The geometry of a bi-Lagrangian manifold

This is a survey on bi-Lagrangian manifolds, which are symplectic manifolds endowed with two transversal Lagrangian foliations. We also study the non-integrable case (i.e., a symplectic manifold endowed with two transversal Lagrangian distributions). We show that many different geometric structures can be attached to these manifolds and we carefully analyse the associated connections. Moreover, we introduce the problem of the intersection of two leaves, one of each foliation, through a point and show a lot of significative examples.Comment: 30 page

The canonical 8-form on manifolds with holonomy group Spin(9)

An explicit expression of the canonical 8-form on a Riemannian manifold with a Spin(9)-structure, in terms of the nine local symmetric involutions involved, is given. The list of explicit expressions of all the canonical forms related to Berger's list of holonomy groups is thus completed. Moreover, some results on Spin(9)-structures as G-structures defined by a tensor and on the curvature tensor of the Cayley planes, are obtained

Multiscale non-adiabatic dynamics with radiative decay, case study on the post-ionization fragmentation of rare-gas tetramers

In this supplementary material, we recollect, for reader's convenience, the general scheme of suggested multiscale model (Sec. 1), and basic informations about approaches used for pilot study: a detailed description of the interaction model (Sec. 2) and dynamical methods used for the dark dynamics step (Sec. 3) reported previously in two preceding studies [1, 2]. In addition, a detailed description of the treatment of radiative processes is also given (Sec. 4).Comment: supplementary material for parent paper; 9 pages, 1 figure; corrected formulae and misleading notation in Sec.4 (pages 7 and 8

Effects of a single session of SMR neurofeedback training on anxiety and cortisol levels

Objectives: According to some studies, a putatively calming effect of EEG neurofeedback training could be useful as a therapeutic tool in psychiatric practice. With the aim of elucidating this possibility, we tested the efficacy of a single session of ¿sensorimotor (SMR)/¿theta neurofeedback training for mood improvement in 32 healthy men, taking into account trainability, independence and interpretability of the results. Methods: A pre-post design, with the following dependent variables, was applied: (i) psychometric measures of mood with regards to anxiety, depression, and anger (Profile of Mood State, POMS, and State Trait Anxiety Inventory, STAI); (ii) biological measures (salivary levels of cortisol); (iii) neurophysiological measures (EEG frequency band power analysis). In accordance with general recommendations for research in neurofeedback, a control group receiving sham neurofeedback was included. Results: Anxiety levels decreased after the real neurofeedback and increased after the sham neurofeedback (P < 0.01, size effect 0.9 for comparison between groups). Cortisol decreased after the experiment in both groups, though with significantly more pronounced effects in the desired direction after the real neurofeedback (P < 0.04; size effect 0.7). The group receiving real neurofeedback significantly enhanced their SMR band (P < 0.004; size effect 0.88), without changes in the theta band. The group receiving sham neurofeedback did not show any EEG changes. Conclusions: The improvement observed in anxiety was greater in the experimental group than in the sham group, confirmed by both subjective (psychometric) measures and objective (biological) measures. This was demonstrated to be associated with the real neurofeedback, though a nonspecific (placebo) effect likely also contributed

Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three

We determine, for all three-dimensional non-unimodular Lie groups equipped with a Lorentzian metric, the set of homogeneous geodesics through a point. Together with the results of [C] and [CM2], this leads to the full classification of three-dimensional Lorentzian g.o. spaces and naturally reductive spaces

The population of deformed bands in 48^{48}Cr by emission of 8^{8}Be from the 32^{32}S + 24^{24}Mg reaction

Using particle-$\gamma$ coincidences we have studied the population of final states after the emission of 2 $\alpha$-particles and of $^{8}$Be in nuclei formed in $^{32}$S+$^{24}$Mg reactions at an energy of $\textrm{E}_{\rm L}(^{32}\textrm{S}) = 130 {\rm MeV}$. The data were obtained in a setup consisting of the GASP $\gamma$-ray detection array and the multidetector array ISIS. Particle identification is obtained from the $\Delta$E and E signals of the ISIS silicon detector telescopes, the $^{8}$Be being identified by the instantaneous pile up of the $\Delta$E and E pulses. $\gamma$-ray decays of the $^{48}$Cr nucleus are identified with coincidences set on 2 $\alpha$-particles and on $^{8}$Be. Some transitions of the side-band with $K^\pi=4^{-}$ show stronger population for $^{8}$Be emission relative to that of 2 $\alpha$-particles (by a factor $1.5-1.8$). This observation is interpreted as due to an enhanced emission of $^{8}$Be into a more deformed nucleus. Calculations based on the extended Hauser-Feshbach compound decay formalism confirm this observation quantitatively.Comment: 17 pages, 9 figures accepted for publication in J. Phys.

Performance of the Fully Digital FPGA-based Front-End Electronics for the GALILEO Array

In this work we present the architecture and results of a fully digital Front End Electronics (FEE) read out system developed for the GALILEO array. The FEE system, developed in collaboration with the Advanced Gamma Tracking Array (AGATA) collaboration, is composed of three main blocks: preamplifiers, digitizers and preprocessing electronics. The slow control system contains a custom Linux driver, a dynamic library and a server implementing network services. The digital processing of the data from the GALILEO germanium detectors has demonstrated the capability to achieve an energy resolution of 1.53 per mil at an energy of 1.33 MeV.Comment: 5 pages, 6 figures, preprint version of IEEE Transactions on Nuclear Science paper submitted for the 19th IEEE Real Time Conferenc