Mathematical treatment of some problems in physiology

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...

From Inverse Problems in Mathematical Physiology to Quantitative Differential Diagnoses

The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patien...

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