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We study the emission of photons from germinating seeds using an experimental technique designed to detect photons of extremely small intensity when the signal/noise ratio is low. We analyze the dark count signal in the absence of germinating seeds as well as the photon emission during the germination process. The technique of analysis adopted here was originally designed to measure the temporal complexity of astrophysical, sociological and physiological processes. The foundation of this method, called Diffusion Entropy Analysis (DEA), rests on Kolmogorov complexity. The updated version of DEA used in this paper is designed to determine if the signal complexity is generated by either non-ergodic crucial events with a non-stationary correlation function or by the infinite memory of a stationary but non-integrable correlation function or by a mixture of both processes. We find that dark count yields the ordinary scaling, thereby showing that no complexity of either kinds may occur in the absence of any seeds in the chamber. In the presence of seeds in the chamber anomalous scaling emerges, reminiscent of that found in neuro-physiological processes. However, this is a mixture of both processes and with the progress of germination the non-ergodic component tends to vanish and complexity is dominated by the stationary infinite memory. We argue that this may be a sign of quantum coherence that according to some authors is the important ingredient of cognition.

We study seismic fluctuations in California and Hindu Kush using Diffusion Entropy Analysis (DEA), a technique designed to detect the action of crucial events in time series generated by complex dynamical systems. The time distance between two consecutive crucial events is described by an inverse power law distribution density with a power index $\mu$ close to the value $\mu = 2$, corresponding to an ideal $1/f$ noise. DEA was used in the recent past to study neurophysiological processes that in the healthy condition are found to generate $1/f$ noise and $\mu$ close to $2$. In this paper we find that the seismic fluctuations in both California and Hindu-Kush of extended areas implying the action of many faults, $\mu \approx 2.1$, while in regions involving the action of only one fault, or of a very small number of faults, $\mu \approx 2.4$. This observation led us the conjectures that the seismic criticality is due to the interaction of many faults. To support this conjecture we adopted a dynamical model for fault dynamics proposed by Brown and Tosatti and we have extended it to describe the interaction between many faults. The DEA applied to surrogate sequences generated by this dynamical model, yields $\mu = 2.1$ for a single fault and $\mu = 2,4$ for many interacting faults, in a good agreement with the observation of real seismic fluctuations. This result supports our conjecture and suggests interesting applications to neurophysiological and sociological processes., Comment: 6 pages, 7 figures

Complexity matching characterizes the role of information in interactions between systems and can be traced back to the 1957 Introduction to Cybernetics by Ross Ashby. We argue that complexity can be expressed in terms of crucial events, which are generated by the processes of spontaneous self-organization. Complex processes, ranging from biological to sociological, must satisfy the homeodynamic condition and host crucial events that have recently been shown to drive the information transport between complex systems. We adopt a phenomenological approach, based on the subordination to periodicity that makes it possible to combine homeodynamics and self-organization induced crucial events. The complexity of crucial events is defined by the waiting-time probability density function (PDF) of the intervals between consecutive crucial events, which have an inverse power law (IPL) PDF $\psi (\tau )\propto 1/(\tau )^{\mu }$ with $1, Comment: 21 pages, 8 figures

Earlier research work on the dynamics of the brain, disclosing the existence of crucial events, is revisited for the purpose of making the action of crucial events, responsible for the 1/f −noise in the brain, compatible with the wave-like nature of the brain processes. We review the relevant neurophysiological literature to make clear that crucial events are generated by criticality. We also show that although criticality generates a strong deviation from the regular wave-like behavior, under the form of Rapid Transition Processes, the brain dynamics also host crucial events in regions of nearly coherent oscillations, thereby making many crucial events virtually invisible. Furthermore, the anomalous scaling generated by the crucial events can be established with high accuracy by means of direct analysis of raw data, suggested by a theoretical perspective not requiring the crucial events to yield a visible physical effect. The latter follows from the fact that periodicity, waves and crucial events are the consequences of a spontaneous process of self-organization. We obtain three main results: (a) the important role of crucial events is confirmed and established with greater accuracy than previously; (b) we demonstrate the theoretical tools necessary to understand the joint action of crucial events and periodicity; (c) we argue that the results of this paper can be used to shed light on the nature of this important process of self-organization, thereby contributing to the understanding of cognition.

The key purpose of this article is to establish a connection between two emerging fields of research in theoretical biology. The former focuses on the concept of criticality borrowed from physics that is expected to be extensible to biology through a robust theoretical approach that although not yet available shall eventually shed light into the origin of cognition. The latter, largely based on the tracking of single molecules diffusing in biological cells, is bringing to the general attention the need to go beyond the ergodic assumption currently done in the traditional statistical physics. We show that replacing critical slowing down with temporal complexity explains why biological systems at criticality are resilient and why long-range correlations are compatible with the free-will condition necessary for the emergence of cognition. Temporal complexity generates ergodicity breakdown and requires new forms of response of complex systems to external stimuli. We concisely illustrate these new forms of information transport and we also address the challenging issue of combining temporal complexity with coherence and renewal with infinite memory.

The mean field for a complex network consisting of a large but finite number of random two-state elements, \(M\), has been shown to satisfy a nonlinear Langevin equation. The noise intensity is inversely proportional to \(\sqrt{M} \). In the limiting case \(M = \infty \), the solution to the Langevin equation exhibits a transition from exponential to inverse power law relaxation as criticality is approached from above or below the critical point. When \(M < \infty \), the inverse power law is truncated by an exponential decay with rate \(\varGamma \), the evaluation of which is the main purpose of this article. An analytic/numeric approach is used to obtain the lowest-order eigenvalues in the spectral decomposition of the solution to the corresponding Fokker–Planck equation and its equivalent Schrodinger equation representation.

