Related papers: Hierarchical Gompertzian growth maps with applicat…
Modeling of growth (or decay) curves arises in many fields such as microbiology, epidemiology, marketing, and econometrics. Parametric forms like Logistic and Gompertz are often used for modeling such monotonic patterns. While useful for…
This work faces the problem of the origin of the logarithmic character of the Gompertzian growth. We show that the macroscopic, deterministic Gompertz equation describes the evolution from the initial state to the final stationary value of…
A macroscopic model of the tumor Gompertzian growth is proposed. This approach is based on the energetic balance among the different cell activities, described by methods of statistical mechanics and related to the growth inhibitor factors.…
A macroscopic model of the tumor Gompertzian growth is proposed. The new approach is based on the energetic balance among the different cell activities, described by methods of statistical mechanics and related to the growth inhibitor…
We derive, in order of magnitude, the observed astrophysical and cosmological scales in the Universe, from neutron stars to superclusters of galaxies, up to, asymptotically, the observed radius of the Universe. This result is obtained by…
A class of models for large-scale evolution and mass extinctions is presented. These models incorporate environmental changes on all scales, from influences on a single species to global effects. This is a step towards a unified picture of…
We introduce a model of a randomly growing interface in multidimensional Euclidean space. The growth model incorporates a random order model as an ingredient of its graphical construction, in a way that replicates the connection between the…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…
We introduce a model of Poincar\'e mappings which represents hierarchical structure of phase spaces for systems with many degrees of freedom. The model yields residence time distribution of power type, hence temporal correlation remains…
A classification in universality classes of broad categories of phenomenologies, belonging to different disciplines, may be very useful for a crossfertilization among them and for the purpose of pattern recognition. We present here a simple…
In this contribution, we investigate hierarchical nature of large-scale structure clustering through the oscillatory nature of the solutions of the Schr\"{o}dinger-like Friedmann equation in a modified gravitational background described by…
Prime numbers appeared in contexts spanning statistical mechanics, quantum mechanics and dynamical systems. However, the mechanisms governing the irregularities observed in their sequence and linking them to physical systems remained…
Hierarchical modeling provides a framework for modeling the complex interactions typical of problems in applied statistics. By capturing these relationships, however, hierarchical models also introduce distinctive pathologies that quickly…
We introduce a class of random graphs with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration model, and on the intra-community level, every vertex in the…
In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This…
This article studies the sequence of iterative degrees of a birational map of the plane. This sequence is known either to be bounded or to have a linear, quadratic or exponential growth. The classification elements of infinite order with a…
The discovery of a population of massive, compact and quiescent early-type galaxies has changed the view on plausible formation scenarios for the present day population of elliptical galaxies. Traditionally assumed formation histories…
Different classes of phenomenological universalities of environment dependent growths have been proposed. The logistic as well as environment dependent West-type allometry based biological growth can be explained in this proposed framework…
The aim of this paper is to present the technique (and its linkage with physics) of overcoming problems connected to modeling social structures, which are typically hierarchical. Hierarchical Linear Models provide a conceptual and…