The Role of Noise in the Spatial Public Goods Game

In this work we aim to analyze the role of noise in the spatial Public Goods Game, one of the most famous games in Evolutionary Game Theory. The dynamics of this game is affected by a number of parameters and processes, namely the topology of interactions among the agents, the synergy factor, and the strategy revision phase. The latter is a process that allows agents to change their strategy. Notably, rational agents tend to imitate richer neighbors, in order to increase the probability to maximize their payoff. By implementing a stochastic revision process, it is possible to control the level of noise in the system, so that even irrational updates may occur. In particular, in this work we study the effect of noise on the macroscopic behavior of a finite structured population playing the Public Goods Game. We consider both the case of a homogeneous population, where the noise in the system is controlled by tuning a parameter representing the level of stochasticity in the strategy revision phase, and a heterogeneous population composed of a variable proportion of rational and irrational agents. In both cases numerical investigations show that the Public Goods Game has a very rich behavior which strongly depends on the amount of noise in the system and on the value of the synergy factor. To conclude, our study sheds a new light on the relations between the microscopic dynamics of the Public Goods Game and its macroscopic behavior, strengthening the link between the field of Evolutionary Game Theory and statistical physics.Comment: 14 pages, 3 figure

Cerebral blood flow estimation from Arterial Spin Labeling MRI with Look-Locker readout: a bayesian approach

Arterial Spin Labeling (ASL) è una tecnica MRI che permette di misurare la perfusione in maniera completamente non invasiva. Diversi modelli sono stati proposti in letteratura per la quantificazione della perfusione (CBF) da acquisizioni ASL. In questo lavoro viene proposto un approccio bayesiano alla quantificazione, in grado di indirizzare al meglio le conoscenze disponibili sui parametri inclusi nel modello. Il modello standard, conosciuto anche come modello di Buxton, è stato consideratoopenEmbargo per motivi di priorità nella ricerca previo accordo con terze part

DebtRank: A microscopic foundation for shock propagation

The DebtRank algorithm has been increasingly investigated as a method to estimate the impact of shocks in financial networks, as it overcomes the limitations of the traditional default-cascade approaches. Here we formulate a dynamical "microscopic" theory of instability for financial networks by iterating balance sheet identities of individual banks and by assuming a simple rule for the transfer of shocks from borrowers to lenders. By doing so, we generalise the DebtRank formulation, both providing an interpretation of the effective dynamics in terms of basic accounting principles and preventing the underestimation of losses on certain network topologies. Depending on the structure of the interbank leverage matrix the dynamics is either stable, in which case the asymptotic state can be computed analytically, or unstable, meaning that at least one bank will default. We apply this framework to a dataset of the top listed European banks in the period 2008 - 2013. We find that network effects can generate an amplification of exogenous shocks of a factor ranging between three (in normal periods) and six (during the crisis) when we stress the system with a 0.5% shock on external (i.e. non-interbank) assets for all banks.Comment: 10 pages, 2 figure

An Information Theoretic approach to Post Randomization Methods under Differential Privacy

Post Randomization Methods (PRAM) are among the most popular disclosure limitation techniques for both categorical and continuous data. In the categorical case, given a stochastic matrix M and a specified variable, an individual belonging to category i is changed to category j with probability Mi,j . Every approach to choose the randomization matrix M has to balance between two desiderata: 1) preserving as much statistical information from the raw data as possible; 2) guaranteeing the privacy of individuals in the dataset. This trade-off has generally been shown to be very challenging to solve. In this work, we use recent tools from the computer science literature and propose to choose M as the solution of a constrained maximization problems. Specifically, M is chosen as the solution of a constrained maximization problem, where we maximize the Mutual Information between raw and transformed data, given the constraint that the transformation satisfies the notion of Differential Privacy. For the general Categorical model, it is shown how this maximization problem reduces to a convex linear programming and can be therefore solved with known optimization algorithms

