Hopf-algebraic deformations of products and Wick polynomials

We present an approach to classical definitions and results on cumulant--moment relations and Wick polynomials based on extensive use of convolution products of linear functionals on a coalgebra. This allows, in particular, to understand the construction of Wick polynomials as the result of a Hopf algebra deformation under the action of linear automorphisms induced by multivariate moments associated to an arbitrary family of random variables with moments of all orders. We also generalise the notion of deformed product in order to discuss how these ideas appear in the recent theory of regularity structures.Comment: Revised and improved Section 9. 29 page

Multi-scale characterisation of material properties of composite fabrics through modal tests

One of the main issues of composite materials is related to the difficulty of characterising the material properties at mesoscopic and microscopic scales. Classical mechanical tests are not able to provide the full set of 3D properties : these tests can provide only the in-plane elastic properties of the constitutive lamina. Therefore, to go beyond the main restrictions imposed by standard destructive tests, this work deals with the problem of characterising the material properties of a multilayer composite plate, through a non-destructive modal test performed at the macro-scale : a multi-scale identification strategy (MSIS) is proposed. The MSIS aims at identifying the constitutive properties by exploiting the information restrained in the composite macroscopic dynamical response. The MSIS relies on the strain energy homogenisation technique of periodic media and on a gradient-based algorithm to perform the solution search. The identification problem is stated as a constrained inverse problem, where the objective function depends upon both experimental and numerical natural frequencies of the specimen. In this background, the optimisation variables are both geometrical and material properties of the constitutive phases composing the representative volume element. The effectiveness of the approach will be proven through a campaign of tests conducted on multilayer composites.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 642121

Shifted substitution in non-commutative multivariate power series with a view toward free probability

We study a particular group law on formal power series in non-commuting variables induced by their interpretation as linear forms on a suitable graded connected word Hopf algebra. This group law is left-linear and is therefore associated to a pre-Lie structure on formal power series. We study these structures and show how they can be used to recast in a group theoretic form various identities and transformations on formal power series that have been central in the context of non-commutative probability theory, in particular in Voiculescu's theory of free probability

Wick polynomials in non-commutative probability: A group-theoretical approach

Wick polynomials and Wick products are studied in the context of non-commutative probability theory. It is shown that free, boolean and conditionally free Wick polynomials can be defined and related through the action of the group of characters over a particular Hopf algebra. These results generalize our previous developments of a Hopf algebraic approach to cumulants and Wick products in classical probability theory

Augmented Reality Application Supporting On-Site Secondary Building Assets Management

none5sinoneA. Corneli, B. Naticchia, A. Carbonari, F. Bosché, L. PrincipiCorneli, A.; Naticchia, B.; Carbonari, A.; Bosché, F.; Principi, L

Fermi constraints on the ejecta speed and prompt emission region of the distant GRB 220101A

GRB 220101A is the most distant gamma-ray burst detected by the Fermi-LAT to date, at a redshift z = 4.618. It is also a very energetic event, with an equivalent isotropic energy of $3.6\times10^{54}$ erg. We jointly analyzed the Fermi/GBM and LAT observations of GRB 220101A with two independent approaches, and found a significant spectral break at sub-100 MeV energies during the prompt emission. The fast variability of the emission suggests that this spectral attenuation is caused by internal opacity to pair creation. Regardless of the nature of the emission processes assumed in the spectral analysis, we infer a moderate value for the jet Lorentz factor, $\Gamma\sim110$, and find that all of the high-energy emission was produced above and near the photosphere, at a distance of $\sim10^{14}$ cm from the central engine. We compare these results with the four other LAT-detected gamma-ray bursts with similar properties.Comment: 15 pages, 4 figures. Accepted for publication in Ap

Multi-scale characterisation of material properties of composite fabrics through modal tests

One of the main issues of composite materials is related to the difficulty of characterising the material properties at mesoscopic and microscopic scales. Classical mechanical tests are not able to provide the full set of 3D properties : these tests can provide only the in-plane elastic properties of the constitutive lamina. Therefore, to go beyond the main restrictions imposed by standard destructive tests, this work deals with the problem of characterising the material properties of a multilayer composite plate, through a non-destructive modal test performed at the macro-scale : a multi-scale identification strategy (MSIS) is proposed. The MSIS aims at identifying the constitutive properties by exploiting the information restrained in the composite macroscopic dynamical response. The MSIS relies on the strain energy homogenisation technique of periodic media and on a gradient-based algorithm to perform the solution search. The identification problem is stated as a constrained inverse problem, where the objective function depends upon both experimental and numerical natural frequencies of the specimen. In this background, the optimisation variables are both geometrical and material properties of the constitutive phases composing the representative volume element. The effectiveness of the approach will be proven through a campaign of tests conducted on multilayer composites.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 642121

Management of tuberculosis: are the practices homogeneous in high-income countries?

Objectives: to evaluate and compare practices regarding the diagnosis, isolation measures, and treatment of tuberculosis (TB) in high-income countries and mainly in Europe. Materials and Methods: a survey was conducted from November 2018 to April 2019 within the European Society of Clinical Microbiology and Infectious Diseases Study Group for Mycobacterial Infections (ESGMYC). The practices observed were compared to the main international guidelines. Results: among 136 ESGMYC members, 64 (17 countries) responded to the questionnaire. In their practice, two (20.7%) or three sputum samples (79.3%) were collected for the diagnosis of pulmonary TB, alternatively induced sputum (n = 37, 67.2%), bronchoscopy (34, 58.6%), and gastric aspirates (15, 25.9%). Nucleic acid amplification tests (NAATs) were performed by 41 (64%) respondents whatever the smear result and by 47 (73%) in case of smear-positive specimens. NAAT and adenosine deaminase measurement were used for extrapulmonary TB diagnosis in 83.6 and 40.4% of cases, respectively. For isolation duration, 21 respondents (42.9%) were keeping isolation until smear negativity. An initial treatment without ethambutol was offered by 14% (n = 9) of respondents. Corticosteroid therapy, cerebrospinal fluid opening pressure testing, and repeated lumbar puncture were carried out for central nervous system TB by 79.6, 51.9, and 46.3% of the respondents, respectively. For patients with human immunodeficiency virus-TB coinfection, the preferred antiretroviral therapy included dolutegravir 50 mg twice a day (56.8%). Comparing with the recommendations of the main guidelines, the practices are not totally consistent. Conclusion: this study shows heterogeneous practices, particularly for diagnosis, and isolation, although rapid molecular testing is implemented in most centers. More standardization might be needed

Distinguishing different stackings in layered materials via luminescence spectroscopy

Despite its simple crystal structure, layered boron nitride features a surprisingly complex variety of phonon-assisted luminescence peaks. We present a combined experimental and theoretical study on ultraviolet-light emission in hexagonal and rhombohedral bulk boron nitride crystals. Emission spectra of high-quality samples are measured via cathodoluminescence spectroscopy, displaying characteristic differences between the two polytypes. These differences are explained using a fully first-principles computational technique that takes into account radiative emission from ``indirect'', finite-momentum, excitons via coupling to finite-momentum phonons. We show that the differences in peak positions, number of peaks and relative intensities can be qualitatively and quantitatively explained, once a full integration over all relevant momenta of excitons and phonons is performed.Comment: Main: 6 pages and 4 figures, Supplementary: 6 pages and 7 figure