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We do mean-field perturbation theory for U(1) lattice gauge theory in the axial gauge, and evaluate corrections from fluctuations up to fourth order for the free energy and plaquette energy. Comparing with similar results previously obtained in the Feynman gauge we find, to those orders studied, a gauge dependence of the size of the first correction term neglected with one exception. This gauge de

The self-similar structure of mode lockings for circle maps is studied by means of the associated Farey trees. We investigate numerically several classes of scaling relations implicit in the Farey organization of mode lockings and discuss the extent to which they lead to universal scaling laws.

We explore the possibility of reducing finite size effects in the weak coupling region of glueball correlations and Wilson loops. Our analysis indicates that twisted boundary conditions do diminish finite size effects and numerical evidence for this is given for the glueball correlation.

We study a model of random surfaces endowed with fermionic degrees of freedom. The critical parameters are estimated using a Monte Carlo simulation method, for the dimensionality d of the embedding space ranging from d=0 to d=10.

A novel modified method for obtaining approximate solutions to difficult optimization problems within the neural network paradigm is presented. We consider the graph partition and the travelling salesman problems. The key new ingredient is a reduction of solution space by one dimension by using graded neurons, thereby avoiding the destructive redundancy that has plagued these problems when using s

A convenient mapping and an efficient algorithm for solving scheduling problems within the neural network paradigm is presented. It is based on a reduced encoding scheme and a mean field annealing prescription which was recently successfully applied to TSP.Most scheduling problems are characterized by a set of hard and soft constraints. The prime target of this work is the hard constraints. In thi

In a recent paper (Gislén et al. 1989) a convenient encoding and an efficient mean field algorithm for solving scheduling problems using a Potts neural network was developed and numerically explored on simplified and synthetic problems. In this work the approach is extended to realistic applications both with respect to problem complexity and size. This extension requires among other things the in

Bosonic strings can be discretized in terms of dynamically triangulatedrandom surfaces. We investigate the possibility of introducing fermionicdegrees of freedom on the surface in terms of Ising spins, which in twodimensions correspond to Majorana fermions. Critical properties of themodel are estimated using finite-size scaling methods.

Myocardial active relaxation and restoring forces are known determinants of left ventricular (LV) diastolic function. We hypothesize the existence of an additional mechanism involved in LV filling, namely, a hydraulic force contributing to the longitudinal motion of the atrioventricular (AV) plane. A prerequisite for the presence of a net hydraulic force during diastole is that the atrial short-ax

Rotor neurons are introduced to encode states living on the surface of a sphere in D dimensions. Such rotors can be regarded as continuous generalizations of binary (Ising) neurons. The corresponding mean field equations are derived, and phase transition properties based on linearized dynamics are given. The power of this approach is illustrated with an optimization problem—placing N identical cha

The Potts Neural Network approach to non-binary discrete optimizationproblems is described. It applies to problems that can be described asa set of elementary 'multiple choice' options. Instead of the conventionalbinary (Ising) neurons, mean field Potts neurons, having several availablestates, are used to describe the elementary degrees of freedom of suchproblems. The dynamics consists of iteratin

A general introduction to the use of feed-back artificial neural networks (ANN) for obtaining good approximate solutions to combinatorial optimization problems is given, assuming no previous knowledge in the field. In particular we emphasize a novel neural mapping technique which efficiently reduces the solution space. This approach maps the problems onto Potts glass rather than spin glass models.

We devise a feed-forward Artificial Neural Network (ANN) procedure for predicting utility loads and present the resulting predictions for two test problems given by ``The Great Energy Predictor Shootout - The First Building Data Analysis and Prediction Competition''. Key ingredients in our approach are a method ($\delta$ -test) for determiningrelevant inputs and the Multilayer Perceptron. These me

The generic relation between continuous polymers and zero-componentEuclidean field-theories is reviewed, and exemplified by polymers withcontact and Coulomb interactions. An analogous relation on thelattice is also discussed, relating the statistics of self-avoidingwalks to a zero-component spin-model.

The recurrent neural network approach to combinatorial optimization has during the last decade evolved into a competitive and versatile heuristic method, that can be used on a wide range of problem types. In the state-of-the-art neural approach the discrete elementary decisions (not necessarily binary) are represented by continuous Potts mean-field neurons, interpolating between the available disc