The backtracking survey propagation algorithm for solving random K-SAT problems

Discrete combinatorial optimization has a central role in many scientific disciplines, however, for hard problems we lack linear time algorithms that would allow us to solve very large instances. Moreover, it is still unclear what are the key features that make a discrete combinatorial optimization problem hard to solve. Here we study random K-satisfiability problems with $K=3,4$, which are known to be very hard close to the SAT-UNSAT threshold, where problems stop having solutions. We show that the backtracking survey propagation algorithm, in a time practically linear in the problem size, is able to find solutions very close to the threshold, in a region unreachable by any other algorithm. All solutions found have no frozen variables, thus supporting the conjecture that only unfrozen solutions can be found in linear time, and that a problem becomes impossible to solve in linear time when all solutions contain frozen variables.Comment: 11 pages, 10 figures. v2: data largely improved and manuscript rewritte

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

Generalized off-equilibrium fluctuation-dissipation relations in random Ising systems

We show that the numerical method based on the off-equilibrium fluctuation-dissipation relation does work and is very useful and powerful in the study of disordered systems which show a very slow dynamics. We have verified that it gives the right information in the known cases (diluted ferromagnets and random field Ising model far from the critical point) and we used it to obtain more convincing results on the frozen phase of finite-dimensional spin glasses. Moreover we used it to study the Griffiths phase of the diluted and the random field Ising models.Comment: 20 pages, 10 figures, uses epsfig.sty. Partially presented at StatPhys XX in a talk by one of the authors (FRT). Added 1 reference in the new versio

Long term effects of mesoglycan on brachial arterial stiffness and MMP-9/TIMP-1 system in patients with metabolic syndrome

Objectives: The aim of this study was to evaluate the chronic effects of mesoglycan on the vascular remodeling in patients with metabolic syndrome (Mets). Background: MetS is defined by a clustering of vascular risk factors that require both pharmacologic and non-pharmacologic interventions, including body weight reductions and physical activity. The correction of vascular remodeling associated with MetS has lately received increasing interest. Methods: Thirty consecutive ambulatory patients affected by MetS were 2:1 randomized in a doubleblind fashion to receive mesoglycan or placebo, respectively. At the beginning and after 90 days of oral treatment we appraised the effects of mesoglycan (50 mg per os bid) or placebo on vascular remodeling, as assessed by the measurement of arterial wall elastic properties. Moreover, the matrix metalloproteinase’s (MMPs) type 9 and tissue inhibitor of metalloproteinase (TIMP) type 1 were analyzed by enzyme-linked immune sorbent assay (ELISA) and gelatin substrate zymography at the beginning of the study and after 90 days of treatment. Results: After 90 days of treatment, a marked improvement of arterial distensibility and compliance was detected in Mesoglycan group, with associated significant reduction of arterial stiffness, and a significant reduction of serum levels of MMP-9 and TIMP-1 and significant reduction of enzyme activity of MMPs. Conclusions: This small, preliminary study shows that mesoglycan exerts relevant effects on vascular remodeling after three-month treatment, in patients affected by metabolic syndrome