Title
Quantitative Evaluation of Neural Networks for NDE Applications Using the ROC Curve

Abstract
The relative operating characteristic (ROC) method is applied to performance evaluation of neural networks. The study was motivated by the need to objectively evaluate neural networks for flaw waveform identification in NDE equipment, and to compare neural network performance with other methods. NDE applications are characterized by noisy real-world data, less- than-perfect detection and a serious problem of false alarm indications. The ROC method is explained by modeling neural network output as exponential probability distributions with two peaks, one near 1 (flaw) and one near 0 (no flaw). 100% POD (probability of detection) can only be achieved when the POFA (probability of false alarm) is also 100%, and if a POFA of 0% is required, the POD also falls to 0%. The ROC curve presents all intermediate performance information in an objective form and depicts the inevitable trade-off in every interpreter, human, neural, or otherwise. The ROC method is applied to the comparison of the performance of a neural network and a threshold-based scheme in classifying real-world eddy current data collected from an aircraft wheel NDE system.

Source: 21st Annual Review of Progress in Quantitative Nondestructive Evaluation, Snowmass CO, 1994

Title
Phase Transitions in Dilute, Locally Connected Neural Networks

Abstract
We report numerical studies of the "memory-loss" phase transition in Hopfield-like symmetric neural networks in which the neurons are connected to all other neurons within a local neighborhood (dense, short-range connectivity). The number of connections per neuron, K, scales as the number of neurons, N, raised to a power less than one (i. e., K ~ Nh, h<1) We use the recently developed Lee- Kosterlitz finite size scaling technique to determine the critical value of h below which the first-order phase transition disappears.

Source: Physical Review A, 45(8) 6135-6138, 1992

Title
Entropic Predictions for Cellular Networks

Abstract
Diverse cellular systems evolve to remarkably similar stationary states. We therefore have studied and simulated a purely topological model. We use a maximum entropy argument to predict that the average number of l-sided cells adjacent to an n-sided cell, Ml(n), will be linear in n. One consequence is the empirically observed linearity of the total number of edges of cells adjacent to an n-sided cell, known as the Aboav-Weaire law. The prevailing justification of that law is shown to be incorrect, and thus the apparently universal experimental slope of ~5 remains unexplained.

Source: Physical Review Letters 67 (13) 1803 , Sept. 23, 1991