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Entropy and Diversity: The Axiomatic Approach

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arxiv 2012.02113 v4 pith:WFKNLUEN submitted 2020-12-03 q-bio.PE cs.ITmath.CAmath.CTmath.ITq-bio.QM

classification q-bio.PEcs.ITmath.CAmath.CTmath.ITq-bio.QM
keywords theorydiversitymathematicalaxiomaticbiologicalbookentropyanalysis
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This book brings new mathematical rigour to the ongoing vigorous debate on how to quantify biological diversity. The question "what is diversity?" has surprising mathematical depth, and breadth too: this book involves parts of mathematics ranging from information theory, functional equations and probability theory to category theory, geometric measure theory and number theory. It applies the power of the axiomatic method to a biological problem of pressing concern, but the new concepts and theorems are also motivated from a purely mathematical perspective. The main narrative thread requires no more than an undergraduate course in analysis. No familiarity with entropy or diversity is assumed.

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Cited by 1 Pith paper

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  1. X-Factor: Quality Is a Dataset-Intrinsic Property

    cs.LG 2025-05 conditional novelty 5.0 of 10

    Across 2,500 class-balanced MNIST subsets and 10 model architectures, test-error Z-scores correlate strongly across models (mean R2=0.82 excluding GNB), supporting dataset quality as an intrinsic property.

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