arXiv subjects

Pablo Villegas

Publications and source records attributed to Pablo Villegas.

At least 37 records · Page 2Linked to original sources

arXiv2024

Laplacian Renormalization Group: An introduction to heterogeneous coarse-graining

The renormalization group (RG) constitutes a fundamental framework in modern theoretical physics. It allows the study of many systems showing states with large-scale correlations and their classification in a relatively small set of universality classes. RG is the most powerful tool for investigating organizational scales within dynamic systems. However, the application of RG techniques to complex networks has presented significant challenges, primarily due to the intricate interplay of correlations on multiple scales. Existing approaches have relied on hypotheses involving hidden geometries and based on embedding complex networks into hidden metric spaces. Here, we present a practical overview of the recently introduced Laplacian Renormalization Group for heterogeneous networks. First, we present a brief overview that justifies the use of the Laplacian as a natural extension for well-known field theories to analyze spatial disorder. We then draw an analogy to traditional real-space renormalization group procedures, explaining how the LRG generalizes the concept of "Kadanoff supernodes" as block nodes that span multiple scales. These supernodes help mitigate the effects of cross-scale correlations due to small-world properties. Additionally, we rigorously define the LRG procedure in momentum space in the spirit of Wilson RG. Finally, we show different analyses for the evolution of network properties along the LRG flow following structural changes when the network is properly reduced.

cond-mat.stat-mech↗

arXiv2024

Evidence of scale-free clusters of vegetation in tropical rainforests

Tropical rainforests exhibit a rich repertoire of spatial patterns emerging from the intricate relationship between the microscopic interaction between species. In particular, the distribution of vegetation clusters can shed much light on the underlying process regulating the ecosystem. Analyzing the distribution of vegetation clusters at different resolution scales, we show the first robust evidence of scale-invariant clusters of vegetation, suggesting the coexistence of multiple intertwined scales in the collective dynamics of tropical rainforests. We use field data and computational simulations to confirm our hypothesis, proposing a predictor that could be particularly interesting to monitor the ecological resilience of the world's 'green lungs'.

cond-mat.stat-mech↗

arXiv2022

Laplacian paths in complex networks: information core emerges from entropic transitions

Complex networks usually exhibit a rich architecture organized over multiple intertwined scales. Information pathways are expected to pervade these scales reflecting structural insights that are not manifest from analyses of the network topology. Moreover, small-world effects correlate with the different network hierarchies complicating the identification of coexisting mesoscopic structures and functional cores. We present a communicability analysis of effective information pathways throughout complex networks based on information diffusion to shed further light on these issues. We employ a variety of brand-new theoretical techniques allowing for: (i) bring the theoretical framework to quantify the probability of information diffusion among nodes, (ii) identify critical scales and structures of complex networks regardless of their intrinsic properties, and (iii) demonstrate their dynamical relevance in synchronization phenomena. By combining these ideas, we evidence how the information flow on complex networks unravels different resolution scales. Using computational techniques, we focus on entropic transitions, uncovering a generic mesoscale object, the information core, and controlling information processing in complex networks. Altogether, this study sheds much light on allowing new theoretical techniques paving the way to introduce future renormalization group approaches based on diffusion distances.

physics.soc-ph↗

arXiv2022

Characterizing spatial point processes by percolation transitions

A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical ecology to analyze, e.g., the spatial percolation of a tree species in a tropical forest or a savanna. Here, we revisit the problem of aggregating random points in continuum systems (from $2$ to $6-$dimensional Euclidean spaces) to analyze the nature of the corresponding percolation transition in spatial point processes. This problem finds a natural description in terms of the canonical ensemble but not in the usual grand-canonical one, customarily employed to describe percolation transitions. This leads us to analyze the question of ensemble equivalence and study whether the resulting canonical continuum percolation transition shares its universal properties with standard percolation transitions, analyzing diverse homogeneous and heterogeneous spatial point processes. We, therefore, provide a powerful tool to characterize and classify a vast class of natural point patterns, revealing their fundamental properties based on percolation phase transitions.

cond-mat.stat-mech↗

arXiv2022

Marginal speed confinement resolves the conflict between correlation and control in natural flocks of birds

Speed fluctuations of individual birds in natural flocks are moderate, due to the aerodynamic and biomechanical constraints of flight. Yet the spatial correlations of such fluctuations are scale-free, namely they have a range as wide as the entire group, a property linked to the capacity of the system to collectively respond to external perturbations. Scale-free correlations and moderate fluctuations set conflicting constraints on the mechanism controlling the speed of each agent, as the factors boosting correlation amplify fluctuations, and vice versa. Here, using a statistical field theory approach, we suggest that a marginal speed confinement that ignores small deviations from the natural reference value while ferociously suppressing larger speed fluctuations, is able to reconcile scale-free correlations with biologically acceptable group's speed. We validate our theoretical predictions by comparing them with field experimental data on starling flocks with group sizes spanning an unprecedented interval of over two orders of magnitude.

