Cecilia Vernia

An analysis of a large dataset on immigrant integration in Spain. The Statistical Mechanics perspective on Social Action

How does immigrant integration in a country change with immigration density? Guided by a statistical mechanics perspective we propose a novel approach to this problem. The analysis focuses on classical integration quantifiers such as the percentage of jobs (temporary and permanent) given to immigrants, mixed marriages, and newborns with parents of mixed origin. We find that the average values of different quantifiers may exhibit either linear or non-linear growth on immigrant density and we suggest that social action, a concept identified by Max Weber, causes the observed non-linearity. Using the statistical mechanics notion of interaction to quantitatively emulate social action, a unified mathematical model for integration is proposed and it is shown to explain both growth behaviors observed. The linear theory instead, ignoring the possibility of interaction effects would underestimate the quantifiers up to 30% when immigrant densities are low, and overestimate them as much when densities are high. The capacity to quantitatively isolate different types of integration mechanisms makes our framework a suitable tool in the quest for more efficient integration policies.

Ultrametricity in the Edwards-Anderson Model

We test the property of ultrametricity for the spin-glass three-dimensional Edwards-Anderson model in zero magnetic field with numerical simulations up to 20(3) spins. We find an excellent agreement with the prediction of the mean field theory. Since ultrametricity is not compatible with a trivial structure of the overlap distribution, our result contradicts the droplet theory.

A stochastic approach for quantifying immigrant integration: the Spanish test case

We apply stochastic process theory to the analysis of immigrant integration. Using a unique and detailed data set from Spain, we study the relationship between local immigrant density and two social and two economic immigration quantifiers for the period 1999?2010. As opposed to the classic time-series approach, by letting immigrant density play the role of ?time? and the quantifier the role of ?space,? it becomes possible to analyse the behavior of the quantifiers by means of continuous time random walks. Two classes of results are then obtained. First, we show that social integration quantifiers evolve following diffusion law, while the evolution of economic quantifiers exhibits ballistic dynamics. Second, we make predictions of best- and worst-case scenarios taking into account large local fluctuations. Our stochastic process approach to integration lends itself to interesting forecasting scenarios which, in the hands of policy makers, have the potential to improve political responses to integration problems. For instance, estimating the standard first-passage time and maximum-span walk reveals local differences in integration performance for different immigration scenarios. Thus, by recognizing the importance of local fluctuations around national means, this research constitutes an important tool to assess the impact of immigration phenomena on municipal budgets and to set up solid multi-ethnic plans at the municipal level as immigration pressures build.

Normally attracting manifolds and periodic behavior in one‐dimensional and two‐dimensional coupled map lattices

We consider diffusively coupled logistic maps in one- and two-dimensional lattices. We investigate periodic behaviors as the coupling parameter varies, i.e., existence and bifurcations of some periodic orbits with the largest domain of attraction. Similarity and differences between the two lattices are shown. For small coupling the periodic behavior appears to be characterized by a number of periodic orbits structured in such a way to give rise to distinct, reverse period-doubling sequences. For intermediate values of the coupling a prominent role in the dynamics is played by the presence of normally attracting manifolds that contain periodic orbits. The dynamics on these manifolds is very weakly hyperbolic, which implies long transients. A detailed investigation allows the understanding of the mechanism of their formation. A complex bifurcation is found which causes an attracting manifold to become unstable. (c) 1994 American Institute of Physics.

ON THE PRESENCE OF NORMALLY ATTRACTING MANIFOLDS CONTAINING PERIODIC OR QUASIPERIODIC ORBITS IN COUPLED MAP LATTICES

The significant presence of normally attracting invariant manifolds, formed by closed curves or two-tori, is investigated in two-dimensional lattices of coupled chaotic maps. In the case of a manifold formed by closed curves, it contains symmetrically placed periodic orbits, with the property of a very weak hyperbolicity along the manifold itself. The resulting dynamics is an extremely slow relaxation to periodic behavior. Analogously, a manifold consisting of two-tori includes very weakly hyperbolic periodic (or quasiperiodic) orbits, which in this case also implies quite a long time before any solution approaches periodicity or quasiperiodicity. The normally attracting manifolds and the contained weak attractors can undergo several global bifurcations. Some of them, including saddle-node bifurcation, period-doubling and Hopf bifurcation, are illustrated. Almost all the asymptotic solutions that we discuss have flat rows or flat columns, which means that they can occur also in one-dimensional lattices.

Asymmetric fluctuation-relaxation paths in FPU models

A recent theory by Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim predicts a temporal asymmetry in the fluctuation-relaxation paths of certain observables of nonequilibrium systems in local thermodynamic equilibrium. We find temporal asymmetries in the fluctuation-relaxation paths of a form of local heat flow, in the nonequilibrium FPU-

Interpolating greedy and reluctant algorithms

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Inverse problem robustness for multi-species mean-field spin models

model of Lepri, Livi and Politi.

Structure of correlations in three dimensional spin glasses

In a standard NP-complete optimization problem, we introduce an interpolating algorithm between the quick decrease along the steepest descent direction (greedy dynamics) and a slow decrease close to the level curves (reluctant dynamics). We find that, for a fixed elapsed computer time, the best performance of the optimization is reached at a special value of the interpolation parameter, considerably improving the results of the pure cases of greedy and reluctant.

On quasiperiodic travelling waves in coupled map lattices

The inverse problem method is tested for a class of mean-field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical parameters,systemsizesandindependentsamples.Weshowhowtoreconstruct the parameter values with a precision of a few per cent.