Hirsch–Plotkin radical of stability groups

AbstractWe study the Hirsch–Plotkin radical of stability groups of (general) subspace series of infinite dimensional vector spaces. We show that in countable dimension and some other cases, the HP-radical of the stability group coincides with the set of all space automorphisms that fix a finite subseries; this implies that the Hirsch–Plotkin radical is a Fitting group. Conversely, we prove that every countable Fitting group, which is either torsion-free or a p-group may be represented as a subgroup of the Hirsch–Plotkin radical of a series stabilizer

Fitting height and lengths of laws in finite solvable groups

Let G be a finite solvable group, and let h(G) denote its Fitting height, namely the length of a shortest normal series in G with nilpotent factors. We show, that any law in G has length at least h(G). This result is then used to improve a previously given bound on the nonsolvable length of finite nonsolvable groups

On simple symplectic alternating algebras and their groups of automorphisms

Let N be any perfect symplectic alternating algebra. We show that N can be embedded into a larger simple alternating algebra S of dimension View the MathML source7⋅(dimN)+6 such that Aut (S)={id}Aut (S)={id}. This answers a question raised in [9]. Building on this result we show moreover that for any finite group G and characteristic c there exists a symplectic alternating algebra L over a field FF of characteristic c such that Aut (L)=GAut (L)=G

Hierarchical physically based machine learning in material science: the case study of spider silk

Multiscale phenomena exhibit complex structure-function relationships, and predicting their macroscopic behavior requires deducing differential equations at different scales. The complexity of these equations and the number of essential parameters make developing effective, predictive models challenging. To overcome this, researchers explore leveraging advanced numerical techniques from artificial intelligence and machine learning. Here, we focus on a fundamental aspect in multiscale phenomena, i.e the recognition of the hierarchical role of variables. By adopting a Pareto front interpretation, we aim to deduce simple and accurate relations for material modeling, starting from experimental multiscale analyses. From a physical point of view, the aim is to deduce information at higher scales from lower scales data, possibly respecting their hierarchical order. A crucial aspect of the proposed approach is the deduction of causality relations among the different variables to be compared with the available theoretical notions and possibly new interpretations resulting by the data modelling. This result in a stepwise approximation going from data modelling to theoretical equations and back to data modelling. To demonstrate the key advantages of our multiscale numerical approach, compared to classical, non-physically based data modelling techniques, we consider the explicit example of spider silk, known for its exceptional properties and bioinspiration potential. Indeed, it presents a complex behavior resulting from mesostructures formed by the aggregation of amino acids at the molecular scale. We argue that, due to the generality of our results, our approach may represent a proof of concept in many fields where multiscale, hierarchical differential equations regulate the observed phenomenon

Human papillomavirus vaccination coverage among adolescents living in southern Italy

Objective: The aim of this study was to estimate HPV vaccination coverage in the target population residing in Sicily, five years after launch of the vaccination campaign, and to analyze its organization in this region. Methods: Regional data as at 31 December 2013, grouped by province, issued by the Regional Health Authority were used. The organization and information materials of the campaign were also assessed (letters, posters, brochures, etc.). Results: The results for Sicily show uptake rates for three doses of HPV vaccination of 56.5%, 55.8%, 58.2%, 55.3% for cohorts born in 1997, 1998, 1999, 2000 respectively, and 56.4% for cohorts born in 1996. These figures highlight the problems encountered during the promotion campaign and vaccination provision. Conclusions: Vaccine uptake in Sicily was lower than national figures for Italy as a whole for all cohorts and both fall far short of the targets set by the National Immunization Prevention Plan 2012-2014. In order to promote vaccination uptake and improve coverage, at both regional and local level, the quality of information should be improved and more communication campaigns be instigated to increase the involvement of professionals