Related papers: Universal growth scaling law determined by dimensi…
The unreduced, universally nonperturbative analysis of arbitrary interaction process, described by a quite general equation, provides the truly complete, "dynamically multivalued" general solution that leads to dynamically derived,…
Compositional understanding is crucial for human intelligence, yet it remains unclear whether contemporary vision models exhibit it. The dominant machine learning paradigm is built on the premise that scaling data and model sizes will…
Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive.…
In this work we analyze the universal scaling functions and the critical exponents at the upper critical dimension of a continuous phase transition. The consideration of the universal scaling behavior yields a decisive check of the value 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…
The population loss of trained deep neural networks often follows precise power-law scaling relations with either the size of the training dataset or the number of parameters in the network. We propose a theory that explains the origins of…
Mathematical modelling of the evolution of the size-spectrum dynamics in aquatic ecosystems was discovered to be a powerful tool to have a deeper insight into impacts of human- and environmental driven changes on the marine ecosystem. In…
In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of…
Urban land growth presents a major sustainability challenge, yet its growth patterns and dynamics remain unclear. We quantified urban land evolution by analyzing its statistical distribution in 14 regions and countries over 29 years. The…
The report considers the dynamics of the global population as the unique case of the Socio-Economic Soft Matter system. This category was introduced for complex systems dominated by mesoscale assemblies, emerging due to the inherent…
We explain the anomaly of election results between large cities and rural areas in terms of urban scaling in the 1948-2016 US elections and in the 2016 EU referendum of the UK. The scaling curves are all universal and depend on a single…
Turbulence is a fundamental flow phenomenon, typically anisotropic at large scales and approximately isotropic at small scales. The classical Kolmogorov scaling laws (2/3, -5/3 and 4/5) have been well-established for turbulence without…
With the number of fully-sequenced genomes now well over a hundred it has become possible to start investigating if there are any quantitative regularities in the genetic make-up of genomes. In (physics/0307001), I originally showed that…
Because of increasing global urbanization and its immediate consequences, including changes in patterns of food demand, circulation and land use, the next century will witness a major increase in the extent of paved roads built worldwide.…
We study the effect of generic spatial anisotropies on the scaling behavior in the Kardar-Parisi-Zhang equation. In contrast to its "conserved" variants, anisotropic perturbations are found to be relevant in d > 2 dimensions, leading to…
Nonequilibrium many-body transient dynamics play an important role in the adaptation of active matter systems environment changes. However, the generic universal behavior of such dynamics is usually elusive and left as open questions. Here,…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…
The paper considers some class of dynamical systems that called density systems. For such systems the derivative of quadratic function depends on so-called density function. The density function is used to set the properties of phase space,…
Neural scaling laws--power-law relationships between generalization errors and characteristics of deep learning models--are vital tools for developing reliable models while managing limited resources. Although the success of large language…
We build networks of genetic similarity in which the nodes are organisms sampled from biological populations. The procedure is illustrated by constructing networks from genetic data of a marine clonal plant. An important feature in the…