Charles R. Willcox

Understanding hierarchical neural network behaviour: a renormalization group approach

A hierarchical neural network model, presented in an earlier paper (Wilcox, 1989), is analysed using a renormalization group (RG) approach. The RG method puts many of the previously found empirical results on a firm theoretical foundation. The functional dependence of the propagation of errors from one level of the hierarchical tree to the next is derived and is shown to exhibit a phase transition. When the probability of entering errors at a given level exceeds some critical value, the error propagation is unbounded and will extend throughout the entire network, whereas below the critical value, the errors remain localized. This result along with individual cluster updating data is used to explain the content-addressability properties of the model.

Dealloying properties of Pt-NiCr thin films on glass

Abstract A dealloying reaction between sputter-deposited platinum and NiCr thin films on Pyrex® glass has been investigated. Using X-ray diffraction, 78 at.% Ni-22 at.% Cr alloy samples with platinum were studied following room temperature, 450 °C and 700 °C anneals. Although no instability was observed at room temperature, cubic Pt3Cr and Ni3Pt intermetallic phases emerged after annealing at 450 °C. These phases were no longer present when the anneal temperature was brought to 700 °C. There was complete dealloying of the NiCr film by the platinum, resulting in the formation of a tertiary alloy of platinum, nickel and chromium having an ordered face-centered tetragonal structure. The dealloying results are in accord with free energy calculations which are also presented. The possibility of an NiCr-glass dealloying reaction was also examined through free energy calculations and by X-ray diffraction indexing of annealed NiCr thin films deposited onto Pyrex and quartz substrates. It was found that the dealloying of NiCr by glass is self-stabilizing, with the extent of dealloying dependent on the type of glass substrate used. In this respect, an interesting anomaly between quartz and Pyrex is reported.