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Tetsuo Mohri - One of the best experts on this subject based on the ideXlab platform.

  • conversion of magnetic freedoms into atomic configurational freedoms within the Cluster Variation Method
    Materials Transactions, 2019
    Co-Authors: Ryo Yamada, Tetsuo Mohri
    Abstract:

    The continuous displacement Cluster Variation Method (CDCVM) has introduced local atomic displacements into the theoretical framework of the Cluster Variation Method (CVM) by viewing an atom displaced from a Bravais lattice point as a particular atomic species located at the lattice point. This idea of conversion from a freedom of local displacements into configurational freedom is extended in this paper to magnetic freedoms. Various magnitudes of local magnetic moments are considered, as well as two spin directions, on up-spins and down-spins. The approach is applied to pure Ni and its Curie temperature is explored with the entropy formula of the tetrahedron approximation in the CVM, using the first-nearest-neighbor pair interaction energies extracted from the total energies of various spin configurations, which are estimated from electronic-structure calculations.

  • Cluster Variation Method as a Theoretical Tool for the Study of Phase Transformation
    Metallurgical and Materials Transactions A, 2017
    Co-Authors: Tetsuo Mohri
    Abstract:

    Cluster Variation Method (CVM) has been widely employed to calculate alloy phase diagrams. The atomistic feature of the CVM is consistent with first-principles electronic structure calculations, and the combination of CVM with electronic structure calculation enables one to formulate free energy from the first-principles. CVM free energy conveys affluent information of a given system, and the second-order derivative traces the stability locus against configurational fluctuation. The kinetic extension of the CVM is the path probability Method (PPM) which is utilized to calculate transformation and relaxation kinetics associated with the temperature change. Hence, the CVM and PPM are coherent Methods to perform a synthetic study from initial non-equilibrium to final equilibrium states. By utilizing CVM free energy as a homogeneous free energy density term, one can calculate the time evolution of ordered domains within the phase field Method. Finally, continuous displacement Cluster Variation Method (CDCVM) is discussed as the recent development of CVM. CDCVM is capable of introducing the local lattice displacement into the free energy. Moreover, it is shown that CDCVM can be extended to study collective atomic displacements leading to displacive phase transformation.

  • Cluster Variation Method
    JOM, 2013
    Co-Authors: Tetsuo Mohri
    Abstract:

    The Cluster Variation Method (CVM) has been widely employed to calculate alloy free energies. The atomistic feature of the CVM is coherent with first-principles electronic structure calculations. In the current manuscript, a detailed derivation of a simple pair approximation is demonstrated, which facilitates the introduction of the concept of atomic correlations. The recent progress of the continuous displacement CVM is briefly introduced.

  • analysis of dislocation core structure in b2 ordered phase by Cluster Variation Method
    Materials Transactions, 2012
    Co-Authors: Yasunori Yamada, Tetsuo Mohri
    Abstract:

    Theoretical framework of the Cluster Variation Method (CVM) is extended in two directions. One is the construction of a supercell in which the basic Clusters are aligned in two dimensional directions. The other one is the introduction of the atomic displacement in the flexible lattice. These extensions of the conventional CVM enable us to calculate a core structure of two parallel superpartial dislocations in B2 ordered phase at finite temperatures. It is shown that a large stacking fault is formed inside the two superpartial dislocations at lower temperatures, while the stacking fault appears outside the superpartial dislocations at higher temperatures. [doi:10.2320/matertrans.MAW201214]

  • theoretical investigation of alloy phase equilibria by continuous displacement Cluster Variation Method
    Solid State Phenomena, 2011
    Co-Authors: Tetsuo Mohri
    Abstract:

    Continuous Displacement Cluster Variation Method is employed to study binary phase equilibria on the two dimensional square lattice with Lennard-Jones type pair potentials. It is confirmed that the transition temperature decreases significantly as compared with the one obtained by conventional Cluster Variation Method. This is ascribed to the distribution of atomic pairs in a wide range of atomic distance, which enables the system to attain the lower free energy. The spatial distribution of atomic species around a Bravais lattice point is visualized. Although the average position of an atom is centred at the Bravais lattice point, the maximum pair probability is not necessarily attained for the pairs located at the neighboring Bravais lattice points. In addition to the real space information, k-space information are calculated in the present study. Among them, the diffuse intensity spectra due to short range ordering and atomic displacement are discussed.

Alessandro Pelizzola - One of the best experts on this subject based on the ideXlab platform.

