Quantifying ethnic segregation in cities through random walks

Sousa, Sandro; Nicosia, Vincenzo

doi:10.48550/arxiv.2010.10462

Cited by 3 publications

(3 citation statements)

References 5 publications

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“…Moreover, interesting insights about the relation between the structure and dynamics on a network have come from the analysis of transient and long trajectories of random walks on graphs, including the statistics of first passage times and coverage times [12,13,[62][63][64], or the systematic study of their fluctuations [65]. However, the potential usefulness of random walks to quantify the heterogeneity of class distributions on networks, either in spatially-embedded systems or in high-dimensional networks, has only recently been hinted to [39,65,66].…”

Section: Discussionmentioning

confidence: 99%

First-passage times to quantify and compare structural correlations and heterogeneity in complex systems

Bassolas¹,

Nicosia²

2020

Preprint

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Virtually all the emergent properties of a complex system are rooted in the non-homogeneous nature of the behaviours of its elements and of the interactions among them. However, the fact that heterogeneity and correlations can appear simultaneously at local, mesoscopic, and global scales, is a concrete challenge for any systematic approach to quantify them in systems of different types. We develop here a scalable and non-parametric framework to characterise the presence of heterogeneity and correlations in a complex system, based on the statistics of random walks over the underlying network of interactions among its units. In particular, we focus on normalised mean first passage times between meaningful pre-assigned classes of nodes, and we showcase a variety of their potential applications. We found that the proposed framework is able to characterise polarisation in voting systems, including the UK Brexit referendum and the roll-call votes in the US Congress. Moreover, the distributions of class mean first passage times can help identifying the key players responsible for the spread of a disease in a social system, and comparing the spatial segregation of US cities, revealing the central role of urban mobility in shaping the incidence of socio-economic inequalities.

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Section: Discussionmentioning

confidence: 99%

First-passage times to quantify and compare structural correlations and heterogeneity in complex systems

Bassolas¹,

Nicosia²

2020

Preprint

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“…Many metrics have been introduced in the literature to discern if the final state is segregated or not [15,22,46,47]. The number of clusters is known to be directly related with the segregation, because a high presence of small clusters indicates a mixing between agents.…”

Section: Metrics Of Segregationmentioning

confidence: 99%

Aging effects in Schelling Segregation model

Abella¹,

Miguel²,

Ramasco³

2022

Preprint

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The Schelling model has become a paradigm in social sciences to explain the emerge of residential spatial segregation even in the presence of high tolerance to mixed neighborhoods by the side of citizens. In particular, we consider a noisy constrained version of the Schelling model, in which agents maximize its satisfaction, related to the composition of the local neighborhood, by infinite-range movements towards satisfying vacancies. We add to it an aging effect by making the probability of agents to move inversely proportional to the time they have been satisfied in their present location. This mechanism simulates the development of an emotional attachment to a location where an agent has been satisfied for a while. The introduction of aging has several major impacts on the model statics and dynamics: the phase transition between a segregated and a mixed phase of the original model disappears, and we observe segregated states with high level of agent satisfaction even for high values of the tolerance. In addition, the new segregated phase is dynamically characterized by a slow power-law coarsening process and by a glassy-like dynamics in which the asymptotic time translational invariance is broken.

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“…In this study, we focus on the class mean first passage times (CMFPT) on a network, defined as the expected time, τ αβ , for a random walker beginning on a node of class α to first arrive at a node of class β . This method has recently been applied to other complex systems to quantify spatial segregation in voting patterns [25], ethnic segregation in UK and US metropolitan areas [26], and to show that internal clustering and spatial heterogeneity of individuals of different ethnic groups contributed to the observed excess of infectious diseases [27]. Here, we leverage the CMFPT to quantify the complex spatial patterns of mutated sub-clonal cells in BaseScope images.…”

Section: Introductionmentioning

confidence: 99%

First passage time analysis of spatial mutation patterns reveals evolutionary dynamics of pre-existing resistance in colorectal cancer

Haughey

Bassolas

Sousa

et al. 2022

Preprint

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The footprint left by early cancer dynamics on the spatial arrangement of tumour cells is poorly understood, and yet could encode information about how therapy resistant sub-clones grew within the expanding tumour. Novel methods of quantifying spatial tumour data at the cellular scale are required to link evolutionary dynamics to the resulting spatial architecture of the tumour. Here, we propose a framework using first passage times of random walks to quantify the complex spatial patterns of tumour cell population mixing. First, using a toy model of cell mixing we demonstrate how first passage time statistics can distinguish between different pattern structures. We then apply our method to simulated patterns of wild-type and mutated tumour cell population mixing, generated using an agent-based model of expanding tumours, to explore how first passage times reflect mutant cell replicative advantage, time of emergence and strength of cell pushing. Finally, we analyse experimentally measured patterns of genetic point mutations in human colorectal cancer, and estimate parameters of early sub-clonal dynamics using our spatial computational model. We uncover a wide range of mutant cell replicative advantages and timings, with the majority of sampled tumours consistent with boundary driven growth or short-range cell pushing. By analysing multiple sub-sampled regions in a small number of samples, we explore how the distribution of inferred dynamics could inform about the initial mutational event. Our results demonstrate the efficacy of first passage time analysis as a new methodology for quantifying cell mixing patterns in vivo, and suggest that patterns of sub-clonal mixing can provide insights into early cancer dynamics.

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Quantifying ethnic segregation in cities through random walks

Cited by 3 publications

References 5 publications

First-passage times to quantify and compare structural correlations and heterogeneity in complex systems

First-passage times to quantify and compare structural correlations and heterogeneity in complex systems

Aging effects in Schelling Segregation model

First passage time analysis of spatial mutation patterns reveals evolutionary dynamics of pre-existing resistance in colorectal cancer

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