A Hopf bundle over a quantum four-sphere from the symplectic group

We construct a quantum version of the SU(2) Hopf bundle $S^7 \to S^4$. The quantum sphere $S^7_q$ arises from the symplectic group $Sp_q(2)$ and a quantum 4-sphere $S^4_q$ is obtained via a suitable self-adjoint idempotent $p$ whose entries generate the algebra $A(S^4_q)$ of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere $S^4$. We compute the fundamental $K$-homology class of $S^4_q$ and pair it with the class of $p$ in the $K$-theory getting the value -1 for the topological charge. There is a right coaction of $SU_q(2)$ on $S^7_q$ such that the algebra $A(S^7_q)$ is a non trivial quantum principal bundle over $A(S^4_q)$ with structure quantum group $A(SU_q(2))$.Comment: 27 pages. Latex. v2 several substantial changes and improvements; to appear in CM

Noncommutative families of instantons

We construct $\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\theta(2,H)$ by $Sp_\theta(2)$.Comment: v2: Minor changes; computation of the pairing at the end of Sect. 5.1 improve

Braided Hopf algebras and gauge transformations II: ∗*-structures and examples

We consider noncommutative principal bundles which are equivariant under a triangular Hopf algebra. We present explicit examples of infinite dimensional braided Lie and Hopf algebras of infinitesimal gauge transformations of bundles on noncommutative spheres. The braiding of these algebras is implemented by the triangular structure of the symmetry Hopf algebra. We present a systematic analysis of compatible $*$-structures, encompassing the quasitriangular case.Comment: 36 page

overexploring and overtreating the axilla

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Dynamic response of aerospace structures by means of refined beam theories

The present paper is devoted to the investigation of the dynamic response of typical aerospace structures subjected to different time-dependent loads. These analyses have been performed using the mode superposition method combined with refined one-dimensional models, which have been developed in the framework of the Carrera Unified Formulation (CUF). The Finite Element Method (FEM) and the principle of virtual displacements are used to compute the stiffness and mass matrices of these models. Using CUF, one has the great advantage to obtain these matrices in terms of fundamental nuclei, which depend neither on the adopted class of beam theory nor on the FEM approximation along the beam axis. In this paper, Taylor-like expansions (TE), Chebyshev expansion (CE) and Lagrange expansion (LE) have been employed in the framework of CUF. In particular, the latter class of polynomials has been used to develop pure translational displacement-based refined beam models, which are referred to as Component Wise (CW). This approach allows to model each structural component as a 1D element. The dynamic response analysis has been carried out for several aerospace structures, including thin-walled, open section and reinforced thin-shells. The capabilities of the proposed models are demonstrated, since this formulation allows to detect shell-like behavior with enhanced performances in terms of computational efforts

PLIERS: a Popularity-Based Recommender System for Content Dissemination in Online Social Networks

In this paper, we propose a novel tag-based recommender system called PLIERS, which relies on the assumption that users are mainly interested in items and tags with similar popularity to those they already own. PLIERS is aimed at reaching a good tradeoff between algorithmic complexity and the level of personalization of recommended items. To evaluate PLIERS, we performed a set of experiments on real OSN datasets, demonstrating that it outperforms state-of-the-art solutions in terms of personalization, relevance, and novelty of recommendations.Comment: Published in SAC '16: Proceedings of the 31st Annual ACM Symposium on Applied Computin

Static and free vibration analysis of laminated beams by refined theory based on Chebyshev Polynomials

This paper presents a new class of refined beam theories for the static and dynamic analyseis of composite structures. These beam models are obtained by implementing higher-order expansions of Chebyshev polynomials for the three components of the displacement field over the beam cross-section. The Carrera Unified Formulation (CUF) is adopted to obtain higher-order beam models. The governing equations are written in terms of fundamental nuclei, which are independent of the choice of the expansion order and the interpolating polynomials. Static and free vibration analysis of laminated beams and thin walled boxes has been carried out. Results obtained with the novel Chebyshev Expansion (CE) model have been compared with those available in the literature. For comparison, Taylor-like Expansion (TE) and Lagrange Expansion (LE) CUF models, commercial codes, analytical and experimental data are exploited. The performances of refined beam models in terms of computational cost and accuracy in comparison to the reference solutions have been assessed. The analysis performed has pointed out the high level of accuracy reached by the refined beam models with lower computational costs than 2D and 3D Finite Elements

A Transfer Learning and Explainable Solution to Detect mpox from Smartphones images

In recent months, the monkeypox (mpox) virus -- previously endemic in a limited area of the world -- has started spreading in multiple countries until being declared a ``public health emergency of international concern'' by the World Health Organization. The alert was renewed in February 2023 due to a persisting sustained incidence of the virus in several countries and worries about possible new outbreaks. Low-income countries with inadequate infrastructures for vaccine and testing administration are particularly at risk. A symptom of mpox infection is the appearance of skin rashes and eruptions, which can drive people to seek medical advice. A technology that might help perform a preliminary screening based on the aspect of skin lesions is the use of Machine Learning for image classification. However, to make this technology suitable on a large scale, it should be usable directly on mobile devices of people, with a possible notification to a remote medical expert. In this work, we investigate the adoption of Deep Learning to detect mpox from skin lesion images. The proposal leverages Transfer Learning to cope with the scarce availability of mpox image datasets. As a first step, a homogenous, unpolluted, dataset is produced by manual selection and preprocessing of available image data. It will also be released publicly to researchers in the field. Then, a thorough comparison is conducted amongst several Convolutional Neural Networks, based on a 10-fold stratified cross-validation. The best models are then optimized through quantization for use on mobile devices; measures of classification quality, memory footprint, and processing times validate the feasibility of our proposal. Additionally, the use of eXplainable AI is investigated as a suitable instrument to both technically and clinically validate classification outcomes.Comment: Submitted to Pervasive and Mobile Computin