We study pattern formation associated with the polarization degree of freedom of the electric fie... more We study pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a nonlinear Kerr medium close to a two-photon resonance, placed inside a ring cavity with flat mirrors and driven by a coherent $\hat x$-polarized plane-wave field. In the self-focusing case, for negative detunings the pattern arises naturally from
Physica A: Statistical Mechanics and its Applications, 2003
We analyze a model of social interaction in one and two-dimensional lattices for a moderate numbe... more We analyze a model of social interaction in one and two-dimensional lattices for a moderate number of features. We introduce an order parameter as a function of the overlap between neighboring sites. In a one-dimensional chain, we observe that the dynamics is consistent with a second order transition, where the order parameter changes continuously and the average domain diverges at the transition point. However, in a two-dimensional lattice the order parameter is discontinuous at the transition point characteristic of a first order transition between an ordered and a disordered state.
Human mobility has been traditionally studied using surveys that deliver snapshots of population ... more Human mobility has been traditionally studied using surveys that deliver snapshots of population displacement patterns. The growing accessibility to ICT information from portable digital media has recently opened the possibility of exploring human behavior at high spatio-temporal resolutions. Mobile phone records, geolocated tweets, check-ins from Foursquare or geotagged photos, have contributed to this purpose at different scales, from cities to countries, in different world areas. Many previous works lacked, however, details on the individuals' attributes such as age or gender. In this work, we analyze credit-card records from Barcelona and Madrid and by examining the geolocated credit-card transactions of individuals living in the two provinces, we find that the mobility patterns vary according to gender, age and occupation. Differences in distance traveled and travel purpose are observed between younger and older people, but, curiously, either between males and females of similar age. While mobility displays some generic features, here we show that sociodemographic characteristics play a relevant role and must be taken into account for mobility and epidemiological modelization.
Conference Digest. 2000 International Quantum Electronics Conference (Cat. No.00TH8504), 2000
Noise-sustained patterns have been recently predicted in several systems including a Kerr cavity ... more Noise-sustained patterns have been recently predicted in several systems including a Kerr cavity and an optical parametric oscillator. In these systems a regime of convective instability can appear, in which a transverse pattern arises as a macroscopic manifestation of amplified and spatially structured quantum noise, with magnification factors of several order of magnitudes. We study quantum correlations in the convective
Lecture Notes in Economics and Mathematical Systems, 2001
A generic property of biological, social and economical networks is their ability to evolve in ti... more A generic property of biological, social and economical networks is their ability to evolve in time, creating and suppressing interactions. We approach this issue within the framework of an adaptive network of agents playing a Prisoner's Dilemma game, where each agent plays with its local neighbors, collects an aggregate payoff and imitates the strategy of its best neighbor. We allow the agents to adapt their local neighborhood according to their satisfaction level and the strategy played. We show that a steady state is reached, where the strategy and network configurations remain stationary. While the fraction of cooperative agents is high in these states, their average payoff is lower than the one attained by the defectors. The system self-organizes in such a way that the structure of links in the network is quite inhomogeneous, revealing the occurrence of cooperator "leaders" with a very high connectivity, which guarantee that global cooperation can be sustained in the whole network. Perturbing the leaders produces drastic changes of the network, leading to global dynamical cascades. These cascades induce a transient oscillation in the population of agents between the nearly all-defectors state and the all-cooperators outcome, before setting again in a state of high global cooperation.
The effect of a temporal modulation at three times the critical frequency on a Hopf bifurcation i... more The effect of a temporal modulation at three times the critical frequency on a Hopf bifurcation is studied in the framework of amplitude equations. We consider a complex Ginzburg-Landau equation with an extra quadratic term, resulting from the strong coupling between the external field and the unstable modes. We show that, by increasing the intensity of the forcing, one passes
The Evolution of Language - Proceedings of the 7th International Conference (EVOLANG7), 2008
In the general context of dynamics of social consensus, we study an agent based model for the com... more In the general context of dynamics of social consensus, we study an agent based model for the competition between two socially equivalent languages, addressing the role of bilingualism and social structure. In a regular network, we study the formation of linguistic domains and their interaction across the boundaries. We also analyse the dynamics on a small world network and on a network with community structure. In all cases, a final scenario of dominance of one language and extinction of the other is obtained (dominance-extinction state). In comparison with the regular network, smaller times for extinction are found in the small world network. In the network with communities instead, the average time for extinction does not give a characteristic time for the dynamics, and metastable states are observed at all time scales.
