A Moser-Trudinger inequality for the singular Toda system

In this paper we prove a sharp version of the Moser-Trudinger inequality for the Euler-Lagrange functional of a singular Toda system, motivated by the study of models in Chern-Simons theory. Our result extends those for the scalar case, as well as for the regular Toda system. We expect this inequality to be a basic tool to attack variationally the existence problem under general assumptions.Comment: 13 pages, accepted on Bulletin of the Institute of Mathematica Academia Sinic

Existence and non-existence results for the SU(3) singular Toda system on compact surfaces

We consider the SU(3) Toda system on a compact surface. We give both existence and non-existence results under some conditions on the parameters. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Pohozaev identities.Comment: 41 pages, 9 figures, accepted on Journal of Functional Analysi

About the Chemical Evolution of dSphs (and the peculiar Globular Cluster Omega Cen)

We present three dimensional hydrodynamical simulations aimed at studying the dynamical and chemical evolution of the interstellar medium (ISM) in isolated dwarf spheroidal galaxies (dSphs). This evolution is driven by the explosion of Type II and Type Ia supernovae, whose different contribution on both the dynamics and chemical enrichment is taken into account. Radiative losses are effective in radiating away the huge amount of energy released by SNe explosions, and the dSph is able to retain most of the gas allowing a long period (>2-3 Gyr) of star formation, as usually observed in this kind of galaxies. We are able to reproduce the stellar metallicity distribution function (MDF) as well as the peculiar chemical properties of strongly O-depleted stars observed in several dSphs. The model also naturally predicts two different stellar populations, with an anti-correlation between [Fe/H] and velocity dispersion, similarly to what observed in the Sculptor and Fornax dSphs. These results derive from the inhomogeneous pollution of the SNe Ia, a distinctive characteristic of our model. We also applied the model to the peculiar globular cluster (GC) Omega Cen in the hypothesis that it is the remnant of a formerly larger stellar system, possibly a dSph.Comment: To appear in the IAU Symposium 255, "Low-Metallicity Star Formation: From the First stars to Dwarf Galaxies", contributed talk, 5 page

Metodi euristici per il Vehicle Routing Problem

Il problema della consegna di prodotti da un deposito/impianto ai clienti mediante una flotta di automezzi è un problema centrale nella gestione di una catena di produzione e distribuzione (supply chain). Questo problema, noto in letteratura come Vehicle Routing Problem (VRP), nella sua versione più semplice consiste nel disegnare per ogni veicolo disponibile presso un dato deposito aziendale un viaggio (route) di consegna dei prodotti ai clienti, che tali prodotti richiedono, in modo tale che (i) la somma delle quantità richieste dai clienti assegnati ad ogni veicolo non superi la capacità del veicolo, (ii) ogni cliente sia servito una ed una sola volta, (iii) sia minima la somma dei costi dei viaggi effettuati dai veicoli. Il VRP è un problema trasversale ad una molteplicità di settori merceologici dove la distribuzione dei prodotti e/o servizi avviene mediante veicoli su gomma, quali ad esempio: distribuzione di generi alimentari, distribuzione di prodotti petroliferi, raccolta e distribuzione della posta, organizzazione del servizio scuolabus, pianificazione della manutenzione di impianti, raccolta rifiuti, etc. In questa tesi viene considerato il Multi-Trip VRP, in cui ogni veicolo può eseguire un sottoinsieme di percorsi, chiamato vehicle schedule (schedula del veicolo), soggetto a vincoli di durata massima. Nonostante la sua importanza pratica, il MTVRP ha ricevuto poca attenzione in letteratura: sono stati proposti diversi metodi euristici e un solo algoritmo esatto di risoluzione, presentato da Mingozzi, Roberti e Toth. In questa tesi viene presentato un metodo euristico in grado di risolvere istanze di MTVRP in presenza di vincoli reali, quali flotta di veicoli non omogenea e time windows. L’euristico si basa sul modello di Prins. Sono presentati inoltre due approcci di local search per migliorare la soluzione finale. I risultati computazionali evidenziano l’efficienza di tali approcci

A general existence result for the Toda system on compact surfaces

In this paper we consider the Toda system of equations on a compact surface, which is motivated by the study of models in non-abelian Chern-Simons theory. We prove a general existence result using variational methods. The same analysis applies to a mean field equation which arises in fluid dynamics.Comment: 28 pages, 1 figure, accepted on Advances in Mathematic

Functional connectivity and neuronal dynamics: insights from computational methods

International audienceBrain functions rely on flexible communication between microcircuits in distinct cortical regions. The mechanisms underlying flexible information routing are still, however, largely unknown. Here, we hypothesize that the emergence of a multiplicity of possible information routing patterns is due to the richness of the complex dynamics that can be supported by an underlying structural network. Analyses of circuit computational models of interacting brain areas suggest that different dynamical states associated with a given connectome mechanistically implement different information routing patterns between system's components. As a result, a fast, network-wide and self-organized reconfiguration of information routing patterns-and Functional Connectivity networks, seen as their proxy-can be achieved by inducing a transition between the available intrinsic dynamical states. We present here a survey of theoretical and modelling results, as well as of sophisticated metrics of Functional Connectivity which are compliant with the daunting task of characterizing dynamic routing from neural data. Theory: Function follows dynamics, rather than structure Neuronal activity conveys information, but which target should this information be-pushed‖ to, or which source should new information be-pulled‖ from? The problem of dynamic information routing is ubiquitous in a distributed information processing system as the brain. Brain functions in general require the control of distributed networks of interregional communication on fast timescales compliant with behavior, but incompatible with plastic modifications of connectivity tracts (Bressler & Kelso, 2001; Varela et al., 2001). This argument led to notions of connectivity based on information exchange-or more generically, an-interaction‖-between brain regions or neuronal populations, rather than based on the underlying STRUCTURAL CONNECTIVITY (SC, i.e. anatomic). An entire zoo of data-driven metrics has been introduced in the literature and this chapter will review some of them. Notwithstanding, they track simple correlation, or directed causal influence (Friston, 2011) or information transfer (Wibral et al., 2014) between time-series of activity. Thes

The impact of privacy and cybersecurity on e-record: The PNR Directive Adoption and the impact of GDPR

Digital transformation means radically change how we manage interaction with everything, including goods, persons and data flows. Cyberspace is by nature borderless and open to everybody, and any sensitive personal info passing through it should be appropriately managed to ensure the protection of the users' identity and other personal records. The Passenger Name Record (EU Directive 2016/681) impacts for travellers, e-wallets for online shoppers, medical e-records for patients, etc., which may contain personal information provided by the users and collected by the service providers during the on-line transaction. While such records need to be shared for the smooth operation of the provided service, evidence shows that such sharing does not always respect the privacy of the data subjects. This paper address this challenge by proposing a comprehensive solution to safeguard and protect such on-line info and to preserve and protect the users’ privacy (GDPR) in order to improve the cybersecurity aspects at EU level with a focus on transports and blockchain