Related papers: Fractal Scaling of Population Counts Over Time Spa…
The relation between critical exponents, characterizing a continuous phase transition, and the fractal structure of physical lines, proliferating at the critical point, is established by considering the two-dimensional O($N$) spin model for…
Although geographic features, such as mountains and coastlines, are fractal, some studies have claimed that the fractal property is not universal. This claim, which is false, is mainly attributed to the strict definition of fractal…
Fractals and multifractals and their associated scaling laws provide a quantification of the complexity of a variety of scale invariant complex systems. Here, we focus on lattice multifractals which exhibit complex exponents associated with…
Is a causal description of human wealth history conceivable? To investigate the matter we introduce a simple causal albeit strongly aggregated model, assuming that the observed wealth growth is mainly driven by human collaborative efforts…
Fractals, 1/f noise, Zipf's law, and the occurrence of large catastrophic events are typical ubiquitous general empirical observations across the individual sciences which cannot be understood within the set of references developed within…
For a long time, many methods are developed to make temporal signal analyses based on time series. However, for geographical systems, spatial signal analyses are as important as temporal signal analyses. Nonstationary spatial and temporal…
We investigate the temporal patterns of human communication and its influence on the spreading of information in social networks. The analysis of mobile phone calls of 20 million people in one country shows that human communication is…
We present a number models describing the sequential deposition of a mixture of particles whose size distribution is determined by the power-law $p(x) \sim \alpha x^{\alpha-1}$, $x\leq l$ . We explicitly obtain the scaling function in the…
A model is presented for the origin of the large scale structure of the universe and their Mass-Radius scaling law; a fractal power law, $M \propto R^D$, with dimension $D=2$, most significantly. The physics is conventional, orthodox, but…
The things surrounding us vary dramatically, which implies that there are far more small things than large ones, e.g., far more small cities than large ones in the world. This dramatic variation is often referred to as fractal or scaling.…
Time evolutions whose infinitesimal generator is a fractional time derivative arise generally in the long time limit. Such fractional time evolutions are considered here for random walks. An exact relationship is given between the…
Taylor's power law (TL) or fluctuation scaling has been verified empirically for the abundances of many species, human and non-human, and in many other fields including physics, meteorology, computer science, and finance. TL asserts that…
Fractal dimension is defined on the base of entropy, including macro state entropy and information entropy. The generalized correlation dimension of multifractals is based on Renyi entropy. However, the mathematical transform from entropy…
We consider the $1d$ one-component plasma (OCP) in thermal equilibrium, consisting of $N$ equally charged particles on a line, with pairwise Coulomb repulsion and confined by an external harmonic potential. We study two observables: (i) the…
The statistical analysis of the lensing effects coupled with the statistical analysis of the number counts is a tool to probe directly the relation between the mass and the light. In particular, some properties of the bias parameter can be…
The ability to directly record human face-to-face interactions increasingly enables the development of detailed data-driven models for the spread of directly transmitted infectious diseases at the scale of individuals. Complete coverage of…
In samples from a heavy-tailed distribution a second-order approximation is often use to approximate the tail function. Based on the parameters of the approximation, an optimal sample fraction can be estimated which is then used to estimate…
The critical behaviour of correlation functions near a boundary is modified from that in the bulk. When the boundary is smooth this is known to be characterised by the surface scaling dimension $\xt$. We consider the case when the boundary…
While conformal predictors reap the benefits of rigorous statistical guarantees on their error frequency, the size of their corresponding prediction sets is critical to their practical utility. Unfortunately, there is currently a lack of…
Traditional population estimation techniques often fail to capture the dynamic fluctuations inherent in urban and rural population movements. Recognizing the need for a high spatiotemporal dynamic population dataset, we propose a method…