We study pattern formation associated with the polarization degree of freedom of the electric fie... more We study pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a nonlinear Kerr medium close to a two-photon resonance, placed inside a ring cavity with flat mirrors and driven by a coherentx-polarized plane-wave field. In the self-focusing case, for negative detunings the pattern arises naturally from a codimension two bifurcation. For a critical value of the field intensity there are two wave numbers that become unstable simultaneously, corresponding to two Turing-like instabilities. Considered alone, one of the instabilities would originate a linearly polarized hexagonal pattern whereas the other instability is of pure vectorial origin and would give rise to an elliptically polarized stripe pattern. We show that the competition between the two wavenumbers can originate different structures, being the detuning a natural selection parameter.
The synchronization of vectorial, noise-sustained structures in nonlinear optical systems is disc... more The synchronization of vectorial, noise-sustained structures in nonlinear optical systems is discussed. In particular, the analysis is made for nondegenerate optical parametric oscillators with walk off. The interplay between walk off and noise fluctuations leads to the formation of noise-sustained transverse patterns in both the signal and idler fields. Despite the fact that both patterns are stochastic macroscopic structures driven by independent sources of noise, their correlation grows with time, finally leading to a spatially distributed time synchronization of noise-sustained structures. A physical explanation of this phenomenon is found by analyzing the linear instability process and the existence of exact nonlinear solutions that show the same correlation.
In many evolutionary algorithms, crossover is the main operator used in generating new individual... more In many evolutionary algorithms, crossover is the main operator used in generating new individuals from old ones. However, the usual mechanism for generating offsprings in spatially structured evolutionary games has to date been clonation. Here we study the effect of incorporating crossover on these models. Our framework is the spatial Continuous Prisoner's Dilemma. For this evolutionary game, it has been reported that occasional errors (mutations) in the clonal process can explain the emergence of cooperation from a non-cooperative initial state. First, we show that this only occurs for particular regimes of low costs of cooperation. Then, we display how crossover gets greater the range of scenarios where cooperative mutants can invade selfish populations. In a social context, where crossover involves a general rule of gradual learning, our results show that the less that is learnt in a single step, the larger the degree of global cooperation finally attained. In general, the effect of step-by-step learning can be more efficient for the evolution of cooperation than a full blast one.
We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction... more We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small world network, we find a transition between an ordered homogeneous state and a disordered state. The transition point is shifted by the degree of spatial disorder of the underlying network, the network disorder favoring ordered configurations. In random scale-free networks the transition is only observed for finite size systems, showing system size scaling, while in the thermodynamic limit only ordered configurations are always obtained. Thus in the thermodynamic limit the transition disappears. However, in structured scale-free networks, the phase transition between an ordered and a disordered phase is restored.
We analyze the effect of cultural drift, modeled as noise, in Axelrod's model for the disseminati... more We analyze the effect of cultural drift, modeled as noise, in Axelrod's model for the dissemination of culture. The disordered multicultural configurations are found to be metastable. This general result is proven rigorously in d = 1, where the dynamics is described in terms of a Lyapunov potential. In d = 2, the dynamics is governed by the average relaxation time T of perturbations. Noise at a rate r T −1 induces monocultural configurations, whereas r T −1 sustains disorder. In the thermodynamic limit, the relaxation time diverges and global polarization persists in spite of a dynamics of local convergence.
We consider a model for a Kerr medium in a planar resonator, which takes into account the vectori... more We consider a model for a Kerr medium in a planar resonator, which takes into account the vectorial character of the radiation field. We analyze the spatial behavior of quantum fluctuations around a steady state, with a roll-pattern configuration in the beam cross section, using a Langevin treatment based on the Wigner representation. The spatial distribution of the quantum fluctuations
We introduce a two layer network model for social coordination incorporating two relevant ingredi... more We introduce a two layer network model for social coordination incorporating two relevant ingredients: a) different networks of interaction to learn and to obtain a pay-off, and b) decision making processes based both on social and strategic motivations. Two populations of agents are distributed in two layers with intralayer learning processes and playing interlayer a coordination game. We find that the skepticism about the wisdom of crowd and the local connectivity are the driving forces to accomplish full coordination of the two populations, while polarized coordinated layers are only possible for all-to-all interactions. Local interactions also allow for full coordination in the socially efficient Pareto-dominant strategy in spite of being the riskier one.
