A Fractional Probability Calculus View of Allometry
The scaling of respiratory metabolism with body size in animals is considered by many to be a fundamental law of nature. An apparent corollary of this law is the scaling of physiologic time with body size, implying that physiologic time is separate and distinct from clock time. However, these are on...
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| Format: | Article |
| Language: | English |
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MDPI AG
2014-04-01
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| Series: | Systems |
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| Online Access: | http://www.mdpi.com/2079-8954/2/2/89 |
| _version_ | 1828113920658767872 |
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| author | Bruce J. West |
| author_facet | Bruce J. West |
| author_sort | Bruce J. West |
| collection | DOAJ |
| description | The scaling of respiratory metabolism with body size in animals is considered by many to be a fundamental law of nature. An apparent corollary of this law is the scaling of physiologic time with body size, implying that physiologic time is separate and distinct from clock time. However, these are only two of the many allometry relations that emerge from empirical studies in the physical, social and life sciences. Herein, we present a theory of allometry that provides a foundation for the allometry relation between a network function and the size that is entailed by the hypothesis that the fluctuations in the two measures are described by a scaling of the joint probability density. The dynamics of such networks are described by the fractional calculus, whose scaling solutions entail the empirically observed allometry relations. |
| first_indexed | 2024-04-11T12:17:29Z |
| format | Article |
| id | doaj.art-ca78eb0bdaa946d9b7fa0b337de24c48 |
| institution | Directory Open Access Journal |
| issn | 2079-8954 |
| language | English |
| last_indexed | 2024-04-11T12:17:29Z |
| publishDate | 2014-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Systems |
| spelling | doaj.art-ca78eb0bdaa946d9b7fa0b337de24c482022-12-22T04:24:15ZengMDPI AGSystems2079-89542014-04-01228911810.3390/systems2020089systems2020089A Fractional Probability Calculus View of AllometryBruce J. West0Mathematics and Information Sciences Directorate, Army Research Office, Research Triangle Park, NC 27709, USAThe scaling of respiratory metabolism with body size in animals is considered by many to be a fundamental law of nature. An apparent corollary of this law is the scaling of physiologic time with body size, implying that physiologic time is separate and distinct from clock time. However, these are only two of the many allometry relations that emerge from empirical studies in the physical, social and life sciences. Herein, we present a theory of allometry that provides a foundation for the allometry relation between a network function and the size that is entailed by the hypothesis that the fluctuations in the two measures are described by a scaling of the joint probability density. The dynamics of such networks are described by the fractional calculus, whose scaling solutions entail the empirically observed allometry relations.http://www.mdpi.com/2079-8954/2/2/89allometryfractional calculusprobability statisticsinverse power lawsLevy statistics |
| spellingShingle | Bruce J. West A Fractional Probability Calculus View of Allometry Systems allometry fractional calculus probability statistics inverse power laws Levy statistics |
| title | A Fractional Probability Calculus View of Allometry |
| title_full | A Fractional Probability Calculus View of Allometry |
| title_fullStr | A Fractional Probability Calculus View of Allometry |
| title_full_unstemmed | A Fractional Probability Calculus View of Allometry |
| title_short | A Fractional Probability Calculus View of Allometry |
| title_sort | fractional probability calculus view of allometry |
| topic | allometry fractional calculus probability statistics inverse power laws Levy statistics |
| url | http://www.mdpi.com/2079-8954/2/2/89 |
| work_keys_str_mv | AT brucejwest afractionalprobabilitycalculusviewofallometry AT brucejwest fractionalprobabilitycalculusviewofallometry |