Multicanonical Cluster Algorithm and the 2-D 7-State Potts Model

I present a hybrid-like two-step algorithm, which combines a microcanonical update of a spin system using demons, with a multicanonical demon refresh. The algorithm is free from the supercritical slowing down that burdens the canonical methods: the exponential increase of the tunnelling time between the metastable states in the first-order phase transitions, when the volume of the system is increased. The demons act as a buffer between the multicanonical heat bath and the spin system, allowing the spin system to be updated with any microcanonical demon procedure, including cluster methods. The cluster algorithm is demonstrated with the 2-dimensional 7-state Potts model, using volumes up to $128^2$. The tunnelling time is found to increase as $L^{1.82}$, where $L$ is the linear dimension of the system.Comment: 14 pages, 8 ps-figures, the flashy one missing to save space+troubles, sorry, the whole thing available from the author. Preprint CERN-TH.6654/9

An improved connectionist activation function for energy minimization

Symmetric networks that are based on energy minimization, such as Boltzmann machines or Hopfield nets, are used extensively for optimization, constraint satisfaction, and approximation of NP-hard problems. Nevertheless, finding a global minimum for the energy function is not guaranteed, and even a local minimum may take an exponential number of steps. We propose an improvement to the standard activation function used for such networks. The improved algorithm guarantees that a global minimum is found in linear time for tree-like subnetworks. The algorithm is uniform and does not assume that the network is a tree. It performs no worse than the standard algorithms for any network topology. In the case where there are trees growing from a cyclic subnetwork, the new algorithm performs better than the standard algorithms by avoiding local minima along the trees and by optimizing the free energy of these trees in linear time. The algorithm is self-stabilizing for trees (cycle-free undirected graphs) and remains correct under various scheduling demons. However, no uniform protocol exists to optimize trees under a pure distributed demon and no such protocol exists for cyclic networks under central demon

Understanding the temperature and the chemical potential using computer simulations

Several Monte Carlo algorithms and applications that are useful for understanding the concepts of temperature and chemical potential are discussed. We then introduce a generalization of the demon algorithm that measures the chemical potential and is suitable for simulating systems with variable particle number.Comment: 23 pages including 6 figure

A multisite microcanonical updating method

We have made a study of several update algorithms using the XY model. We find that sequential local overrelaxation is not ergodic at the scale of typical Monte Carlo simulation time. We have introduced a new multisite microcanonical update method, which yields results compatible with those of random overrelaxation and the microcanonical demon algorithm, which are very much slower, all being incompatible with the sequential overrelaxation results.Comment: 13 pages, 4 figure

A Bayesian Approach to Manifold Topology Reconstruction

In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated

An Improved Activation Function for Energy Minimization

Symmetric networks that are based on energy minimization, such as Boltzmann machines or Hopfield nets, are used extensively for optimization, constraint satisfaction, and approximation of NP-hard problems. Nevertheless, finding a global minimum for the energy function is not guaranteed, and even a local minimum may take an exponential number of steps. We propose and improvement to the standard activation function used for such networks. The improved algorithm guarantees that a global minimum is found in linear time for tree-like subnetworks. The algorithm is uniform and does not assume that the network is a tree. It performs no worse than the standard algorithms for any network topology. In the case where there are trees growing from a cyclic subnetwork, the new algorithm performs better than the standard algorithms by avoiding local minima along the trees and by optimizing the energy of these trees in linear time. The algorithm is self-stabilizing for trees (cycle-free undirected graphs) and remains correct under various scheduling demons. However, no uniform protocol exists to optimze trees under a pure distributed demon and no such protocol exists for cyclic networks under central demon

A Hybrid Demon Algorithm for the Two-Dimensional Orthogonal Strip Packing Problem

This paper develops a hybrid demon algorithm for a two-dimensional orthogonal strip packing problem. This algorithm combines a placement procedure based on an improved heuristic, local search, and demon algorithm involved in setting one parameter. The hybrid algorithm is tested on a wide set of benchmark instances taken from the literature and compared with other well-known algorithms. The computation results validate the quality of the solutions and the effectiveness of the proposed algorithm