background: with the increasing concern for health and nutrition, dietary fat has attracted considerable attention. the composition of fatty acids in the diet is important because they are associated with major diseases including cancers, diabetes, and cardiovascular disease. the fatty acid synthase (fasn) and stearoyl-coa desaturase (delta-9-desaturase) (scd) genes affect fatty acid compositio...

The standard method in optimization problems consists in a random search of the global minimum: a neuron network relaxes in the nearest local minimum from some randomly chosen initial configuration. This procedure is to be repeated many times in order to find as deep an energy minimum as possible. However the question about the reasonable number of such random starts and whether the result of t...

The standard method in optimization problems consists in a random search of the global minimum: a neuron network relaxes in the nearest local minimum from some randomly chosen initial configuration. This procedure is to be repeated many times in order to find as deep energy minimum as possible. However the question about the reasonable number of such random starts and if the result of the searc...

We investigate the local chromatic number of shift graphs and prove that it is close to their chromatic number. This implies that the gap between the directed local chromatic number of an oriented graph and the local chromatic number of the underlying undirected graph can be arbitrarily large. We also investigate the minimum possible directed local chromatic number of oriented versions of “topo...

Consider the multi-homogeneous homotopy continuation method for solving a system of polynomial equations. For any partition of variables, the multi-homogeneous Bézout number bounds the number of isolated solution curves one has to follow in the method. This paper presents a local search method for finding a partition of variables with minimal multi-homogeneous Bézout number. As with any other l...

We study on-line backpropagation and show that the existing theoretical descriptions are strictly valid only on relatively short time scales or in the vicinity of (local) minima of the backpropagation error potential. Qualitative global features (e.g., why is it much easier to escape from local minima than from global minima) may also be explained by these local descriptions, but the current ap...

Local minima in the error surfaces of feed-forward neural networks are signiicant because they may entrap gradient based training algorithms. Recent results have identiied conditions under which local minima do not occur. The present paper considers three distinct deenitions of local minimum, concluding that a new deenition, called regional minimum, corresponds most closely to intuition. Using ...

The determination of a stable molecular structure can often be formulated in terms of calculating the global (or approximate global) minimum of a potential energy function. Computing the global minimum of this function is very difficult because it typically has a very large number of local minima which may grow exponentially with molecule size. The optimization method presented involves collect...

An algorithm for finding an approximate global minimum of a funnel shaped function with many local minima is described. It is applied to compute the minimum energy docking position of a ligand with respect to a protein molecule. The method is based on the iterative use of a convex, general quadratic approximation that underestimates a set of local minima, where the error in the approximation is...

A computational study of the electronic structure and stability of complexes formed between Zeolite Y and boric acid was carried out at the HF and B3LYP levels using 6-31G* basis set. Five structures located as local minimum in PES of complex (structures d, e, f, g, and h). The most stable structure is formed due to hydrogen bonding between two hydroxyl of boric acid and both oxygen of ...