cond-mat.stat-mech↗

arXiv2022

Laplacian Renormalization Group for heterogeneous networks

The renormalization group is the cornerstone of the modern theory of universality and phase transitions, a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its network counterpart is particularly challenging due to correlations between intertwined scales. To date, the explorations are based on hidden geometries hypotheses. Here, we propose a Laplacian RG diffusion-based picture in complex networks, defining both the Kadanoff supernodes' concept, the momentum space procedure, \emph{á la Wilson}, and applying this RG scheme to real networks in a natural and parsimonious way.

cond-mat.stat-mech↗

arXiv2021

The broad edge of synchronisation: Griffiths effects and collective phenomena in brain networks

Many of the amazing functional capabilities of the brain are collective properties stemming from the interactions of large sets of individual neurons. In particular, the most salient collective phenomena in brain activity are oscillations, which require the synchronous activation of many neurons. Here, we analyse parsimonious dynamical models of neural synchronisation running on top of synthetic networks that capture essential aspects of the actual brain anatomical connectivity such as a hierarchical-modular and core-periphery structure. These models reveal the emergence of complex collective states with intermediate and flexible levels of synchronisation, halfway in the synchronous-asynchronous spectrum. These states are best described as broad Griffiths-like phases, i.e. an extension of standard critical points that emerge in structurally heterogeneous systems. We analyse different routes (bifurcations) to synchronisation and stress the relevance of 'hybrid-type transitions' to generate rich dynamical patterns. Overall, our results illustrate the complex interplay between structure and dynamics, underlining key aspects leading to rich collective states needed to sustain brain functionality.

q-bio.NC↗

arXiv2021

Emergent spatial patterns of coexistence in species-rich plant communities

Statistical Physics has proved essential to analyze multi-agent environments. Motivated by the empirical observation of various non-equilibrium features in Barro Colorado and other ecological systems, we analyze a plant-species abundance model, presenting analytical evidence of scale-invariant plant clusters and non-trivial emergent modular correlations. Such first theoretical confirmation of a scale-invariant region, based on percolation processes, reproduces the key features in actual ecological ecosystems and can confer the most stable equilibrium for ecosystems with vast biodiversity.

cond-mat.stat-mech↗

arXiv2021

Hybrid-type synchronization transitions: where marginal coherence, scale-free avalanches, and bistability live together

The human cortex is never at rest but in a state of sparse and noisy neural activity that can be detected at broadly diverse resolution scales. It has been conjectured that such a state is best described as a critical dynamical process -- whose nature is still not fully understood -- where scale-free avalanches of activity emerge at the edge of a phase transition. In particular, some works suggest that this is most likely a synchronization transition, separating synchronous from asynchronous phases. Here, by investigating a simplified model of coupled excitable oscillators describing the cortex dynamics at a mesoscopic level, we investigate the possible nature of such a synchronization phase transition. Within our modeling approach, we conclude that -- in order to reproduce all key empirical observations, such as scale-free avalanches and bistability, on which fundamental functional advantages rely -- the transition to collective oscillatory behavior needs to be of an unconventional hybrid type, with mixed features of type-I and type-II excitability, opening the possibility for a particularly rich dynamical repertoire.

cond-mat.stat-mech↗

arXiv2021

CoMo: A novel co-moving 3D camera system

Motivated by the theoretical interest in reconstructing long 3D trajectories of individual birds in large flocks, we developed CoMo, a co-moving camera system of two synchronized high speed cameras coupled with rotational stages, which allow us to dynamically follow the motion of a target flock. With the rotation of the cameras we overcome the limitations of standard static systems that restrict the duration of the collected data to the short interval of time in which targets are in the cameras common field of view, but at the same time we change in time the external parameters of the system, which have then to be calibrated frame-by-frame. We address the calibration of the external parameters measuring the position of the cameras and their three angles of yaw, pitch and roll in the system "home" configuration (rotational stage at an angle equal to 0deg and combining this static information with the time dependent rotation due to the stages. We evaluate the robustness and accuracy of the system by comparing reconstructed and measured 3D distances in what we call 3D tests, which show a relative error of the order of 1%. The novelty of the work presented in this paper is not only on the system itself, but also on the approach we use in the tests, which we show to be a very powerful tool in detecting and fixing calibration inaccuracies and that, for this reason, may be relevant for a broad audience.

