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

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

Wigner-Weyl isomorphism for quantum mechanics on Lie groups

The Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group $G$ is developed in detail. Several New features are shown to arise which have no counterparts in the familiar Cartesian case. Notable among these is the notion of a `semiquantised phase space', a structure on which the Weyl symbols of operators turn out to be naturally defined and, figuratively speaking, located midway between the classical phase space $T^*G$ and the Hilbert space of square integrable functions on $G$. General expressions for the star product for Weyl symbols are presented and explicitly worked out for the angle-angular momentum case.Comment: 32 pages, Latex2

The Schwinger Representation of a Group: Concept and Applications

The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the Schwinger oscillator construction for SU(2), and its relevance in several quantum mechanical contexts is highlighted. The Schwinger representations for $SU(2), SO(3)$ and SU(n) for all $n$ are constructed via specific carrier spaces and group actions. In the SU(2) case connections to the oscillator construction and to Majorana's theorem on pure states for any spin are worked out. The role of the Schwinger Representation in setting up the Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group is brought out.Comment: Latex, 17 page

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

Rapid System to Detect Variants of SARS-CoV-2 in Nasopharyngeal Swabs

Currently, the reference method for identifying the presence of variants of SARS-CoV-2 is whole genome sequencing. Although it is less expensive than in the past, it is still time-consuming, and interpreting the results is difficult, requiring staff with specific skills who are not always available in diagnostic laboratories. The test presented in this study aimed to detect, using traditional real-time PCR, the presence of the main variants described for the spike protein of the SARS-CoV-2 genome. The primers and probes were designed to detect the main deletions that characterize the different variants. The amplification targets were deletions in the S gene: 25-27, 69-70, 241-243, and 157-158. In the ORF1a gene, the deletion 3675-3677 was chosen. Some of these mutations can be considered specific variants, while others can be identified by the simultaneous presence of one or more deletions. We avoided using point mutations in order to improve the speed of the test. Our test can help clinical and medical microbiologists quickly recognize the presence of variants in biological samples (particularly nasopharyngeal swabs). The test can also be used to identify variants of the virus that could potentially be more diffusive as well as not responsive to the vaccine

Criminological and Medico-legal Aspects in Homicidal and Suicidal Sharp Force Fatalities

The interpretation of sharp force fatality dynamics may be difficult in some cases, but a contribution to analysis of the phenomenon may be provided by case studies. Therefore, the purpose of our study is focused on identifying, in observed sharp force fatalities, reliable parameters that can differentiate a homicidal and suicidal manner of death, with particular reference to criminological parameters. Data derived from sharp force fatality cases in Padua and Venice from 1997 to 2019, anonymized and collected in Excel, included personal, circumstantial, clinical, and psychopathological\u2013criminological data, as well as crime scene investigation, necroscopic, and toxicological data. Statistical analyses were performed using chi-square and Wilcoxon rank-sum tests. Possible predictors of homicide were analyzed by logistic regression. Six parameters (bloodstains distant from the body, clothing lacerations, hesitation/defense wounds, number of injuries, and potential motives) were significantly different in the two groups (p\ua0<\ua00.05). An independent statistical association between potential motives explaining the crime (p\ua0<\ua00.001; OR 27.533) and homicide on multiple logistic regression analysis was highlighted. The absence of clothing lacerations was inversely related to homicide (p\ua0=\ua00.002, OR 0.092). To the best of our knowledge, this is one of very few Italian studies concerning the differential diagnosis between homicidal and suicidal sharp force fatalities. The dynamics of the event is established in most cases by the integrated evaluation of data from crime scene investigation and the autopsy. Nevertheless, in an atypical scenario, a psychopathological\u2013criminological analysis may provide essential elements, and particular attention should be given to the identification of potential explanatory motives

Generalized Weyl systems and kappa-Minkowski space

We introduce the notion of generalized Weyl system, and use it to define *-products which generalize the commutation relations of Lie algebras. In particular we study in a comparative way various *-products which generalize the k-Minkowski commutation relations.Comment: 21 pages, minor corrections and references adde