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A mean field feedback artificial neural network (ANN) algorithm is developed and explored for the set covering problem. A convenient encoding of the inequality constraints is achieved by means of a multilinear penalty function. An approximate energy minimum is obtained by iterating a set of mean field equations, in combination with annealing. The approach is numerically tested against a set of pub
A novel artificial neural network approach to constraint satisfaction problems is presented. Based on information-theoretical considerations, it differs from a conventional mean-field approach in the form of the resulting free energy. The method, implemented as an annealing algorithm, is numerically explored on a testbed of K-SAT problems. The performance shows a dramatic improvement over that of
The fusion of secretory vesicles and granules with the cell membrane prior to the release of their content into the extracellular space requires a transient increase of free Ca2+ concentration in the vicinity of the fusion site. Usually there is a short temporal delay in the onset of the actual fusion of membranes with reference to the rising free Ca2+ levels. This delay is described as a latency
A novel method is presented and explored within the framework of Potts neural networks for solving optimization problems with a non-trivial topology, with the airline crew scheduling problem as a target application. The key ingredient to handle the topological complications is a propagator defined in terms of Potts neurons. The approach is tested on artificial problems generated with two real-worl
Monte Carlo simulations and variational calculations using a Gaussian ansatz are applied to a model consisting of a flexible linear polyelectrolyte chain as well as to an intrinsically stiff chain with up to 1000 charged monomers. Addition of salt is treated implicitly through a screened Coulomb potential for the electrostatic interactions. For the flexible model the electrostatic persistence leng
A Potts feedback neural network approach for finding good solutions to resource allocation problems with a nonfixed topology is presented. As a target application, the airline crew scheduling problem is chosen. The topological complication is handled by means of a propagator defined in terms of Potts neurons. The approach is tested on artificial random problems tuned to resemble real-world conditi
Variational methods are used to calculate structural and thermodynamical properties of a titrating polyelectrolyte in a discrete representation. In the variational treatment, the Coulomb potentials are emulated by harmonic repulsive forces between all monomers; the force constants are used as variational parameters. The accuracy of the variational approach is tested against Monte Carlo data. Excel
A variational method for computing conformational properties of molecules with Lennard-Jones potentials for the monomer-monomer interactions is presented. The approach is tailored to deal with angular degrees of freedom, rotors, and consists of the iterative solution of a set of deterministic equations with an annealing in temperature. The singular short-distance behavior of the Lennard-Jones pote
We consider the thermodynamics of a uniformly charged polyelectrolyte with harmonic bonds. For such a system there is at high temperatures an approximate scaling of global properties like the end-to-end distance and the interaction energy with the chain length divided by the temperature. This scaling is broken at low temperatures by the ultraviolet divergence of the Coulomb potential. By introduci
A new Monte Carlo method for computing thermodynamical properties of very large polyelectrolytes is presented. It is based on a renormalization group relating the original polymer to a smaller system, where, in addition to the naively rescaled forces, a corrective nearest-neighbor interaction originating from the short distance Coulomb cutoff is introduced. The method is derived for low T but is i
Monte Carlo simulations have been used to study three different models for linear, titrating polyelectrolytes in a salt-free environment: (i) a rigid polymer with rigid bonds (rigid rod); (ii) a flexible polymer with rigid bonds; and (iii) a flexible polymer with flexible bonds. The use of a very efficient pivot algorithm has made it possible to simulate very long chains, with up to several thousa
A variational approach, based on a discrete representation of the chain, is used to calculate free energy and conformational properties in polyelectrolytes. The true bond and Coulomb potentials are approximated by a trial isotropic harmonic energy containing force constants between all monomer-pairs as variational parameters. By a judicious choice of representation and the use of incremental matri
A deterministic algorithm for calculating polymer properties is presented. It is based on a variational approach where the bond and Coulomb potentials are approximated by a quadratic trial energy. The parameters which describe average atom positions and Gaussian fluctuations, are the solutions of matrix equations. By a judicious choice of parameter representations and the use of incremental matrix
A recently suggested geometrical embedding of Bethe-type lattices (branched polymers) in the hyperbolic plane [R. Mosseri and J. F. Sadoc, J. Phys. Lett. 43, L249 (1982); J. A. de Miranda-Neto and F. Moraes, J. Phys. I. France 2, 1657 (1992)] is shown to be only a special case of a whole continuum of possible realizations that preserve some of the symmetries of the Bethe lattice. The properties of
The Apollonian tiling of the plane into circles is analyzed with respect to its group properties. The relevant group, which is noncompact and discrete, is found to be identical to the symmetry group of a particular geometric tree graph in hyperbolic three-space. A linear recursive method to compute the radii is obtained. Certain modifications of the problem are investigated, and relations to other
We use the cooling method and the lattice approximation to study the form and properties of the minimum action configurations for the SU(2) Yang-Mills theory on a space-time torous with twist k=m=(1, 1, 1).
We analyze the finite size effects for the source method in pure lattice gauge theory at weak coupling. They are found to be strongly suppressed by twisting the boundary conditions, for SU(3) by typically an order of magnitude.
We compute the energy levels of an SU(2) Yang-Mills field in perturbation theory to order g2, for a box of finite size and symmetric twist m=(1, 1, 1). A cubic-invariant spectrum results, with almost degenerate E++ and T2 ++ levels. Various suggestions for further MC measurements are made.
A construction that relates circle maps of mutually reciprocal winding number, belonging to the same criticality class, is presented. It is explicitly invariant under smooth conjugations of either map, and displays a series of remarkable properties, in spite of its simplicity.
We discuss the Langevin equation for a complex Boltzmann distribution, allowing for modifications of the process. The relation between the two different time development operators involved is analyzed, with emphasis on their spectra.
