Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs

We consider the adjacency matrix $A$ of a large random graph and study fluctuations of the function $f_n(z,u)=\frac{1}{n}\sum_{k=1}^n\exp\{-uG_{kk}(z)\}$ with $G(z)=(z-iA)^{-1}$. We prove that the moments of fluctuations normalized by $n^{-1/2}$ in the limit $n\to\infty$ satisfy the Wick relations for the Gaussian random variables. This allows us to prove central limit theorem for $\hbox{Tr}G(z)$ and then extend the result on the linear eigenvalue statistics $\hbox{Tr}\phi(A)$ of any function $\phi:\mathbb{R}\to\mathbb{R}$ which increases, together with its first two derivatives, at infinity not faster than an exponential.Comment: 22 page

Linear and nonlinear post-processing of numerically forecasted surface temperature

International audienceIn this paper we test different approaches to the statistical post-processing of gridded numerical surface air temperatures (provided by the European Centre for Medium-Range Weather Forecasts) onto the temperature measured at surface weather stations located in the Italian region of Puglia. We consider simple post-processing techniques, like correction for altitude, linear regression from different input parameters and Kalman filtering, as well as a neural network training procedure, stabilised (i.e. driven into the absolute minimum of the error function over the learning set) by means of a Simulated Annealing method. A comparative analysis of the results shows that the performance with neural networks is the best. It is encouraging for systematic use in meteorological forecast-analysis service operations

An application of the saturated attractor analysis to three typical models Lect

The saturated attractor analysis, an approach proposed first in [FP] for a comprehensive study of the dynamics of the Linsker model and then successfully applied to the dynamic link model[FT1], is further developed here. By a unified approach to the Hopfield model, the Linsker model and the dynamic link model, three typical models in the field of the neural networks, we show a way to choose the parameters of these dynamics in order to obtain any chosen saturated attractor which is general enough in most applications. We generalize our previous results for the Linsker model and the dynamic link model with the clipping function to the case of the sigmoid like function. Our results allow us for the first time to understand the underlying mechanism among these models and thus to furnish a useful guidance in the further possible applications. The past decade has seen an explosive growth in the studies of neural networks, the theory underlying learning and computing in networks has developed into a mature subfield existing somewhere between mathematics, physics, computer science and neurobiology. In part this was the result of many deep and interesting theoretical exposition in physics and mathematics, for example, the application of th