Formation of the frozen core in critical Boolean Networks

We investigate numerically and analytically the formation of the frozen core in critical random Boolean networks with biased functions. We demonstrate that a previously used efficient algorithm for obtaining the frozen core, which starts from the nodes with constant functions, fails when the number of inputs per node exceeds 4. We present computer simulation data for the process of formation of the frozen core and its robustness, and we show that several important features of the data can be derived by using a mean-field calculation

Scaling laws in critical random Boolean networks with general in- and out-degree distributions

We evaluate analytically and numerically the size of the frozen core and various scaling laws for critical Boolean networks that have a power-law in- and/or out-degree distribution. To this purpose, we generalize an efficient method that has previously been used for conventional random Boolean networks and for networks with power-law in-degree distributions. With this generalization, we can also deal with power-law out-degree distributions. When the power-law exponent is between 2 and 3, the second moment of the distribution diverges with network size, and the scaling exponent of the nonfrozen nodes depends on the degree distribution exponent. Furthermore, the exponent depends also on the dependence of the cutoff of the degree distribution on the system size. Altogether, we obtain an impressive number of different scaling laws depending on the type of cutoff as well as on the exponents of the in- and out-degree distributions. We confirm our scaling arguments and analytical considerations by numerical investigations

Regional Imbalances and Aggregate Performance in a Leading Sector Model of the Labour Market: An analysis of Italian data 1977-1991

This paper presents a model in which wages throughout the economy depend only on the labour market conditions in some low-unemployment sector. In equilibrium, a labour demand shift towards the primary sector tends to raise the unemployment rate everywhere else in the economy and leaves wages unchanged. Overall this implies an increase in aggregate unemployment. Based on SHIW micro data for the period 1977-1991 we find that wages in Italy depend only on the tightness of the labour market in the North. We estimate that around 15% of the increase in aggregate unemployment in Italy can be explained by a shift in labour demand in favour of the North not matched by an equal shift in labour supply.

Regional Mismatch and Unemployment: Theory and Evidence from Italy, 1977-1998

This paper describes the functioning of a two-region economy characterized by asymmetric wage-setting. Labor market tightness in one region (the leading-region) affects wages in the whole economy. In equilibrium, net labor demand shifts towards the leading region raise unemployment in the rest of the economy and leave regional wages unchanged, causing an increase in aggregate unemployment. This model has some success in explaining the evolution of regional unemployment rates in Italy during the period 1977-1998. Based on SHIW micro data on earnings and ISTAT data on unemployment rates we find strong evidence that wages in Italy only respond to labor market tightness in the North. We estimate that around one third of the increase in aggregate unemployment in Italy can be explained by regional mismatch, mainly due to an excess labor supply growth in the South.regional imbalances; wage curve; unemployment.

Self-similar gelling solutions for the coagulation equation with diagonal kernel

We consider Smoluchowski's coagulation equation in the case of the diagonal kernel with homogeneity $\gamma>1$. In this case the phenomenon of gelation occurs and solutions lose mass at some finite time. The problem of the existence of self-similar solutions involves a free parameter $b$, and one expects that a physically relevant solution (i.e. nonnegative and with sufficiently fast decay at infinity) exists for a single value of $b$, depending on the homogeneity $\gamma$. We prove this picture rigorously for large values of $\gamma$. In the general case, we discuss in detail the behaviour of solutions to the self-similar equation as the parameter $b$ changes

Multiclass latent locally linear support vector machines

Kernelized Support Vector Machines (SVM) have gained the status of off-the-shelf classifiers, able to deliver state of the art performance on almost any problem. Still, their practical use is constrained by their computational and memory complexity, which grows super-linearly with the number of training samples. In order to retain the low training and testing complexity of linear classifiers and the exibility of non linear ones, a growing, promising alternative is represented by methods that learn non-linear classifiers through local combinations of linear ones. In this paper we propose a new multi class local classifier, based on a latent SVM formulation. The proposed classifier makes use of a set of linear models that are linearly combined using sample and class specific weights. Thanks to the latent formulation, the combination coefficients are modeled as latent variables. We allow soft combinations and we provide a closed-form solution for their estimation, resulting in an efficient prediction rule. This novel formulation allows to learn in a principled way the sample specific weights and the linear classifiers, in a unique optimization problem, using a CCCP optimization procedure. Extensive experiments on ten standard UCI machine learning datasets, one large binary dataset, three character and digit recognition databases, and a visual place categorization dataset show the power of the proposed approach

Monte Carlo determination of the critical coupling in ϕ24\phi^4_2 theory

We use lattice formulation of $\phi^4$ theory in order to investigate non--perturbative features of its continuum limit in two dimensions. In particular, by means of Monte Carlo calculations, we obtain the critical coupling constant $g/\mu^2$ in the continuum, where $g$ is the {\em unrenormalised} coupling. Our final result is $g/\mu^2=11.15(6)(3)$.Comment: Version published on Phys. Rev. D. We added a reference and modified a couple of sentence

QCD Hard Scattering and the Sign of the Spin Asymmetry A_LL^pi

Recent preliminary PHENIX data are consistent with a negative and sizable longitudinal double-spin asymmetry A_LL^pi for pi^0 production at moderate transverse momentum p_perp \simeq 1 - 4 GeV and central rapidity. By means of a systematic investigation of the relevant degrees of freedom we show that the perturbative QCD framework at leading power in p_perp produces at best a very small negative asymmetry in this kinematic range.Comment: 4 pages, 3 figures, final version published in PRL (only minor changes; note: title changed in published version