Parallel Tempering for the planted clique problem

The theoretical information threshold for the planted clique problem is $2\log_2(N)$, however no polynomial algorithm is known to recover a planted clique of size $O(N^{1/2-\epsilon})$, $\epsilon>0$. In this paper we will apply a standard method for the analysis of disordered models, the Parallel-Tempering (PT) algorithm, to the clique problem, showing numerically that its time-scaling in the hard region is indeed polynomial for the analyzed sizes. We also apply PT to a different but connected model, the Sparse Planted Independent Set problem. In this situation thresholds should be sharper and finite size corrections should be less important. Also in this case PT shows a polynomial scaling in the hard region for the recovery.Comment: 12 pages, 5 figure

Real Space Renormalization Group Theory of Disordered Models of Glasses

We develop a real space renormalisation group analysis of disordered models of glasses, in particular of the spin models at the origin of the Random First Order Transition theory. We find three fixed points respectively associated to the liquid state, to the critical behavior and to the glass state. The latter two are zero-temperature ones; this provides a natural explanation of the growth of effective activation energy scale and the concomitant huge increase of relaxation time approaching the glass transition. The lower critical dimension depends on the nature of the interacting degrees of freedom and is higher than three for all models. This does not prevent three dimensional systems from being glassy. Indeed, we find that their renormalisation group flow is affected by the fixed points existing in higher dimension and in consequence is non-trivial. Within our theoretical framework the glass transition results to be an avoided phase transition.Comment: 6 pages, 3 figure

The Super-Potts glass: a new disordered model for glass-forming liquids

We introduce a new disordered system, the Super-Potts model, which is a more frustrated version of the Potts glass. Its elementary degrees of freedom are variables that can take M values and are coupled via pair-wise interactions. Its exact solution on a completely connected lattice demonstrates that for large enough M it belongs to the class of mean-field systems solved by a one step replica symmetry breaking Ansatz. Numerical simulations by the parallel tempering technique show that in three dimensions it displays a phenomenological behaviour similar to the one of glass-forming liquids. The Super-Potts glass is therefore the first long-sought disordered model allowing one to perform extensive and detailed studies of the Random First Order Transition in finite dimensions. We also discuss its behaviour for small values of M, which is similar to the one of spin-glasses in a field.Comment: 6 pages, 3 figure

Spin Glass in a Field: a New Zero-Temperature Fixed Point in Finite Dimensions

By using real space renormalisation group (RG) methods we show that spin-glasses in a field display a new kind of transition in high dimensions. The corresponding critical properties and the spin-glass phase are governed by two non-perturbative zero temperature fixed points of the RG flow. We compute the critical exponents, discuss the RG flow and its relevance for three dimensional systems. The new spin-glass phase we discovered has unusual properties, which are intermediate between the ones conjectured by droplet and full replica symmetry breaking theories. These results provide a new perspective on the long-standing debate about the behaviour of spin-glasses in a field.Comment: 5 pages, 3 figure

Monte Carlo algorithms are very effective in finding the largest independent set in sparse random graphs

The effectiveness of stochastic algorithms based on Monte Carlo dynamics in solving hard optimization problems is mostly unknown. Beyond the basic statement that at a dynamical phase transition the ergodicity breaks and a Monte Carlo dynamics cannot sample correctly the probability distribution in times linear in the system size, there are almost no predictions nor intuitions on the behavior of this class of stochastic dynamics. The situation is particularly intricate because, when using a Monte Carlo based algorithm as an optimization algorithm, one is usually interested in the out of equilibrium behavior which is very hard to analyse. Here we focus on the use of Parallel Tempering in the search for the largest independent set in a sparse random graph, showing that it can find solutions well beyond the dynamical threshold. Comparison with state-of-the-art message passing algorithms reveals that parallel tempering is definitely the algorithm performing best, although a theory explaining its behavior is still lacking.Comment: 14 pages, 12 figure

