A new approach to the study of non-linear non-autonomous systems

In this paper, a new approach to the study of non-linear, non-autonomous systems is presented. The method outlined is based on the idea of solving the governing differential equations of order n by a process of successive reduction of their order. This is achieved by the use of “differential transformation functions”. The value of the technique presented in the study of problems arising in the field of non-linear mechanics and the like, is illustrated by means of suitable examples drawn from different fields such as vibrations, rigid body dynamics, etc.

A new model for drainage of static foams

Existing theories of foam drainage assume bubbles as pentagonal dodecahedrons, though a close-packed structure built with cells of this shape is not space-filling. The present work develops a theory for calculating drainage rates based on the more realistic beta-tetrakaidecahedral shape for the bubbles. In contrast with the earlier works, three types of films, and Plateau borders had to be considered in view of the more complex shape used in the present work. The exchange of liquid between Plateau borders was treated in a way different From earlier theories, using the idea that the volume of junctions of Plateau borders is negligible. For foams made of large bubble sizes, the present model performs as well as the previous models, but when bubble size is small, its predictions of drainage rates from static foams are in better agreement with the experimental observations.

Role of feedback in mammalian vision: a new hypothesis and a computational model

This paper presents a novel hypothesis on the function of massive feedback pathways in mammalian visual systems. We propose that the cortical feature detectors compete not for the right to represent the output at a point, but for exclusive rights to abstract and represent part of the underlying input. Feedback can do this very naturally. A computational model that implements the above idea for the problem of line detection is presented and based on that we suggest a functional role for the thalamo-cortical loop during perception of lines. We show that the model successfully tackles the so called Cross problem. Based on some recent experimental results, we discuss the biological plausibility of our model. We also comment on the relevance of our hypothesis (on the role of feedback) to general sensory information processing and recognition. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.