cs.CV↗

arXiv2020

Self-organized bistability and its possible relevance for brain dynamics

Self-organized bistability (SOB) is the counterpart of 'self-organized criticality' (SOC), for systems tuning themselves to the edge of bistability of a discontinuous phase transition, rather than to the critical point of a continuous one. The equations defining the mathematical theory of SOB turn out to bear strong resemblance to a (Landau-Ginzburg) theory recently proposed to analyze the dynamics of the cerebral cortex. This theory describes the neuronal activity of coupled mesoscopic patches of cortex, homeostatically regulated by short-term synaptic plasticity. The theory for cortex dynamics entails, however, some significant differences with respect to SOB, including the lack of a (bulk) conservation law, the absence of a perfect separation of timescales and, the fact that in the former, but not in the second, there is a parameter that controls the overall system state (in blatant contrast with the very idea of self-organization). Here, we scrutinize --by employing a combination of analytical and computational tools-- the analogies and differences between both theories and explore whether in some limit SOB can play an important role to explain the emergence of scale-invariant neuronal avalanches observed empirically in the cortex. We conclude that, actually, in the limit of infinitely slow synaptic-dynamics, the two theories become identical, but the timescales required for the self-organization mechanism to be effective do not seem to be biologically plausible. We discuss the key differences between self-organization mechanisms with/without conservation and with/without infinitely separated timescales. In particular, we introduce the concept of 'self-organized collective oscillations' and scrutinize the implications of our findings in neuroscience, shedding new light into the problems of scale invariance and oscillations in cortical dynamics.

cond-mat.stat-mech↗

arXiv2020

Evolution in the Debian GNU/Linux software network: analogies and differences with gene regulatory networks

Biological networks exhibit intricate architectures deemed to be crucial for their functionality. In particular, gene regulatory networks, which play a key role in information processing in the cell, display non-trivial architectural features such as scale-free degree distributions, high modularity, and low average distance between connected genes. Such networks result from complex evolutionary and adaptive processes difficult to track down empirically. On the other hand, there exists detailed information on the developmental (or evolutionary) stages of open-software networks that result from self-organized growth across versions. Here, we study the evolution of the Debian GNU/Linux software network, focusing on the changes of key structural and statistical features over time. Our results show that evolution has led to a network structure in which the out-degree distribution is scale-free and the in-degree distribution is a stretched exponential. In addition, while modularity, directionality of information flow, and average distance between elements grew, vulnerability decreased over time. These features resemble closely those currently shown by gene regulatory networks, suggesting the existence of common adaptive pathways for the architectural design of information-processing networks. Differences in other hierarchical aspects point to system-specific solutions to similar evolutionary challenges.

physics.soc-ph↗

arXiv2019

Time-series thresholding and the definition of avalanche size

Avalanches whose sizes and durations are distributed as power laws appear in many contexts. Here, we show that there is a hidden peril in thresholding continuous times series --either from empirical or synthetic data-- for the detection of avalanches. In particular, we consider two possible alternative definitions of avalanche size used e.g. in the empirical determination of avalanche exponents in the analysis of neural-activity data. By performing analytical and computational studies of an Ornstein-Uhlenbeck process (taken as a guiding example) we show that if (i) relatively large threshold values are employed to determine the beginning and ending of avalanches and if (ii) --as sometimes done in the literature-- avalanche sizes are defined as the total area (above zero) of the avalanche, then true asymptotic scaling behavior is not seen, instead the observations are dominated by transient effects. These can induce misinterpretations of the resulting scaling regimes as well as to a wrong assignation of universality classes.

cond-mat.dis-nn↗

arXiv2019

Jensen's force and the statistical mechanics of cortical asynchronous states

The cortex exhibits self-sustained highly-irregular activity even under resting conditions, whose origin and function need to be fully understood. It is believed that this can be described as an "asynchronous state" stemming from the balance between excitation and inhibition, with important consequences for information-processing, though a competing hypothesis claims it stems from critical dynamics. By analyzing a parsimonious neural-network model with excitatory and inhibitory interactions, we elucidate a noise-induced mechanism called "Jensen's force" responsible for the emergence of a novel phase of arbitrarily-low but self-sustained activity, which reproduces all the experimental features of asynchronous states. The simplicity of our framework allows for a deep understanding of asynchronous states from a broad statistical-mechanics perspective and of the phase transitions to other standard phases it exhibits, opening the door to reconcile, asynchronous-state and critical-state hypotheses. We argue that Jensen's forces are measurable experimentally and might be relevant in contexts beyond neuroscience.

cond-mat.dis-nn↗

arXiv2018

Non-normality, reactivity, and intrinsic stochasticity in neural dynamics: a non-equilibrium potential approach

