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A simple classical non-local dynamical system with random initial conditions and an output projecting the state variable on selected axes has been defined to mimic a two-channel quantum coincidence experiment. Non-locality is introduced by a parameter connecting the initial conditions to the selection of the projection axes. The statistics of the results shows violations up to 100% of the Bell's inequality, in the form of Clauser-Horne- Shimony-Holt (CHSH), strongly depending on the non-locality parameter. Discussions on the parallelism with Bohmian mechanics are given., Comment: 11 pages, 7 Figures

We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental parametrized optimal control problems are usually studied for different configurations described by several physical and/or geometrical parameters representing different phenomena and structures. The solution of parametrized problems requires a demanding computational effort. In order to save com- putational time, we rely on reduced basis techniques as a reliable and rapid tool to solve parametrized problems. We introduce general parametrized linear quadratic optimal control problems, and the saddle-point structure of their optimality system. Then, we propose a POD-Galerkin reduction of the optimality system. Finally, we test the resulting method on two environmental applications: a pollutant control in the Gulf of Trieste, Italy and a solution tracking governed by quasi-geostrophic equations, in its linear and nonlinear version, describing North Atlantic Ocean dynamic. The two experiments underline how reduced order methods are a reliable and convenient tool to manage several environmental optimal control problems, for different mathematical models, geographical scale as well as physical meaning., Comment: A section 5 concerning the optimal control governed by nonlinear quasi-geostrophic equations has been added

A two-layer quasi-geostrophic flow is quite insulated from the surrounding fluid, while the layers interact each other by means of the modulation of the interface between them and of the turbulence affecting the layers in the proximity of the interface. In this framework, the time evolution of the circulation of the flow along the lateral boundaries (upper and lower) is investigated under the assumption of arbitrary initial conditions. The analytic solution shows the glue-like behaviour of turbulence, which is parameterized in the standard way (Pedosky, 1996): initially the glue is wet and each layer evolves almost independently of the other while, for times far enough from that initial, the glue hardens and the system converges to a singlelayer one. Indeed, the circulation of the thinner layer tends to adjust itself in a parallel way with respect to the thicker layer and the final circulation of the consequent single-layer system is given by the average of the initial circulations, each being weighted by the thickness of the related layer.

The first aim of this work is to construct a Finite Elements model for quasi-geostrophic equation. This model is analyzed through FEniCS interface. As a second purpose, it shows the potential of the control theory to treat Data Assimilation large scale problems. In section one the finite element approximation of the quasi-geostrophic model is described. In section two some numerical results on different domains are shown. In section three a comparison between Navier Stokes model and quasi-geostrophic one is discussed. Last section is dedicated to a more complex data assimilation/control problem based on quasi-geostrophic equations, to test possible developments and improvements.

The observed pseudo-periodic reversal of the upper layer circulation of the Ionian Sea has been assumed to be related to some internal feedback processes (density driven) by the so called BiOS (Adriatic-Ionian Bimodal Oscillating System) hypothesis. The mechanism seems to be very well described by a non-linear oscillator dynamical system. By setting the state variables as the salinity of Adriatic deep water and the sea level anomaly in the Ionian region a Van der Pol equation has been obtained. The periodic cycle so obtained is of the order of a decade as observed in the data. Furthermore, a periodic term, which mimics the decadal variability of the forcing (mainly atmospheric), produces a period doubling phenomenon which is typical of the forced Van der Pol oscillator. By considering also a stochastic gaussian noise acting as a forcing and a decadal periodic input term, having an amplitude much smaller than the noise variance, a sub-harmonic stochastic resonance appears in the solution for a certain range of the values of the parameters. This yields the possibility of a longer time scale variability of the BiOS mechanism., Comment: 10 Figures

The concept of quantum correlation matrix for observables leads to the application of the PCA (Principal Component Analysis) also for quantum system in Hilbert space. It is shown that, in the case of a 2x2 spin system where the observables are the Pauli matrices and a polarization vector is acting on the density matrix, meaningful results can be obtained by the PCA in terms of qubit properties. In particular, it is shown that by choosing, for example, the (x,z) spinors, the axes of the principal components (PC) coincide with the circular polarization basis on the Block Sphere.

Perfect synchronicity in $N$-player games is a useful theoretical dream, but communication delays are inevitable and may result in asynchronous interactions. Some systems such as financial markets are asynchronous by design, and yet most theoretical models assume perfectly synchronized actions. We propose a general method to transform standard models of adaptive agents into asynchronous systems while preserving their global structure under some conditions. Using the Minority Game as an example, we find that the phase and fluctuations structure of the standard game subsists even in maximally asynchronous deterministic case, but that it disappears if too much stochasticity is added to the temporal structure of interaction. Allowing for heterogeneous communication speeds and activity patterns gives rise to a new information ecology that we study in details., Comment: 6 pages, 7 figures. New version removed a section and found a new phase transition

We review the recent approaches to modelling financial markets based on multi-agent systems. After a brief summary of the basic stylised facts observed in real-market time-series we discuss some simple agent-based systems which are currently used to model financial markets. One of the most prominent examples is here the Minority Game (MG), which we address in some more detail. After a brief discussion of its basic setup and general phenomenology we summarise the main findings of the statistical mechanics analysis and discuss the emergence of stylised facts in extensions of the MG near their phase transitions between efficient and predictable regimes. We then turn towards more realistic variants which comprise heterogeneous populations of agents, with different memory capabilities, different inclinations to trade and varying expectations on the future evolution of the market. Finally we give a short outlook on potential future work in this area., Comment: review article, 27 pages, 13 figures

Minority games where groups of agents remember, react or incorporate information with different timescales are investigated. We study how their respective gains depend on their timescales for standard models and games with no public information, and support our findings by analytical arguments whenever possible., Comment: 13 pages, 11 figures

We study the asymptotic macroscopic properties of the mixed majority-minority game, modeling a population in which two types of heterogeneous adaptive agents, namely ``fundamentalists'' driven by differentiation and ``trend-followers'' driven by imitation, interact. The presence of a fraction f of trend-followers is shown to induce (a) a significant loss of informational efficiency with respect to a pure minority game (in particular, an efficient, unpredictable phase exists only for f<1/2), and (b) a catastrophic increase of global fluctuations for f>1/2. We solve the model by means of an approximate static (replica) theory and by a direct dynamical (generating functional) technique. The two approaches coincide and match numerical results convincingly., Comment: 19 pages, 3 figures