Inference on copula-based correlation structures

We propose an extension of the approach provided by Kluppelberg and Kuhn (2009) for inference on second-order structure moments. As in Kluppelberg and Kuhn (2009) we adopt a copula-based approach instead of assuming normal distribution for the variables, thus relaxing the equality in distribution assumption. A new copula-based estimator for structure moments is investigated. The methodology provided by Kluppelberg and Kuhn (2009) is also extended considering the copulas associated with the family of Eyraud-Farlie-Gumbel-Morgenstern distribution functions (Kotz, Balakrishnan, and Johnson, 2000, Equation 44.73). Finally, a comprehensive simulation study and an application to real financial data are performed in order to compare the different approaches.

1963-1968. Dall'avvento dell'amministrazione di Lyndon B. Johnson al Trattato di Non-Proliferazione. gli Stati Uniti, la Francia, la NATO e l'Europa agli esordi della distensione. Storia di una "non-crisi" transatlantica e della riorganizzazione dell'Alleanza.

The aim of this proposal is to explain the paradigm of the American foreign policy during the Johnson Administration, especially toward Europe, within the NATO framework, and toward URSS, in the context of the détente, just emerged during the decade of the sixties. During that period, after the passing of the J. F. Kennedy, President L. B. Johnson inherited a complex and very high-powered world politics, which wanted to get a new phase off the ground in the transatlantic relations and share the burden of the Cold war with a refractory Europe. Known as the grand design, it was a policy that needed the support of the allies and a clear purpose which appealed to the Europeans. At first, President Johnson detected in the problem of the nuclear sharing the good deal to make with the NATO allies. At the same time, he understood that the United States needed to reassert their leadeship within the new stage of relations with the Soviet Union. Soon, the “transatlantic bargain” became something not so easy to dealt with. The Federal Germany wanted to say a word in the nuclear affairs and, why not, put the finger on the trigger of the atlantic nuclear weapons. URSS, on the other hand, wanted to keep Germany down. The other allies did not want to share the onus of the defense of Europe, at most the responsability for the use of the weapons and, at least, to participate in the decision-making process. France, which wanted to detach herself from the policy of the United States and regained a world role, added difficulties to the manage of this course of action. Through the years of the Johnson’s office, the divergences of the policies placed by his advisers to gain the goal put the American foreign policy in deep water. The withdrawal of France from the organization but not from the Alliance, give Washington a chance to carry out his goal. The development of a clear-cut disarm policy leaded the Johnson’s administration to the core of the matter. The Non-proliferation Treaty signed in 1968, solved in a business-like fashion the problem with the allies. The question of nuclear sharing faded away with the acceptance of more deep consultative role in the nuclear affairs by the allies, the burden for the defense of Europe became more bearable through the offset agreement with the FRG and a new doctrine, the flexible response, put an end, at least formally, to the taboo of the nuclear age. The Johnson’s grand design proved to be different from the Kennedy’s one, but all things considered, it was more workable. The unpredictable result was a real détente with the Soviet Union, which, we can say, was a merit of President Johnson.

Spectrum reconstruction from a scattering measurement using the adjoint Boltzmann transport equation for photons

Quality control of medical radiological systems is of fundamental importance, and requires efficient methods for accurately determine the X-ray source spectrum. Straightforward measurements of X-ray spectra in standard operating require the limitation of the high photon flux, and therefore the measure has to be performed in a laboratory. However, the optimal quality control requires frequent in situ measurements which can be only performed using a portable system. To reduce the photon flux by 3 magnitude orders an indirect technique based on the scattering of the X-ray source beam by a solid target is used. The measured spectrum presents a lack of information because of transport and detection effects. The solution is then unfolded by solving the matrix equation that represents formally the scattering problem. However, the algebraic system is ill-conditioned and, therefore, it is not possible to obtain a satisfactory solution. Special strategies are necessary to circumvent the ill-conditioning. Numerous attempts have been done to solve this problem by using purely mathematical methods. In this thesis, a more physical point of view is adopted. The proposed method uses both the forward and the adjoint solutions of the Boltzmann transport equation to generate a better conditioned linear algebraic system. The procedure has been tested first on numerical experiments, giving excellent results. Then, the method has been verified with experimental measurements performed at the Operational Unit of Health Physics of the University of Bologna. The reconstructed spectra have been compared with the ones obtained with straightforward measurements, showing very good agreement.

Master Equation: Biological Applications and Thermodynamic Description

It is well known that many realistic mathematical models of biological systems, such as cell growth, cellular development and differentiation, gene expression, gene regulatory networks, enzyme cascades, synaptic plasticity, aging and population growth need to include stochasticity. These systems are not isolated, but rather subject to intrinsic and extrinsic fluctuations, which leads to a quasi equilibrium state (homeostasis). The natural framework is provided by Markov processes and the Master equation (ME) describes the temporal evolution of the probability of each state, specified by the number of units of each species. The ME is a relevant tool for modeling realistic biological systems and allow also to explore the behavior of open systems. These systems may exhibit not only the classical thermodynamic equilibrium states but also the nonequilibrium steady states (NESS). This thesis deals with biological problems that can be treat with the Master equation and also with its thermodynamic consequences. It is organized into six chapters with four new scientific works, which are grouped in two parts: (1) Biological applications of the Master equation: deals with the stochastic properties of a toggle switch, involving a protein compound and a miRNA cluster, known to control the eukaryotic cell cycle and possibly involved in oncogenesis and with the propose of a one parameter family of master equations for the evolution of a population having the logistic equation as mean field limit. (2) Nonequilibrium thermodynamics in terms of the Master equation: where we study the dynamical role of chemical fluxes that characterize the NESS of a chemical network and we propose a one parameter parametrization of BCM learning, that was originally proposed to describe plasticity processes, to study the differences between systems in DB and NESS.

L'amministrazione Johnson e le origini della distensione. 1964-1968

La tesi analizza una parte della politica estera dell’amministrazione Johnson, e più specificamente l’avvio del dialogo con l’Urss in materia di non proliferazione e controllo degli armamenti e la revisione della China policy, inquadrando entrambe nell’adattamento della cold war strategy all’evoluzione sistema internazionale, argomentando che la distensione intesa come rilassamento delle tensioni e ricerca di terreno comune per il dialogo, fosse perlomeno uno degli strumenti politici che l’amministrazione scelse di usare. Il primo capitolo analizza i cambiamenti che interessarono il Blocco sovietico e il movimento comunista internazionale tra la fine degli anni Cinquanta e l’inizio degli anni Sessanta, soprattutto la rottura dell’alleanza sino-sovietica, e l’impatto che essi ebbero sul sistema bipolare su cui si basava la Guerra Fredda. Il capitolo secondo affronta più specificamente l’evoluzione delle relazioni tra Stati Uniti e Unione Sovietica, il perseguimento di una politica di distensione, dopo la crisi dei missili cubani, e in che relazione si trovasse ciò con lo status della leadership sovietica a seguito dei cambiamenti che avevano avuto luogo. Soffermandosi sulla questione del controllo degli armamenti e sul percorso che portò alla firma del Trattato di Non-proliferazione, si analizza come la nuova rotta intrapresa col dialogo sulle questioni strategiche sia stato anche un cambiamento di rotta in generale nella concezione della Guerra Fredda e l’introduzione della distensione come strumento politico. Il terzo capitolo affronta la questione della modifica della politica verso Pechino e il processo tortuoso e contorto attraverso cui l’amministrazione Johnson giunse a distaccarsi dalla China policy seguita sino ad allora.