arXiv subjects

Paolo Grigolini

Publications and source records attributed to Paolo Grigolini.

At least 37 records · Page 2Linked to original sources

arXiv2016

Ergodicity Breaking and Localization

We study the joint action of the non-Poisson renewal events (NPR) yielding Continuous Time Random Walk (CTRW) with index alpha < 1 and two different generators of Hurst coefficient H not equal to 0.5, one generating fractional Brownian motion (FBM) and another scaled Brownian motion (SBM). We discuss the ergodicity breaking emerging from these joint actions and we find that in both cases the adoption of time averages leads to localization. In the case of the joint action of NPR and SBM, localization occurs when SBM would produce sub-diffusion. The joint action of NPR and FBM, on the contrary, may lead to localization when FBM would be a source of super-diffusion. We argue that the second effect might require a refinement of the theoretical perspective about determinism and randomness.

cond-mat.stat-mech↗

arXiv2016

Non-Ergodic Complexity Management

Linear response theory, the backbone of non-equilibrium statistical physics, has recently been extended to explain how and why non-ergodic renewal processes are insensitive to simple perturbations, such as in habituation. It was established that a permanent correlation resulted between an external stimulus and the response of a complex system generating non-ergodic renewal processes, when the stimulus is a similar non-ergodic process. This is the principle of complexity management, whose proof relies on ensemble distribution functions. Herein we extend the proof to the non-ergodic case using time averages and a single time series, hence making it usable in real life situations where ensemble averages cannot be performed because of the very nature of the complex systems being studied.

nlin.AO↗

arXiv2015

Imitation-Induced Criticality: Network Reciprocity and Psycho-logical Reward

The nodes of a regular two-dimensional lattice play a game based on the joint action of two distinct levels. At the first step of the game, using a random prescription half players are assigned the cooperation and half the defection state. At the bottom level the strategy choice is done on the mere basis of imitation according to the homo imitans principle, generating a form of collective intelligence that makes the system sensitive to the criteria determining the strategy choice adopted at the top level. The units of the top level, in fact, play the prisoner's dilemma game and are allowed to update their strategy either by selecting the strategy of the most successful nearest neighbor, success model, or merely on the basis of the criterion of the best financial benefit, selfishness model. The intelligence emerging from imitation-induced criticality leads in the former case to the extinction of defection and in the latter case to the extinction of cooperation. The former case is interpreted as a form of network reciprocity enhanced by the imitation-induced criticality and contributing to the evolution towards cooperation. We perturb the selfishness model with a form of morality pressure, exerted by a psychological reward Lambda for cooperation, to establish the sensitivity of collective intelligence to morality. We find that when Lambda gets a crucial value Lambda-c, exceeding the temptation to cheat, the system makes a transition from the supercritical defection state to the critical regime, with the warning that an excess of morality and religion pressure may annihilate the criticality-induced resilience of the system.

physics.soc-ph↗

arXiv2015

The Value of Conflict in Stable Social Networks

A cooperative network model of sociological interest is examined to determine the sensitivity of the global dynamics to having a fraction of the members behaving uncooperatively, that is, being in conflict with the majority. We study a condition where in the absence of these uncooperative individuals, the contrarians, the control parameter exceeds a critical value and the network is frozen in a state of consensus. The network dynamics change with variations in the percentage of contrarians, resulting in a balance between the value of the control parameter and the percentage of those in conflict with the majority. We show that the transmission of information from a network $B$ to a network $A$, with a small fraction of lookout members in $A$ who adopt the behavior of $B$, becomes maximal when both networks are assigned the same critical percentage of contrarians.

physics.soc-ph↗

arXiv2014

Fractional calculus ties the microscopic and macroscopic scales of complex network dynamics

A two-state master equation based decision making model has been shown to generate phase transitions, to be topologically complex and to manifest temporal complexity through an inverse power-law probability distribution function in the switching times between the two critical states of consensus. These properties are entailed by the fundamental assumption that the network elements in the decision making model imperfectly imitate one another. The process of subordination establishes that a single network element can be described by a fractional master equation whose analytic solution yields the observed inverse power-law probability distribution obtained by numerical integration of the two-state master equation to a high degree of accuracy.

