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A mathematics for medicine: The Network Effect.

West BJ - Front Physiol (2014)

Bottom Line: Therefore, when what had originally been made as a simplifying assumption or a working hypothesis becomes foundational to understanding the operation of physiologic networks it is in the best interests of science to replace or at least update that assumption.The observed ubiquity of inverse power laws in physiology entails the need for a new calculus, one that describes the dynamics of fractional phenomena and captures the fractal properties of the statistics of physiological time series.We identify these properties as a necessary consequence of the complexity resulting from the network dynamics and refer to them collectively as The Network Effect.

View Article: PubMed Central - PubMed

Affiliation: Mathematics and Information Science Directorate, Army Research Office Research Triangle Park, NC, USA.

ABSTRACT
The theory of medicine and its complement systems biology are intended to explain the workings of the large number of mutually interdependent complex physiologic networks in the human body and to apply that understanding to maintaining the functions for which nature designed them. Therefore, when what had originally been made as a simplifying assumption or a working hypothesis becomes foundational to understanding the operation of physiologic networks it is in the best interests of science to replace or at least update that assumption. The replacement process requires, among other things, an evaluation of how the new hypothesis affects modern day understanding of medical science. This paper identifies linear dynamics and Normal statistics as being such arcane assumptions and explores some implications of their retirement. Specifically we explore replacing Normal with fractal statistics and examine how the latter are related to non-linear dynamics and chaos theory. The observed ubiquity of inverse power laws in physiology entails the need for a new calculus, one that describes the dynamics of fractional phenomena and captures the fractal properties of the statistics of physiological time series. We identify these properties as a necessary consequence of the complexity resulting from the network dynamics and refer to them collectively as The Network Effect.

No MeSH data available.


Four PDF's are plotted on log-linear graph paper. The parabolic solid curve is a Normal PDF and the dashed is a Laplace PDF. The broader of the two remaining distributions is the Gumbel PDF given by Equation (4). The remaining extrema distribution is that of Fréchet (1927) and is discussed subsequently.
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Figure 1: Four PDF's are plotted on log-linear graph paper. The parabolic solid curve is a Normal PDF and the dashed is a Laplace PDF. The broader of the two remaining distributions is the Gumbel PDF given by Equation (4). The remaining extrema distribution is that of Fréchet (1927) and is discussed subsequently.

Mentions: Figure 1 compares the Normal and the Laplace (1810) PDF's to that of Gumbel as well as to a second type of extreme value PDF due to Fréchet (1927). Note that a PDF is obtained from the negative derivative of the probability so that for the Gumbel PDF we obtain from Equation (3)


A mathematics for medicine: The Network Effect.

West BJ - Front Physiol (2014)

Four PDF's are plotted on log-linear graph paper. The parabolic solid curve is a Normal PDF and the dashed is a Laplace PDF. The broader of the two remaining distributions is the Gumbel PDF given by Equation (4). The remaining extrema distribution is that of Fréchet (1927) and is discussed subsequently.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4260484&req=5

Figure 1: Four PDF's are plotted on log-linear graph paper. The parabolic solid curve is a Normal PDF and the dashed is a Laplace PDF. The broader of the two remaining distributions is the Gumbel PDF given by Equation (4). The remaining extrema distribution is that of Fréchet (1927) and is discussed subsequently.
Mentions: Figure 1 compares the Normal and the Laplace (1810) PDF's to that of Gumbel as well as to a second type of extreme value PDF due to Fréchet (1927). Note that a PDF is obtained from the negative derivative of the probability so that for the Gumbel PDF we obtain from Equation (3)

Bottom Line: Therefore, when what had originally been made as a simplifying assumption or a working hypothesis becomes foundational to understanding the operation of physiologic networks it is in the best interests of science to replace or at least update that assumption.The observed ubiquity of inverse power laws in physiology entails the need for a new calculus, one that describes the dynamics of fractional phenomena and captures the fractal properties of the statistics of physiological time series.We identify these properties as a necessary consequence of the complexity resulting from the network dynamics and refer to them collectively as The Network Effect.

View Article: PubMed Central - PubMed

Affiliation: Mathematics and Information Science Directorate, Army Research Office Research Triangle Park, NC, USA.

ABSTRACT
The theory of medicine and its complement systems biology are intended to explain the workings of the large number of mutually interdependent complex physiologic networks in the human body and to apply that understanding to maintaining the functions for which nature designed them. Therefore, when what had originally been made as a simplifying assumption or a working hypothesis becomes foundational to understanding the operation of physiologic networks it is in the best interests of science to replace or at least update that assumption. The replacement process requires, among other things, an evaluation of how the new hypothesis affects modern day understanding of medical science. This paper identifies linear dynamics and Normal statistics as being such arcane assumptions and explores some implications of their retirement. Specifically we explore replacing Normal with fractal statistics and examine how the latter are related to non-linear dynamics and chaos theory. The observed ubiquity of inverse power laws in physiology entails the need for a new calculus, one that describes the dynamics of fractional phenomena and captures the fractal properties of the statistics of physiological time series. We identify these properties as a necessary consequence of the complexity resulting from the network dynamics and refer to them collectively as The Network Effect.

No MeSH data available.