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ARS Home » Research » Publications at this Location » Publication #243549

Title: Magnetic resonance spectra and statistical geometry

item Earle, Keith
item Sahu, Indra Dev
item Mainali, Laxman
item Schneider, David

Submitted to: Applied Magnetic Resonance
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 7/6/2009
Publication Date: 11/17/2009
Citation: Earle, K.A., Sahu, I., Mainali, L., Schneider, D.J. 2009. Magnetic resonance spectra and statistical geometry. Applied Magnetic Resonance. 37:865-880.

Interpretive Summary: Fitting equations describing a theoretical model to experimental data is a very difficult problem with many practical implications. This paper presents a novel approach to this general problem based on a synthesis of existing methods in common use in electrical engineering, mathematics and statistics. Several examples are explicitly worked out that demonstrate how the general methodology can be applied to concrete problems in chemistry.

Technical Abstract: Methods of statistical geometry are introduced which allow one to estimate, on the basis of computable criteria, the conditions under which maximally informative data may be collected. We note the important role of constraints that introduce curvature into parameter space and discuss the appropriate mathematical tools for treating curvature effects. Channel capacity, a term from communication theory, is suggested as a useful figure of merit for estimating the information content of spectra in the presence of noise. The tools introduced here are applied to the case of a model nitroxide system as a concrete example, but we stress that the methods described here are of general utility.