Related papers: The Rank-Size Scaling Law and Entropy-Maximizing P…
Easy and intuitive navigability is of central importance in cities. The actual scale-free networking of urban street networks in their topological space, where navigation information is encoded by mapping roads to nodes and junctions to…
The axiomatic structure of the $\kappa$-statistcal theory is proven. In addition to the first three standard Khinchin--Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
The minimization of Fisher's information (MFI) approach of Frieden et al. [Phys. Rev. E {\bf 60} 48 (1999)] is applied to the study of size distributions in social groups on the basis of a recently established analogy between scale…
We consider a generic system composed of a fixed number of particles distributed over a finite number of energy levels. We make only general assumptions about system's properties and the entropy. System's constraints other than fixed number…
Analyzing and modeling the mobility process with tour behavior is fundamental to understanding a wide range of complex systems, including animal foraging, human mobility and freight transportation. However, despite their importance, the…
The scaling exponent of a hierarchy of cities used to be regarded as a fractal parameter. The Pareto exponent was treated as the fractal dimension of size distribution of cities, while the Zipf exponent was treated as the reciprocal of the…
Statistical mechanics descriptions of the second law of thermodynamics generally imply point-like particles driven by a dissipative overall mechanism for their simultaneous time-evolution. As the number of involved particles grows larger,…
The p-median problem is a common model for optimal facility location. The task is to place p facilities (e.g., warehouses or schools) in a heterogeneously populated space such that the average distance from a person's home to the nearest…
The shape of urban settlements plays a fundamental role in their sustainable planning. Properly defining the boundaries of cities is challenging and remains an open problem in the Science of Cities. Here, we propose a worldwide model to…
Recent work has shown that, in generative modeling, cross-entropy loss improves smoothly with model size and training compute, following a power law plus constant scaling law. One challenge in extending these results to reinforcement…
In this paper we combine statistical analysis of large text databases and simple stochastic models to explain the appearance of scaling laws in the statistics of word frequencies. Besides the sublinear scaling of the vocabulary size with…
How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…
Zipf's law predicts a power-law relationship between word rank and frequency in language communication systems, and is widely reported in texts yet remains enigmatic as to its origins. Computer simulations have shown that language…
The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions…
City-size distributions follow an approximate power law in various countries despite high volatility in relative city sizes over time. Our empirical evidence for the United States and Japan indicates that the scaling law stems from a…
The statistical characterization of the distribution of visible matter in the universe is a central problem in modern cosmology. In this respect, a crucial question still lacking a definitive answer concerns how large are the greatest…
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…
We consider a system composed of a fixed number of particles with total energy smaller or equal to some prescribed value. The particles are non-interacting, indistinguishable and distributed over fixed number of energy levels. The energy…
It exists a large class of systems for which the traditional notion of extensivity breaks down. From experimental examples we induce two general hypothesis concerning such systems. In the first the existence of an internal coordinate system…