Related papers: Toward a deeper understanding of a basic cascade
Recent discussion of the possibility to study intermittency in individual events of high multiplicity by A. Bialas and myself is reported. In the framework of $\alpha-$model it is found that, for a cascade long enough, the dispersion of…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
Markovian properties of a discrete random multiplicative cascade model of log-normal type are discussed. After taking small-scale resummation and breaking of the ultrametric hierarchy into account, qualitative agreement with Kramers-Moyal…
This is our current research perspective on models providing insight into statistical mechanics. It is necessarily personal, emphasizing our own interest in simulation as it developed from the National Laboratories' work to the worldwide…
The complex dynamics of physical systems can often be modeled with stochastic differential equations. However, computational constraints inhibit the estimation of dynamics from large time-series datasets. I present a method for estimating…
This paper is the forth part of our series of work, is devoted to the analysis on the multiscales and cascade aspects of the statistical theory of isotropic turbulence based on the new Sedov-type solution. In this paper, we use the explicit…
Many complex systems have natural representations as multi-layer networks. While these formulations retain more information than standard single-layer network models, there is not yet a fully developed theory for computing network metrics…
The characterization of intermittency in turbulence has its roots in the K62 theory, and if no proper definition is to be found in the literature, statistical properties of intermittency were studied and models were developed in attempt to…
Detecting anomalies in link streams that represent various kinds of interactions is an important research topic with crucial applications. Because of the lack of ground truth data, proposed methods are mostly evaluated through their ability…
In recent years, machine learning models have been increasingly applied to spectroscopic datasets for chemical and biomedical analysis. For their successful adoption, particularly in clinical and safety-critical settings, professionals and…
We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…
The possibility to study intermittency in a single event of high multiplicity is investigated in the framework of the $\alpha-$model. It is found that, for cascade long enough, the dispersion of intermittency exponents obtained from…
Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are…
We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been already understood. Our motivating examples come from systems…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
In this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a $b$-cotangent model. We provide physical interpretations of the singular symplectic geometry underlying in…
We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. We develop a new importance-sampling procedure in simulation, based on rare events around "holes", that enables us to access bootstrap…
We introduce a variant of continuous random cascade models that extends former constructions introduced by Barral-Mandelbrot and Bacry-Muzy in the sense that they can be supported by sets of arbitrary fractal dimension. The so introduced…
Turbulent cascades characterize the transfer of energy injected by a random force at large scales towards the small scales. In hydrodynamic turbulence, when the Reynolds number is large, the velocity field of the fluid becomes irregular and…
Multiplicative cascades have been used in turbulence to generate fields with multifractal statistics and long-range correlations. Examples of continuous and causal stochastic processes which generate such a random field have been carefully…