Studio dell'utilizzo di feedback uditivo nell'esecuzione di task motori

In seguito ad un ictus, frequentemente nei pazienti si denota una perdita della funzionalità motoria e della capacità di controllo del movimento stesso. Tale situazione, in sede di riabilitazione, viene evidenziata ad esempio con la misura di opportuni parametri cinematici nell'esecuzione di movimenti. Il feedback è un componente essenziale della riabilitazione, in particolare il feedback uditivo su parametri cinematici può risultare uno strumento molto utile per un migliore e più pronto recupero della capacità motoria. Lo scopo di questo studio è quello di investigare gli effetti che diversi tipi di feedback audio portano nell'esecuzione di alcuni movimenti riabilitativi da parte dei pazienti. E' stata presa in considerazione una popolazione di venti soggetti sani, privi di alcun tipo di menomazione motoria. Tre tipi di feedback audio sono stati sviluppati e forniti online durante l'esecuzione di sei esercizi di target tracking. Tutti i parametri cinematici di interesse dell'intero esercizio sono stati memorizzati per consentire la visualizzazione in momenti successivi dello stesso esercizio, e la valutazione dell'accuratezza dell'inseguimento attraverso il calcolo di svariati indici di errore. Sono stati comparati indici relativi ad esercizi di audio diverso ma eseguiti dallo stesso soggetto e la valutazione dell'effetto del feedback uditivo è stata ottenuta per mezzo di un test statistico sull'intero gruppo di soggettiope

Quantitative MRI for measuring myelin content in human spinal cord

The aim of this thesis is to progress the state-of-the art of quantitative Magnetic Resonance Imaging (MRI) in the human spinal cord, with particular focus on methods sensitive to myelin content. Myelin is a fundamental structure of the central nervous system, ensuring the correct transmission of action potentials along neuronal axons, affected in a number of neurological disorders, first and foremost Multiple Sclerosis (MS). MRI methods to assess myelin in the spinal cord have found limited development, despite the primary involvement of the spinal cord in demyelinating diseases, such as MS where the characterization of spinal cord pathology is key for a better diagnosis, understanding of pathological processes, and evaluation of neuroprotective and reparative treatments. In this thesis, we develop novel methods for the spinal cord to measure parameters that are known to correlate with myelin content, namely the longitudinal relaxation time (T₁) and quantitative Magnetization Transfer (qMT) parameters, and we compare them with a large set of myelin sensitive MRI indices in the post mortem MS spinal cord. The thesis is structured as follows: chapter 1 states the problem this thesis attempts to address and provides background information regarding the involvement of the spinal cord in MS; chapter 2 reviews the basic principles of MRI and introduces the theory behind the measurement of surrogate indices of myelin content with MRI; chapter 3 reviews an existing imaging sequence for the spinal cord, extends its use for measuring myelin sensitive parameters and discusses potential improvements for in vivo applications; chapter 4 and chapter 5 propose novel efficient methods to measure T₁ and qMT parameters in vivo in the spinal cord; and chapter 6 evaluates the performance of the methods developed in the previous chapter, together with other prospective myelin mapping methods, in the healthy and MS post mortem human spinal cord

Pathways towards instability in financial networks

Following the financial crisis of 2007–2008, a deep analogy between the origins of instability in financial systems and complex ecosystems has been pointed out: in both cases, topological features of network structures influence how easily distress can spread within the system. However, in financial network models, the details of how financial institutions interact typically play a decisive role, and a general understanding of precisely how network topology creates instability remains lacking. Here we show how processes that are widely believed to stabilize the financial system, that is, market integration and diversification, can actually drive it towards instability, as they contribute to create cyclical structures which tend to amplify financial distress, thereby undermining systemic stability and making large crises more likely. This result holds irrespective of the details of how institutions interact, showing that policy-relevant analysis of the factors affecting financial stability can be carried out while abstracting away from such details