Relative influence of gaze and static arm position in the Superior Parietal Lobule of the macaque monkey during reaching

The superior parietal lobule (SPL) of macaques is classically described as an associative cortex implicated in visuospatial perception, planning and control of reaching and grasping movements (De Vitis et al., 2019; Galletti et al., 2003, 2018, 2022; Fattori et al., 2017; Hadjidimitrakis et al., 2015). These processes are the result of the integration of signals related to different sensory modalities. During a goal-directed action, eye and limb information are combined to ensure that the hand is transported at the gazed target location and the arm is maintained steady in the final position. The SPL areas V6A, PEc and PE contain cells sensitive to the direction of gaze and limb position but less is known about the degree of independent encoding of these signals. In this thesis, we evaluated the influence of eye and arm position information upon single neuron activity of areas V6A, PEc and PE during the holding period after the execution of arm reaching movement, when the gaze and hand are both still at the reach target. Two male macaques (Macaca fascicularis) performed a reaching task while single unit activity was recorded from areas V6A, PEc and PE. We found that neurons in all these areas were modulated by eye and static arm positions with a joint encoding of gaze and somatosensory signals in V6A and PEc and a mostly separate processing of the two signals in PE. The elaboration of this information reflects the functional gradient found in the SPL with the caudal sector characterized by visuo-somatic properties in comparison to the rostral sector dominated by somatosensory signals. This evidence well agree also with the recent reallocation of areas V6A and PEc in Brodmann’s area 7 depending on their similar structural and functional features with respect to PE belonging to Brodmann’s area 5 (Gamberini et al., 2020).

Probabilistic tomography of atmospheric parameters from GNSS data

The objective of the work is the evaluation of the potential capabilities of navigation satellite signals to retrieve basic atmospheric parameters. A capillary study have been performed on the assumptions more or less explicitly contained in the common processing steps of navigation signals. A probabilistic procedure has been designed for measuring vertical discretised profiles of pressure, temperature and water vapour and their associated errors. Numerical experiments on a synthetic dataset have been performed with the main objective of quantifying the information that could be gained from such approach, using entropy and relative entropy as testing parameters. A simulator of phase delay and bending of a GNSS signal travelling across the atmosphere has been developed to this aim.

Correlations and Quantum Dynamics of 1D Fermionic Models: New Results for the Kitaev Chain with Long-Range Pairing

In the first part of the thesis, we propose an exactly-solvable one-dimensional model for fermions with long-range p-wave pairing decaying with distance as a power law. We studied the phase diagram by analyzing the critical lines, the decay of correlation functions and the scaling of the von Neumann entropy with the system size. We found two gapped regimes, where correlation functions decay (i) exponentially at short range and algebraically at long range, (ii) purely algebraically. In the latter the entanglement entropy is found to diverge logarithmically. Most interestingly, along the critical lines, long-range pairing breaks also the conformal symmetry. This can be detected via the dynamics of entanglement following a quench. In the second part of the thesis we studied the evolution in time of the entanglement entropy for the Ising model in a transverse field varying linearly in time with different velocities. We found different regimes: an adiabatic one (small velocities) when the system evolves according the instantaneous ground state; a sudden quench (large velocities) when the system is essentially frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations (also as a function of the velocity). Finally, we discussed the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.