We study spatiotemporal pattern formation associated with the polarization degree of freedom of t... more We study spatiotemporal pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a Kerr medium in a cavity with flat mirrors and driven by a coherent plane-wave field. We consider linearly as well as elliptically polarized driving fields, and situations of self-focusing and self-defocusing. For the case of self-defocusing and a linearly polarized driving field, there is a stripe pattern orthogonally polarized to the driving field. Such a pattern changes into a hexagonal pattern for an elliptically polarized driving field. The range of driving intensities for which the pattern is formed shrinks to zero with increasing ellipticity. For the case of self-focusing, changing the driving field ellipticity leads from a linearly polarized hexagonal pattern ͑for linearly polarized driving͒ to a circularly polarized hexagonal pattern ͑for circularly polarized driving͒. Intermediate situations include a modified Hopf bifurcation at a finite wave number, leading to a time dependent pattern of deformed hexagons and a codimension 2 Turing-Hopf instability resulting in an elliptically polarized stationary hexagonal pattern. Our numerical observations of different spatiotemporal structures are described by appropriate model and amplitude equations.
The Journal of Artificial Societies and Social Simulation, 2007
We study the effects of different forms of information feedback associated with mass media on an ... more We study the effects of different forms of information feedback associated with mass media on an agent-agent based model of the dynamics of cultural dissemination. In addition to some processes previously considered, we also examine a model of local mass media influence in cultural dynamics. Two mechanisms of information feedback are investigated: (i) direct mass media influence, where local or
Fluorescence spectra indicate that pyrene is solubilized in a non-polar region in lead(II) decano... more Fluorescence spectra indicate that pyrene is solubilized in a non-polar region in lead(II) decanoate. The local fluidity of the probe in the L a and liquid phases, monitored by excimer formation, is comparable to that of aliphatic hydrocarbons at the same temperature, and the microviscosity is an order of magnitude lower than the bulk viscosity of the soap.
We study pattern formation associated with the polarization degree of freedom of the electric fie... more We study pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a nonlinear Kerr medium close to a two-photon resonance, placed inside a ring cavity with flat mirrors and driven by a coherent $\hat x$-polarized plane-wave field. In the self-focusing case, for negative detunings the pattern arises naturally from
Physica A: Statistical Mechanics and its Applications, 2003
We analyze a model of social interaction in one and two-dimensional lattices for a moderate numbe... more We analyze a model of social interaction in one and two-dimensional lattices for a moderate number of features. We introduce an order parameter as a function of the overlap between neighboring sites. In a one-dimensional chain, we observe that the dynamics is consistent with a second order transition, where the order parameter changes continuously and the average domain diverges at the transition point. However, in a two-dimensional lattice the order parameter is discontinuous at the transition point characteristic of a first order transition between an ordered and a disordered state.
Human mobility has been traditionally studied using surveys that deliver snapshots of population ... more Human mobility has been traditionally studied using surveys that deliver snapshots of population displacement patterns. The growing accessibility to ICT information from portable digital media has recently opened the possibility of exploring human behavior at high spatio-temporal resolutions. Mobile phone records, geolocated tweets, check-ins from Foursquare or geotagged photos, have contributed to this purpose at different scales, from cities to countries, in different world areas. Many previous works lacked, however, details on the individuals' attributes such as age or gender. In this work, we analyze credit-card records from Barcelona and Madrid and by examining the geolocated credit-card transactions of individuals living in the two provinces, we find that the mobility patterns vary according to gender, age and occupation. Differences in distance traveled and travel purpose are observed between younger and older people, but, curiously, either between males and females of similar age. While mobility displays some generic features, here we show that sociodemographic characteristics play a relevant role and must be taken into account for mobility and epidemiological modelization.
