Contents tagged “allometry”

There are 4 contents with the tag “allometry”:

  1. Which first principles for mathematical modelling in biology?

    Which first principles for mathematical modelling in biology?

    Rendiconti di Matematica e delle sue Applicazioni

    Like theoretical physics, theoretical biology is not just mathematical modeling. Instead, it should strive to find principles to frame experiments and models.

    Abstract

    Like theoretical physics, theoretical biology is not just mathematical modeling. Instead, theoretical biology should strive to find suitable first principles to ground the understanding of biological phenomena and ultimately frame biological experiments and mathematical models. First principles in physics are expressed in terms of symmetries and the associated conservations, on the one side, and optimization on the other side. In biology, we argue instead that a strong notion of variation is fundamental. This notion encompasses new possibilities and the historicity of biological phenomena. By contrast, the relative regularity of some aspects of biological organisms, which we call constraints, should be regarded as the consequence of a mutual stabilization of the parts of organisms. We exemplify several aspects of this framework with the modeling of allometric relationships. Our change of perspective leads to reconsider the meaning of measurements and the structure of the space of description.

    Keywords: Allometry, first principles, Historicity, invariants, theoretical biology, Variability

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  2. Perspectives on Organisms: Biological time, symmetries and singularities

    Perspectives on Organisms: Biological time, symmetries and singularities

    This authored monograph introduces a genuinely theoretical approach to biology. Starting point is the investigation of empirical biological scaling including their variability, which is found in the literature, e.g. allometric relationships, fractals, etc. The book then analyzes two different...

    Abstract

    This authored monograph introduces a genuinely theoretical approach to biology. Starting point is the investigation of empirical biological scaling including their variability, which is found in the literature, e.g. allometric relationships, fractals, etc. The book then analyzes two different aspects of biological time: first, a supplementary temporal dimension to accommodate proper biological rhythms; secondly, the concepts of protension and retention as a means of local organization of time in living organisms. Moreover, the book investigates the role of symmetry in biology, in view of its ubiquitous importance in physics. In relation with the notion of extended critical transitions, the book proposes that organisms and their evolution can be characterized by continued symmetry changes, which accounts for the irreducibility of their historicity and variability. The authors also introduce the concept of anti-entropy as a measure for the potential of variability, being equally understood as alterations in symmetry. By this, the book provides a mathematical account of Gould’s analysis of phenotypic complexity with respect to biological evolution. The target audience primarily comprises researchers interested in new theoretical approaches to biology, from physical, biological or philosophical backgrounds, but the book may also be beneficial for graduate students who want to enter this field.

    Citation
    Longo, G., and Maël Montévil. 2014. Perspectives on Organisms: Biological Time, Symmetries and Singularities. Lecture Notes in Morphogenesis. Heidelberg: Springer. https://doi.org/10.1007/978-3-642-35938-5
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  3. The Inert vs. the Living State of Matter: Extended Criticality, Time Geometry, Anti-Entropy — an overview

    The Inert vs. the Living State of Matter: Extended Criticality, Time Geometry, Anti-Entropy — an overview

    Frontiers in Physiology

    The physical singularity of life phenomena is analyzed by a comparison with the theories of the inert with a focus on criticality, time, and anti-entropy.

    Abstract

    The physical singularity of life phenomena is analyzed by means of comparison with the driving concepts of theories of the inert. We outline conceptual analogies, transferals of methodologies and theoretical instruments between physics and biology, in addition to indicating significant differences and sometimes logical dualities. In order to make biological phenomenalities intelligible, we introduce theoretical extensions to certain physical theories. In this synthetic paper, we summarize and propose a unified conceptual framework for the main conclusions drawn from work spanning a book and several articles, quoted throughout.

    Keywords: criticality, biological time, anti-entropy, theoretical biology, symmetry, allometry, incompleteness

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  4. A 2-dimensional geometry for biological time

    A 2-dimensional geometry for biological time

    Progress in Biophysics and Molecular Biology

    We frame several features of biological time with a 2-d manifold to accommodate autonomous biological rhythms both for individuals and comparisons.

    Abstract

    This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of life, such as rhythms, both physical (circadian, seasonal …) and properly biological (heart beating, respiration, metabolic …). In particular, the role of biological rhythms do not seem to have any counterpart in mathematical formalization of physical clocks, which are based on frequencies along the usual (possibly thermodynamical, thus oriented) time. We then suggest a functional representation of biological time by a 2-dimensional manifold as a mathematical frame for accommodating autonomous biological rhythms. The “visual” representation of rhythms so obtained, in particular heart beatings, will provide, by a few examples, hints towards possible applications of our approach to the understanding of interspecific differences or intraspecific pathologies. The 3- dimensional embedding space, needed for purely mathematical reasons, allows to introduce a suitable extra-dimension for “representation time”, with a cognitive significance.

    Keywords: Biological rhythms, Allometry, Biological rhythms, Circadian rhythms, Heartbeats, Rate variability

    Citation
    Bailly, F., G. Longo, and Maël Montévil. 2011. “A 2-Dimensional Geometry for Biological Time.” Progress in Biophysics and Molecular Biology 106 (3): 474–84. https://doi.org/10.1016/j.pbiomolbio.2011.02.001
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