Related papers: Universal growth scaling law determined by dimensi…
Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
Publicly traded companies are fundamental units of contemporary economies and markets and are important mechanisms through which humans interact with their environments. Understanding the general properties that underlie the processes of…
We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…
Understanding how size influences the internal characteristics of a system is a crucial concern across various fields. Concepts like scale invariance, universalities, and fractals are fundamental to this inquiry and find application in…
Life systems are complex and hierarchical, with diverse components at different scales, yet they sustain themselves, grow, and evolve over time. How can a theory of such complex biological states be developed? Here we note that for a…
The objective of statistical physics is to understand macroscopic behavior of a many-body system from the interactions of the constituents of that system. When many-body systems reach critical states, simple universal and scaling behaviors…
We study the growth dynamics of the size of manufacturing firms considering competition and normal distribution of competency. We start with the fact that all components of the system struggle with each other for growth as happened in real…
Diffusion processes are central to human interactions. One common prediction of the current modeling frameworks is that initial spreading dynamics follow exponential growth. Here, we find that, ranging from mobile handsets to automobiles,…
In the present work, via computational simulation we study the statistical distribution of people versus number of steps acquired by them in a learning process, considering Darwin classical theory of evolution, i.e. competition, learning…
Universality in the behavior of complex systems often reveals itself in the form of scale-invariant distributions that are essentially independent of the details of the microscopic dynamics. A representative paradigm of complex behavior in…
Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality.…
Cities are often compared through scaling laws, usually expressed as power-law relations between population size and aggregate urban quantities related to infrastructure, socioeconomic activity, or environmental impacts. These laws are…
Predicting dynamic behaviors is one of the goals of science in general as well as essential to many specific applications of human knowledge to real world systems. Here we introduce an analytic approach using the sigmoid growth curve to…
In the past many papers have appeared which simulated surface growth with different growth models. The results showed that, if models differed only slightly in their `growth' rules, the resulting surfaces may belong to different…
Deep neural networks exhibit empirical neural scaling laws, with error decreasing as a power law with increasing model or data size, across a wide variety of architectures, tasks, and datasets. This universality suggests that scaling laws…
We have studied the kinetics of cluster formation for dynamical systems of dimensions up to $n=8$ interacting through elastic collisions or coalescence. These systems could serve as possible models for gas kinetics, polymerization and…
When a system is brought to a metastable state, nuclei of the equilibrium phase form and grow. This is the well-known nucleation and growth of first-order phase transitions. Near a critical point of a continuous phase transition, critical…
We develop a ``unified'' model that describes both ``micro'' and ``macro'' evolutions within a single theoretical framework. The eco-system is described as a dynamic network; the population dynamics at each node of this network describes…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…