In this paper a new method is suggested for learning and generalization with a general one-hidden layer feedforward neural network. This scheme encompasses the use of a linear combination of heterogeneous nodes having randomly prescribed parameter values. The learning of the parameters is realized through adaptive stochastic optimization using a generalization data set. The learning of the linear coefficients in the linear combination of nodes is achieved with a linear regression method using data from the training set. One node is learned at a time. The method allows for choosing the proper number of net nodes, and is computationally efficient. The method was tested on mathematical examples and real problems from materials science and technology.

This paper focuses on estimating real and quantum potentials from financial commodities. The log returns of six common commodities are considered. We find that some phenomena, such as the vertical potential walls and the time scale issue of the variation on returns, also exists in commodity markets. By comparing the quantum and classical potentials, we attempt to demonstrate that the information within these two types of potentials is different. We believe this empirical result is consistent with the theoretical assumption that quantum potentials (when embedded into social science contexts) may contain some social cognitive or market psychological information, while classical potentials mainly reflect 'hard' market conditions. We also compare the two potential forces and explore their relationship by simply estimating the Pearson correlation between them. The Medium or weak interaction effect may indicate that the cognitive system among traders may be affected by those 'hard' market conditions.