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The use of brain images as markers for diseases or behavioral differences is challenged by the small effects size and the ensuing lack of power, an issue that has incited researchers to rely more systematically on large cohorts. Coupled…
Social media outlets such as Twitter constitute valuable data sources for understanding human activities in the virtual world from a geographic perspective. This paper examines spatial distribution of tweets and densities within cities. The…
The recent availability of electronic datasets containing large volumes of communication data has made it possible to study human behavior on a larger scale than ever before. From this, it has been discovered that across a diverse range of…
A fractal method to detect, locate and quantify chaos in multi-dimensional-conservative-closed systems, based on the creation of artificial exits, is presented. The method is invariant under space-time changes of coordinates and can be used…
Culturomics was recently introduced as the application of high-throughput data collection and analysis to the study of human culture. Here we make use of this data by investigating fluctuations in yearly usage frequencies of specific words…
The famous Laplace's Demon is not only of strict physical determinism, but also related to the power of differential equations. When deterministically extended structures are taken into consideration, it is admissible that fractals are…
On the one hand, the large scale structure of matter is arguably scale invariant, and, on the other hand, halos and voids are recognized as prominent features of that structure. To unify both approaches, we propose to model the dark matter…
The description of large temporal graphs requires effective methods giving an appropriate mesoscopic partition. Many approaches exist today to detect communities in static graphs. However, many networks are intrinsically dynamical, and need…
We give exact relations for certain types of the hierarchic fractal structures. In the blatant distinction from regular networks of the "small world" (SW) topology [1], regular fractal networks manifests the logarithmic dependence of the…
Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Based on the idea from general fractals and scaling,…
Self-similarity is the essence of fractal images and, as such, characterizes natural stochastic textures. This paper is concerned with the property of self-similarity in the statistical sense in the case of fully-textured images that…
The spatial distributions of cities fall into two groups: one is the simple distribution with characteristic scale (e.g. exponential distribution), and the other is the complex distribution without characteristic scale (e.g. power-law…
Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…
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…
For the first time the systems of cities in seven countries or regions among the largest in the world (China, India, Brazil, Europe, the Former Soviet Union (FSU), the United States and South Africa) are made comparable through the building…
Recent developments in extracting and processing biological and clinical data are allowing quantitative approaches to studying living systems. High-throughput sequencing, expression profiles, proteomics, and electronic health records are…
In order to understand characteristics common to distributions which have both fractal and non-fractal scale regions in a unified framework, we introduce a concept of typical scale. We employ a model of 2d gravity modified by the $R^2$ term…
The distribution of living languages is investigated and scaling relations are found for the diversity of languages as a function of the country area and population. These results are compared with data from Ecology and from computer…
Naive scale invariance is not a true property of natural images. Natural monochrome images posses a much richer geometrical structure, that is particularly well described in terms of multiscaling relations. This means that the pixels of a…
Degree distributions of graph representations for compact urban patterns are scale-dependent. Therefore, the degree statistics alone does not give us the enough information to reach a qualified conclusion on the structure of urban spatial…