Criticality and the Onset of Ordering in the Standard Vicsek Model

Experimental observations of animal collective behavior have shown stunning evidence for the emergence of large-scale cooperative phenomena resembling phase transitions in physical systems. Indeed, quantitative studies have found scale-free correlations and critical behavior consistent with the occurrence of continuous, second-order phase transitions. The Standard Vicsek Model (SVM), a minimal model of self-propelled particles in which their tendency to align with each other competes with perturbations controlled by a noise term, appears to capture the essential ingredients of critical flocking phenomena. In this paper, we review recent finite-size scaling and dynamical studies of the SVM, which present a full characterization of the continuous phase transition through dynamical and critical exponents. We also present a complex network analysis of SVM flocks and discuss the onset of ordering in connection with XY-like spin models.Comment: 15 pages, 4 figures. To appear in Interface Focu

Complex Network Structure of Flocks in the Standard Vicsek Model

In flocking models, the collective motion of self-driven individuals leads to the formation of complex spatiotemporal patterns. The Standard Vicsek Model (SVM) considers individuals that tend to adopt the direction of movement of their neighbors under the influence of noise. By performing an extensive complex network characterization of the structure of SVM flocks, we show that flocks are highly clustered, assortative, and non-hierarchical networks with short-tailed degree distributions. Moreover, we also find that the SVM dynamics leads to the formation of complex structures with an effective dimension higher than that of the space where the actual displacements take place. Furthermore, we show that these structures are capable of sustaining mean-field-like orientationally ordered states when the displacements are suppressed, thus suggesting a linkage between the onset of order and the enhanced dimensionality of SVM flocks.Comment: 26 pages, 11 figures. To appear in J. Stat. Phy

Continuous-space automaton model for pedestrian dynamics

An off-lattice automaton for modeling pedestrian dynamics is presented. Pedestrians are represented by disks with variable radius that evolve following predefined rules. The key feature of our approach is that although positions and velocities are continuous, forces do not need to be calculated. This has the advantage that it allows using a larger time step than in force-based models. The room evacuation problem and circular racetrack simulations quantitatively reproduce the available experimental data, both for the specific flow rate and for the fundamental diagram of pedestrian traffic with an outstanding performance. In this last case, the variation of two free parameters (r min and rmax) of the model accounts for the great variety of experimental fundamental diagrams reported in the literature. Moreover, this variety can be interpreted in terms of these model parameters.Fil: Baglietto, Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Parisi, Daniel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto Tecnológico de Buenos Aires; Argentin

Noisy multistate voter model for flocking in finite dimensions

We study a model for the collective behavior of self-propelled particles subject to pairwise copying interactions and noise. Particles move at a constant speed v on a two-dimensional space and, in a single step of the dynamics, each particle adopts the direction of motion of a randomly chosen neighboring particle within a distance R=1, with the addition of a perturbation of amplitude eta (noise). We investigate how the global level of particles' alignment (order) is affected by their motion and the noise amplitude eta. In the static case scenario v=0 where particles are fixed at the sites of a square lattice and interact with their first neighbors, we find that for any noise eta > 0 the system reaches a steady state of complete disorder in the thermodynamic limit, while for eta=0 full order is eventually achieved for a system with any number of particles N. Therefore, the model displays a transition at zero noise when particles are static, and thus there are no ordered steady states for a finite noise ( eta>0). We show that the finite-size transition noise vanishes with Nas eta_c^(1D)~ N^-1 and eta_c^(2D)~ (N lnN)^-1/2 in one- and two-dimensional lattices, respectively, which is linked to known results on the behavior of a type of noisy voter model for catalytic reactions. When particles are allowed to move in the space at a finite speed v>0, an ordered phase emerges, characterized by a fraction of particles moving in a similar direction. The system exhibits an order-disorder phase transition at a noise amplitude eta_c >0 that is proportional to v, and that scales approximately as eta_c ~ v(-lnv)^-1/2 for v<<1. These results show that the motion of particles is able to sustain a state of global order in a system with voter-like interactions.Fil: Loscar, Ernesto Selim. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Baglietto, Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Vazquez, Federico. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentin

Density-based clustering: A 'landscape view' of multi-channel neural data for inference and dynamic complexity analysis

Two, partially interwoven, hot topics in the analysis and statistical modeling of neural data, are the development of efficient and informative representations of the time series derived from multiple neural recordings, and the extraction of information about the connectivity structure of the underlying neural network from the recorded neural activities. In the present paper we show that state-space clustering can provide an easy and effective option for reducing the dimensionality of multiple neural time series, that it can improve inference of synaptic couplings from neural activities, and that it can also allow the construction of a compact representation of the multi-dimensional dynamics, that easily lends itself to complexity measures. We apply a variant of the 'mean-shift' algorithm to perform state-space clustering, and validate it on an Hopfield network in the glassy phase, in which metastable states are largely uncorrelated from memories embedded in the synaptic matrix. In this context, we show that the neural states identified as clusters' centroids offer a parsimonious parametri-zation of the synaptic matrix, which allows a significant improvement in inferring the synaptic couplings from the neural activities. Moving to the more realistic case of a multi-modular spiking network, with spike-frequency adaptation inducing history-dependent effects, we propose a procedure inspired by Boltzmann learning, but extending its domain of application, to learn inter-module synaptic couplings so that the spiking network reproduces a prescribed pattern of spatial correlations; we then illustrate, in the spiking network, how clustering is effective in extracting relevant features of the network's state-space landscape. Finally, we show that the knowledge of the cluster structure allows casting the multi-dimensional neural dynamics in the form of a symbolic dynamics of transitions between clusters; as an illustration of the potential of such reduction, we define and analyze a measure of complexity of the neural time series.Instituto de Física de Líquidos y Sistemas Biológico

