Current research lines
Self-organized
criticality
Lattice
models of pulse-coupled oscillators
Application
to economic models
Communication
in complex networks
Synchronization in complex networks
The phenomenon known as self-organized criticality is related to systems which spontaneously (self organized) evolve towards a stationary state without time and length characteristic scales; it is named critical because their analogies with critical phenomena, widely studied in equilibrium. The main differences are that now one deals with non-equilibrium systems, and hence equilibrium statistical mechanics can not be used, and that criticality appears without the necessity of tuning any external parameter. Follow this link to view some simple models.
Within this subject our contributions can be split in two distinct parts:
Collaborations:
One of the central points of our research has been the study of biological rhythms, together with other dynamical aspects related to the cooperative behavior of extended populations. Particularly, our analysis has been emphasized on the study of the mechanisms that are behind phenomena like synchronization of the activity of these populations as well as the formation of spatio-temporal structures. A characteristic example observed in nature is a population of fireflies.
To carry out these analysis we consider populations of oscillators, coupled through a nonlinear interaction, in low-dimensionality lattices. Two different types of model have to be distinguished:
Collaborations:
During the last years we have been collaborating with Prof. Fernando Vega-Redondo, an economist from the University of Alicante.
As physicists our contribution in this subject has been to apply concepts and tools widely used in nonequilibrium statistical mechanics, as those described above, to the study of the complex behavior of interacting economic agents.
We have studied a model of a socio-economic environment in a one-dimensional regular lattice, where each agent is characterized by a certain technological level. Depending on their neighbors' level, a given agent can decide to change her own level inducing collective events (avalanches). The probability distribution of the sizes of these avalanches has a power-law shape. Characterizing the evolution of the system by a conveniently chosen variable, we find that the system self-organizes in an optimal way in the critical region of parameter space. This behavior is robust, in the sense that it does not depend on the details of the microscopic dynamics of the agents, but just on certain constraints.
We are currently investigating other properties of this system. For instance, validity of scaling laws, profile roughness, limitation in the number of agents that are allowed to innovate (quenched disorder), higher dimensional lattices, effect of introducing costs in the decisions, ...
Right now, we are starting a line of research which concerns mainly the effect of the interaction paths between the agents. Up to now we have considered the agents in a perfect one-dimensional ring or in a square two-dimensional lattice. It is well known that slight changes in the interaction paths between the agents leads to completely novel macroscopic behaviors. Examples of new topologies are small-world networks, scale-free networks, random networks, and so on. Our interest is the study of how the dynamics is affected by this kind of topologies. On the one hand, we want to analyze the effect of a quenched (fixed in time) randomness, and on the other hand the effect of dynamical changes in the links between the agents. This dynamics can be either randomly or purpose generated. We believe that in these cases new macroscopic behaviors will emerge that can be very interesting from a practical point of view.
Collaborations:
Our interest in this subject is focused on the behavior of complex structures formed by elements (or agents) that interact with each other via communication processes. This framework is specially adequate to study e.g. Internet flow, traffic networks, river networks, and even communication flows in organizations.
We have proposed a simple model that includes only the basic ingredients present in a communication process between two elements: (i) information packets to be transmitted (delivered) and (ii) communication channels with finite capacity to transmit the packets. The model reproduces the main characteristics of the flow of information packets in a network and it is simple enough to allow analytical characterization.
We can apply these ideas to the task of organizational design. It is interesting to notice that for a given hierarchical structure it is possible to calculate the maximum amount of information packets that can be generated at each time step without collapsing the organization. Two main features are observed: (i) the maximum number of packets per unit time the organization can deal with does not depend on the number of levels in the hierarchical structure and (ii) this critical number of packets is a monotonically increasing function of the branching factor, thus suggesting that, for a fixed size of the organization, the optimal structure is the flattest one, with only two levels. A different scenario arises when the more realistic situation of costly connections is considered by introducing a cost factor in the definition of agents capability. Although, as in the previous case, the maximum amount of information the organization is able to handle does not depend on the number of levels, it is not a monotonically increasing function of the branching factor. Thus the flattest structure is not the best in general. Actually, the steepness of the optimal structure is tuned by the intensity of the cost factor. As may be expected, the higher the cost of the connections, the steeper the optimal structure and vice versa.
A different subjects where this
framework can be applied is to the innovation capacity of an organization.
Thinking of an innovation as a combination of two complementary ideas that
randomly appear in different nodes of an organization.
On of the main issues in this type
of problem is to find the optimal structure for networks with some
restrictions. We have studied:
·
Parameterized networks: networks built according
to different mechanisms (square regular lattice, small-world, preferential
attachment,…). Results.
·
General framework: optimization algorithm that search for the
best network with a fixed number of nodes and links. Results.
Collaborations:
We have also the
statistical properties of different social networks. The examples are:
Social networks as those we have analized have several properties in common: a high clustering coefficient, positive degree correlations, and the existence of well defined communities. In order to explain the wide appearance of these characteristics we have also proposed a model where the attachment between nodes is based on the distance in a social space.
Collaborations:
Various physical, social, and biological systems generate complex fluctuations with correlations across multiple time scales. In physiologic systems, these long-range correlations are altered with disease and aging. Such correlated fluctuations in living systems have been attributed to the interaction of multiple control systems; however, the mechanisms underlying this behavior remain unknown. We have shown that a number of distinct classes of dynamical behaviors, including correlated fluctuations characterized by 1/f scaling of their power spectra, can emerge in networks of simple signaling units. We found that, under general conditions, complex dynamics can be generated by systems fulfilling the following two requirements, (i) a ‘‘small-world’’ topology and (ii) the presence of noise. Our findings support two notable conclusions. First, complex physiologic-like signals can be modeled with a minimal set of components; and second, systems fulfilling conditions i and ii are robust to some degree of degradation (i.e., they will still be able to generate 1/f dynamics).
Collaborations:
Concerning again the complex patterns of interactions that have been found in many natural, social and technological systems, we have studied the interplay between dynamics and topology. In particular, we have focused our research on the way topology, in terms of the communities that are formed at different scales, affects the dynamics of the complete system, in terms of the partial synchronization achieved between the different topological groups. We have modelized the dynamics through the Kuramoto model for which a stationary solution in which all the oscillators are completelly synchronized exists. Click here for a more detailed information and application to several computer-generated networks..
Collaborations: