The rst-order system least-squares methodology represents an alternative to standard mixed nite element methods. Among its advantages is the fact that the nite element spaces approximating the pressure and ux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropiate error measure. This paper studies the rst-order system least-squa...

We present a new approach for solving certain innnite sets of rst order uniication problems represented by term schemes. Within the framework of second-order equational logic solving such scheme uniication problems amounts exactly to solving (variable-)restricted uniication problems. Finally, we show how this approach yields a generic solution technique for innnitely many ordinary rst-order uni...

We examine the representational capabilities of first-order and second-order single-layer recurrent neural networks (SLRNN's) with hard-limiting neurons. We show that a second-order SLRNN is strictly more powerful than a first-order SLRNN. However, if the first-order SLRNN is augmented with output layers of feedforward neurons, it can implement any finite-state recognizer, but only if state-spl...

The quasispecies model describes processes related to the origin of life and viral evolutionary dynamics. We discuss how the error catastrophe that reflects the transition from localized to delocalized quasispecies population is affected by catalytic replication of different reaction orders. Specifically, we find that 2 order mechanisms lead to 1 order discontinuous phase transitions in the via...

The processing of texture patterns has been characterized by a model that first filters the image to isolate one texture component, then applies a rectifying nonlinearity that converts texture variation into intensity variation, and finally processes the resulting pattern with mechanisms similar to those used in processing luminance-defined images (spatial-frequency- and orientation-tuned filte...