Numerical integration based on trivariate C 2 quartic spline quasi-interpolants

In this paper we consider the space generated by the scaled translates of the trivariate C ² quartic box spline B defined by a set X of seven directions, that forms a regular partition of the space into tetrahedra. Then, we construct new cubature rules for 3D integrals, based on spline quasi-interpolants expressed as linear combinations of scaled translates of B and local linear functionals. We give weights and nodes of the above rules and we analyse their properties. Finally, some numerical tests and comparisons with other known integration formulas are presented.     

On entropy weak solutions of Hughes’ model for pedestrian motion

We consider a generalized version of Hughes’ macroscopic model for crowd motion in the one-dimensional case. It consists in a scalar conservation law accounting for the conservation of the number of pedestrians, coupled with an eikonal equation giving the direction of the flux depending on pedestrian density. As a result of this non-trivial coupling, we have to deal with a conservation law with space–time discontinuous flux, whose discontinuity depends non-locally on the density itself. We propose a definition of entropy weak solution, which allows us to recover a maximum principle. Moreover, we study the structure of the solutions to Riemann-type problems, and we construct them explicitly for small times, depending on the choice of the running cost in the eikonal equation. In particular, aiming at the optimization of the evacuation time, we propose a strategy that is optimal in the case of high densities. All results are illustrated by numerical simulations.     

Differences in brain regions of three mice strains identified by label-free micro-Raman

The analysis of different central nervous system regions is interesting and necessary as each one is involved in specific physiological processes and pathologies. On that matter, differences in the chemical composition between the same brain regions in different mice strains have been reported. In this sense, the development of a simple method for the identification of these regions depending on their chemical composition becomes relevant. Raman microspectroscopy, a non-destructive analytical chemical approach for biological samples, is a widely used method for qualitative, quantitative, and structural analysis in biochemical research. Ten brain structures in three different mice strains (Triple transgenic for Alzheimer Disease, 3xTgAD; Cluster 57 black 6, C57BL/6; and the Swiss strain, CD1) were analyzed, and variations among samples from several brain regions were found. Particularly, the pattern of signals from the hippocampus, the prefrontal and temporal cortices, the basal forebrain, the striatum, the cerebellum, and the hypothalamus was discernable. Interestingly, notable signals regarding non-peptide small neurotransmitters were observed, including those related to acetylcholine. These bands were present in the Raman spectra of the basal forebrain and prefrontal cortex in the three mice strains, consistent with the relative abundance of this neurotransmitter in those regions. However, signals with lower intensities appeared in the basal forebrain of C57BL/6 in comparison with the same tissue of the other two strains. In addition, the Raman intensity of bands assigned to catecholamines in the striatum was lower in the 3xTgAD than those from both CD1 and C57BL/6 mice strains. This approach, as well as the reported differences, has potential application for designing analysis on specific murine models of brain diseases.     

An efficient numerical tool for dose deposition prediction applied to synchrotron medical imaging and radiation therapy

Medical imaging and radiation therapy are widely used synchrotron‐based techniques which have one thing in common: a significant dose delivery to typically biological samples. Among the ways to provide the experimenters with image guidance techniques indicating optimization strategies, Monte Carlo simulation has become the gold standard for accurately predicting radiation dose levels under specific irradiation conditions. A highly important hampering factor of this method is, however, its slow statistical convergence. A track length estimator (TLE) module has been coded and implemented for the first time in the open‐source Monte Carlo code GATE/Geant4. Results obtained with the module and the procedures used to validate them are presented. A database of energy‐absorption coefficients was also generated, which is used by the TLE calculations and is now also included in GATE/Geant4. The validation was carried out by comparing the TLE‐simulated doses with experimental data in a synchrotron radiation computed tomography experiment. The TLE technique shows good agreement versus both experimental measurements and the results of a classical Monte Carlo simulation. Compared with the latter, it is possible to reach a pre‐defined statistical uncertainty in about two to three orders of magnitude less time for complex geometries without loss of accuracy.     

A Nyström interpolant for some weakly singular nonlinear Volterra integral equations

We consider a second kind weakly singular nonlinear Volterra–Hammerstein integral equation defined by a compact operator and derive a Nyström type interpolant of the solution based on Gauss–Radau nodes. We prove the convergence of the interpolant and derive convergence estimates. For equations with nonlinearity of algebraic kind, we improve the rate of convergence by using a smoothing transformation. Some numerical examples are given.     

Microstructural and thermal characterization of neolithic ceramics

The aim of this research was to characterize some Neolithic ceramic finds collected during an excavation carried out at Lugo di Grezzana (Verona, Italy). Pottery shards with different paste and tempers were analyzed to better understand the manufacturing and firing technologies used for their production. Another task of the study was to determine whether highly refined artefacts, found in the site and resembling figulina-type ceramics, were of local production or imported from other places in the north of Italy, where the production of this sort of product has already been unambiguously assessed. Several results emerged from this investigation, providing indications on the finds from this Neolithic settlement and, therefore, on the technological expertise achieved by the primitive community. Moreover, a comparative study carried out on refined ceramic products found in Lugo and genuine figulina items from other northern Italian sites suggests that no trading exchange and commercial routes existed among those primitive communities.     

Efficient catalyst-free tricomponent synthesis of new spiro[cyclohexane-1,4′-pyrazolo[3,4-e][1, 4]thiazepin]-7′(6′H)-ones

A series of spirocyclohexane-1,4′-pyrazolothiazepinones were synthesized by one-pot multicomponent cyclocondensation reactions between 5-amino-1-arylpyrazoles, cyclohexanone and mercaptoacetic acid with good yields and easy purification protocols. Some control experiments involving isolation of reaction intermediates were performed leading to the proposal of three alternative mechanistic pathways conducting to the named spiroheterocycles. All target molecules were fully characterized by IR, NMR, melting point and HRMS.