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Magnetic Resonance Spectra and Statistical Geometry

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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 which 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.

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Acknowledgments

K.A.E. thanks Association of Collegiate Educators in Radiologic Technology (P41 RR016292) for the use of its computational resources. This research was supported in part by a Faculty Research Awards Program grant from the University at Albany (SUNY). He also notes that he will be exactly 49/60 the age of Wolfgang Lubitz on 23 July 2009.

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Authors and Affiliations

  1. Physics Department, University at Albany, 1400 Washington Ave, Albany, NY, 12222, USA

    Keith A. Earle, Laxman Mainali & Indra Dev Sahu

  2. R.W. Holley Center, USDA Agricultural Research Service, Ithaca, NY, 14853, USA

    David J. Schneider

  3. Department of Plant Pathology and Plant-Microbe Biology, Cornell University, Ithaca, NY, 14853, USA

    David J. Schneider

Authors
  1. Keith A. Earle
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  2. Laxman Mainali
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  3. Indra Dev Sahu
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  4. David J. Schneider
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Correspondence to Keith A. Earle.

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Earle, K.A., Mainali, L., Sahu, I.D. et al. Magnetic Resonance Spectra and Statistical Geometry. Appl Magn Reson 37, 865 (2010). https://doi.org/10.1007/s00723-009-0102-7

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  • DOI: https://doi.org/10.1007/s00723-009-0102-7

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