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We derive and analyze transport equations for the energy density o f w aves of any kind in a random medium. The equations take account of nonuniformities of the background medium, scattering by random inhomogeneities, polarization e ects, coupling of di erent t ypes of waves, etc. We also show that di usive behavior occurs on long time and distance scales and we determine the di usion coe cients. The results are specialized to acoustic, electromagnetic, and elastic waves. The analysis is based on the governing equations of motion and uses the Wigner distribution.

The visual cortex of many adult mammals has patches of cells that receive inputs driven by the right eye alternating with patches that receive inputs driven by the left eye. These ocular dominance patches (or "columns") form during early life as a consequence of competition between the activity patterns of the two eyes. A mathematical model of several biological mechanisms that can account for this development is presented. Analysis of this model reveals the conditions under which ocular dominance segregation will occur and determines the resulting patch width. Simulations of the model also exhibit other phenomena associated with early visual development, such as topographic refinement of cortical receptive fields, the confinement of input cell connections to patches, monocular deprivation plasticity including a critical period, and the effect of artificially induced strabismus. The model can be used to predict the results of proposed experiments and to discriminate among various mechanisms of plasticity.

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the force per unit length exerted on the body by the fluid. The novelty is that the body is permitted to twist and dilate in addition to undergoing the translating, bending and stretching, which have been considered by others. The method of derivation is relatively simple, and the resulting integral equation does not involve the limiting processes which occur in the previous work.