We show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural. In order to convince the reader that it is mathematically natural, we show the time asymptotic behavior can be easily understood in this framework. We use the intuition

The development of stimulus selectivity in the primary sensory cortex of higher vertebrates is considered in a general mathematical framework. A synaptic evolution scheme of a new kind is proposed in which incoming patterns rather than converging afferents compete. The change in the efficacy of a

A novel method of incorporating shape information into the image segmentation process is presented. We introduce a representation for deformable shapes and define a probability distribution over the variances of a set of training shapes. The segmentation process embeds an initial curve as the zero

This paper addresses the problem of parametric representation and estimation of complex planar curves in 2-D, surfaces in 3-D and nonplanar space curves in 3-D. Curves and surfaces can be defined either parametrically or implicitly, and we use the latter representation. A planar curve is the set

The stochastic simulation algorithm ͑SSA͒ is an essentially exact procedure for numerically simulating the time evolution of a well-stirred chemically reacting system. Despite recent major improvements in the efficiency of the SSA, its drawback remains the great amount of computer time

-Volterra equation of ecology and the quasispecies equation of molecular evolution.

The Fokker--Planck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of time--dependent systems in which randomness plays a role. In this paper

This paper describes a physically-based rendering system tailored to the demands of lighting design and architecture. The simulation uses a light-backwards ray-tracing method with extensions to efficiently solve the rendering equation under most conditions. This includes specular, diffuse

This paper addresses feedback stabilization problems for linear time-invariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation

The soil moisture characteristic may be modeled as a power curve combined with a short parabolic section near saturation to represent gradual air entry. This two-part functionmtogether with a power function relating soil moisture and hydraulic conductivitymis used to derive a formula