Integrated surveying for the archaeological documentation of a neolithic site

It has been tested the applicability of integrated surveys (remote sensing, digital photogrammetry and terrestrial laser scanning (TLS)) in order to verify, through gradual and successive steps, how geomatic techniques can get 3D results with metric value combined with a quality content for an archaeological site. In particular, the data have been collected during the excavation campaign of Neolithic archaeological site in Taranto. The possibilities to scan articulated forms, in the presence of curve, concavity and convexity, and jutting parts rotate, characterized by alterations, through the acquisition of a dense points cloud makes the technique TLS needed in archaeology. Through the photogrammetric technique the laser data has been integrated concerning some details found on the site for which it has been required a higher degree of detail. The photogrammetric data has been acquired with the calibrated camera. The processing of the acquired data and their integration has been made possible to study an important archeological site, in its totality, from small scale (general site framework) to large scale (3D model with a high degree of detail) and to structure a multi-temporal database for simplified data management

One-loop topological expansion for spin glasses in the large connectivity limit

We apply for the first time a new one-loop topological expansion around the Bethe solution to the spin-glass model with field in the high connectivity limit, following the methodological scheme proposed in a recent work. The results are completely equivalent to the well known ones, found by standard field theoretical expansion around the fully connected model (Bray and Roberts 1980, and following works). However this method has the advantage that the starting point is the original Hamiltonian of the model, with no need to define an associated field theory, nor to know the initial values of the couplings, and the computations have a clear and simple physical meaning. Moreover this new method can also be applied in the case of zero temperature, when the Bethe model has a transition in field, contrary to the fully connected model that is always in the spin glass phase. Sharing with finite dimensional model the finite connectivity properties, the Bethe lattice is clearly a better starting point for an expansion with respect to the fully connected model. The present work is a first step towards the generalization of this new expansion to more difficult and interesting cases as the zero-temperature limit, where the expansion could lead to different results with respect to the standard one.Comment: 8 pages, 1 figur

Ensemble renormalization group for disordered systems

We propose and study a renormalization group transformation that can be used also for models with strong quenched disorder, like spin glasses. The method is based on a mapping between disorder distributions, chosen such as to keep some physical properties (e.g., the ratio of correlations averaged over the ensemble) invariant under the transformation. We validate this ensemble renormalization group by applying it to the hierarchical model (both the diluted ferromagnetic version and the spin glass version), finding results in agreement with Monte Carlo simulations.Comment: 7 pages, 10 figure

R&D Subsidization effect and network centralization. Evidence from an agent-based micro-policy simulation

This paper presents an agent-based micro-policy simulation model assessing public R&D policy effect when R&D and non-R&D performing companies are located within a network. We set out by illustrating the behavioural structure and the computational logic of the proposed model; then, we provide a simulation experiment where the pattern of the total level of R&D activated by a fixed amount of public support is analysed as function of companies’ network topology. More specifically, the suggested simulation experiment shows that a larger “hubness” of the network is more likely accompanied with a decreasing median of the aggregated total R&D performance of the system. Since the aggregated firm idiosyncratic R&D (i.e., the part of total R&D independent of spillovers) is slightly increasing, we conclude that positive cross-firm spillover effects - in the presence of a given amount of support - have a sizeable impact within less centralized networks, where fewer hubs emerge. This may question the common wisdom suggesting that larger R&D externality effects should be more likely to arise when few central champions receive a support

The interbank market after August 2007: what has changed, and why?

The outbreak of the financial crisis coincided with a sharp increase of worldwide interbank interest rates. We analyze the micro and macroeconomic determinants of this phenomenon, finding that before August 2007 interbank rates were insensitive to borrower characteristics, whereas afterwards they became reactive to borrowers’ creditworthiness. At the same time, conditions for large borrowers became relatively more favorable, both before and after the failure of Lehman Brothers. This suggests that banks have become more discerning in their lending, a welcome change, but that moral hazard considerations related to the â€too big to fail†argument should remain a main concern for central banks.Interbank markets, Spreads, Financial crisis