  • Exactness of the Cluster Variation Method and factorization of the equilibrium probability for the Wako–Saitô–Muñoz–Eaton model of protein folding
    Journal of Statistical Mechanics: Theory and Experiment, 2005
    Co-Authors: Alessandro Pelizzola
    Abstract:

    I study the properties of the equilibrium probability distribution of a protein folding model originally introduced by Wako and Saito, and later reconsidered by Munoz and Eaton. The model is a one-dimensional model with binary variables and many-body, long-range interactions, which has been solved exactly through a mapping to a two-dimensional model of binary variables with local constraints. Here I show that the equilibrium probability of this two-dimensional model factors into the product of local Cluster probabilities, each raised to a suitable exponent. The Clusters involved are single sites, nearest-neighbour pairs and square plaquettes, and the exponents are the coefficients of the entropy expansion of the Cluster Variation Method. As a consequence, the Cluster Variation Method is exact for this model.

  • exactness of the Cluster Variation Method and factorization of the equilibrium probability for the wako saito munoz eaton model of protein folding
    Journal of Statistical Mechanics: Theory and Experiment, 2005
    Co-Authors: Alessandro Pelizzola
    Abstract:

    I study the properties of the equilibrium probability distribution of a protein folding model originally introduced by Wako and Saito, and later reconsidered by Munoz and Eaton. The model is a one-dimensional model with binary variables and many-body, long-range interactions, which has been solved exactly through a mapping to a two-dimensional model of binary variables with local constraints. Here I show that the equilibrium probability of this two-dimensional model factors into the product of local Cluster probabilities, each raised to a suitable exponent. The Clusters involved are single sites, nearest-neighbour pairs and square plaquettes, and the exponents are the coefficients of the entropy expansion of the Cluster Variation Method. As a consequence, the Cluster Variation Method is exact for this model.

  • Cluster Variation Method in statistical physics and probabilistic graphical models
    arXiv: Statistical Mechanics, 2005
    Co-Authors: Alessandro Pelizzola
    Abstract:

    The Cluster Variation Method (CVM) is a hierarchy of approximate Variational techniques for discrete (Ising--like) models in equilibrium statistical mechanics, improving on the mean--field approximation and the Bethe--Peierls approximation, which can be regarded as the lowest level of the CVM. In recent years it has been applied both in statistical physics and to inference and optimization problems formulated in terms of probabilistic graphical models. The foundations of the CVM are briefly reviewed, and the relations with similar techniques are discussed. The main properties of the Method are considered, with emphasis on its exactness for particular models and on its asymptotic properties. The problem of the minimization of the Variational free energy, which arises in the CVM, is also addressed, and recent results about both provably convergent and message-passing algorithms are discussed.

  • Accurate results for Ising models from large order Cluster Variation Method
    AIP Conference Proceedings, 2001
    Co-Authors: Alessandro Pelizzola, M. Pretti
    Abstract:

    The Cluster Variation Method is a powerful hierarchy of mean-field-like approximations for Ising-like lattice models, which is known to give results that are particularly accurate at high and/or low temperature and converge to the exact ones as the size of the Clusters taken into account gets larger. Here we show how these properties can be exploited to obtain non-classical, quite accurate estimates of quantities characterizing the critical behavior of the ordinary Ising model and the ground state of the triangular Ising antiferromagnet.

  • Cluster Variation Method and disorder varieties of two dimensional ising like models
    Physical Review B, 2000
    Co-Authors: Alessandro Pelizzola
    Abstract:

    I show that the Cluster Variation Method, long used as a powerful hierarchy of approximations for discrete (Ising-like) two-dimensional lattice models, yields exact results on the disorder varieties which appear when competitive interactions are put into these models. I consider, as an example, the plaquette approximation of the Cluster Variation Method for the square lattice Ising model with nearest-neighbor, next-nearest-neighbor, and plaquette interactions, and, after rederiving known results, report simple closed-form expressions for the pair and plaquette correlation functions.

H J Kappen - One of the best experts on this subject based on the ideXlab platform.

  • The Cluster Variation Method for efficient linkage analysis on extended pedigrees.
    BMC bioinformatics, 2006
    Co-Authors: Cornelis A Albers, Martijn A R Leisink, H J Kappen
    Abstract:

    Computing exact multipoint LOD scores for extended pedigrees rapidly becomes infeasible as the number of markers and untyped individuals increase. When markers are excluded from the computation, significant power may be lost. Therefore accurate approximate Methods which take into account all markers are desirable. We present a novel Method for efficient estimation of LOD scores on extended pedigrees. Our approach is based on the Cluster Variation Method, which deterministically estimates likelihoods by performing exact computations on tractable subsets of variables (Clusters) of a Bayesian network. First a distribution over inheritances on the marker loci is approximated with the Cluster Variation Method. Then this distribution is used to estimate the LOD score for each location of the trait locus. First we demonstrate that significant power may be lost if markers are ignored in the multi-point analysis. On a set of pedigrees where exact computation is possible we compare the estimates of the LOD scores obtained with our Method to the exact LOD scores. Secondly, we compare our Method to a state of the art MCMC sampler. When both Methods are given equal computation time, our Method is more efficient. Finally, we show that CVM scales to large problem instances. We conclude that the Cluster Variation Method is as accurate as MCMC and generally is more efficient. Our Method is a promising alternative to approaches based on MCMC sampling.

