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The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally treelike, and sparse covariance matrices. We derive a closed set of equations from which the density of eigenvalues can be efficiently calculated. Within this approach, the… (More)

- Carlotta Martelli, Andrea De Martino, Enzo Marinari, Matteo Marsili, Isaac Pérez Castillo
- Proceedings of the National Academy of Sciences…
- 2009

Understanding the organization of reaction fluxes in cellular metabolism from the stoichiometry and the topology of the underlying biochemical network is a central issue in systems biology. In this task, it is important to devise reasonable approximation schemes that rely on the stoichiometric data only, because full-scale kinetic approaches are… (More)

Quite generally, constraint-based metabolic flux analysis describes the space of viable flux configurations for a metabolic network as a high-dimensional polytope defined by the linear constraints that enforce the balancing of production and consumption fluxes for each chemical species in the system. In some cases, the complexity of the solution space can… (More)

We study the statistics of the condition number κ = λmax/λmin (the ratio between largest and smallest squared singular values) of N × M Gaussian random matrices. Using a Coulomb fluid technique, we derive analytically and for large N the cumulative P[κ < x] and tail-cumulative P[κ > x] distributions of κ. We find that these distributions decay as P[κ < x] ≈… (More)

In this letter, we introduce a novel message-passing algorithm for a class of problems which can be mathematically understood as estimating volume-related properties of random polytopes. Unlike the usual approach consisting in approximating the real-valued cavity marginal distributions by a few parameters, we propose a weighted message-passing algorithm to… (More)

- Francesco A Massucci, Isaac Pérez Castillo, Conrad Pérez, Vicente
- 2010

The technological innovation of the experimental techniques involved in molecular biology allows nowadays to perform experiments almost unimaginable a few decades ago. Among these a particularly interesting role is played by single molecule manipulation experiments, aiming at understanding the mechanical properties of the fundamental bricks of life. DNA… (More)

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