arXiv subjects

Gabriel Baglietto

Publications and source records attributed to Gabriel Baglietto.

8 recordsLinked to original sources

arXiv2021

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, with the addition of a perturbation of amplitude $η$ (noise). We investigate how the global level of particles' alignment (order) is affected by their motion and the noise amplitude $η$. 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 $η_c>0$ the system reaches a steady state of complete disorder in the thermodynamic limit, while for $η=0$ 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 ($η>0$). We show that the finite-size transition noise vanishes with $N$ as $η_c^{1D} \sim N^{-1}$ and $η_c^{2D} \sim \left(N \ln N \right)^{-1/2}$ 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 $η_c>0$ that is proportional to $v$, and that scales approximately as $η_c \sim v \, (-\ln v)^{-1/2}$ for $v \ll 1$. These results show that the motion of particles is able to sustain a state of global order in a system with voter-like interactions.

physics.soc-ph↗

arXiv2019

A multi-state 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 multi-state 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 multi-state 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 $\langle ψ\rangle \simeq 6/(π^2 η^2 N)$ for $η\ll 1$ and $η^2 N \gtrsim 1$, and thus the system becomes totally disordered in the thermodynamic limit $N \to \infty$. We also show that $\langle ψ\rangle \simeq 1-1.64 \, η^2 N$ in the vanishing small error limit $η\to 0$, 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.

physics.soc-ph↗

arXiv2019

Flocking dynamics with voter-like interactions

We study the collective motion of a large set of self-propelled particles subject to voter-like interactions. Each particle moves on a two-dimensional space at a constant speed in a direction that is randomly assigned initially. Then, at every step of the dynamics, each particle adopts the direction of motion of a randomly chosen neighboring particle. We investigate the time evolution of the global alignment of particles measured by the order parameter $φ$, until complete order $φ=1.0$ is reached (polar consensus). We find that $φ$ increases as $t^{1/2}$ for short times and approaches exponentially fast to $1.0$ for long times. Also, the mean time to consensus $τ$ varies non-monotonically with the density of particles $ρ$, reaching a minimum at some intermediate density $ρ_{\tiny \mbox{min}}$. At $ρ_{\tiny \mbox{min}}$, the mean consensus time scales with the system size $N$ as $τ_{\tiny \mbox{min}} \sim N^{0.765}$, and thus the consensus is faster than in the case of all-to-all interactions (large $ρ$) where $τ=2N$. We show that the fast consensus, also observed at intermediate and high densities, is a consequence of the segregation of the system into clusters of equally-oriented particles which breaks the balance of transitions between directional states in well mixed systems.

physics.soc-ph↗

arXiv2018

Heterogeneity promotes first to second order phase transition on flocking systems

We have considered a variation of the Vicsek model with vectorial noise where each one of the agents have their own noise amplitude normally distributed around a mean value, $μ$, with standard deviation $σ$. First-order phase transition are observed for standard deviation $0\leqσ<σ_{tri}\approx0.11$, whereas for larger values, up to $σ=0.3$, a continuous phase transition occurs. For values of $σ$ in the interval $0.15\leqσ\leq0.30$ the continuous nature of the observed transition is characterized by means of finite-size scaling techniques, that also allow us to estimate the exponents driving the transition. A study of bands stability suggests that no band can form in this regime. Inspired by biological facts, the perception heterogeneity introduced in the model trough $σ$, allow us to tune the collective behaviour of the system.

cond-mat.soft↗

arXiv2017

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

Simultaneous recordings from N electrodes generate N-dimensional time series that call for efficient representations to expose relevant aspects of the underlying dynamics. Binning the time series defines neural activity vectors that populate the N-dimensional space as a density distribution, especially informative when the neural dynamics performs a noisy path through metastable states (often a case of interest in neuroscience); this makes clustering in the N-dimensional space a natural choice. We apply a variant of the 'mean-shift' algorithm to perform such clustering, and validate it on an Hopfield network in the glassy phase, in which metastable states are uncorrelated from memory attractors. The neural states identified as clusters' centroids are then used to define a parsimonious parametrization of the synaptic matrix, which allows a significant improvement in inferring the synaptic couplings from neural activities. We next consider the more realistic case of a multi-modular spiking network, with spike-frequency adaptation (SFA) inducing history-dependent effects; we develop 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. After clustering the activity generated by multi-modular spiking networks, we represent their multi-dimensional dynamics as the symbolic sequence of the clusters' centroids, which naturally lends itself to complexity estimates that provide information on memory effects like those induced by SFA. To obtain a relative complexity measure we compare the Lempel-Ziv complexity of the actual centroid sequence to the one of Markov processes sharing the same transition probabilities between centroids; as an illustration, we show that the dependence of such relative complexity on the time scale of SFA.

q-bio.NC↗

arXiv2013

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.

cond-mat.stat-mech↗

arXiv2013

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 $α$ 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, 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.

cond-mat.stat-mech↗

arXiv2012

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.

cond-mat.stat-mech↗