  • The Cluster Variation Method for Efficient Linkage Analysis on Extended Pedigrees
    BMC Bioinformatics, 2006
    Co-Authors: Cornelis A Albers, Martijn A R Leisink, H J Kappen
    Abstract:

    Background Computing exact multipoint LOD scores for extended pedigrees rapidly becomes infeasible as the number of markers and untyped individuals increase. When markers are excluded from the computation, significant power may be lost. Therefore accurate approximate Methods which take into account all markers are desirable. Methods We present a novel Method for efficient estimation of LOD scores on extended pedigrees. Our approach is based on the Cluster Variation Method, which deterministically estimates likelihoods by performing exact computations on tractable subsets of variables (Clusters) of a Bayesian network. First a distribution over inheritances on the marker loci is approximated with the Cluster Variation Method. Then this distribution is used to estimate the LOD score for each location of the trait locus. Results First we demonstrate that significant power may be lost if markers are ignored in the multi-point analysis. On a set of pedigrees where exact computation is possible we compare the estimates of the LOD scores obtained with our Method to the exact LOD scores. Secondly, we compare our Method to a state of the art MCMC sampler. When both Methods are given equal computation time, our Method is more efficient. Finally, we show that CVM scales to large problem instances. Conclusion We conclude that the Cluster Variation Method is as accurate as MCMC and generally is more efficient. Our Method is a promising alternative to approaches based on MCMC sampling.

  • novel iteration schemes for the Cluster Variation Method
    Neural Information Processing Systems, 2001
    Co-Authors: H J Kappen, Wim Wiegerinck
    Abstract:

    The Cluster Variation Method is a class of approximation Methods containing the Bethe and Kikuchi approximations as special cases. We derive two novel iteration schemes for the Cluster Variation Method. One is a fixed point iteration scheme which gives a significant improvement over loopy BP. mean field and TAP Methods on directed graphical models. The other is a gradient based Method, that is guaranteed to converge and is shown to give useful results on random graphs with mild frustration. We conclude that the Methods are of significant practical value for large inference problems.

  • NIPS - Novel iteration schemes for the Cluster Variation Method
    2001
    Co-Authors: H J Kappen, Wim Wiegerinck
    Abstract:

    The Cluster Variation Method is a class of approximation Methods containing the Bethe and Kikuchi approximations as special cases. We derive two novel iteration schemes for the Cluster Variation Method. One is a fixed point iteration scheme which gives a significant improvement over loopy BP. mean field and TAP Methods on directed graphical models. The other is a gradient based Method, that is guaranteed to converge and is shown to give useful results on random graphs with mild frustration. We conclude that the Methods are of significant practical value for large inference problems.

Tohru Morita - One of the best experts on this subject based on the ideXlab platform.

L R Evangelista - One of the best experts on this subject based on the ideXlab platform.

  • Cluster Variation Method for the blume emery griffiths model
    Journal of Magnetism and Magnetic Materials, 1992
    Co-Authors: Carla Buzano, L R Evangelista
    Abstract:

    Abstract The Cluster Variation Method (CVM) in its recent formulation using the Moebius inversion is utilized to investigate the critical properties of the Blume-Emery-Griffiths model. We consider as the basic Cluster an nn pair. Particular attention is devoted to the reentrant phenomenon.

  • Cluster Variation Method in the analysis of spin-1 models
    1991
    Co-Authors: C. Buzano, L R Evangelista
    Abstract:

    The Cluster Variation Method, in its recent formulation using the Moebius inversion, is applied to the study of the critical properties of the spin-1 BlumeCapel model. In order to stress the various steps of the approximation a face-centered-cubic lattice is considered and the free energy of the system is written in several degrees of approximations: single site (one-body), pair (two-body), triangle (three-body), tetrahedron (four-body). The case of the pair approximation is discussed in detail and the resulting phase diagram is compared with that obtained using other Methods. The behavior of the dipolar and quadrupolar order parameters and of the pair-correlation functions is examined in three typical cases: second order transition, first order transition, no transitions.