Spatially embedded dynamics and complexity

Buckley, Christopher L.; Bullock, Seth; Barnett, Lionel

doi:10.1002/cplx.20337

“…Key examples are offered by [5] in their work modeling the tendency of molecules to organize into mutually self‐reinforcing “hypercycles” [6], and by [7] in the context of trying to understand how biological populations of simple creatures might evolve to exhibit cooperative tendencies (see [8], this volume, for more details of both models). In each case, the system being modeled was unable to exhibit organized complex behavior when its constituent parts were well‐mixed.…”

Section: Space As An Enabling Constraintmentioning

confidence: 99%

“…Bullock et al [20] explore the effect of structural constraints arising from spatial embedding on several network properties including giant component formation, degree correlation and the presence of scale free and small world properties. Buckley et al [8] focus on the effect of spatial embedding on the dynamic complexity of networks. They investigate a measure of complexity inspired by the balance between modularity and integration in neural systems [21, 22] and demonstrate how the constraints arising from spatial embedding increase interaction complexity relative to comparable nonspatial networks.…”

Section: Contents Of This Special Issuementioning

confidence: 99%

Spatial embedding as an enabling constraint: Introduction to a special issue of complexity on the topic of “Spatial Organization”

Bullock

¹

,

Geard

²

2010

Complexity

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We introduce and discuss the role of spatial embedding as an enabling constraint on complex system structure and function.Key words: complexity, space, spatial embedding, networks, Space as an Enabling ConstraintThe vast majority of real-world complex systems are extended in space. Some parts are close together, others are far apart. Moreover, the tendency for particular system parts to interact is partly determined by the distances that separate them. Consequently, there is considerable evidence that this spatial embedding has a significant impact on both the structural and functional organisation of complex systems. Spatial constraints are implicated in the way that populations of termites construct their impressive mounds [15,16], the way in which species of plants compete for light [8], and even the way in which genes are packed onto linear strands of DNA [18]. Moreover, we are beginning to understand that this influence is not neutral, but can sometimes be positive, with spatially embedded systems enjoying an improved ability to effectively organise in order to support useful functionality.Key examples are offered by [5] in their work modelling the tendency of molecules to organise into mutually self-reinforcing "hypercycles" [11], and by [9] in the context of trying to understand how biological populations of simple creatures might evolve to exhibit co-operative tendencies (see [6], this volume, for more details of both models). In each case, the system being Preprint submitted to Complexity April 22, 2010 modelled was unable to exhibit organised complex behaviour when its constituent parts were well-mixed. However, when each system was extended over a two-dimensional space such that its parts could only interact with their close spatial neighbours, the systems were able to spontaneously achieve and maintain functional organisation in the face of exploitative disturbance. Spatial embedding enabled each population (of modelled molecular species or simple simulated creatures) to structure itself in such a way as to maintain co-operative functional organisation through exploiting the "useful" asymmetries that space introduces into the ecology of interactions [7]. These results suggest an intriguing possibility: might understanding the role of spatial embedding help us to better deal with problems concerning a wide range of spatially embedded complex systems? For instance, how to organise the built environment such that community coherence is consolidated rather than fragmented [4]; how to arrange social care processes such that they are vital and integrated [17]; how to engineer accountability in virtual communities [12]; how to achieve bioremediation using bacterial biofilm communities [19]; and how to improve the resilience of the infrastructural systems upon which we rely [10], etc. Could the influence of spatial embedding in these contexts, when properly understood, allow and encourage individuals to organise in a way that makes good solutions easier to achieve?It is in this sense that space sh...

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“…The behaviour of such models is sensitive to these choices regarding how interactions are structured, with, for instance, spatial embedding often encouraging complex organised behaviour where it would not otherwise arise (e.g., Boerlijst and Hogeweg, 1991;Di Paolo, 2000;Buckley et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

Contagion on Networks with Self-Organised Community Structure

Antonioni¹,

Bullock²,

Darabos³

et al. 2015

07/20/2015-07/24/2015

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Living systems are organised in space. This imposes constraints on both their structural form and, consequently, their dynamics. While artificial life research has demonstrated that embedding an adaptive system in space tends to have a significant impact on its behaviour, we do not yet have a full account of the relevance of spatiality to living self-organisation.Here, we extend the REDS model of spatial networks with self-organised community structure to include the "small world" effect. We demonstrate that REDS networks can become small worlds with the introduction of a small amount of random rewiring. We then explore how this rewiring influences two simple dynamic processes representing the contagious spread of infection or information.We show that epidemic outbreaks arise more easily and spread faster on REDS networks compared to standard random geometric graphs (RGGs). Outbreaks spread even faster on small world REDS networks (due to their shorter path lengths) but initially find it more difficult to establish themselves (due to their reduced community structure). Overall, we find that small world REDS networks, with their combination of short characteristic path length, positive assortativity, strong community structure and high clustering, are more susceptible to a range of contagion dynamics than RGGs, and that they offer a useful abstract model for studying dynamics on spatially organised living systems.

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“…Despite this, many models of living systems either assume that the system is well-mixed, with every interaction between system components equally valid, or specify that the interactions within a system are embedded on a regular lattice. The behaviour of such models is sensi-tive to these choices regarding how interactions are structured, with, for instance, spatial embedding often encouraging complex organised behaviour where it would not otherwise arise (e.g., Boerlijst and Hogeweg, 1991;Di Paolo, 2000;Buckley et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

Contagion on Networks with Self-Organised Community Structure

Antonioni

¹

,

Bullock

²

,

Darabos

³

et al. 2015

07/20/2015-07/24/2015

Self Cite

0

View full text Add to dashboard Cite

Living systems are organised in space. This imposes constraints on both their structural form and, consequently, their dynamics. While artificial life research has demonstrated that embedding an adaptive system in space tends to have a significant impact on its behaviour, we do not yet have a full account of the relevance of spatiality to living self-organisation.Here, we extend the REDS model of spatial networks with self-organised community structure to include the "small world" effect. We demonstrate that REDS networks can become small worlds with the introduction of a small amount of random rewiring. We then explore how this rewiring influences two simple dynamic processes representing the contagious spread of infection or information.We show that epidemic outbreaks arise more easily and spread faster on REDS networks compared to standard random geometric graphs (RGGs). Outbreaks spread even faster on small world REDS networks (due to their shorter path lengths) but initially find it more difficult to establish themselves (due to their reduced community structure). Overall, we find that small world REDS networks, with their combination of short characteristic path length, positive assortativity, strong community structure and high clustering, are more susceptible to a range of contagion dynamics than RGGs, and that they offer a useful abstract model for studying dynamics on spatially organised living systems.

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Spatially embedded dynamics and complexity

Cited by 4 publications

References 38 publications

Spatial embedding as an enabling constraint: Introduction to a special issue of complexity on the topic of “Spatial Organization”

Spatial embedding as an enabling constraint: Introduction to a special issue of complexity on the topic of “Spatial Organization”

Contagion on Networks with Self-Organised Community Structure

Contagion on Networks with Self-Organised Community Structure

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