Related papers: Hierarchical Gompertzian growth maps with applicat…
Increasing inhomogeneity due to gravitational clumping reflects increasing gravitational entropy in a time evolving universe. Starting from an ensemble of uniformly distributed particles it is demonstrated that gravitational clustering is…
Cell size control and homeostasis is a major topic in cell biology yet to be fully understood. Several growth laws like the timer, adder, and sizer were proposed, and mathematical approaches that model cell growth and division were…
Growth-fragmentation processes describe systems of particles in which each particle may grow larger or smaller, and divide into smaller ones as time proceeds. Unlike previous studies, which have focused mainly on the self-similar case, we…
Due to their relevance to geophysical systems, the investigation of multiscale systems through the lens of statistical mechanics has gained popularity in recent years. The aim of our work is the characterization of the nonequilibrium…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
Roughly speaking, let us say that a map between metric spaces is large scale conformal if it maps packings by large balls to large quasi-balls with limited overlaps. This quasi-isometry invariant notion makes sense for finitely generated…
Recently, we developed a theory of a geometrically growing system. Here we show that the theory can explain some phenomena of power-law distribution including classical demographic and economic and novel pandemic instances, without…
We consider the set of all 2-step recurrences (difference equations) that are given by linear fractional maps. These give birational maps of the plane. We determine the degree growth of these birational maps. We find the all the maps in…
This work is focused on constructing space-time covariance functions through a hierarchical mixture approach that can serve as building blocks for capturing complex dependency structures. This hierarchical mixture approach provides a…
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…
The photometric evolution of galaxies in a hierarchically clustering universe is investigated. The study is based on high resolution numerical simulations which include the effects of gas dynamics, shock heating, radiative cooling and a…
To understand large, connected systems, we cannot only zoom into the details. We also need to see the large-scale features from afar. One way to take a step back and get the whole picture is to model the systems as a network. However, many…
We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with Hermitian matrices whose elements perform a random walk in the space of complex numbers, satisfy certain partial…
Considering the flexibility and applicability of Bayesian modeling, in this work we revise the main characteristics of two hierarchical models in a regression setting. We study the full probabilistic structure of the models along with the…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal…
An extension of coupled maps is given which allows for the growth of the number of elements, and is inspired by the cell differentiation problem. The growth of elements is made possible first by clustering the phases, and then by…
The ghost-free theory of massive gravity with two dynamical metrics has been shown to produce viable cosmological expansion, where the late-time acceleration of the Universe is due to the finite range of the gravitational interaction rather…
We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to…