nlin.AO↗

arXiv2013

Collective behavior and evolutionary games - An introduction

This is an introduction to the special issue titled "Collective behavior and evolutionary games" that is in the making at Chaos, Solitons & Fractals. The term collective behavior covers many different phenomena in nature and society. From bird flocks and fish swarms to social movements and herding effects, it is the lack of a central planner that makes the spontaneous emergence of sometimes beautifully ordered and seemingly meticulously designed behavior all the more sensational and intriguing. The goal of the special issue is to attract submissions that identify unifying principles that describe the essential aspects of collective behavior, and which thus allow for a better interpretation and foster the understanding of the complexity arising in such systems. As the title of the special issue suggests, the later may come from the realm of evolutionary games, but this is certainly not a necessity, neither for this special issue, and certainly not in general. Interdisciplinary work on all aspects of collective behavior, regardless of background and motivation, and including synchronization and human cognition, is very welcome.

physics.soc-ph↗

arXiv2012

Cooperation in Neural Systems: Bridging Complexity and Periodicity

Inverse power law distributions are generally interpreted as a manifestation of complexity, and waiting time distributions with power index μ< 2 reflect the occurrence of ergodicity breaking renewal events. In this Letter we show how to combine these properties with the apparently foreign clocklike nature of biological processes. We use a two-dimensional regular network of leaky integrate-and-fire neurons, each of which is linked to its four nearest neighbors, to show that both complexity and periodicity are generated by locality breakdown: links of increasing strength have the effect of turning local into long-range interaction, thereby generating first time complexity and then time periodicity. Increasing the density of neuron firings reduces the influence of periodicity thus creating a cooperation-induced distinctly non-Poisson renewal condition.

nlin.AO↗

arXiv2012

Role of Committed Minorities in Times of Crisis

We use a Cooperative Decision Making (CDM) model to study the effect of committed minorities on group behavior in time of crisis. The CDM model has been shown to generate consensus through a phase-transition process that at criticality establishes long-range correlations among the individuals within a model society. In a condition of high consensus, the correlation function vanishes, thereby making the network recover the ordinary locality condition. However, this state is not permanent and times of crisis occur when there is an ambiguity concerning a given social issue. The correlation function within the cooperative system becomes similarly extended as it is observed at criticality. This combination of independence (free will) and long-range correlation makes it possible for very small but committed minorities to produce substantial changes in social consensus.

physics.soc-ph↗

arXiv2011

Transmission of Information between Complex Networks: 1/f-Resonance

We study the transport of information between two complex networks with similar properties. Both networks generate non-Poisson renewal fluctuations with a power-law spectrum 1/f^(3-μ), the case μ= 2 corresponding to ideal 1/f-noise. We denote by μ_S and μ_P the power-law indexes of the network "system" of interest S and the perturbing network P respectively. By adopting a generalized fluctuation-dissipation theorem (FDT) we show that the ideal condition of 1/f-noise for both networks corresponds to maximal information transport. We prove that to make the network S respond when μ_S < 2 we have to set the condition μ_P < 2. In the latter case, if μ_P < μ_S, the system S inherits the relaxation properties of the perturbing network. In the case where μ_P > 2, no response and no information transmission occurs in the long-time limit. We consider two possible generalizations of the fluctuation-dissipation theorem and show that both lead to maximal information transport in the condition of 1/f-noise.

cond-mat.stat-mech↗

arXiv2010

Beyond the Death of Linear Response: 1/f optimal information transport

Non-ergodic renewal processes have recently been shown by several authors to be insensitive to periodic perturbations, thereby apparently sanctioning the death of linear response, a building block of nonequilibrium statistical physics. We show that it is possible to go beyond the ``death of linear response" and establish a permanent correlation between an external stimulus and the response of a complex network generating non-ergodic renewal processes, by taking as stimulus a similar non-ergodic process. The ideal condition of 1/f-noise corresponds to a singularity that is expected to be relevant in several experimental conditions.

cond-mat.stat-mech↗

arXiv2007

A fluctuating environment as a source of periodic modulation

We study the intermittent fluorescence of a single molecule, jumping from the "light on" to the "light off" state, as a Poisson process modulated by a fluctuating environment. We show that the quasi-periodic and quasi-deterministic environmental fluctuations make the distribution of the times of sojourn in the "light off" state depart from the exponential form, and that their succession in time mirrors environmental dynamics. As an illustration, we discuss some recent experimental results, where the environmental fluctuations depend on enzymatic activity.

