Rémi Monasson

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Heuristic methods for solution of problems in the NP-complete class of decision problems often reach exact solutions, but fail badly at ‘‘phase boundaries,’’ across which the decision to be reached changes from almost always having one value to almost always having a different value. We report an analytic solution and experimental investigations of the(More)
We introduce a procedure to infer the interactions among a set of binary variables, based on their sampled frequencies and pairwise correlations. The algorithm builds the clusters of variables contributing most to the entropy of the inferred Ising model and rejects the small contributions due to the sampling noise. Our procedure successfully recovers(More)
A variational approach to finite connectivity spin-glass-like models is developed and applied to describe the structure of optimal solutions in random satisfiability problems. Our variational scheme accurately reproduces the known replica symmetric results and also allows for the inclusion of replica symmetry breaking effects. For the 3-SAT problem, we find(More)
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer science and statistical physics. This review aims at presenting the tools and concepts designed by physicists to deal(More)
Complexity of neural systems often makes impracticable explicit measurements of all interactions between their constituents. Inverse statistical physics approaches, which infer effective couplings between neurons from their spiking activity, have been so far hindered by their computational complexity. Here, we present 2 complementary, computationally(More)
Various approaches have explored the covariation of residues in multiple-sequence alignments of homologous proteins to extract functional and structural information. Among those are principal component analysis (PCA), which identifies the most correlated groups of residues, and direct coupling analysis (DCA), a global inference method based on the maximum(More)
An analysis of the average properties of a local search procedure (RandomWalkSAT) for the satisfaction of random Boolean constraints is presented. Depending on the ratio alpha of constraints per variable, reaching a solution takes a time T(res) growing linearly [T(res) approximately tau(res)(alpha)N, alpha<alpha(d)] or exponentially (T(res) approximately(More)