{"title":"Optimal representation in biological systems.","authors":"Subhash Kak","doi":"10.1007/s12064-025-00444-9","DOIUrl":null,"url":null,"abstract":"<p><p>An optimal representation constitutes an efficient set. It is known that for an aggregating system if the cost of representation increases linearly with the number of bases, ternary coding is superior to binary, and coding in e is optimal. This paper investigates the relative efficiency of bases for the cases when the cost complexity is affine (slope-intercept linear), exponential, and logistic and presents new results. It is shown that for representation of structure in logistic maps, which applies often to biological systems and is true for input-output maps of neurons, the optimal base value is near 1.7632, which is consistent with the unary and space coding of information in songbirds. It is shown that the mathematical basis of this result is the solution to the equation <math> <mrow> <msup><mrow><mi>b</mi></mrow> <mi>b</mi></msup> <mo>=</mo> <mi>e</mi> <mo>.</mo></mrow></math></p>","PeriodicalId":54428,"journal":{"name":"Theory in Biosciences","volume":" ","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory in Biosciences","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1007/s12064-025-00444-9","RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BIOLOGY","Score":null,"Total":0}
引用次数: 0
Abstract
An optimal representation constitutes an efficient set. It is known that for an aggregating system if the cost of representation increases linearly with the number of bases, ternary coding is superior to binary, and coding in e is optimal. This paper investigates the relative efficiency of bases for the cases when the cost complexity is affine (slope-intercept linear), exponential, and logistic and presents new results. It is shown that for representation of structure in logistic maps, which applies often to biological systems and is true for input-output maps of neurons, the optimal base value is near 1.7632, which is consistent with the unary and space coding of information in songbirds. It is shown that the mathematical basis of this result is the solution to the equation
一个最优表示构成一个有效集合。众所周知，对于聚合系统，如果表示成本随着基数的数量线性增加，则三进制编码优于二进制编码，并且e编码是最优的。本文研究了代价复杂度为仿射（斜截线性）、指数和逻辑的情况下基的相对效率，并给出了新的结果。研究表明，对于逻辑图中结构的表示，最优基值接近1.7632，这与鸣禽信息的一元编码和空间编码是一致的，逻辑图常用于生物系统，也适用于神经元的输入-输出映射。结果表明，该结果的数学基础是方程b b = e的解。
期刊介绍：
Theory in Biosciences focuses on new concepts in theoretical biology. It also includes analytical and modelling approaches as well as philosophical and historical issues. Central topics are:
Artificial Life;
Bioinformatics with a focus on novel methods, phenomena, and interpretations;
Bioinspired Modeling;
Complexity, Robustness, and Resilience;
Embodied Cognition;
Evolutionary Biology;
Evo-Devo;
Game Theoretic Modeling;
Genetics;
History of Biology;
Language Evolution;
Mathematical Biology;
Origin of Life;
Philosophy of Biology;
Population Biology;
Systems Biology;
Theoretical Ecology;
Theoretical Molecular Biology;
Theoretical Neuroscience & Cognition.
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