Examples of Hodge Laplacians on quantum spheres

Using a non canonical braiding over the 3d left covariant calculus we present a family of Hodge operators on the quantum SU(2) and its homogeneous quantum two-sphere.Comment: 7 pages, evolving the subject of a talk at the conference "FuninGeo" 2011, Ischia (Italy

Warped Products and Yang-Mills equations on non commutative spaces

This paper presents a non self-dual solution of the Yang-Mills equations on a non commutative version of the classical $R^4_q\backslash\{0\}$, so generalizing the classical meron solution first introduced by de Alfaro, Fubini and Furlan in 1976. The basic tool for that is a generalization to non commutative spaces of the classical notion of warped products between metric spaces.Comment: 18 page

Calculi, Hodge operators and Laplacians on a quantum Hopf fibration

We describe Laplacian operators on the quantum group SUq (2) equipped with the four dimensional bicovariant differential calculus of Woronowicz as well as on the quantum homogeneous space S2q with the restricted left covariant three dimensional differential calculus. This is done by giving a family of Hodge dualities on both the exterior algebras of SUq (2) and S2q . We also study gauged Laplacian operators acting on sections of line bundles over the quantum sphere.Comment: v3, one reference corrected, one reference added. 31 page

Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces

We equip a family of algebras whose noncommutativity is of Lie type with a derivation based differential calculus obtained, upon suitably using both inner and outer derivations, as a reduction of a redundant calculus over the Moyal four dimensional space.Comment: 18 page

Gauged Laplacians on quantum Hopf bundles

We study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe `excitations moving on the quantum sphere' in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect.Comment: v2: latex; 32 pages. Papers re-organized; no major changes, several minor ones. Commun. Math. Phys. In pres

The quantum Cartan algebra associated to a bicovariant differential calculus

We associate to any (suitable) bicovariant differential calculus on a quantum group a Cartan Hopf algebra which has a left, respectively right, representation in terms of left, respectively right, Cartan calculus operators. The example of the Hopf algebra associated to the $4D_+$ differential calculus on $SU_q(2)$ is described.Comment: 20 pages, no figures. Minor corrections in the example in Section 4

Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients

We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank approximations and the cyclic reduction method. The setup and application phases of the preconditioner achieve log-linear complexity in memory footprint and number of operations, and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment. Numerical experiments with linear systems that feature symmetry and nonsymmetry, definiteness and indefiniteness, constant and variable coefficients demonstrate the preconditioner applicability and robustness. Furthermore, it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations, and the tuning of the admissibility condition parameter. Together, these parameters allow for optimization of the memory requirements and performance of the preconditioner.Comment: 24 pages, Elsevier Journal of Computational and Applied Mathematics, Dec 201

Fooling the eyes: the influence of a sound-induced visual motion illusion on eye movements

The question of whether perceptual illusions influence eye movements is critical for the long-standing debate regarding the separation between action and perception. To test the role of auditory context on a visual illusion and on eye movements, we took advantage of the fact that the presence of an auditory cue can successfully modulate illusory motion perception of an otherwise static flickering object (sound-induced visual motion effect). We found that illusory motion perception modulated by an auditory context consistently affected saccadic eye movements. Specifically, the landing positions of saccades performed towards flickering static bars in the periphery were biased in the direction of illusory motion. Moreover, the magnitude of this bias was strongly correlated with the effect size of the perceptual illusion. These results show that both an audio-visual and a purely visual illusion can significantly affect visuo-motor behavior. Our findings are consistent with arguments for a tight link between perception and action in localization tasks

Protecting juvenile defendants in the trial and from the trial: special safeguards in EU and Italian regulations

Both the Directive 2016/800/EU and the Italian national law on juvenile criminal trial (presidential decree no. 448/1988) aim to provide specific safeguards for young suspects and defendants to protect their fragile and still-developing personality, and to ensure that any crime allegedly committed by the minor is an isolated incident in their past. These safeguards are required throughout criminal proceedings, especially during the trial stage, which can be confusing and overwhelming for a juvenile and may seriously impact their development. The trial phase – along with the precautionary limitation of personal freedom – seems to be the most dangerous procedural segment for children’s personalities. The trial is where the justice ‘play’ comes to life on its main stage, with its whole ritual, language, and characters. When attempting to identify safeguards intended to operate during the trial phase, two main fields seem to emerge: one focuses on the issue of assistance, which has to be more profound due to the unique nature of juvenile personality and experience of life; while the other one aims to protect children’s privacy so that their public image will be shielded as much as possible from the negative consequences of the trial. The article first focuses on these aspects by analysing legal regulations and the jurisprudence. In some cases, Italian legal regulation exceeds European directive standards, serving as a model for other legal systems. However, even though the internal regulation formally matches the EU requirement in some instances, it needs further improvement. Also, in terms of the law in action, the Italian jurisprudential approach sometimes weakens the safeguards provided by law, demonstrating the need for different interpretative solutions that are adequate to respect children’s rights fully. In the light of such issues, the author suggests some exegetical solutions