Attractors, statistics and fluctuations of the dynamics of the Schelling’s model for social segregation

Cortez, Vasco; Medina, Pablo; Goles, Éric; Zarama, Roberto; Rica, Sergio

doi:10.1140/epjb/e2014-50603-5

Cited by 16 publications

(12 citation statements)

References 11 publications

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“…In the late forties, Sakoda introduced in his Ph.D. thesis [10] a first general discrete dynamical model for social interactions and published later [11], at the same time of the well-known Schelling's social segregation model [12,13], which is, as we will show, only a special class already included in the original Sakoda model. The particular case of the Schelling segregation model and its variations have been studied widely through agent based models [9,[14][15][16][17][18][19][20][21][22][23]. However, the Sakoda dynamics and its underlying richness, which explain other different social phenomena far from segregation, are mostly unknown; thus they have not been, to the best of our knowledge, studied previously in a deeper manner.…”

Section: Introductionmentioning

confidence: 99%

Self-Organized Societies: On the Sakoda Model of Social Interactions

Medina¹,

Goles

Zarama³

et al. 2017

Complexity

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We characterize the behavior and the social structures appearing from a model of general social interaction proposed by Sakoda. The model consists of two interacting populations in a two-dimensional periodic lattice with empty sites. It contemplates a set of simple rules that combine attitudes, ranges of interactions, and movement decisions. We analyze the evolution of the 45 different interaction rules via a Potts-like energy function which drives the system irreversibly to an equilibrium or a steady state. We discuss the robustness of the social structures, dynamical behaviors, and the existence of spatial long range order in terms of the social interactions and the equilibrium energy.

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Section: Introductionmentioning

confidence: 99%

Self-Organized Societies: On the Sakoda Model of Social Interactions

Medina¹,

Goles

Zarama³

et al. 2017

Complexity

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“…In [10,11] the density function of energy differences ∆E and average magnetization M for different time steps of the model is shown when the Schelling model is approached as a thermodynamic system. These models provide a great deal of insight into the phase changes of the system which delivers a potentially invaluable method to detect paradigm changes in the macrostates.…”

Section: Introductionmentioning

confidence: 99%

“…Their main strength is in determining the changes in the value of the parameters of the model which can affect the spatial arrangements under the premise that those values can be mapped to values observed in a real world scenario (a task which is another challenge in itself). To monitor the state of the system [10], uses the energy per site, E / N . The results show a reduction in the energy over the system as the residents in satisfied states will cease to move.…”

Section: Introductionmentioning

confidence: 99%

“…These differences in the measures applied to monitor the Schelling model trajectory can be seen in a comparison of the figures produced in [2,10], which represent the degree of residential homogeneity satisfaction across the lattice for the time steps. Although they have similar starting and final points, as defined by the dynamics, the trajectories followed are different based upon the measures used to evaluate the overall homogeneity between these points.…”

Section: Introductionmentioning

confidence: 99%

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Examining the Schelling Model Simulation through an Estimation of Its Entropy

Mantzaris

Marich

Halfman

2018

Entropy

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The Schelling model of segregation allows for a general description of residential movements in an environment modeled by a lattice. The key factor is that occupants change positions until they are surrounded by a designated minimum number of similarly labeled residents. An analogy to the Ising model has been made in previous research, primarily due the assumption of state changes being dependent upon the adjacent cell positions. This allows for concepts produced in statistical mechanics to be applied to the Schelling model. Here is presented a methodology to estimate the entropy of the model for different states of the simulation. A Monte Carlo estimate is obtained for the set of macrostates defined as the different aggregate homogeneity satisfaction values across all residents, which allows for the entropy value to be produced for each state. This produces a trace of the estimated entropy value for the states of the lattice configurations to be displayed with each iteration. The results show that the initial random placements of residents have larger entropy values than the final states of the simulation when the overall homogeneity of the residential locality is increased.

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“…This model revealed how, even with relatively high levels of tolerance for mixity, a system of agents located at sites on a grid would eventually evolve towards patterns of segregation, with the two communities "living" in distinct parts of the grid. Schelling's model has given rise to a vast literature on segregation across a wide range of disciplines [3,11,12,15,17,21,25,[30][31][32][33]40], and notably in statistical physics, where analogies with certain interacting particle systems have been put to fruitful use [10,13,16,19,20,24,36,37,41,43]. However, rare are the instances in which real-world data has been compared with theoretical results other than stylized facts [5,22,23].…”

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confidence: 99%

Multidimensional urban segregation: toward a neural network measure

Olteanu

Hazan

Cottrell

et al. 2019

Neural Comput & Applic

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We introduce a multidimensional, neural-network approach to reveal and measure urban segregation phenomena, based on the Self-Organizing Map algorithm (SOM). The multidimensionality of SOM allows one to apprehend a large number of variables simultaneously, defined on census or other types of statistical blocks, and to perform clustering along them. Levels of segregation are then measured through correlations between distances on the neural network and distances on the actual geographical map. Further, the stochasticity of SOM enables one to quantify levels of heterogeneity across census blocks. We illustrate this new method on data available for the city of Paris.

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Attractors, statistics and fluctuations of the dynamics of the Schelling’s model for social segregation

Cited by 16 publications

References 11 publications

Self-Organized Societies: On the Sakoda Model of Social Interactions

Self-Organized Societies: On the Sakoda Model of Social Interactions

Examining the Schelling Model Simulation through an Estimation of Its Entropy

Multidimensional urban segregation: toward a neural network measure

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