Power grids exhibit patterns of reaction to outages similar to complex networks. Blackout sequences follow power laws, as complex systems operating near a critical point. Here, the tolerance of electric power grids to both accidental and malicious outages is analyzed in the framework of complex network theory. In particular, the quantity known as efficiency is modified by introducing a new concept of distance between nodes. As a result, a new parameter called net-ability is proposed to evaluate the performance of power grids. A comparison between efficiency and net-ability is provided by estimating the vulnerability of sample networks, in terms of both the metrics.

The Hurst exponent H of long range correlated series can be estimated by means of the Detrending Moving Average (DMA) method. A computational tool defined within the algorithm is, with y n (i) = 1/n k y(i − k) the moving average, n the moving average window and N the dimension of the stochastic series y(i).This ability relies on the property of σ 2 DM A to scale as n 2H . Here, we analytically show that σ 2 DM A is equivalent to C H n 2H for n ≫ 1 and provide an explicit expression for C H .

A method for estimating the cross-correlation C xy (τ ) of long-range correlated series x(t) and y(t), at varying lags τ and scales n, is proposed. For fractional Brownian motions with Hurst exponents H 1 and H 2 , the asymptotic expression of C xy (τ ) depends only on the lag τ (wide-sense stationarity) and scales as a power of n with exponent H 1 + H 2 for τ → 0. The method is illustrated on (i ) financial series, to show the leverage effect; (ii ) genomic sequences, to estimate the correlations between structural parameters along the chromosomes.

We show how non-compact (quantum 2d AdS) space-time emerges for specific ratios of the square of the boundary cosmological constant to the cosmological constant in 2d Euclidean quantum gravity.

A consistent formulation of a fully supersymmetric theory on the lattice has been a long standing challenge. In recent years there has been a renewed interest on this problem with different approaches. At the basis of the formulation we present in the following there is the Dirac-Kähler twisting procedure, which was proposed in the continuum for a number of theories, including N = 4 SUSY in four dimensions. Following the formalism developed in recent papers, an exact supersymmetric theory with two supercharges on a one dimensional lattice is realized using a matrix-based model. The matrix structure is obtained from the shift and clock matrices used in two dimensional non-commutative field theories. The matrix structure reproduces on a one dimensional lattice the expected modified Leibniz rule. Recent claims of inconsistency of the formalism are discussed and shown not to be relevant.

In this work, higher-order moving average polynomials are defined by straightforward generalization of the standard moving average. The self-similarity of the polynomials is analyzed for fractional Brownian series and quantified in terms of the Hurst exponent H by using the detrending moving average method. We prove that the exponent H of the fractional Brownian series and of the detrending moving average variance asymptotically agree for the first-order polynomial. Such asymptotic values are compared with the results obtained by the simulations. The higher-order polynomials correspond to trend estimates at shorter time scales as the degree of the polynomial increases. Importantly, the increase of polynomial degree does not require to change the moving average window. Thus trends at different time scales can be obtained on data sets with the same size. These polynomials could be interesting for those applications relying on trend estimates over different time horizons (financial markets) or on filtering at different frequencies (image analysis).

Following the approach developed by some of the authors in recent papers and using a matrix representation for the superfields, we formulate an exact supersymmetric theory with two supercharges on a one dimensional lattice. In the superfield formalism supersymmetry transformations are uniquely defined and do not suffer of the ambiguities recently pointed out by some authors. The action can be written in a unique way and it is invariant under all supercharges. A modified Leibniz rule applies when supercharges act on a superfield product and the corresponding Ward identities take a modified form but hold exactly at least at the tree level, while their validity in presence of radiative corrections is still an open problem and is not considered here. * arianos@to.infn.it † dadda@to.infn.it ‡

Inspired by the interpretation of two dimensional Yang-Mills theory on a cylinder as a random walk on the gauge group, we point out the existence of a large N transition which is the gauge theory analogue of the cutoff transition in random walks. The transition occurs in the strong coupling region, with the 't Hooft coupling scaling as alpha*log(N), at a critical value of alpha (alpha = 4 on the sphere). The two phases below and above the transition are studied in detail. The effective number of degrees of freedom and the free energy are found to be proportional to N^(2-alpha/2) below the transition and to vanish altogether above it. The expectation value of a Wilson loop is calculated to the leading order and found to coincide in both phases with the strong coupling value.Comment: 23 pages, 3 figure