Conference Digest. 2000 International Quantum Electronics Conference (Cat. No.00TH8504), 2000
Noise-sustained patterns have been recently predicted in several systems including a Kerr cavity ... more Noise-sustained patterns have been recently predicted in several systems including a Kerr cavity and an optical parametric oscillator. In these systems a regime of convective instability can appear, in which a transverse pattern arises as a macroscopic manifestation of amplified and spatially structured quantum noise, with magnification factors of several order of magnitudes. We study quantum correlations in the convective
Lecture Notes in Economics and Mathematical Systems, 2001
A generic property of biological, social and economical networks is their ability to evolve in ti... more A generic property of biological, social and economical networks is their ability to evolve in time, creating and suppressing interactions. We approach this issue within the framework of an adaptive network of agents playing a Prisoner's Dilemma game, where each agent plays with its local neighbors, collects an aggregate payoff and imitates the strategy of its best neighbor. We allow the agents to adapt their local neighborhood according to their satisfaction level and the strategy played. We show that a steady state is reached, where the strategy and network configurations remain stationary. While the fraction of cooperative agents is high in these states, their average payoff is lower than the one attained by the defectors. The system self-organizes in such a way that the structure of links in the network is quite inhomogeneous, revealing the occurrence of cooperator "leaders" with a very high connectivity, which guarantee that global cooperation can be sustained in the whole network. Perturbing the leaders produces drastic changes of the network, leading to global dynamical cascades. These cascades induce a transient oscillation in the population of agents between the nearly all-defectors state and the all-cooperators outcome, before setting again in a state of high global cooperation.
The effect of a temporal modulation at three times the critical frequency on a Hopf bifurcation i... more The effect of a temporal modulation at three times the critical frequency on a Hopf bifurcation is studied in the framework of amplitude equations. We consider a complex Ginzburg-Landau equation with an extra quadratic term, resulting from the strong coupling between the external field and the unstable modes. We show that, by increasing the intensity of the forcing, one passes
The Evolution of Language - Proceedings of the 7th International Conference (EVOLANG7), 2008
In the general context of dynamics of social consensus, we study an agent based model for the com... more In the general context of dynamics of social consensus, we study an agent based model for the competition between two socially equivalent languages, addressing the role of bilingualism and social structure. In a regular network, we study the formation of linguistic domains and their interaction across the boundaries. We also analyse the dynamics on a small world network and on a network with community structure. In all cases, a final scenario of dominance of one language and extinction of the other is obtained (dominance-extinction state). In comparison with the regular network, smaller times for extinction are found in the small world network. In the network with communities instead, the average time for extinction does not give a characteristic time for the dynamics, and metastable states are observed at all time scales.
We study pattern formation associated with the polarization degree of freedom of the electric fie... more We study pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a nonlinear Kerr medium close to a two-photon resonance, placed inside a ring cavity with flat mirrors and driven by a coherentx-polarized plane-wave field. In the self-focusing case, for negative detunings the pattern arises naturally from a codimension two bifurcation. For a critical value of the field intensity there are two wave numbers that become unstable simultaneously, corresponding to two Turing-like instabilities. Considered alone, one of the instabilities would originate a linearly polarized hexagonal pattern whereas the other instability is of pure vectorial origin and would give rise to an elliptically polarized stripe pattern. We show that the competition between the two wavenumbers can originate different structures, being the detuning a natural selection parameter.
The synchronization of vectorial, noise-sustained structures in nonlinear optical systems is disc... more The synchronization of vectorial, noise-sustained structures in nonlinear optical systems is discussed. In particular, the analysis is made for nondegenerate optical parametric oscillators with walk off. The interplay between walk off and noise fluctuations leads to the formation of noise-sustained transverse patterns in both the signal and idler fields. Despite the fact that both patterns are stochastic macroscopic structures driven by independent sources of noise, their correlation grows with time, finally leading to a spatially distributed time synchronization of noise-sustained structures. A physical explanation of this phenomenon is found by analyzing the linear instability process and the existence of exact nonlinear solutions that show the same correlation.
In many evolutionary algorithms, crossover is the main operator used in generating new individual... more In many evolutionary algorithms, crossover is the main operator used in generating new individuals from old ones. However, the usual mechanism for generating offsprings in spatially structured evolutionary games has to date been clonation. Here we study the effect of incorporating crossover on these models. Our framework is the spatial Continuous Prisoner's Dilemma. For this evolutionary game, it has been reported that occasional errors (mutations) in the clonal process can explain the emergence of cooperation from a non-cooperative initial state. First, we show that this only occurs for particular regimes of low costs of cooperation. Then, we display how crossover gets greater the range of scenarios where cooperative mutants can invade selfish populations. In a social context, where crossover involves a general rule of gradual learning, our results show that the less that is learnt in a single step, the larger the degree of global cooperation finally attained. In general, the effect of step-by-step learning can be more efficient for the evolution of cooperation than a full blast one.
