Biomarkers in chronic obstructive pulmonary diseases. Clinical and functional correlations.

Asthma and chronic obstructive pulmonary disease (COPD) are two distinct lung diseases with distinctive clinical and inflammatory features. A proportion of asthmatic patients experience a fixed airflow obstruction that persists despite optimal pharmacologic treatment for reasons that are still largely unknown. We found that patients with asthma and COPD sharing a similar fixed airflow obstruction have an increased lung function decline and frequency of exacerbations. Nevertheless, the decline in lung function is associated with specific features of the underlying inflammation. Airway inflammation increases during asthma exacerbation and disease severity. Less is known about the correlations between symptoms and airway inflammation in COPD patients. We found that there is no correlation between symptoms and lung function in COPD patients. Nevertheless symptoms changes are associated with specific inflammatory changes: cough is associated with an increase of sputum neutrophils in COPD, dyspnoea is associated with an increase of eosinophils. The mechanisms of this correlation remain unknown. Neutrophils inflammation is associated with bacterial colonization in stable COPD. Is not known whether inhaled corticosteroids might facilitate bacterial colonization in COPD patients. We found that the use of inhaled corticosteroids in COPD patients is associated with an increase of airway bacterial load and with an increase of airway pathogen detection. Bacterial and viral infections are the main causes of COPD and asthma exacerbations. Impaired innate immune responses to rhinovirus infections have been described in adult patients with atopic asthma. Whether this impaired immune condition is present early in life and whether is modulated by a concomitant atopic condition is currently unknown. We found that deficient innate immune responses to rhinovirus infection are already present early in life in atopic patients without asthma and in asthmatic subjects. These findings generalize the scenario of increased susceptibility to viral infections to other Th2 oriented conditions.

Quantum Correlations in Field Theory and Integrable Systems

In this thesis we will investigate some properties of one-dimensional quantum systems. From a theoretical point of view quantum models in one dimension are particularly interesting because they are strongly interacting, since particles cannot avoid each other in their motion, and you we can never ignore collisions. Yet, integrable models often generate new and non-trivial solutions, which could not be found perturbatively. In this dissertation we shall focus on two important aspects of integrable one- dimensional models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum quench. The first part of the thesis will be therefore devoted to the study of the entanglement entropy in one- dimensional integrable systems, with a special focus on the XYZ spin-1/2 chain, which, in addition to being integrable, is also an interacting model. We will derive its Renyi entropies in the thermodynamic limit and its behaviour in different phases and for different values of the mass-gap will be analysed. In the second part of the thesis we will instead study the dynamics of correlators after a quantum quench , which represent a powerful tool to measure how perturbations and signals propagate through a quantum chain. The emphasis will be on the Transverse Field Ising Chain and the O(3) non-linear sigma model, which will be both studied by means of a semi-classical approach. Moreover in the last chapter we will demonstrate a general result about the dynamics of correlation functions of local observables after a quantum quench in integrable systems. In particular we will show that if there are not long-range interactions in the final Hamiltonian, then the dynamics of the model (non equal- time correlations) is described by the same statistical ensemble that describes its statical properties (equal-time correlations).

Max Abraham's and Tullio Levi-Civita's approach to Einstein Theory of Relativity

This work deals with the theory of Relativity and its diffusion in Italy in the first decades of the XX century. Not many scientists belonging to Italian universities were active in understanding Relativity, but two of them, Max Abraham and Tullio Levi-Civita left a deep mark. Max Abraham engaged a substantial debate against Einstein between 1912 and 1914 about electromagnetic and gravitation aspects of the theories. Levi-Civita played a fundamental role in giving Einstein the correct mathematical instruments for the General Relativity formulation since 1915. This work, which doesn't have the aim of a mere historical chronicle of the events, wants to highlight two particular perspectives: on one hand, the importance of Abraham-Einstein debate in order to clarify the basis of Special Relativity, to observe the rigorous logical structure resulting from a fragmentary reasoning sequence and to understand Einstein's thinking; on the other hand, the originality of Levi-Civita's approach, quite different from the Einstein's one, characterized by the introduction of a method typical of General Relativity even to Special Relativity and the attempt to hide the two Einstein Special Relativity postulates.

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.