design & Selection 19:555-562. 2. Aspeborg H, Coutinho PM, Wang Y, Brumer H, Henrissat B. 2012. Evolution, substrate specificity and subfamily classification of glycoside hydrolase family 5 (GH5). Bmc Evolutionary Biology 12. 3. Matsuzawa T, Saito Y, Yaoi K. 2014. Key amino acid residues for the endo-processive activity of GH74 xyloglucanase. FEBS Lett 588:1731-8