Biomedical subjects

Riccardo Zecchina

Publications and source records attributed to Riccardo Zecchina.

7 recordsLinked to original sources

PubMed2006

Statistical mechanics of combinatorial auctions.

Combinatorial auctions are formulated as frustrated lattice gases on sparse random graphs, allowing the determination of the optimal revenue by methods of statistical physics. Transitions between computationally easy and hard regimes are found and interpreted in terms of the geometric structure of the space of solutions. We introduce an iterative algorithm to solve intermediate and large instances, and discuss competing states of optimal revenue and maximal number of satisfied bidders. The algorithm can be generalized to the hard phase and to more sophisticated auction protocols.

Algorithms↗

PubMed2006

Learning by message passing in networks of discrete synapses.

We show that a message-passing process allows us to store in binary "material" synapses a number of random patterns which almost saturate the information theoretic bounds. We apply the learning algorithm to networks characterized by a wide range of different connection topologies and of size comparable with that of biological systems (e.g., [EQUATION: SEE TEXT]). The algorithm can be turned into an online-fault tolerant-learning protocol of potential interest in modeling aspects of synaptic plasticity and in building neuromorphic devices.

Action Potentials↗

PubMed2005

Source coding by efficient selection of ground-state clusters.

We analyze the geometrical structure of clusters of ground states which appear in many frustrated systems over random graphs. Focusing on the regime of connectivities where the number of clusters is exponential in the size of the problems, we identify an appropriate generalization of the survey propagation equations efficiently exploring the geometry. The possibility of selecting different clusters has also computational consequences. As a proof of concept here we show how a well-known physical system can be used to perform nontrivial data compression, for which we introduce a unique compression scheme. Performances are optimized when the number of well-separated clusters is maximal in the underlying physical model.

Journal Article↗

PubMed2005

Lossy data compression with random gates.

We introduce a new protocol for a lossy data compression algorithm which is based on constraint satisfaction gates. We show that the theoretical capacity of algorithms built from standard parity-check gates converges exponentially fast to the Shannon's bound when the number of variables seen by each gate increases. We then generalize this approach by introducing random gates. They have theoretical performances nearly as good as parity checks, but they offer the great advantage that the encoding can be done in linear time using the survey inspired decimation algorithm, a powerful algorithm for constraint satisfaction problems derived from statistical physics.

Journal Article↗

PubMed2004

Minimizing energy below the glass thresholds.

Focusing on the optimization version of the random K -satisfiability problem, the MAX- K -SAT problem, we study the performance of the finite energy version of the survey propagation algorithm. We show that a simple (linear time) backtrack decimation strategy is sufficient to reach configurations well below the lower bound for the dynamic threshold energy and very close to the analytic prediction for the optimal ground states. A comparative numerical study on one of the most efficient local search procedures is also given.

Journal Article↗

PubMed2002

Random K-satisfiability problem: from an analytic solution to an efficient algorithm.

We study the problem of satisfiability of randomly chosen clauses, each with K Boolean variables. Using the cavity method at zero temperature, we find the phase diagram for the K=3 case. We show the existence of an intermediate phase in the satisfiable region, where the proliferation of metastable states is at the origin of the slowdown of search algorithms. The fundamental order parameter introduced in the cavity method, which consists of surveys of local magnetic fields in the various possible states of the system, can be computed for one given sample. These surveys can be used to invent new types of algorithms for solving hard combinatorial optimizations problems. One such algorithm is shown here for the K=3 satisfiability problem, with very good performances.

Journal Article↗

PubMed2002

Optimizing searches via rare events.

Randomized search algorithms for hard combinatorial problems exhibit a large variability of performances. We study the different types of rare events which occur in such out-of-equilibrium stochastic processes and we show how they cooperate in determining the final distribution of running times. As a by-product of our analysis we show how search algorithms are optimized by random restarts.

Journal Article↗