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Urban Transfer Entropy across Scales.

Murcio R, Morphet R, Gershenson C, Batty M - PLoS ONE (2015)

Bottom Line: Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity between scales is important in determining how the interplay of local/regional urban policies may affect the distribution of urban settlements.In order to quantify these relationships, we follow an information theoretic approach using the concept of Transfer Entropy.The results indicate how different policies could affect urban morphology in terms of the information generated across geographical scales.

View Article: PubMed Central - PubMed

Affiliation: Centre for Advanced Spatial Analysis, University College London, London, United Kingdom.

ABSTRACT
The morphology of urban agglomeration is studied here in the context of information exchange between different spatio-temporal scales. Urban migration to and from cities is characterised as non-random and following non-random pathways. Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity between scales is important in determining how the interplay of local/regional urban policies may affect the distribution of urban settlements. In order to quantify these relationships, we follow an information theoretic approach using the concept of Transfer Entropy. Our analysis is based on a stochastic urban fractal model, which mimics urban growing settlements and migration waves. The results indicate how different policies could affect urban morphology in terms of the information generated across geographical scales.

No MeSH data available.


Three different stages in our model evolution.From right to left we can observe structures formed at (A) t1(t = 50) (B) t5(t = 250) and (C) t10(t = 500). Consolidated structures Ci(t) = 1 are shown in black, while non-consolidated ones Ci(t) = 2 are shown in white. The red circumference around the London area is the area of influence defined around the initial seed. Source: Black and white structures compiled by authors; Coastline made with Natural Earth. Free vector and raster map data @ naturalearthdata.com
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pone.0133780.g001: Three different stages in our model evolution.From right to left we can observe structures formed at (A) t1(t = 50) (B) t5(t = 250) and (C) t10(t = 500). Consolidated structures Ci(t) = 1 are shown in black, while non-consolidated ones Ci(t) = 2 are shown in white. The red circumference around the London area is the area of influence defined around the initial seed. Source: Black and white structures compiled by authors; Coastline made with Natural Earth. Free vector and raster map data @ naturalearthdata.com

Mentions: We defined a set of four thresholds T equal to 4.0, 4.5, 5.0 and 6.0 relating to the difficulty of development actually occurring, which are determined by physical or policy factors. We fixed the length of the simulation to t = 500 iterations as this gives sufficient time for patterns to emerge. At time t = 0 all grid positions, except the seed, have a potential Pi(0) = εi. To represent the importance of the historical accident across time, its initial potential is Pseed(0) = 20 which remains constant through all the iterations, so Eq 8 is never applied to the seed cell and its potential always exceeds the threshold. A typical configuration obtained with this model is shown in Fig 1. As our approach is stochastic we performed 1000 runs per configuration in order to derive robust statistics. All the quantities and measures derived are then the averaged over each configuration. We refer the reader to [22, 23] for examples in which aspects of this model have been applied.


Urban Transfer Entropy across Scales.

Murcio R, Morphet R, Gershenson C, Batty M - PLoS ONE (2015)

Three different stages in our model evolution.From right to left we can observe structures formed at (A) t1(t = 50) (B) t5(t = 250) and (C) t10(t = 500). Consolidated structures Ci(t) = 1 are shown in black, while non-consolidated ones Ci(t) = 2 are shown in white. The red circumference around the London area is the area of influence defined around the initial seed. Source: Black and white structures compiled by authors; Coastline made with Natural Earth. Free vector and raster map data @ naturalearthdata.com
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4514628&req=5

pone.0133780.g001: Three different stages in our model evolution.From right to left we can observe structures formed at (A) t1(t = 50) (B) t5(t = 250) and (C) t10(t = 500). Consolidated structures Ci(t) = 1 are shown in black, while non-consolidated ones Ci(t) = 2 are shown in white. The red circumference around the London area is the area of influence defined around the initial seed. Source: Black and white structures compiled by authors; Coastline made with Natural Earth. Free vector and raster map data @ naturalearthdata.com
Mentions: We defined a set of four thresholds T equal to 4.0, 4.5, 5.0 and 6.0 relating to the difficulty of development actually occurring, which are determined by physical or policy factors. We fixed the length of the simulation to t = 500 iterations as this gives sufficient time for patterns to emerge. At time t = 0 all grid positions, except the seed, have a potential Pi(0) = εi. To represent the importance of the historical accident across time, its initial potential is Pseed(0) = 20 which remains constant through all the iterations, so Eq 8 is never applied to the seed cell and its potential always exceeds the threshold. A typical configuration obtained with this model is shown in Fig 1. As our approach is stochastic we performed 1000 runs per configuration in order to derive robust statistics. All the quantities and measures derived are then the averaged over each configuration. We refer the reader to [22, 23] for examples in which aspects of this model have been applied.

Bottom Line: Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity between scales is important in determining how the interplay of local/regional urban policies may affect the distribution of urban settlements.In order to quantify these relationships, we follow an information theoretic approach using the concept of Transfer Entropy.The results indicate how different policies could affect urban morphology in terms of the information generated across geographical scales.

View Article: PubMed Central - PubMed

Affiliation: Centre for Advanced Spatial Analysis, University College London, London, United Kingdom.

ABSTRACT
The morphology of urban agglomeration is studied here in the context of information exchange between different spatio-temporal scales. Urban migration to and from cities is characterised as non-random and following non-random pathways. Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity between scales is important in determining how the interplay of local/regional urban policies may affect the distribution of urban settlements. In order to quantify these relationships, we follow an information theoretic approach using the concept of Transfer Entropy. Our analysis is based on a stochastic urban fractal model, which mimics urban growing settlements and migration waves. The results indicate how different policies could affect urban morphology in terms of the information generated across geographical scales.

No MeSH data available.