A Fractional Probability Calculus View of Allometry

West, Bruce J.

doi:10.3390/systems2020089

Cited by 6 publications

(5 citation statements)

References 115 publications

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“…Considering all L levels for both inactive and active metabolic rates, b is predicted to show a V-or U-shaped relationship with L [22,30]. No other current mechanistic model makes this prediction (but for a possible explanation based on fractional probability calculus, see [19,20]).…”

Section: Covariation Of the Elevation (L) And Slope (B) Of Metabolic mentioning

confidence: 98%

“…Not surprisingly, frequent attempts have been made to use the quantitative methods of physics, a field which focuses largely on natural laws, to explain Kleiber's law (e.g., [6][7][8][9][10][11][12][13][14][15][16][17]). However, these mostly deterministic explanations (but see [18][19][20]) have failed to explain fully the marked diversity of metabolic scaling relationships that actually exists in the living world (b ranging between ~0 to >1, but mostly between 2/3 and 1 [21][22][23][24][25]). Thus, there has been a need for new theoretical approaches to explain this diversity.…”

Section: Introductionmentioning

confidence: 99%

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Scaling of Metabolic Scaling within Physical Limits

Glazier

2014

Systems

204

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Both the slope and elevation of scaling relationships between log metabolic rate and log body size vary taxonomically and in relation to physiological or developmental state, ecological lifestyle and environmental conditions. Here I discuss how the recently proposed metabolic-level boundaries hypothesis (MLBH) provides a useful conceptual framework for explaining and predicting much, but not all of this variation. This hypothesis is based on three major assumptions: (1) various processes related to body volume and surface area exert state-dependent effects on the scaling slope for metabolic rate in relation to body mass; (2) the elevation and slope of metabolic scaling relationships are linked; and (3) both intrinsic (anatomical, biochemical and physiological) and extrinsic (ecological) factors can affect metabolic scaling. According to the MLBH, the diversity of metabolic scaling relationships occurs within physical boundary limits related to body volume and surface area. Within these limits, specific metabolic scaling slopes can be predicted from the metabolic level (or scaling elevation) of a species or group of species. In essence, metabolic scaling itself scales with metabolic level, which is in turn contingent on various intrinsic and extrinsic conditions operating in physiological or evolutionary time. The MLBH represents a "meta-mechanism" or collection of multiple, specific mechanisms that have contingent, state-dependent effects. As such, the MLBH is Darwinian in approach (the theory of natural selection is also meta-mechanistic), in contrast to currently influential metabolic scaling theory that is Newtonian in approach (i.e., based on unitary deterministic laws). Furthermore, the MLBH can be viewed as part of a more general theory that includes other mechanisms that may also affect metabolic scaling.

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Section: Covariation Of the Elevation (L) And Slope (B) Of Metabolic mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Scaling of Metabolic Scaling within Physical Limits

Glazier

2014

Systems

204

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“…Maximization of organism metabolic capacity and internal efficiency via maximized exchange surface area scaling and minimized internal transport distances and times are related to fractal geometry and might be a reason for its abundance in biology ( West et al. 1999b ; West 2014 ). Also, there is a close connection between plant root fractal dimension and drought stress ( Wang et al.…”

Section: Scale-free Systems In General and In Naturementioning

confidence: 99%

The fractal brain: scale-invariance in structure and dynamics

et al. 2022

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The past 40 years have witnessed extensive research on fractal structure and scale-free dynamics in the brain. Although considerable progress has been made, a comprehensive picture has yet to emerge, and needs further linking to a mechanistic account of brain function. Here, we review these concepts, connecting observations across different levels of organization, from both a structural and functional perspective. We argue that, paradoxically, the level of cortical circuits is the least understood from a structural point of view and perhaps the best studied from a dynamical one. We further link observations about scale-freeness and fractality with evidence that the environment provides constraints that may explain the usefulness of fractal structure and scale-free dynamics in the brain. Moreover, we discuss evidence that behavior exhibits scale-free properties, likely emerging from similarly organized brain dynamics, enabling an organism to thrive in an environment that shares the same organizational principles. Finally, we review the sparse evidence for and try to speculate on the functional consequences of fractality and scale-freeness for brain computation. These properties may endow the brain with computational capabilities that transcend current models of neural computation and could hold the key to unraveling how the brain constructs percepts and generates behavior.

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“…Furthermore, by using the uniform fractional probability density function, the classical probability axioms are validated for a fractional probability measure. For more details, the reader is recommended to consult the research works presented in [19,27] The idea of local fractional calculus [22,32,33], which was first proposed by Kolwankar and Gangal [14] based on the Riemann-Liouville fractional derivative [13], was employed to deal with non-differentiable problems in science and engineering [29]. Yang et al [28,29,30,31] presented the logical generalizations of the definitions to the subject of local derivative on fractals.…”

Section: A Brief Review Of Prerequisites Based On Local Fractionalmentioning

confidence: 99%

Mittag-leffler string stability of singularly perturbed stochastic systems within local fractal space

Sayevand

2019

Mathematical Modelling and Analysis

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In this paper, we define a new type of string stability based on Mittag-Leffler function so-called Mittag-Leffler (p\alpha)-string stability. This kind of stability for a class of singularly perturbed stochastic systems of fractional order will be considered. The fractional derivative in these systems is in the local sense. String stability indicates uniform boundedness of the interconnected system if the initial cases of interconnected system be uniformly bounded. The deduction of the sufficient conditions of stability is based on a mixture of the concept of the Mittag-Leffler stability with the notion of p-mean string stability of singularly perturbed stochastic systems. In the sequel, our purpose is to investigate the full order system in their lower order subsystems, i.e., the reduced order system and the boundary layer correction.

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A Fractional Probability Calculus View of Allometry

Cited by 6 publications

References 115 publications

Scaling of Metabolic Scaling within Physical Limits

Scaling of Metabolic Scaling within Physical Limits

The fractal brain: scale-invariance in structure and dynamics

Mittag-leffler string stability of singularly perturbed stochastic systems within local fractal space

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