Interfacing biology, category theory and mathematical statistics

Pastor, Dominique; Beurier, Erwan; Ehresmann, Andrée; Waldeck, Roger

doi:10.4204/eptcs.323.9

Cited by 1 publication

(4 citation statements)

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“…We expect that this preliminary work along with our purely mathematical results in [18] can lay the groundwork to derive models of "fractal-like" holarchies, in the continuation of research works such as [3,4,8,26] among others. We can also expect that our approach could be beneficial to theoretical biology in the sought for new models for real components of the immune system, at di↵erent scales, from the molecule to the organism scale [25].…”

Section: Discussionmentioning

confidence: 78%

“…As such, these families should be convenient to model holons whose degenerative properties in signal detection and communication allow them to evolve with resilience in fluctuating contexts. A formal proof of this result can be achieved by mimicking the reasoning followed in [18]. It is not provided here because it would require a significant amount of additional material.…”

Section: A Multiplicity Of Families Of Update Functionsmentioning

confidence: 99%

Section: A Multiplicity Of Families Of Update Functionsmentioning

confidence: 99%

“…for signal detection in interference and noise A first attempt to embrace both the MP and the design of optimal tests within the same framework is provided in [18] from a pure statistical point of view. In what follows, we use arguments similar to those given in [18] to exhibit families of update functions that satisfy the MP. As a convenient shortcut, we hereafter say that these families of update functions are "degenerate" as compared to each other, as a reminder of the corresponding biological notion.…”

Section: A Multiplicity Of Families Of Update Functionsmentioning

confidence: 99%

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A multiplicity of statistical models for modeling the degeneracy of living communicating holons

2022

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Communicating living systems detect and process a multiplicity of events with degeneracy, to continuously cope with environmental aleatoric incertitude. The concept of holon, communicating at various scales of living organizations, is hereafter formalized through dynamical systems driven by the multiplicity of statistical models. Then, the stimulus-response of elementary biological holons can be modeled by memoryless Boolean automata with different signal processing methods, in presence of noise and stochastic interference. Detection of a specified signal, to update the automaton state, can be performed via multiple families of update functions, with differentiated balances between sensitivity and specificity in presence of interference: (i) Neyman-Pearson update functions provide the best possible sensitivity to detect the signal of interest in absence of interference, but cannot guarantee a desired specificity; (ii) by detecting large amplitudes of any signal in noise, update functions based on Random Distortion Testing yield a suboptimal sensitivity to detect the signal in noise, but guarantee a wanted specificity even in presence of interference. Thus, statistical inference theories offer functional and structural redundancy and open prospects to model fractal-like holarchies, via networks of communicating degenerated automata, to feature properties of the immune system.

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