Related papers: Ultrametric dynamics for the closed fractal-cluste…
In this work, we investigate the global structural properties and fractality of 1,876 open clusters (OCs) in different environments, including 1,145 singles, 392 pairs, and 339 groups. We analyze cluster mass, age, size, concentration, and…
The morphology of urban agglomeration is studied here in the context of information exchange between different spatio-temporal scales. Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity…
An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a hierarchical embedding. Such hierarchical structure can be global in the data set, or…
The equilibrium size distribution function of clusters (nanoparticles) in the system of finite number of molecules (atoms) in finite closed volume with constant total energy (isolated system) is found using methods of statistical…
We propose a dynamical scheme for the combined processes of fragmentation and merging as a model system for cluster dynamics in nature and society displaying scale invariant properties. The clusters merge and fragment with rates…
The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An…
It is shown that preferential concentrations of inertial (finite-size) particle suspensions in turbulent flows follow from the dissipative nature of their dynamics. In phase space, particle trajectories converge toward a dynamical fractal…
Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition…
The formation, movement and gluing of clusters can be described through a system of non local balance laws. Here, the well posedness of this system is obtained, as well as various stability estimates. Remarkably, qualitative properties of…
Complex-dynamical fractal is a hierarchy of permanently, chaotically changing versions of system structure, obtained as the unreduced, causally probabilistic general solution of arbitrary interaction problem (physics/0305119,…
Policy-makers are often faced with the task of distributing a limited supply of resources. To support decision-making in these settings, statisticians are confronted with two challenges: estimands are defined by allocation strategies that…
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale…
For many externally driven complex systems neither the noisy driving force, nor the internal dynamics are a priori known. Here we focus on systems for which the time dependent activity of a large number of components can be monitored,…
Hierarchical clustering is a powerful tool for exploratory data analysis, organizing data into a tree of clusterings from which a partition can be chosen. This paper generalizes these ideas by proving that, for any reasonable hierarchy, one…
Fractal structures and non-Gaussian velocity distributions are characteristic properties commonly observed in virialized self-gravitating systems such as galaxies or interstellar molecular clouds. We study the origin of these properties…
A paradigmatic nonhyperbolic dynamical system exhibiting deterministic diffusion is the smooth nonlinear climbing sine map. We find that this map generates fractal hierarchies of normal and anomalous diffusive regions as functions of the…
We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite time interval as a high-dimensional data point and then cluster these data…
We investigate the thermodynamics as well as the population dynamics of ecosystems based on a stochastic approach in which the number of individuals of the several species of the ecosystem are treated as stochastic variables. The several…
In many self-organising systems the ability to extract necessary resources from the external environment is essential to the system's growth and survival. Examples include the extraction of sunlight and nutrients in organic plants, of…
The competition for resources is a defining feature of microbial communities. In many contexts, from soils to host-associated communities, highly diverse microbes are organized into metabolic groups or guilds with similar resource…