We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction... more We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small world network, we find a transition between an ordered homogeneous state and a disordered state. The transition point is shifted by the degree of spatial disorder of the underlying network, the network disorder favoring ordered configurations. In random scale-free networks the transition is only observed for finite size systems, showing system size scaling, while in the thermodynamic limit only ordered configurations are always obtained. Thus in the thermodynamic limit the transition disappears. However, in structured scale-free networks, the phase transition between an ordered and a disordered phase is restored.
We analyze the effect of cultural drift, modeled as noise, in Axelrod's model for the disseminati... more We analyze the effect of cultural drift, modeled as noise, in Axelrod's model for the dissemination of culture. The disordered multicultural configurations are found to be metastable. This general result is proven rigorously in d = 1, where the dynamics is described in terms of a Lyapunov potential. In d = 2, the dynamics is governed by the average relaxation time T of perturbations. Noise at a rate r T −1 induces monocultural configurations, whereas r T −1 sustains disorder. In the thermodynamic limit, the relaxation time diverges and global polarization persists in spite of a dynamics of local convergence.
We consider a model for a Kerr medium in a planar resonator, which takes into account the vectori... more We consider a model for a Kerr medium in a planar resonator, which takes into account the vectorial character of the radiation field. We analyze the spatial behavior of quantum fluctuations around a steady state, with a roll-pattern configuration in the beam cross section, using a Langevin treatment based on the Wigner representation. The spatial distribution of the quantum fluctuations
We introduce a two layer network model for social coordination incorporating two relevant ingredi... more We introduce a two layer network model for social coordination incorporating two relevant ingredients: a) different networks of interaction to learn and to obtain a pay-off, and b) decision making processes based both on social and strategic motivations. Two populations of agents are distributed in two layers with intralayer learning processes and playing interlayer a coordination game. We find that the skepticism about the wisdom of crowd and the local connectivity are the driving forces to accomplish full coordination of the two populations, while polarized coordinated layers are only possible for all-to-all interactions. Local interactions also allow for full coordination in the socially efficient Pareto-dominant strategy in spite of being the riskier one.
We study spatiotemporal pattern formation associated with the polarization degree of freedom of t... more We study spatiotemporal pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a Kerr medium in a cavity with flat mirrors and driven by a coherent plane-wave field. We consider linearly as well as elliptically polarized driving fields, and situations of self-focusing and self-defocusing. For the case of self-defocusing and a linearly polarized driving field, there is a stripe pattern orthogonally polarized to the driving field. Such a pattern changes into a hexagonal pattern for an elliptically polarized driving field. The range of driving intensities for which the pattern is formed shrinks to zero with increasing ellipticity. For the case of self-focusing, changing the driving field ellipticity leads from a linearly polarized hexagonal pattern ͑for linearly polarized driving͒ to a circularly polarized hexagonal pattern ͑for circularly polarized driving͒. Intermediate situations include a modified Hopf bifurcation at a finite wave number, leading to a time dependent pattern of deformed hexagons and a codimension 2 Turing-Hopf instability resulting in an elliptically polarized stationary hexagonal pattern. Our numerical observations of different spatiotemporal structures are described by appropriate model and amplitude equations.
The Journal of Artificial Societies and Social Simulation, 2007
We study the effects of different forms of information feedback associated with mass media on an ... more We study the effects of different forms of information feedback associated with mass media on an agent-agent based model of the dynamics of cultural dissemination. In addition to some processes previously considered, we also examine a model of local mass media influence in cultural dynamics. Two mechanisms of information feedback are investigated: (i) direct mass media influence, where local or
Fluorescence spectra indicate that pyrene is solubilized in a non-polar region in lead(II) decano... more Fluorescence spectra indicate that pyrene is solubilized in a non-polar region in lead(II) decanoate. The local fluidity of the probe in the L a and liquid phases, monitored by excimer formation, is comparable to that of aliphatic hydrocarbons at the same temperature, and the microviscosity is an order of magnitude lower than the bulk viscosity of the soap.
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Papers by Maxi Miguel