R J Baxter 1982 London: Academic xii + 486 pp price £43.60 Over the past few years there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them. Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944.

Exactly Solved Models in Statistical Mechanics

Annals of physics

Personalized learning full-path recommendation model based on LSTM neural networks

This chapter surveys common clustering algorithms widely used in the data mining community in light of chemometrics. It starts with taxonomy of clustering algorithms, and discusses two common clustering approaches – partitioning clustering and hierarchical clustering – in detail. Several variants of these clustering methods are presented and their strengths and weaknesses are addressed. This chapter continues to overview hybrid clustering approaches combining partitioning clustering and hierarchical clustering, and concludes with a quick overview on constrained clustering.

Common Clustering Algorithms

Neural Network World

Generalized Bragg-Williams equation for systems with an arbitrary long-range interaction

We consider two models of Hopfield-like associative memory with q-valued neurons: Potts-glass neural network (PGNN) and parametrical neural network (PNN). In these models neurons can be in more than two different states. The models have the record characteristics of its storage capacity and noise immunity, and significantly exceed the Hopfield model. We present a uniform formalism allowing us to describe both PNN and PGNN. This networks inherent mechanisms, responsible for outstanding recognizing properties, are clarified.

http://ieeexplore.ieee.org/iel5/9486/30097/01380051.pdf

Vector-neuron models of associative memory

We consider two models of Hopfield-like associative memory with $q$-valued neurons: Potts-glass neural network (PGNN) and parametrical neural network (PNN). In these models neurons can be in more than two different states. The models have the record characteristics of its storage capacity and noise immunity, and significantly exceed the Hopfield model. We present a uniform formalism allowing us to describe both PNN and PGNN. This networks inherent mechanisms, responsible for outstanding recognizing properties, are clarified.

Vector-Neuron Models of Associative Memory

Here we apply the n -vicinity method of approximate calculation of the partition function to an Ising Model with the nearest neighbor interaction on D -dimensional hypercube lattice We solve the equation of state for an arbitrary dimension D and analyze the behavior of the free energy As expected, for large dimensions ( D ≥ 3 ) the system demonstrates a phase transition of the second kind In this case, we obtain a simple analytical expression for the critical value of the inverse temperature When 3 ≤ D ≤ 7 this expression is in a very good agreement with the results of computer simulations In the case of small dimensions ( D = 1 , 2 ), there is a noticeable discrepancy with the known exact results

Applicability of n-vicinity method for calculation of free energy of Ising model

We develop a formalism allowing us to describe operating of a network based on the parametrical four-wave mixing process that is well-known in nonlinear optics. It is shown that the storage capacity of such a network is higher compared with the Potts-glass neural networks.

Leonid Litinskii

Papers

Generalized Bragg-Williams equation for systems with an arbitrary long-range interaction

Vector-neuron models of associative memory

Vector-Neuron Models of Associative Memory

Applicability of n-vicinity method for calculation of free energy of Ising model

Parametrical neural network based on the four-wave mixing process