Neurophysiological, molecular and pathophysiological aspects of synthetic torpor

Synthetic torpor is a peculiar physiological condition resembling natural torpor, in which even non-hibernating species can be induced through different pharmacological approaches. The growing interest in the induction of a safe synthetic torpor state in non-hibernating species stems from the possible applications that it may have in a translational perspective. In particular, the deeper understanding of the functional changes occurring during and after synthetic torpor may lead to the standardization of a safe procedure to be used also in humans and to the implementation of new therapeutic strategies. Some of the most interesting and peculiar characteristics of torpor that should be assessed in synthetic torpor and may have a translational relevance are: the reversible hyperphosphorylation of neuronal Tau protein, the strong and extended neural plasticity, which may be related to Tau regulatory processes, and the development of radioresistance. In this respect, in the present thesis, rats were induced into synthetic torpor by the pharmacological inhibition of the raphe pallidus, a key brainstem thermoregulatory area, in order to assess: i) whether a reversible hyperphosphorylation of Tau protein occurs at the spinal cord level, also testing the possible involvement of microglia activation in this phenomenon; ii) sleep quality after synthetic torpor and its possible involvement in the process of Tau dephosphorylation; iii) whether synthetic torpor has radioprotective properties, by assessing histopathological and molecular features in animals exposed to X-rays irradiation. The results showed that: i) a reversible hyper-phosphorylation of Tau protein also occurs in synthetic torpor in the dorsal horns of the spinal cord; ii) sleep regulation after synthetic torpor seems to be physiological, and sleep deprivation speeds up Tau dephosphorylation; iii) synthetic torpor induces a consistent increase in radioresistance, as shown by analyses at both histological and molecular level.

Non perturbative aspects of non equilibrium physics in two dimensional models

The present manuscript focuses on out of equilibrium physics in two dimensional models. It has the purpose of presenting some results obtained as part of out of equilibrium dynamics in its non perturbative aspects. This can be understood in two different ways: the former is related to integrability, which is non perturbative by nature; the latter is related to emergence of phenomena in the out of equilibirum dynamics of non integrable models that are not accessible by standard perturbative techniques. In the study of out of equilibirum dynamics, two different protocols are used througout this work: the bipartitioning protocol, within the Generalised Hydrodynamics (GHD) framework, and the quantum quench protocol. With GHD machinery we study the Staircase Model, highlighting how the hydrodynamic picture sheds new light into the physics of Integrable Quantum Field Theories; with quench protocols we analyse different setups where a non-perturbative description is needed and various dynamical phenomena emerge, such as the manifistation of a dynamical Gibbs effect, confinement and the emergence of Bloch oscillations preventing thermalisation.

Homological and Hodge-theoretic aspects of matroids and polymatroids

In the first part of this thesis, we study the action of the automorphism group of a matroid on the homology space of the co-independent complex. This representation turns out to be isomorphic, up to tensoring with the sign representation, with that on the homology space associated with the lattice of flats. In the case of the cographic matroid of the complete graph, this result has application in algebraic geometry: indeed De Cataldo, Heinloth and Migliorini use this outcome to study the Hitchin fibration. In the second part, on the other hand, we use ideas from algebraic geometry to prove a purely combinatorial result. We construct a Leray model for a discrete polymatroid with arbitrary building set and we prove a generalized Goresky-MacPherson formula. The first row of the model is the Chow ring of the polymatroid; we prove Poincaré duality, Hard-Lefschetz theorem and Hodge-Riemann relations for the Chow ring.