Related papers: Scaling of Geographic Space as a Universal Rule fo…
Performance of standard processes over large distributed networks typically scales with the size of the network. For example, in planar topologies where nodes communicate with their natural neighbors, the scaling factor is $O(n)$, where $n$…
Driven by access to large volumes of movement data, the study of human mobility has grown rapidly over the past decades. The field has shown that human mobility is scale-free, proposed models to generate scale-free moving distance…
We present a broad, phenomenological picture of the distribution of the length of open space linear segments, $l$, derived from maps of 36 cities in 14 different countries. By scaling the Zipf plot of $l$, we obtain two master curves for a…
A range of early studies have been conducted to illustrate human mobility patterns using different tracking data, such as dollar notes, cell phones and taxicabs. Here, we explore human mobility patterns based on massive tracking data of US…
The big jump principle is a well established mathematical result for sums of independent and identically distributed random variables extracted from a fat tailed distribution. It states that the tail of the distribution of the sum is the…
Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the…
Multiple-scale and broad-scale assessments often require rescaling the original data to a consistent grain size for analysis. Rescaling categorical raster data by spatial aggregation is common in large area ecological assessments. However,…
We report about universality of rank-integration distributions of open spaces in city space syntax similar to the famous rank-size distributions of cities (Zipf's law). We also demonstrate that the degree of choice an open space represents…
The traditional concept of space in geography is based on the notion of distance. Where there is a spatial analysis, there is a distance measurement. However, the precondition for effective distance-based space is that the geographical…
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.…
Human development has far-reaching impacts on the surface of the globe. The transformation of natural land cover occurs in different forms and urban growth is one of the most eminent transformative processes. We analyze global land cover…
Image geolocalization is the task of identifying the location depicted in a photo based only on its visual information. This task is inherently challenging since many photos have only few, possibly ambiguous cues to their geolocation.…
I discuss the universal aspects of scaling in period-doubling sequences in families of maps of the real line possessing non-integer degree. I show that the scaling behaviour in both the orbital and parameter spaces is governed by the same…
The universal scaling law of cortical morphology describes cortical folding as the covariance of average grey matter thickness, pial surface area, and exposed surface area. It applies for mammalian species, humans, and across lobes, however…
We characterise the learning of a mixture of two clouds of data points with generic centroids via empirical risk minimisation in the high dimensional regime, under the assumptions of generic convex loss and convex regularisation. Each cloud…
This paper addresses the problem of Generalized Category Discovery (GCD) under a long-tailed distribution, which involves discovering novel categories in an unlabelled dataset using knowledge from a set of labelled categories. Existing…
Zipf's law is the most common statistical distribution displaying scaling behavior. Cities, populations or firms are just examples of this seemingly universal law. Although many different models have been proposed, no general theoretical…
Over the last few decades power law distributions have been suggested as forming generative mechanisms in a variety of disparate fields, such as, astrophysics, criminology and database curation. However, fitting these heavy tailed…
Deep neural networks exhibit empirical neural scaling laws, with error decreasing as a power law with increasing model or data size, across a wide variety of architectures, tasks, and datasets. This universality suggests that scaling laws…
It is now well established that galaxies are biased tracers of the distribution of matter, although it is still not known what form this bias takes. In local bias models the propensity for a galaxy to form at a point depends only on the…