cond-mat.soft↗

arXiv2007

Brain, Music and non-Poisson Renewal Processes

In this paper we show that both music composition and brain function, as revealed by the Electroencephalogram (EEG) analysis, are renewal non-Poisson processes living in the non-ergodic dominion. To reach this important conclusion we process the data with the minimum spanning tree method, so as to detect significant events, thereby building a sequence of times, which is the time series to analyze. Then we show that in both cases, EEG and music composition, these significant events are the signature of a non-Poisson renewal process. This conclusion is reached using a techniques of statistical analysis recently developed by our group, the Aging Experiment (AE). First, we find that in both cases the distances between two consecutive events are described by non-exponential histograms, thereby proving the non-Poisson nature of these processes. The corresponding survival probabilities $Ψ(t)$ are well fitted by stretched exponentials ($Ψ(t) \propto exp(-(γt)^α$), with $0.5 <α<1$.) The second step rests on the adoption of the AE, which shows that these are renewal processes. We show that the renewal stretched exponential is the emerging tip of an iceberg, whose underwater part has slow tails with an inverse power law structure with power index $μ= 1 + α$. We find that both EEG and music composition yield $μ< 2$. On the basis of the recently discovered complexity matching effect, according to which a complex system $S$ with $μ_S < 2$ responds only to a complex driving signal $P$ with $μ_P = μ_S$, we conclude that the results of our analysis may explain the influence of music on human brain.

q-bio.NC↗

arXiv2006

Response of Complex Systems to Complex Perturbations: the Complexity Matching Effect

The dynamical emergence (and subsequent intermittent breakdown) of collective behavior in complex systems is described as a non-Poisson renewal process, characterized by a waiting-time distribution density $ψ(τ)$ for the time intervals between successively recorded breakdowns. In the intermittent case $ψ(t)\sim t^{-μ}$, with complexity index $μ$. We show that two systems can exchange information through complexity matching and present theoretical and numerical calculations describing a system with complexity index $μ_{S}$ perturbed by a signal with complexity index $μ_{P}$. The analysis focuses on the non-ergodic (non-stationary) case $μ\leq 2$ showing that for $μ_{S}\geq μ_{P}$, the system $S$ statistically inherits the correlation function of the perturbation $P$. The condition $μ_{P}=μ_{S}$ is a resonant maximum for correlation information exchange.

cond-mat.stat-mech↗

arXiv2006

Renewal Aging as Emerging Property of Phase Synchronization

In this letter we examine a model recently proposed to produce phase synchronization [K. Wood et al, Phys. Rev. Lett. 96, 145701 (2006)] and we show that the onset to synchronization corresponds to the emergence of an intermittent process that is non-Poisson and renewal at the same time. We argue that this makes the model appropriate for the physics of blinking quantum dots, and the dynamics of human brain as well.

cond-mat.stat-mech↗

arXiv2006

Aging in Financial Market

We analyze the data of the Italian and U.S. futures on the stock markets and we test the validity of the Continuous Time Random Walk assumption for the survival probability of the returns time series via a renewal aging experiment. We also study the survival probability of returns sign and apply a coarse graining procedure to reveal the renewal aspects of the process underlying its dynamics.

physics.soc-ph↗

arXiv2006

Renewal aging and linear response

We study the linear response to an external perturbation of a renewal process, in an aging condition that, with no perturbation, would yield super-diffusion. We use the phenomenological approach to the linear response adopted in earlier work of other groups, and we find that aging may have the effect of annihilating any sign of coherent response to harmonic perturbation. We also derive the linear response using dynamic arguments and we find a coherent response, although with an intensity dying out very slowly. In the case of a step-like perturbation the dynamic arguments yield in the long-time limit a steady signal whose intensity may be significantly smaller than the phenomenological approach prediction.

cond-mat.stat-mech↗

arXiv2005

Fluorescence intermittency in blinking quantum dots: renewal or slow modulation?

We study time series produced by the blinking quantum dots, by means of an aging experiment, and we examine the results of this experiment in the light of two distinct approaches to complexity, renewal and slow modulation. We find that the renewal approach fits the result of the aging experiment, while the slow modulation perspective does not. We make also an attempt at establishing the existence of an intermediate condition.

cond-mat.stat-mech↗

arXiv2005

Linear response to perturbation of non-exponential renewal processes

We study the linear response of a two-state stochastic process, obeying renewal condition, by means of a stochastic rate equation equivalent to a master equation with infinite memory. We show that the condition of perennial aging makes the response to coherent perturbation vanish in the long-time limit.

cond-mat.stat-mech↗