Gregarious vs Individualistic Behavior in Vicsek Swarms and the Onset of First-Order Phase Transitions

The Standard Vicsek Model (SVM) is a minimal nonequilibrium model of self-propelled particles that appears to capture the essential ingredients of critical flocking phenomena. In the SVM, particles tend to align with each other and form ordered flocks of collective motion; however, perturbations controlled by a noise term lead to a noise-driven, continuous order-disorder phase transition. In this work, we extend the SVM by introducing a parameter $\alpha$ that allows particles to be individualistic instead of gregarious, i.e. to choose a direction of motion independently of their neighbors. By focusing on the small-noise regime, we show that a relatively small probability of individualistic motion (around 10%) is sufficient to drive the system from a Vicsek-like ordered phase to a disordered phase. Despite the fact that the $\alpha-$extended Model preserves the O(n) symmetry, the interaction range, as well as the dimensionality of the underlying SVM, this novel phase transition is found to be discontinuous (first-order), an intriguing manifestation of the richness of the nonequilibrium flocking/swarming phenomenon.Comment: 13 pages, 6 figures. To appear in Physica

Multistate voter model with imperfect copying

The voter model with multiple states has found applications in areas as diverse as population genetics, opinion formation, species competition, and language dynamics, among others. In a single step of the dynamics, an individual chosen at random copies the state of a random neighbor in the population. In this basic formulation, it is assumed that the copying is perfect, and thus an exact copy of an individual is generated at each time step. Here, we introduce and study a variant of the multistate voter model in mean field that incorporates a degree of imperfection or error in the copying process, which leaves the states of the two interacting individuals similar but not exactly equal. This dynamics can also be interpreted as a perfect copying with the addition of noise: a minimalistic model for flocking. We found that the ordering properties of this multistate noisy voter model, measured by a parameter ψ in [0,1], depend on the amplitude η of the copying error or noise and the population size N . In the case of perfect copying η = 0 , the system reaches an absorbing configuration with complete order ( ψ = 1 ) for all values of N . However, for any degree of imperfection η > 0 , we show that the average value of ψ at the stationary state decreases with N as ⟨ ψ ⟩ ≃ 6 / ( π 2 η 2 N ) for η ≪ 1 and η 2 N ≳ 1 , and thus the system becomes totally disordered in the thermodynamic limit N → ∞ . We also show that ⟨ ψ ⟩ ≃ 1 − π 2 6 η 2 N in the vanishing small error limit η → 0 , which implies that complete order is never achieved for η > 0 . These results are supported by Monte Carlo simulations of the model, which allow to study other scenarios as well.Fil: Vazquez, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; ArgentinaFil: Loscar, Ernesto Selim. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Baglietto, Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentin

Gregarious versus individualistic behavior in Vicsek swarms and the onset of first-order phase transitions

The standard Vicsek model (SVM) is a minimal non-equilibrium model of self-propelled particles that appears to capture the essential ingredients of critical flocking phenomena. In the SVM, particles tend to align with each other and form ordered flocks of collective motion; however, perturbations controlled by a noise term lead to a noisedriven continuous order–disorder phase transition. In this work, we extend the SVM by introducing a parameter α that allows particles to be individualistic instead of gregarious, i.e. to choose a direction of motion independently of their neighbors. By focusing on the small-noise regime, we show that a relatively small probability of individualistic motion (around 10%) is sufficient to drive the system from a Vicsek-like ordered phase to a disordered phase. Despite the fact that the α-extended model preserves the O(n) symmetry and the interaction range, as well as the dimensionality of the underlying SVM, this novel phase transition is found to be discontinuous (first order), an intriguing manifestation of the richness of the non-equilibrium flocking/swarming phenomenon.Instituto de Física de Líquidos y Sistemas BiológicosFacultad de IngenieríaFacultad de Ciencias Exacta

Charge and spin correlations in the monopole liquid

A monopole liquid is a spin system with a high density of magnetic charges but no magnetic-charge order. We study such a liquid over an Ising pyrochlore lattice, where a single topological charge or monopole sits in each tetrahedron. Restricting the study to the case with no magnetic field applied we show that, in spite of the liquidlike correlations between charges imposed by construction constraints, the spins are uncorrelated like in a perfect paramagnet. We calculate a massive residual entropy for this phase (ln(2)/2, a result which is exact in the thermodynamic limit), implying a free Ising-like variable per tetrahedron. After defining a simple model Hamiltonian for this system (the balanced monopole liquid) we study its thermodynamics. Surprisingly, this monopole liquid remains a perfect paramagnet at all temperatures. Thermal disorder can then be simply and quantitatively interpreted as single charge dilution, by the excitation of neutral sites and double monopoles. The addition of the usual nearest neighbors interactions favoring neutral ´2in-2out´ excitations as a perturbation maintains the same ground state but induces short-range (topological) order by thermal disorder. While it decreases charge-charge correlations, pair spin correlations - resembling those in spin ice - appear on increasing temperature. This helps us to see in another light the dipolarlike correlations present in spin ices at unexpectedly high temperatures. On the other side, favoring double excitations strengthens the charges short range order and its associated spin correlations. Finally, we discuss how the monopole liquid can be related to other systems and materials where different phases of monopole matter have been observed.Fil: Slobinsky, Demian Gustavo. Universidad Tecnológica Nacional; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Baglietto, Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Borzi, Rodolfo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentin