Inverse problem for the mean-field monomer-dimer model with attractive interaction

The inverse problem method is tested for a class of monomer-dimer statistical mechanics models that contain also an attractive potential and display a mean-field critical point at a boundary of a coexistence line. The inversion is obtained by analytically identifying the parameters in terms of the correlation functions and via the maximum-likelihood method. The precision is tested in the whole phase space and, when close to the coexistence line, the algorithm is used together with a clustering method to take care of the underlying possible ambiguity of the inversion.

[1]  Geoffrey E. Hinton,et al.  A Learning Algorithm for Boltzmann Machines , 1985, Cogn. Sci..

[2]  H. Nishimori.  Statistical Physics of Spin Glasses and Information Processing , 2001 .

[3]  J. Smillie,et al.  Semi-parabolic Bifurcations in Complex Dimension Two , 2017 .

[4]  P. Contucci,et al.  Inverse problem robustness for multi-species mean-field spin models , 2012, 1211.0465.

[5]  R. Peierls.  On Ising's model of ferromagnetism , 1936, Mathematical Proceedings of the Cambridge Philosophical Society.

[6]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[7]  L. Zdeborová,et al.  Thermodynamic origin of order parameters in mean‐field models of spin glasses , 2005, cond-mat/0504132.

[8]  A. Barra,et al.  An analysis of a large dataset on immigrant integration in Spain. The Statistical Mechanics perspective on Social Action , 2013, Scientific Reports.

[9]  P. Contucci,et al.  The exact solution of a mean-field monomer-dimer model with attractive potential , 2014 .

[10]  P. Contucci,et al.  Limit Theorems for Monomer–Dimer Mean-Field Models with Attractive Potential , 2015, 1506.04241.

[11]  西森 秀稔.  Statistical physics of spin glasses and information processing : an introduction , 2001 .

[12]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[13]  R. Monasson,et al.  Small-correlation expansions for the inverse Ising problem , 2008, 0811.3574.

[14]  F. Ricci-Tersenghi,et al.  Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states. , 2015, Physical review. E.

[15]  J. Berg,et al.  Mean-field theory for the inverse Ising problem at low temperatures. , 2012, Physical review letters.

[16]  Ron Aharoni,et al.  Matchings in infinite graphs , 1988, J. Comb. Theory, Ser. B.

[17]  Sean Hughes,et al.  Clustering by Fast Search and Find of Density Peaks , 2016 .

[18]  Lenka Zdeborová,et al.  The number of matchings in random graphs , 2006, ArXiv.

[19]  Sunil J Rao,et al.  Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis , 2003 .

[20]  P. Contucci,et al.  A mean-field monomer-dimer model with attractive interaction. The exact solution , 2013, 1311.6551.

[21]  Some properties of mobile and immobile adsorbed films , 1938 .

[22]  Simona Cocco,et al.  Fast inference of interactions in assemblies of stochastic integrate-and-fire neurons from spike recordings , 2011, Journal of Computational Neuroscience.

[23]  J. Hertz,et al.  Ising model for neural data: model quality and approximate methods for extracting functional connectivity. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Marc Lelarge,et al.  Matchings on infinite graphs , 2011, 1102.0712.

[25]  Rory A. Fisher,et al.  Theory of Statistical Estimation , 1925, Mathematical Proceedings of the Cambridge Philosophical Society.

[26]  Muneki Yasuda,et al.  Inverse Problem in Pairwise Markov Random Fields Using Loopy Belief Propagation , 2012 .

[27]  S. Stenholm.  Information, Physics and Computation, by Marc Mézard and Andrea Montanari , 2010 .

[28]  M. Sipser,et al.  Maximum matching in sparse random graphs , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[29]  G. Patterson,et al.  Children and Divorce , 1991, Science.

[30]  P. Contucci,et al.  Enhancing participation to health screening campaigns by group interactions , 2015, Scientific Reports.

[31]  W. DeGrado,et al.  A thermodynamic scale for the helix-forming tendencies of the commonly occurring amino acids. , 1990, Science.