The e-Dimensionality Information Principle
Data, Representation, and Algorithms
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Product details:
- Edition number 1
- Publisher Chapman and Hall
- Date of Publication 8 April 2026
- ISBN 9781041224303
- Binding Hardback
- No. of pages212 pages
- Size 234x156 mm
- Language English
- Illustrations 45 Illustrations, black & white; 62 Illustrations, color; 22 Halftones, color; 45 Line drawings, black & white; 40 Line drawings, color; 22 Tables, black & white 700
Categories
Short description:
- Analyses algorithms that generate optimal dimensionality fractals of different kinds, ranging from linear structures to three-dimensional ones.
- Useful in simulation of natural phenomena, and they lead to novel methods of optimization.
Long description:
This book is based on an information-theoretic result according to which optimal information is associated with e-dimensionality. Drawing on the principle that nature chooses optimal solutions, it demonstrates that noninteger dimensionality provides a unifying framework for understanding diverse phenomena across physics, cosmology, biology, engineering, and data science. The work explores how optimal information representation naturally leads to scale-invariance and self-similarity – characteristics observed throughout natural systems, from fractals and genetic structures to evolutionary processes and neural networks. This book:
• Reveals why three-way logic is superior to binary logic in natural systems and provides an information-theoretic rationale for the power laws frequently encountered across scientific applications
• Explains fundamental biological mysteries, including the non-uniform groupings of codons in the genetic code (ranging from one to six per amino acid), and offers novel insights into chromatin geometry and evolutionary dynamics
• Addresses the reproducibility crisis in biomedical research by proposing new significance testing approaches based on noninteger dimensionality that move beyond traditional binary hypothesis testing methods
Written for researchers and graduate students in electrical engineering, computer science, physics, and biology, this work serves as both an advanced textbook for senior-level and graduate courses and a research resource providing fresh perspectives on longstanding problems across multiple disciplines.
MoreTable of Contents:
1. Information and optimal representation. 2. The intrinsic dimensionality of data. 3. Fractals with optimal information dimension. 4. Self-similarity, maximum entropy principle, and the genetic code. 5. Information optimality and the geometry of chromatin. 6. Autonomous cognitive agents in a neural network. 7. Evolutionary stages in the universe. 8. Nonlocal noise and self-decoherence. 9. Significance testing in natural and biological systems. 10. Epilogue.
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