Computational study of resting state network dynamics

Lo scopo di questa tesi è quello di mostrare, attraverso una simulazione con il software The Virtual Brain, le più importanti proprietà della dinamica cerebrale durante il resting state, ovvero quando non si è coinvolti in nessun compito preciso e non si è sottoposti a nessuno stimolo particolare. Si comincia con lo spiegare cos’è il resting state attraverso una breve revisione storica della sua scoperta, quindi si passano in rassegna alcuni metodi sperimentali utilizzati nell’analisi dell’attività cerebrale, per poi evidenziare la differenza tra connettività strutturale e funzionale. In seguito, si riassumono brevemente i concetti dei sistemi dinamici, teoria indispensabile per capire un sistema complesso come il cervello. Nel capitolo successivo, attraverso un approccio ‘bottom-up’, si illustrano sotto il profilo biologico le principali strutture del sistema nervoso, dal neurone alla corteccia cerebrale. Tutto ciò viene spiegato anche dal punto di vista dei sistemi dinamici, illustrando il pionieristico modello di Hodgkin-Huxley e poi il concetto di dinamica di popolazione. Dopo questa prima parte preliminare si entra nel dettaglio della simulazione. Prima di tutto si danno maggiori informazioni sul software The Virtual Brain, si definisce il modello di network del resting state utilizzato nella simulazione e si descrive il ‘connettoma’ adoperato. Successivamente vengono mostrati i risultati dell’analisi svolta sui dati ricavati, dai quali si mostra come la criticità e il rumore svolgano un ruolo chiave nell'emergenza di questa attività di fondo del cervello. Questi risultati vengono poi confrontati con le più importanti e recenti ricerche in questo ambito, le quali confermano i risultati del nostro lavoro. Infine, si riportano brevemente le conseguenze che porterebbe in campo medico e clinico una piena comprensione del fenomeno del resting state e la possibilità di virtualizzare l’attività cerebrale

Advanced estimates of regional accounts: an alternative approach by spatial panels

The policies related to regional economic activity developed by European Union (EU) and the role played by regions as economic subject have determined a bigger set of disaggregated statistics at macroeconomic level. The methodologies used nowadays by the Italian national institute of statistics (ISTAT) are based on an information set build on the basis of inner statistical surveys and other external sources. The estimates of regional accounts carried out on the complete information set require an amount of time bigger than the one expected for the already mentioned aims. A strong need to carry out advanced estimates of regional accounts in a quicker time has emerged. The Kalman filter could be the right tool if we use a short time series span. Since it is available a larger data set from ISTAT web site (www.istat.it) from 1980 up to 2004, a different approach will be performed here, and is mainly based on Spatial Panel recently used by Elhorst and Baltagi. SAR (simultaneous autocorrelation model) and SEM (simultaneous error model) will be used. In a similar fashion the first log differences of ULA (units of labour) will be used to forecast the first log differences of four value added branches at constant prices. Finally some conclusions will be drawn on the performances of SAR and SEMspatial panel data models, regional accounts

Mixed symmetry tensors in the worldline formalism

We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which - by adding a suitable Chern-Simons term to the particle action - can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U(F) "flavour" symmetry on the worldline particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young Tableau. In particular the occupation numbers of the wavefunction - i.e. the lengths of the columns (rows) of the Young Tableau - are fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We suggest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.Comment: 1+32 page

Contingent Claim Pricing In A Dual Expected Utility Theory Framework

This paper investigates the price for contingent claims in a dual expected utility theory framework, the dual price, considering complete arbitrage-free nancial markets. In this framework this dual price is obtained, for the rst time in the literature, without any comonotonicity hypothesis and for contingent claims written on n underlying assets following generic Itô processes. An application is also considered assuming geometric brownian motion for the underlying assets and the Wang transform as distortion function.Contingent Claims Pricing, Dual Utility Theory, Wang Transform.

Is Quantum Gravity a Chern-Simons Theory?

We propose a model of quantum gravity in arbitrary dimensions defined in terms of the BV quantization of a supersymmetric, infinite dimensional matrix model. This gives an (AKSZ-type) Chern-Simons theory with gauge algebra the space of observables of a quantum mechanical Hilbert space H. The model is motivated by previous attempts to formulate gravity in terms of non-commutative, phase space, field theories as well as the Fefferman-Graham curved analog of Dirac spaces for conformally invariant wave equations. The field equations are flat connection conditions amounting to zero curvature and parallel conditions on operators acting on H. This matrix-type model may give a better defined setting for a quantum gravity path integral. We demonstrate that its underlying physics is a summation over Hamiltonians labeled by a conformal class of metrics and thus a sum over causal structures. This gives in turn a model summing over fluctuating metrics plus a tower of additional modes-we speculate that these could yield improved UV behavior.Comment: 22 pages, LaTeX, 3 figures, references added, version to appear in PR

A route to explain water anomalies from results on an aqueous solution of salt

In this paper we investigate the possibility to detect the hypothesized liquid-liquid critical point of water in supercooled aqueous solutions of salts. Molecular dynamics computer simulations are conducted on bulk TIP4P water and on an aqueous solution of sodium chloride in TIP4P water, with concentration c = 0.67 mol/kg. The liquid-liquid critical point is found both in the bulk and in the solution. Its position in the thermodynamic plane shifts to higher temperature and lower pressure for the solution. Comparison with available experimental data allowed us to produce the phase diagrams of both bulk water and the aqueous solution as measurable in experiments. Given the position of the liquid-liquid critical point in the solution as obtained from our simulations, the experimental determination of the hypothesized liquid-liquid critical point of water in aqueous solutions of salts appears possible.Comment: 5 pages, 6 figures. Accepted for publication on the Journal of Chemical Physics (2010)

Dressed scalar propagator in a non-abelian background from the worldline formalism

We study the propagator of a colored scalar particle in the background of a non-abelian gauge field using the worldline formalism. It is obtained by considering the open worldline of a scalar particle with extra degrees of freedom needed to take into account the color charge of the particle, which we choose to be in the fundamental representation of the gauge group. Specializing the external gauge field to be given by a sum of plane waves, i.e. a sum of external gluons, we produce a master formula for the scalar propagator with an arbitrary number of gluons directly attached to the scalar line, akin to similar formulas derived in the literature for the case of the scalar particle performing a loop. Our worldline description produces at the same time the situation in which the particle has a color charge given by an arbitrarily chosen symmetric or antisymmetric tensor product of the fundamental.Comment: 21 pages, 1 figure; title modified, discussion improved, references added, main results unchanged. Matches version published in PR