A simple spatiotemporal evolution model of a transmission power grid

In this paper, we present a model for the spatial and temporal evolution of a particularly large human-made network: the 400-kV French transmission power grid. This is based on 1) an attachment procedure that diminishes the connection probability between two nodes as the network grows and 2) a coupled cost function characterizing the available budget at every time step. Two differentiated and consecutive processes can be distinguished: a first global space-filling process and a secondary local meshing process that increases connectivity at a local level. Results show that even without power system engineering design constraints (i.e., population and energy demand), the evolution of a transmission network can be remarkably explained by means of a simple attachment procedure. Given a distribution of resources and a time span, the model can also be used to generate the probability distribution of cable lengths at every time step, thus facilitating network planning. Implications for network's fragility are suggested as a starting point for new design perspectives in this kind of infrastructures.Peer ReviewedPostprint (author's final draft

Evolving protein interaction networks through gene duplication

The topology of the proteome map revealed by recent large-scale hybridization methods has shown that the distribution of protein–protein interactions is highly heterogeneous, with many proteins having few edges while a few of them are heavily connected. This particular topology is shared by other cellular networks, such as metabolic pathways, and it has been suggested to be responsible for the high mutational homeostasis displayed by the genome of some organisms. In this paper we explore a recent model of proteome evolution that has been shown to reproduce many of the features displayed by its real counterparts. The model is based on gene duplication plus re-wiring of the newly created genes. The statistical features displayed by the proteome of well-known organisms are reproduced and suggest that the overall topology of the protein maps naturally emerges from the two leading mechanisms considered by the model.Preprin

Pattern formation and optimization in army ant raids

Army ant colonies display complex foraging raid patterns involving thousands of individuals communicating through chemical trails. In this paper we explore, by means of a simple search algorithm, the properties of these trails in order to test the hypothesis that their structure reflects an optimized mechanism for exploring and exploiting food resources. The raid patterns of three army ant species, {em Eciton hamatum}, {em Eciton burchelli} and {em Eciton rapax}, are analysed. The respective diets of these species involve large but rare, small but common, and a combination of large but rare and small but common, food sources. Using a model proposed by Deneubourg and collaborators, we simulate the formation of raid patterns in response to different food distributions. Our results indicate that the empirically observed raid patterns maximise return on investment, that is, the amount of food brought back to the nest per unit of energy expended, for each of the diets. Moreover, the values of the parameters that characterise the three optimal pattern-generating mechanisms are strikingly similar. Therefore the same behavioural rules at the individual level can produce optimal colony-level patterns. The evolutionary implications of these findings are discussed.Postprint (published version

A Computational characterization of collective chaos

We suggest that the interaction of a Globally Coupled Map (GCM) with an individual element inside the system is, from a computational point of view, indistinguishable of a mu,epsilon-dependent noise in the turbulent region of the phase space. Therefore, we can use the framework of Computational Mechanics to give a measure that clearly separates the ordered from the turbulent phases. Furthermore, our procedure is able to detect a small ordered domain inside the turbulent phase. These results reinforce the view of GCMs as properly defined mean field models of complex nonlinear networks.Preprin

Mean field theory of fluid neural networks

Fluid Neural Networks (FNN) are a mathematical framework where the phenomenon of self-synchronization in ant colonies can be explained, predicting the model a critical density, i.e. a density where oscillations appear, observed in real ant colonies. However, up to now all results have been solely numerical. In this paper we put forward a simpler FNN with the same phenomenology as the original one, but an analytical approximation can be performed in such a way that critical densities can be computed, offering a good approximation to the numerical ones.Postprint (published version

Self-synchronization and task fulfilment in ant colonies

Some authors have hypothesized that the observed self-synchronized activity in ant colonies provides some adaptive advantages, and, in particular, it has been suggested that task realization may benefit from this ordered temporal pattern of behavior (Robinson, 1992; Hatcher {em et al.}, 1992). In this paper we use a model of self-synchronized activity (the Fluid Neural Network) to suggest that with self-synchronized patterns of activity a task may be fulfiled more effectively than with non-synchronized activity, at the same average level of activity per individual.Postprint (published version

Self-synchronization and task fulfilment in ant colonies

Some authors have hypothesized that the observed self-synchronized activity in ant colonies provides some adaptive advantages, and, in particular, it has been suggested that task realization may benefit from this ordered temporal pattern of behavior (Robinson, 1992; Hatcher {em et al.}, 1992). In this paper we use a model of self-synchronized activity (the Fluid Neural Network) to suggest that with self-synchronized patterns of activity a task may be fulfiled more effectively than with non-synchronized activity, at the same average level of activity per individual

Evidence of a noise induced transition in fluid neural networks

Submitted to Physica D. Focusing on a phenomenon observed in the temporal patterns of activity behavior of Leptothorax ants, we introduce the notion of Noise Induced Computation. We study, from a Noise Induced Transition perspective, the emergent property of autosynchronization in ant colonies, using to model this phenomenon the formalism of Fluid Neural Networks. It is known that through this autosynchronization, ants attain, as a global computational property, a mechanism for information exchange known from computer science as mutual exclusion. We have numerical evidence that this happens at the critical point of the noise induced transition.Postprint (published version

Self-synchronization and task fulfilment in ant colonies

Some authors have hypothesized that the observed self-synchronized activity in ant colonies provides some adaptive advantages, and, in particular, it has been suggested that task realization may benefit from this ordered temporal pattern of behavior (Robinson, 1992; Hatcher {em et al.}, 1992). In this paper we use a model of self-synchronized activity (the Fluid Neural Network) to suggest that with self-synchronized patterns of activity a task may be fulfiled more effectively than with non-synchronized activity, at the same average level of activity per individual

A Computational characterization of collective chaos

We suggest that the interaction of a Globally Coupled Map (GCM) with an individual element inside the system is, from a computational point of view, indistinguishable of a mu,epsilon-dependent noise in the turbulent region of the phase space. Therefore, we can use the framework of Computational Mechanics to give a measure that clearly separates the ordered from the turbulent phases. Furthermore, our procedure is able to detect a small ordered domain inside the turbulent phase. These results reinforce the view of GCMs as properly defined mean field models of complex nonlinear networks