Related papers: Universal City-size distributions through rank ord…

The urban road networks of the 20 largest German cities have been analysed, based on a detailed database providing the geographical positions as well as the travel-times for network sizes up to 37,000 nodes and 87,000 links. As the human…

Whereas most dimensionality reduction techniques (e.g. PCA, ICA, NMF) for multivariate data essentially rely on linear algebra to a certain extent, summarizing ranking data, viewed as realizations of a random permutation $\Sigma$ on a set…

Time evolutions of number of cities, population of cities, world population, and size distribution of present languages are studied in terms of a new model, where population of each city increases by a random rate and decreases by a random…

Ignoring the differences between countries, human reproductive and dispersal behaviors can be described by some standardized models, so whether there is a universal law of population growth hidden in the abundant and unstructured data from…

Cities are characterized by concentrating population, economic activity and services. However, not all cities are equal and a natural hierarchy at local, regional or global scales spontaneously emerges. In this work, we introduce a method…

Two measurements are employed to quantitatively investigate the scaling properties of the spatial distribution of urban facilities, the K function by number counting and the variance-mean relationship with the method of expanding bins. The…

We approach the Generalized Beta (GB) family of distributions using a mean-reverting stochastic differential equation (SDE) for a power of the variable, whose steady-state (stationary) probability density function (PDF) is a modified GB…

Expected urban population doubling calls for a compelling theory of the city. Random walks and diffusions defined on spatial city graphs spot hidden areas of geographical isolation in the urban landscape going downhill. First--passage time…

The distributed subgradient method (DSG) is a widely discussed algorithm to cope with large-scale distributed optimization problems in the arising machine learning applications. Most exisiting works on DSG focus on ideal communication…

Scaling of geographic space refers to the fact that for a large geographic area its small constituents or units are much more common than the large ones. This paper develops a novel perspective to the scaling of geographic space using large…

Grouped data in form of income shares have been conventionally used to estimate income inequality due to the lack of availability of individual records. Most prior research on economic inequality relies on lower bounds of inequality…

An important issue in the study of cities is defining a metropolitan area, as different definitions affect the statistical distribution of urban activity. A commonly employed method of defining a metropolitan area is the Metropolitan…

Crime rates per capita are used virtually everywhere to rank and compare cities. However, their usage relies on a strong linear assumption that crime increases at the same pace as the number of people in a region. In this paper, we…

Randomized rankings have been of recent interest to achieve ex-ante fairer exposure and better robustness than deterministic rankings. We propose a set of natural axioms for randomized group-fair rankings and prove that there exists a…

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…

As buildings are central to the social and environmental sustainability of human settlements, high-quality geospatial data are necessary to support their management and planning. Authorities around the world are increasingly collecting and…

We explain Kossovsky's generalization of Benford's law which is a formula that approximates the distribution of leftmost digits in finite sequences of natural data and apply it to six sequences of data including populations of US cities and…

In this paper, we develop a novel approach to measuring urban sprawl based on street nodes and naturally defined urban boundaries, both extracted from massive volunteered geographic information OpenStreetMap databases through some…

In recent decades the world has experienced rates of urban growth unparalleled in any other period of history and this growth is shaping the environment in which an increasing proportion of us live. In this paper we use a longitudinal…

Given that a group of cities follows a scaling law connecting urban population with socio-economic or infrastructural metrics (transversal scaling), should we expect that each city would follow the same behavior over time (longitudinal…