The Feynman propagator from a single path.

We show that it is possible to construct the Feynman propagator for a free particle in one dimension, without quantization, from a single continuous space-time path.

Information loss in the continuum limit and Schrödinger's equation in an electromagnetic field.

Since the time of Einstein's work on Brownian motion it has been known that random walks provide a microscopic model for the diffusion equation. Less well known is the fact that some instances of Schrödinger's equation occur naturally in the description of the statistics of these same walks and thus have classical contexts which are distinct from their usual association with quantum mechanics. An interesting feature of these models is the fact that the information which relates Schrödinger's equation to its classical context is not contained in the partial differential equation itself, but is lost in the continuum limit which gives rise to the equation. In this article we illustrate the above by showing that Schrödinger's equation for a particle in an electromagnetic field in 1 + 1 dimension occurs as a continuum limit of a description of a classical system of point particles on a lattice. The derivation shows that the information lost in the continuum limit is necessary to link the mathematics to the physical context of the equation.

Comparison of neural networks and regression-based methods for temperature retrievals.

Two methods for performing clear-air temperature retrievals from simulated radiances for the Atmospheric Infrared Sounder are investigated. Neural networks are compared with a well-known linear method in which regression is performed after a change of bases. With large channel sets, both methods can rapidly perform clear-air retrievals over a variety of climactic conditions with an overall RMS error of less than 1 K. The Jacobian of the neural network is compared with the Jacobian (the regression coefficients) of the linear method, revealing a more fine-scale variation than expected from the underlying physics, particularly for the neural net. Some pragmatic information concerning the application ofneural nets to retrieval problems is also included.