On the analysis and interpretation of inhomogeneous quadratic forms as receptive fields

In this paper we introduce some mathematical and numerical tools to analyze and interpret inhomogeneous quadratic forms. The resulting characterization is in some aspects similar to that given by experimental studies of cortical cells, making it particularly suitable for application to second-order approximations and theoretical models of physiological receptive fields. We first discuss two ways of analyzing a quadratic form by visualizing the coefficients of its quadratic and linear term directly and by considering the eigenvectors of its quadratic term. We then present an algorithm to compute the optimal excitatory and inhibitory stimuli, i.e. the stimuli that maximize and minimize the considered quadratic form, respectively, given a fixed energy constraint. The analysis of the optimal stimuli is completed by considering their invariances, which are the transformations to which the quadratic form is most insensitive. We introduce a test to determine which of these are statistically significant. Next we propose a way to measure the relative contribution of the quadratic and linear term to the total output of the quadratic form. Furthermore, we derive simpler versions of the above techniques in the special case of a quadratic form without linear term and discuss the analysis of such functions in previous theoretical and experimental studies. In the final part of the paper we show that for each quadratic form it is possible to build an equivalent two-layer neural network, which is compatible with (but more general than) related networks used in some recent papers and with the energy model of complex cells. We show that the neural network is unique only up to an arbitrary orthogonal transformation of the excitatory and inhibitory subunits in the first layer

Prediction of the functional properties of ceramic materials from composition using artificial neural networks

We describe the development of artificial neural networks (ANN) for the prediction of the properties of ceramic materials. The ceramics studied here include polycrystalline, inorganic, non-metallic materials and are investigated on the basis of their dielectric and ionic properties. Dielectric materials are of interest in telecommunication applications where they are used in tuning and filtering equipment. Ionic and mixed conductors are the subjects of a concerted effort in the search for new materials that can be incorporated into efficient, clean electrochemical devices of interest in energy production and greenhouse gas reduction applications. Multi-layer perceptron ANNs are trained using the back-propagation algorithm and utilise data obtained from the literature to learn composition-property relationships between the inputs and outputs of the system. The trained networks use compositional information to predict the relative permittivity and oxygen diffusion properties of ceramic materials. The results show that ANNs are able to produce accurate predictions of the properties of these ceramic materials which can be used to develop materials suitable for use in telecommunication and energy production applications