Review article: Scaling, dynamical regimes, and stratification. How long does weather last? How big is a cloud? [PDF]
Nonlinear Processes in Geophysics, 2023 Until the 1980s, scaling notions were restricted to self-similar homogeneous special cases. I review developments over the last decades, especially in multifractals and generalized scale invariance (GSI).
S. Lovejoy
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Elliptic Self Similar Stochastic Processes [PDF]
Revista Matemática Iberoamericana, 1999 Let M be a random measure and L be an elliptic pseudo-differential operator on \mathbb{R}^d
Benassi, Albert, Roux, Daniel
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A Drive towards Thermodynamic Efficiency for Dissipative Structures in Chemical Reaction Networks
Entropy, 2021 Dissipative accounts of structure formation show that the self-organisation of complex structures is thermodynamically favoured, whenever these structures dissipate free energy that could not be accessed otherwise.
Kai Ueltzhöffer +3 more
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Can power-law scaling and neuronal avalanches arise from stochastic dynamics? [PDF]
PLoS ONE, 2010 The presence of self-organized criticality in biology is often evidenced by a power-law scaling of event size distributions, which can be measured by linear regression on logarithmic axes. We show here that such a procedure does not necessarily mean that
Jonathan Touboul, Alain Destexhe
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On copulas of self-similar Ito processes
Dependence Modeling, 2021 We characterize the cumulative distribution functions and copulas of two-dimensional self-similar Ito processes, with randomly correlated Wiener margins, as solutions of certain elliptic partial differential equations.
Jaworski Piotr, Krzywda Marcin
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Circadian KaiC phosphorylation: a multi-layer network. [PDF]
PLoS Computational Biology, 2009 Circadian KaiC phosphorylation in cyanobacteria reconstituted in vitro recently initiates a series of studies experimentally and theoretically to explore its mechanism.
Congxin Li +3 more
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Time scales in epigenetic dynamics and phenotypic heterogeneity of embryonic stem cells. [PDF]
PLoS Computational Biology, 2013 A remarkable feature of the self-renewing population of embryonic stem cells (ESCs) is their phenotypic heterogeneity: Nanog and other marker proteins of ESCs show large cell-to-cell variation in their expression level, which should significantly ...
Masaki Sasai +4 more
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Estimation of stopping times for stopped self-similar random processes [PDF]
, 2021 Let X=(Xt)t≥0 be a known process and T an unknown random time independent of X. Our goal is to derive the distribution of T based on an iid sample of XT. Belomestny and Schoenmakers (Stoch Process Appl 126(7):2092–2122, 2015) propose a solution based the
Schulmann, Viktor
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Identifying Arguments of Space-Time Fractional Diffusion: Data-Driven Approach
Frontiers in Applied Mathematics and Statistics, 2020 A plethora of complex dynamical systems from disordered media to biological systems exhibit mathematical characteristics (e.g., long-range dependence, self-similar and power law magnitude increments) that are well-fitted by fractional partial ...
Mohamed Ridha Znaidi +3 more
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The 𝑀-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey
International Journal of Differential Equations, 2010 In the present review we survey the properties of a transcendental function of the Wright type, nowadays known as 𝑀-Wright function, entering as a probability density in a relevant class of self-similar stochastic processes that we generally refer to as ...
Francesco Mainardi +2 more
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