Functional and neural mechanisms of intertemporal choice

People are daily faced with intertemporal choice, i.e., choices differing in the timing of their consequences, frequently preferring smaller-sooner rewards over larger-delayed ones, reflecting temporal discounting of the value of future outcomes. This dissertation addresses two main goals. New evidence about the neural bases of intertemporal choice is provided. Following the disruption of either the medial orbitofrontal cortex or the insula, the willingness to wait for larger-delayed outcomes is affected in odd directions, suggesting the causal involvement of these areas in regulating the value computation of rewards available with different timings. These findings were also supported by a reported imaging study. Moreover, this dissertation provides new evidence about how temporal discounting can be modulated at a behavioral level through different manipulations, e.g., allowing individuals to think about the distant time, pairing rewards with aversive events, or changing their perceived spatial position. A relationship between intertemporal choice, moral judgements and aging is also discussed. All these findings link together to support a unitary neural model of temporal discounting according to which signals coming from several cortical (i.e., medial orbitofrontal cortex, insula) and subcortical regions (i.e., amygdala, ventral striatum) are integrated to represent the subjective value of both earlier and later rewards, under the top-down regulation of dorsolateral prefrontal cortex. The present findings also support the idea that the process of outcome evaluation is strictly related to the ability to pre-experience and envision future events through self-projection, the anticipation of visceral feelings associated with receiving rewards, and the psychological distance from rewards. Furthermore, taking into account the emotions and the state of arousal at the time of decision seems necessary to understand impulsivity associated with preferring smaller-sooner goods in place of larger-later goods.

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.

Essays on the Axiomatic Theory of Matching

This dissertation mimics the Turkish college admission procedure. It started with the purpose to reduce the inefficiencies in Turkish market. For this purpose, we propose a mechanism under a new market structure; as we prefer to call, semi-centralization. In chapter 1, we give a brief summary of Matching Theory. We present the first examples in Matching history with the most general papers and mechanisms. In chapter 2, we propose our mechanism. In real life application, that is in Turkish university placements, the mechanism reduces the inefficiencies of the current system. The success of the mechanism depends on the preference profile. It is easy to show that under complete information the mechanism implements the full set of stable matchings for a given profile. In chapter 3, we refine our basic mechanism. The modification on the mechanism has a crucial effect on the results. The new mechanism is, as we call, a middle mechanism. In one of the subdomain, this mechanism coincides with the original basic mechanism. But, in the other partition, it gives the same results with Gale and Shapley's algorithm. In chapter 4, we apply our basic mechanism to well known Roommate Problem. Since the roommate problem is in one-sided game patern, firstly we propose an auxiliary function to convert the game semi centralized two-sided game, because our basic mechanism is designed for this framework. We show that this process is succesful in finding a stable matching in the existence of stability. We also show that our mechanism easily and simply tells us if a profile lacks of stability by using purified orderings. Finally, we show a method to find all the stable matching in the existence of multi stability. The method is simply to run the mechanism for all of the top agents in the social preference.

Proof theory of quantified modal logics

We introduce labelled sequent calculi for indexed modal logics. We prove that the structural rules of weakening and contraction are height-preserving admissible, that all rules are invertible, and that cut is admissible. Then we prove that each calculus introduced is sound and complete with respect to the appropriate class of transition frames.