Intrinsic stochasticity can induce highly non-trivial effects on dynamical systems, including stochastic and coherence resonance, noise induced bistability, noise-induced oscillations, to name but a few. In this paper we revisit a mechanism first investigated in the context of neuroscience by which relatively small demographic (intrinsic) fluctuations can lead to the emergence of avalanching behavior in systems that are deterministically characterized by a single stable fixed point (up state). The anomalously large response of such systems to stochasticity stems (or is strongly associated with) the existence of a "non-normal" stability matrix at the deterministic fixed point, which may induce the system to be "reactive". Here, we further investigate this mechanism by exploring the interplay between non-normality and intrinsic (demographic) stochasticity, by employing a number of analytical and computational approaches. We establish, in particular, that the resulting dynamics in this type of systems cannot be simply derived from a scalar potential but, additionally, one needs to consider a curl flux which describes the essential non-equilibrium nature of this type of noisy non-normal systems. Moreover, we shed further light on the origin of the phenomenon, introduce the novel concept of "non-linear reactivity", and rationalize of the observed the value of the emerging avalanche exponents.

cond-mat.dis-nn↗

arXiv2018

Landau-Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization

Understanding the origin, nature, and functional significance of complex patterns of neural activity, as recorded by diverse electrophysiological and neuroimaging techniques, is a central challenge in neuroscience. Such patterns include collective oscillations emerging out of neural synchronization as well as highly heterogeneous outbursts of activity interspersed by periods of quiescence, called "neuronal avalanches." Much debate has been generated about the possible scale invariance or criticality of such avalanches and its relevance for brain function. Aimed at shedding light onto this, here we analyze the large-scale collective properties of the cortex by using a mesoscopic approach following the principle of parsimony of Landau-Ginzburg. Our model is similar to that of Wilson-Cowan for neural dynamics but crucially, includes stochasticity and space; synaptic plasticity and inhibition are considered as possible regulatory mechanisms. Detailed analyses uncover a phase diagram including down-state, synchronous, asynchronous, and up-state phases and reveal that empirical findings for neuronal avalanches are consistently reproduced by tuning our model to the edge of synchronization. This reveals that the putative criticality of cortical dynamics does not correspond to a quiescent-to-active phase transition as usually assumed in theoretical approaches but to a synchronization phase transition, at which incipient oscillations and scale-free avalanches coexist. Furthermore, our model also accounts for up and down states as they occur (e.g., during deep sleep). This approach constitutes a framework to rationalize the possible collective phases and phase transitions of cortical networks in simple terms, thus helping to shed light on basic aspects of brain functioning from a very broad perspective.

q-bio.NC↗

arXiv2017

A simple unified view of branching process statistics: random walks in balanced logarithmic potentials

We revisit the problem of deriving the mean-field values of avalanche critical exponents in systems with absorbing states. These are well-known to coincide with those of an un-biased branching process. Here, we show that for at least 4 different universality classes (directed percolation, dynamical percolation, the voter model or compact directed percolation class, and the Manna class of stochastic sandpiles) this common result can be obtained by mapping the corresponding Langevin equations describing each of these classes into a random walker confined close to the origin by a logarithmic potential. Many of the results derived here appear in the literature as independently derived for individual universality classes or for the branching process. However, the emergence of non-universal continuously-varying exponent values --which, as shown here, stems fro the presence of small external driving, that might induce avalanche merging-- has not been noticed (or emphasized) in the past. We believe that a simple an unified perspective as the one presented here can (i) help to clarify the overall picture, (ii) underline the super-universality of the behavior as well as the dependence on external driving, and (iii) help avoiding the common existing confusion between un-biased branching processes (equivalent to a random walker in a balanced logarithmic potential) and standard (un-confined) random walkers.

cond-mat.dis-nn↗

arXiv2016

Intrinsic noise and deviations from criticality in Boolean gene-regulatory networks

Gene regulatory networks can be successfully modeled as Boolean networks. A much discussed hypothesis says that such model networks reproduce empirical findings the best if they are tuned to operate at criticality, i.e. at the borderline between their ordered and disordered phases. Critical networks have been argued to lead to a number of functional advantages such as maximal dynamical range, maximal sensitivity to environmental changes, as well as to an excellent trade off between stability and flexibility. Here, we study the effect of noise within the context of Boolean networks trained to learn complex tasks under supervision. We verify that quasi-critical networks are the ones learning in the fastest possible way --even for asynchronous updating rules-- and that the larger the task complexity the smaller the distance to criticality. On the other hand, when additional sources of intrinsic noise in the network states and/or in its wiring pattern are introduced, the optimally performing networks become clearly subcritical. These results suggest that in order to compensate for inherent stochasticity, regulatory and other type of biological networks might become subcritical rather than being critical, all the most if the task to be performed has limited complexity.

q-bio.MN↗