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Intrinsic limits on dimension calculations
Institution:1. Section of Gastroenterology, Fox Chase Cancer Center, Philadelphia, Pennsylvania, USA;2. Department of Pathology, Brigham and Women''s Hospital, Boston, Massachusetts, USA;3. Department of Gastroenterology, Dartmouth-Hitchcock Medical Center, Lebanon, New Hampshire, USA;4. Department of Gastroenterology, VA Medical Center, White River Junction, Vermont, USA;1. Department of Physical Sciences, Earth and Environment, Via Roma 56, I-53100 Siena, Italy;2. INFN Sezione di Pisa, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy;3. Department of Physics, University of Pisa, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy;4. Department of Physics and Astronomy, University of Padova, Padova, Italy, and INFN-Padova, 35131 Padova, Italy;5. Fondazione Bruno Kessler (FBK), I-38122 Trento, Italy;1. Institute of Philosophy, Czech Academy of Sciences, Czech Republic;2. Institute of Philosophy, Pontifical Catholic University of Valparaíso, Chile;1. Theoretical Molecular Science Laboratory, RIKEN, Wako, Saitama, Japan;2. Interdisciplinary Theoretical Science Research Group (iTHES), RIKEN, Wako, Saitama, Japan;3. Quantitative Biology Center, RIKEN, Kobe, Hyogo, Japan;4. Advanced Institute for Computational Science, RIKEN, Kobe, Hyogo, Japan;5. Laboratory of Membrane Molecular Biology, Graduate School of Biological Sciences, Nara Institute of Science and Technology, Nara, Japan;6. Department of Biophysics and Biochemistry, The University of Tokyo, Tokyo, Japan;1. Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Brazil;2. Multinational Organization Network Sponsoring Translational and Epidemiological Research (MONSTER) Initiative, Salvador, Brazil;3. Faculdade de Tecnologia e Ciências (FTC), Salvador, Brazil;4. Universidade Salvador (UNIFACS), Laureate Universities, Salvador, Brazil;5. Escola Bahiana de Medicina e Saúde Pública (EBMSP), Salvador, Brazil
Abstract:The combined influences of boundary effects at large scales and nonzero nearest neighbor separations at small scales are used to compute intrinsic limits on the minimum size of a data set required for calculation of scaling exponents. A lower bound on the number of points required for a reliable estimation of the correlation exponent is given in terms of the dimension of the object and the desired accuracy. A method of estimating the correlation integral computed from a finite sample of a white noise signal is given.
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