Get Gröbner Bases and Convex Polytopes PDF

By Bernd Sturmfels

ISBN-10: 0821804871

ISBN-13: 9780821804872

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This is a simple method for avoiding double counts, and its particular strength is that it is completely independent of the size and shape of the objects being counted. That is, with this method, the two parameters, size and number, cannot be confused. If the two sections are physically separate sections (the 'physical disector') then the process is difficult because the two sections need to be precisely matched so that objects on one section can be matched against objects on the next section. Furthermore, the method often cannot be used on archival material where complete series may not be available, either because different stains were used for adjacent sections, or sections were not mounted as complete series.

1). I f all o f the profiles in the s a m p l e d parts o f the sections are c o u n t e d (profile counts), then the severity o f this bias, and the extent to w h i c h it can be r e c o g n i z e d and c o r r e c t e d d e p e n d s on h o w m u c h the o b s e r v e r k n o w s about the shape and the size o f the objects and the thickness o f the sections. T h e less one k n o w s about the shape and the Fig. 1. Schema to represent the use of the Abercrombie correction for a profile count.

Given the danger that the term 'assumption-free', when applied to a quantitative method, will lead to a false sense of security about the reliability of the results and their interpretation, it may be best for the term to he avoided altogether and replaced by a thoughtful and complete account of the tissues that have been used, and the methods employed to avoid a biased result. Acknowledgements We thank Dr. B. Pawley for helpful discussions of some of the optical problems, Dr. W. Stretton for helpful comments on an earlier draft, and Dr.

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Gröbner Bases and Convex Polytopes by Bernd Sturmfels

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