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International Journal of Clinical Medicine Research

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Erroneous Definition of the Information Dimension in Two Medical Applications

International Journal of Clinical Medicine Research
Vol.4 , No. 6, Publication Date: Nov. 16, 2017, Page: 72-75

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Authors

[1]	Eric Rosenberg, AT&T Labs, Middletown, NJ, USA.

Abstract

Schizophrenia, Asthma, Information Dimension, Entropy, Fractals, Complex Networks

Keywords

The information dimension d_I of a geometric object (e.g., grey matter) is one of several fractal dimensions that have been used in medicine. The information dimension d_I is computed from N data points (e.g., pixels or voxels) by imposing a uniform grid (with grid box size s) covering the N points, measuring the number of points in each box of the grid, computing the resulting probability distribution, computing the entropy H(s) associated with this probability distribution

Reference

[01]	F. A. Bais and J. D. Farmer, “The Physics of Information”, chapter in Philosophy of Information, edited by P. Adriaans and J. van Benthem (Elsevier, Oxford, United Kingdom, 2008).
[02]	S. R. Boser, H. Park, S. F. Perry, M. C. Menache, and F. H. Y. Green, “Fractal Geometry of Airway Remodelling in Human Asthma”, American Journal of Respiratory and Critical Care Medicine 172 (2005) pp. 817-823.
[03]	L. da F. Costa, F. A. Rodrigues, G. Travieso and P. R. Villas Boas, “Characterization of Complex Networks: A Survey of Measurements”, Advances in Physics 56 (2007) pp. 167-242.
[04]	J. D. Farmer, “Dimension, Fractal Measures, and Chaotic Dynamics”, in Evolution of Order and Chaos, Springer Series in Synergetics 17 (1982) pp. 228-246.
[05]	J. D. Farmer, “Information Dimension and the Probabilistic Structure of Chaos”, Z. Naturforsch. 37a (1982) pp. 1304-1325.
[06]	J. Goni, O. Sporns, H. Cheng, M. Aznarez-Sanado, Y. Wang, S. Josa, G. Arrondo, V. P. Mathews, T. A. Hummer, W. G. Kronenberger, A. Avena-Koenigsberger, A. J. Saykin, and M. A. Pastor, “Robust Estimation of Fractal Measures for Characterizing the Structural Complexity of the Human Brain: Optimization and Reproducibility”, NeuroImage 83 (2013) pp. 646-657.
[07]	P. Grassberger, “Generalized Dimensions of Strange Attractors”, Physics Letters 97A (1983) pp. 227-230.
[08]	P. Grassberger and I. Procaccia, “Characterization of Strange Attractors”, Physical Review Letters 50 (1983) pp. 346-349.
[09]	P. Grassberger and I. Procaccia, “Measuring the Strangeness of Strange Attractors”, Physica 9D (1983) pp. 189-208.
[10]	J. M. Halley, S. Hartley, A. S. Kallimanis, W. E. Kunin, J. J. Lennon, and S. P. Sgardelis, “Uses and Abuses of Fractal Methodology in Ecology", Ecology Letters 7 (2004) pp. 254-271.
[11]	H. G. E. Hentschel and I. Procaccia, “The Infinite Number of Generalized Dimensions of Fractals and Strange Attractors”, Physica D 8 (1983) pp. 435-444.
[12]	E. A. Karuza, S. L. Thompson-Schill, and D. S. Bassett, “Local Patterns to Global Architectures: Influences of Network Topology on Human Learning", Trends in Cognitive Sciences 20 (2016) pp. 629-640.
[13]	H. O. Peitgen, H. Jurgens, and D. Saupe, Chaos and Fractals (Springer-Verlag, New York, 1992).
[14]	E. Rosenberg, “Maximal Entropy Coverings and the Information Dimension of a Complex Network”, Physics Letters A 381 (2017) pp. 574-580.
[15]	E. Rosenberg, “Minimal Partition Coverings and Generalized Dimensions of a Complex Network”, Physics Letters A 381 (2017) pp. 1659-1664.
[16]	E. Rosenberg, “Non-monotonicity of the Generalized Dimensions of a Complex Network”, Physics Letters A 381 (2017) pp. 2222-2229.
[17]	M. Rubinov and O. Sporns, “Complex Network Measures of Brain Connectivity: Uses and Interpretations”, NeuroImage 52 (2010) pp. 1059-1069.
[18]	D. Ruelle, “Deterministic Chaos: The Science and the Fiction (The 1989 Claude Bernard Lecture)”, Proc. R. Soc. Lond. A 427 (1990) pp. 241-248.
[19]	C. Song, L. K. Gallos, S. Havlin, and H. A. Makse, “How to Calculate the Fractal Dimension of a Complex Network: the Box Covering Algorithm”, Journal of Statistical Mechanics: Theory and Experiment (2007) P03006.
[20]	J. Theiler, “Estimating Fractal Dimension”, J. Optical Society of America A 7 (1990) pp. 1055-1073.
[21]	G. Zhao, K. Denisova, P. Sehatpour, J. Long, W. Gui, J. Qiao, D. C. Javitt, and Z. Wang, “Fractal Dimension Analysis of Subcortical Gray Matter Structures in Schizophrenia”, PLOS ONE 11 (2016) e0155415.