Julien Randon-Furling

A Schelling model with switching agents: decreasing segregation via random allocation and social mobility

AbstractWe study the behaviour of a Schelling-class system in which a fraction f of spatially-fixed switching agents is introduced. This new model allows for multiple interpretations, including: (i) random, non-preferential allocation (e.g. by housing associations) of given, fixed sites in an open residential system, and (ii) superimposition of social and spatial mobility in a closed residential system. We find that the presence of switching agents in a segregative Schelling-type dynamics can lead to the emergence of intermediate patterns (e.g. mixture of patches, fuzzy interfaces) as the ones described in [E. Hatna, I. Benenson, J. Artif. Soc. Social. Simul. 15, 6 (2012)]. We also investigate different transitions between segregated and mixed phases both at f = 0 and along lines of increasing f, where the nature of the transition changes.

From urban segregation to spatial structure detection

We develop a ‘multifocal’ approach to reveal spatial dissimilarities in cities, from the most local scale to the metropolitan one. Think, for instance, of a statistical variable that may be measured at different scales, e.g. ethnic group proportions, social housing rate, income distribution, or public transportation network density. Then, to any point in the city there corresponds a sequence of values for the variable, as one zooms out around the starting point, all the way up to the whole city – as if with a varifocal camera lens. The sequences thus produced encode spatial dissimilarities in a precise manner: how much they differ from perfectly random sequences is indeed a signature of the underlying spatial structure. We introduce here a mathematical framework that allows to analyse this signature, and we provide a number of illustrative examples.

Maxima of two random walks: universal statistics of lead changes

We investigate statistics of lead changes of the maxima of two discrete-time random walks in one dimension. We show that the average number of lead changes grows as

Multidimensional urban segregation: An exploratory case study

\pi^{-1}\ln(t)

From Urban Segregation to Spatial Pattern Detection.

in the long-time limit. We present theoretical and numerical evidence that this asymptotic behavior is universal. Specifically, this behavior is independent of the jump distribution: the same asymptotic underlies standard Brownian motion and symmetric Levy flights. We also show that the probability to have at most n lead changes behaves as

Multidimensional Urban Segregation - Toward A Neural Network Measure.

t^{-1/4}[\ln t]^n

From Urban Segregation to Multifocal Pattern Detection

for Brownian motion and as

A network model for the propagation of Hepatitis C

t^{-\beta(\mu)}[\ln t]^n

Facets on the convex hull of d-dimensional Brownian and Lévy motion

for symmetric Levy flights with index

A network model for the propagation of Hepatitis C with HIV co-infection

\mu