The true reinforced random walk with bias

We consider a self-attracting random walk in dimension d=1, in presence of a field of strength s, which biases the walker toward a target site. We focus on the dynamic case (true reinforced random walk), where memory effects are implemented at each time step, differently from the static case, where memory effects are accounted for globally. We analyze in details the asymptotic long-time behavior of the walker through the main statistical quantities (e.g. distinct sites visited, end-to-end distance) and we discuss a possible mapping between such dynamic self-attracting model and the trapping problem for a simple random walk, in analogy with the static model. Moreover, we find that, for any s>0, the random walk behavior switches to ballistic and that field effects always prevail on memory effects without any singularity, already in d=1; this is in contrast with the behavior observed in the static model.Comment: to appear on New J. Phy

Reaction networks as systems for resource allocation: A variational principle for their non-equilibrium steady states

Within a fully microscopic setting, we derive a variational principle for the non-equilibrium steady states of chemical reaction networks, valid for time-scales over which chemical potentials can be taken to be slowly varying: at stationarity the system minimizes a global function of the reaction fluxes with the form of a Hopfield Hamiltonian with Hebbian couplings, that is explicitly seen to correspond to the rate of decay of entropy production over time. Guided by this analogy, we show that reaction networks can be formally re-cast as systems of interacting reactions that optimize the use of the available compounds by competing for substrates, akin to agents competing for a limited resource in an optimal allocation problem. As an illustration, we analyze the scenario that emerges in two simple cases: that of toy (random) reaction networks and that of a metabolic network model of the human red blood cell. © 2012 De Martino et al

Potential theory results for a class of PDOs admitting a global fundamental solution

We outline several results of Potential Theory for a class of linear par-tial differential operators L of the second order in divergence form. Under essentially the sole assumption of hypoellipticity, we present a non-invariant homogeneous Harnack inequality for L; under different geometrical assumptions on L (mainly, under global doubling/Poincar\ue9 assumptions), it is described how to obtainan invariant, non-homogeneous Harnack inequality. When L is equipped with a global fundamental solution \u393, further Potential Theory results are available (such as the Strong Maximum Principle). We present some assumptions on L ensuring that such a \u393 exists

Riverberazioni psicotiche in un'équipe psichiatrica.

L'articolo riporta lo studio condotto parallelamente sui pazienti ricoverati in un ospedale psichiatrico e sull'equipe curante, in occasione di un riassetto assistenziale e terapeutico rabilitativo del reparto psichiatric

Boundary regularity problems for some elliptic-parabolic equations

In this note we review some recent results in [64, 95, 96] concerning necessary and sufficient conditions for the regularity of boundary points relatively to the Dirichlet problem for linear degenerate-parabolic operators with well-behaved fundamental solutions. The main focus is on Wiener-type criteria for a class of operators whose degeneracy is controlled by Hormander vector fields

A Wiener test \ue0 la Landis for evolutive H\uf6rmander operators

In this paper we prove a Wiener-type characterization of boundary regularity, in the spirit of a classical result by Landis, for a class of evolutive H\uf6rmander operators. We actually show the validity of our criterion for a larger class of degenerate-parabolic operators with a fundamental solution satisfying suitable two-sided Gaussian bounds. Our condition is expressed in terms of a series of balayages or, (as it turns out to be) equivalently, Riesz-potentials

Attività psichiatrica: aspetti gestionali ed aspetti culturali

il contributo presenta una riflessione sulle modificazioni che si stanno producendo nei servizi psichiatrici e le ripercussioni di queste sulle strategie terapeutiche adottat

Tre bambini nel labirinto fobico-ossessivo

L'articolo riguarda la ricostruzione dei percorsi psicoterapeutici di tre bambini con sintomi fobico-ossessivi e ne descrive la diversa evoluzione in relazione alle configurazioni mentali ed affettive dei bambini stessi