Population-based local search for protein folding simulation in the MJ energy model and cubic lattices.

We present experimental results on benchmark problems in 3D cubic lattice structures with the Miyazawa-Jernigan energy function for two local search procedures that utilise the pull-move set: (i) population-based local search (PLS) that traverses the energy landscape with greedy steps towards (potential) local minima followed by upward steps up to a certain level of the objective function; (ii) simulated annealing with a logarithmic cooling schedule (LSA). The parameter settings for PLS are derived from short LSA-runs executed in pre-processing and the procedure utilises tabu lists generated for each member of the population. In terms of the total number of energy function evaluations both methods perform equally well, however, PLS has the potential of being parallelised with an expected speed-up in the region of the population size. Furthermore, both methods require a significant smaller number of function evaluations when compared to Monte Carlo simulations with kink-jump moves.

Stochastic protein folding simulation in the three-dimensional HP-model.

We present results from three-dimensional protein folding simulations in the HP-model on ten benchmark problems. The simulations are executed by a simulated annealing-based algorithm with a time-dependent cooling schedule. The neighbourhood relation is determined by the pull-move set. The results provide experimental evidence that the maximum depth D of local minima of the underlying energy landscape can be upper bounded by D

Bounded-depth threshold circuits for computer-assisted CT image classification.

We present a stochastic algorithm that computes threshold circuits designed to discriminate between two classes of computed tomography (CT) images. The algorithm employs a partition of training examples into several classes according to the average grey scale value of images. For each class, a sub-circuit is computed, where the first layer of the sub-circuit is calculated by a new combination of the Perceptron algorithm with a special type of simulated annealing. The algorithm is evaluated for the case of liver tissue classification. A depth-five threshold circuit (with pre-processing: depth-seven) is calculated from 400 positive (abnormal findings) and 400 negative (normal liver tissue) examples. The examples are of size n=14,161 (119 x 119) with an 8 bit grey scale. On test sets of 100 positive and 100 negative examples (all different from the learning set) we obtain a correct classification close to 99%. The total sequential run-time to compute a depth-five circuit is about 75h up to 230h on a SUN Ultra 5/360 workstation, depending on the width of the threshold circuit at depth-three. In our computational experiments, the depth-five circuits were calculated from three simultaneous runs for depth-four circuits. The classification of a single image is performed within a few seconds.

Logarithmic simulated annealing for X-ray diagnosis.

We present a new stochastic learning algorithm and first results of computational experiments on fragments of liver CT images. The algorithm is designed to compute a depth-three threshold circuit, where the first layer is calculated by an extension of the Perceptron algorithm by a special type of simulated annealing. The fragments of CT images are of size 119x119 with eight bit grey levels. From 348 positive (focal liver tumours) and 348 negative examples a number of hypotheses of the type w(1)x(1)+. . .;+w(n)x(n)>/=theta were calculated for n=14161. The threshold functions at levels two and three were determined by computational experiments. The circuit was tested on various sets of 50+50 additional positive and negative examples. For depth-three circuits, we obtained a correct classification of about 97%. The input to the algorithm is derived from the DICOM standard representation of CT images. The simulated annealing procedure employs a logarithmic cooling schedule c(k)=Gamma/ln(k+2), where Gamma is a parameter that depends on the underlying configuration space. In our experiments, the parameter Gamma is chosen according to estimations of the maximum escape depth from local minima of the associated energy landscape.