About the ergodic regime in the analogical Hopfield neural networks. Moments of the partition function

In this paper we introduce and exploit the real replica approach for a minimal generalization of the Hopfield model, by assuming the learned patterns to be distributed accordingly to a standard unit Gaussian. We consider the high storage case, when the number of patterns is linearly diverging with the number of neurons. We study the infinite volume behavior of the normalized momenta of the partition function. We find a region in the parameter space where the free energy density in the infinite volume limit is self-averaging around its annealed approximation, as well as the entropy and the internal energy density. Moreover, we evaluate the corrections to their extensive counterparts with respect to their annealed expressions. The fluctuations of properly introduced overlaps, which act as order parameters, are also discussed.Comment: 15 page

Spin Glass Computations and Ruelle's Probability Cascades

We study the Parisi functional, appearing in the Parisi formula for the pressure of the SK model, as a functional on Ruelle's Probability Cascades (RPC). Computation techniques for the RPC formulation of the functional are developed. They are used to derive continuity and monotonicity properties of the functional retrieving a theorem of Guerra. We also detail the connection between the Aizenman-Sims-Starr variational principle and the Parisi formula. As a final application of the techniques, we rederive the Almeida-Thouless line in the spirit of Toninelli but relying on the RPC structure.Comment: 20 page

A(e⃗,e′p⃗)(\vec{e},e'\vec{p})B responses: from bare nucleons to complex nuclei

We study the occurrence of factorization in polarized and unpolarized observables in coincidence quasi-elastic electron scattering. Starting with the relativistic distorted wave impulse approximation, we reformulate the effective momentum approximation and show that the latter leads to observables which factorize under some specific conditions. Within this framework, the role played by final state interactions and, in particular, by the spin-orbit term is explored. Connection with the nonrelativistic formalism is studied in depth. Numerical results are presented to illustrate the analytical derivations and to quantify the differences between factorized and unfactorized approaches.Comment: 26 pages, 5 figures. Improved and extended version. To be published in Phys. Rev.

Unitized regenerative polymeric fuel cell modeling

The research's objective is to have a single machine to function as fuel cell and electrolyser based and needs, that is to say, unitized regenerative fuel cell (when fed to the machine with electric power and water flows will be obtained and H2 and O2 and conversely when the machine is fuelled with H2 and O2 will get water, heat and electricity) The study focuses on polymeric fuel cells and polymeric electrolysers. The development of this machine will make a very significant cost reduction (currently to use hydrogen as an energy store needed the electrolyser and fuel cell) as a single machine may replace the fuel cell and electrolyser. The achievement of the objective mentioned above, have been going by completing a series of stages. The stages addressed in this work are: ¿ A first stage, which will be studied in detail the polymeric fuel cells and polymeric electrolysers, in order to see the similarities between the machines and to design the unitized regenerative fuel cell. ¿ A second stage of simulation, which will develop models to show the behaviour of the unitized regenerative fuel cell and compare results with those obtained from the theoretical. ¿ A third stage of model verification generated polymer fuel cells and electrolyzers polymer on the market

Hints on the quadrupole deformation of the Δ\Delta(1232)

The E2/M1 ratio (EMR) of the $\Delta$(1232) is extracted from the world data in pion photoproduction by means of an Effective Lagrangian Approach (ELA).This quantity has been derived within a crossing symmetric, gauge invariant, and chiral symmetric Lagrangian model which also contains a consistent modern treatment of the $\Delta$(1232) resonance. The \textit{bare} s-channel $\Delta$(1232) contribution is well isolated and Final State Interactions (FSI) are effectively taken into account fulfilling Watson's theorem. The obtained EMR value, EMR$=(-1.30\pm0.52)$%, is in good agreement with the latest lattice QCD calculations [Phys. Rev. Lett. 94, 021601 (2005)] and disagrees with results of current quark model calculations.Comment: Enlarged conclusions and explanations on the E2/M1 ratio. Figure 3 improved. References updated. 5 pages. 3 figures. 2 tables. Accepted for publication in Physical Review

Local Spin Glass Order in 1D

We study the behavior of one dimensional Kac spin glasses as function of the interaction range. We verify by Montecarlo numerical simulations the crossover from local mean field behavior to global paramagnetism. We investigate the behavior of correlations and find that in the low temperature phase correlations grow at a faster rate then the interaction range. We completely characterize the growth of correlations in the vicinity of the mean-field critical region