Some mathematical problems in retrograde nerve degeneration

Some Mathematical Problems in Artificial

The purpose of this essay is to sketch a few mathematical problems arising in artificial intelligence, with the hope that some may appeal to mathematicians, logicians, or theoretical computer scientists. I have thought about these problems off and on for some time, though mostly off, and am now attempting to set some of them down in response to conversations with Merrick Furst and Joseph Bates,...

Mathematical analysis of some bone remodelling problems

Bone remodelling aims to understand the relationship between the morphology of the bone and the applied mechanical loads, and it is based on the fact that the bone has the ability to adapt itself to the load conditions to which it is bearing. This adaptation process, including modelling and remodelling mechanisms, has an enormous effect on the overall behaviour and health of the entire body. Fo...

On some spectral problems of mathematical physics

The article contains a brief survey of some spectral problems of mathematical physics that have been arising recently in optics, mesoscopic systems, quantum chaos, and other areas. In particular, problems of photonic crystal theory, waveguides, and quantum graphs are addressed. This text is a modified version of the lectures delivered at the Pan-American Advanced Studies Institute (PASI) on Par...

Some Problems in the Theory of Dynamical Systems & Mathematical Physics *

Retrograde Axonal Degeneration in Parkinson Disease

In spite of tremendous research efforts we have not yet achieved two of our principal therapeutic goals in the treatment of Parkinson's disease (PD), to prevent its onward progression and to provide restoration of systems that have already been damaged by the time of diagnosis. There are many possible reasons for our inability to make progress. One possibility is that our efforts thus far may n...