Related papers: Universal growth scaling law determined by dimensi…
With the number of sequenced genomes now over one hundred, and the availability of rough functional annotations for a substantial proportion of their genes, it has become possible to study the statistics of gene content across genomes. Here…
This paper investigates the role of size in biological organisms. More specifically, how the energy demand, expressed by the metabolic rate, changes according to the mass of an organism. Empirical evidence suggests a power-law relation…
Neural scaling laws have revolutionized the design and optimization of large-scale AI models by revealing predictable relationships between model size, dataset volume, and computational resources. Early research established power-law…
We study size and growth distributions of products and business firms in the context of a given industry. Firm size growth is analyzed in terms of two basic mechanisms, i.e. the increase of the number of new elementary business units and…
Universal scaling in the power-law size distribution of pelagic fish schools is established. The power-law exponent of size distributions is extracted through the data collapse. The distribution depends on the school size only through the…
Like all natural systems, great societies and their cultures emerge by a growth process from their environments, developing, organized, and behaving as wholes with their internal designs linked with their external worlds. So the general…
Fundamental laws of human mobility have been extensively studied, yet we are still lacking a comprehensive understanding of the mobility patterns of sharing conveyances. Since travellers would highly probably no longer possess their own…
We have previously reported that a 'universal' growth law with fixed scaling exponent p, as proposed by West and collaborators for all living organisms, appears to be able to describe also the growth of tumors in vivo. Here, we investigate…
A good understanding of cities is crucial to implement urban planning policies leading to social and economic sustainability and an efficient use of resources. While urban concentration has been associated with both positive and negative…
Given the right set of circumstances, ultracold quantum gases are able to change character and condense into a liquid state of quantum droplets. The size distribution of the droplets is determined dynamically in the condensation process. A…
Understanding scaling relations of social and environmental attributes of urban systems is necessary for effectively managing cities. Urban scaling theory (UST) has assumed that population density scales positively with city size. We…
The production of waste as a consequence of human activities is one of the most fundamental challenges facing our society and global ecological systems. Waste generation is rapidly increasing, with corresponding shifts in the structure of…
The interaction of all mobile species with their environment hinges on their movement patterns: the places they visit and how frequently they go there. In human society, where the prevalent form of cohabitation is in cities, the highly…
Universal scaling laws of fluctuations (the $\Delta$-scaling laws) can be derived for equilibrium and off-equilibrium systems when combined with the finite-size scaling analysis. In any system in which the second-order critical behavior can…
The current science of cities can provide a useful foundation for future urban policies, provided that these proposals have been validated by correct observations of the diversity of situations in the world. However, international…
Hierarchies can be modeled by a set of exponential functions, from which we can derive a set of power laws indicative of scaling. The solution to a scaling relation equation is always a power law. The scaling laws are followed by many…
When data is plentiful, the loss achieved by well-trained neural networks scales as a power-law $L \propto N^{-\alpha}$ in the number of network parameters $N$. This empirical scaling law holds for a wide variety of data modalities, and may…
In this communication, the approach of phenomenological universalities of growth are considered to describe the behaviour of a system showing oscillatory growth. Two phenomenological classes are proposed to consider the behaviour of a…
We consider a simple variant of the von Neumann model of an expanding economy, in which multiple producers make goods according to their production function. The players trade their goods at the market and then use the bundles acquired for…
Critical, or scale independent, systems are so ubiquitous, that gaining theoretical insights on their nature and properties has many direct repercussions in social and natural sciences. In this report, we start from the simplest possible…