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- Rémi Monasson, Riccardo Zecchina, Scott Kirkpatrick, Bart Selman, Lidror Troyansky
- Random Struct. Algorithms
- 1999

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)

The random K-satisfiability problem, consisting in verifying the existence of an assignment of N Boolean variables that satisfy a set of M5aN random logical clauses containing K variables each, is studied using the replica symmetric framework of diluted disordered systems. We present an exact iterative scheme for the replica symmetric functional order… (More)

- Simona Cocco, Rémi Monasson
- Physical review letters
- 2011

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)

- Giulio Biroli, Rémi Monasson, Martin Weigt
- ArXiv
- 1999

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)

Abstract We present a systematic small-correlation expansion to solve the inverse Ising problem and find a set of couplings and fields corresponding to a given set of correlations and magnetizations. Couplings are calculated up to the third order in the correlations for generic magnetizations and to the seventh order in the case of zero magnetizations; in… (More)

- Olivier C. Martin, Rémi Monasson, Riccardo Zecchina
- Theor. Comput. Sci.
- 2001

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)

A unifying theory of the denaturation transition of DNA, driven by temperature T or induced by an external mechanical torque Γ is presented. Our model couples in a geometrical way the hydrogen-bond opening and the untwisting of the helicoidal molecular structure. Using the transfer matrix method, we show that denaturation corresponds to a first-order phase… (More)

- Simona Cocco, Stanislas Leibler, Rémi Monasson
- Proceedings of the National Academy of Sciences…
- 2009

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)

- Simona Cocco, Rémi Monasson, Martin Weigt
- PLoS Computational Biology
- 2013

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)

- Guilhem Semerjian, Rémi Monasson
- Physical review. E, Statistical, nonlinear, and…
- 2003

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)