A large number of optimization algorithms have been developed by researchers to solve a variety of complex problems in operations management area. We present a novel optimization algorithm belonging to the class of swarm intelligence optimization methods. The algorithm mimics the decision making process of human groups and exploits the dynamics of such a process as a tool for complex combinatorial problems. In order to achieve this aim, we employ a properly modified version of a recently published decision making model [64,65], to model how humans in a group modify their opinions driven by self-interest and consensus seeking. The dynamics of such a system is governed by three parameters: (i) the reduced temperature βJ, (ii) the self-confidence of each agent β′, (iii) the cognitive level 0 ≤ p ≤ 1 of each agent. Depending on the value of the aforementioned parameters a critical phase transition may occur, which triggers the emergence of a superior collective intelligence of the population. Our algorithm exploits such peculiar state of the system to propose a novel tool for discrete combinatorial optimization problems. The benchmark suite consists of the NK - Kauffman complex landscape, with various sizes and complexities, which is chosen as an exemplar case of classical NP-complete optimization problem. A comparison with genetic algorithms (GA), simulated annealing (SA) as well as with a multiagent version of SA is presented in terms of efficacy in finding optimal solutions. In all cases our method outperforms the others, particularly in presence of limited knowledge of the agent.

We study the connection between multi-fractality and crucial events. Multi-fractality is frequently used as a measure of physiological variability. Crucial events are known to play a fundamental role in the transport of information between complex networks. To establish a connection we focus on the special case of heartbeat time series and on the search for a diagnostic prescription to distinguish healthy from pathologic subjects. Over the last twenty years two apparently different diagnostic techniques have been established: the first is based on the observation that the multi-fractal spectrum of healthy patients is broader than the multi-fractal spectrum of pathologic subjects; the second is based on the observation that heartbeat dynamics are a superposition of crucial and Poisson events, with pathologic patients hosting Poisson events with larger probability than the healthy patients. In this paper, we prove that increasing the percentage of Poisson events hosted by heartbeats has the effect of making their multi-fractal spectrum narrower, thereby establishing that the two different diagnostic techniques are compatible with one another and, at the same time, establishing a dynamic interpretation of multi-fractal processes that has been previously overlooked., Comment: 9 pages and 11 figures. Submitted to PRE

We study two different forms of fluctuation-dissipation processes generating anomalous relaxations to equilibrium of an initial out of equilibrium condition, the former being based on a stationary although very slow correlation function and the latter characterized by the occurrence of crucial events, namely, non-Poisson renewal events, incompatible with the stationary condition. Both forms of regression to equilibrium have the same non-exponential Mittag-Leffler structure. We analyze the single trajectories of the two processes by recording the time distances between two consecutive origin re-crossings and establishing the corresponding waiting time probability density function (PDF), $\psi(t)$. In the former case, with no crucial events, $\psi(t)$ is exponential and in the latter case, with crucial events, $\psi(t)$ is an inverse power law PDF with a diverging first moment. We discuss the consequences that this result is expected to have for the correct interpretation of some anomalous relaxation processes., Comment: 13 pages, 7 figures

A spinlike model mimicking human behavior in groups is employed to investigate the dynamics of the decision-making process. Within the model, the temporal evolution of the state of systems is governed by a time-continuous Markov chain. The transition rates of the resulting master equation are defined in terms of the change of interaction energy between the neighboring agents (change of the level of conflict) and the change of a locally defined agent fitness. Three control parameters can be identified: (i) the social interaction strength βJ measured in units of social temperature, (ii) the level of confidence β^{'} that each individual has on his own expertise, and (iii) the level of knowledge p that identifies the expertise of each member. Based on these three parameters, the phase diagrams of the system show that a critical transition front exists where a sharp and concurrent change in fitness and consensus takes place. We show that at the critical front, the information leakage from the fitness landscape to the agents is maximized. This event triggers the emergence of the collective intelligence of the group, and in the end it leads to a dramatic improvement in the decision-making performance of the group. The effect of size M of the system is also investigated, showing that, depending on the value of the control parameters, increasing M may be either beneficial or detrimental.

We introduce a form of Self-Organized Criticality (SOC) inspired by the new generation of evolutionary game theory, which ranges from physiology to sociology. The single individuals are the nodes of a composite network, equivalent to two interacting subnetworks, one leading to strategy choices made by the individuals under the influence of the choices of their nearest neighbors and the other measuring the Prisoner's Dilemma Game payoffs of these choices. The interaction between the two networks is established by making the imitation strength K increase or decrease according to whether the last two payoffs increase or decrease upon increasing or decreasing K. Although each of these imitation strengths is selected selfishly, and independently of the others as well, the social system spontaneously evolves towards the state of cooperation. Criticality is signaled by temporal complexity, namely the occurrence of non-Poisson renewal events, the time intervals between two consecutive crucial events being given by an inverse power law index miu = 1.3 rather than by avalanches with an inverse power law distribution as in the original form of SOC. This new phenomenon is herein labeled self-organized temporal criticality (SOTC). We compare this bottom-up self-organization process to the adoption of a global choice rule based on assigning to all the units the same value K, with the time evolution of common K being determined by consciousness of the social benefit, a top-down process implying the action of a leader. In this case self-organization is impeded by large intensity fluctuations and the global social benefit turns out to be much weaker. We conclude that the SOC model of this paper fits the requests of a manifesto recently proposed by a number of European social scientists.

The model of the current paper is an extension of a previous publication, wherein we used the leaky integrate-and-fire model on a regular lattice with periodic boundary conditions, and introduced the temporal complexity as a genuine signature of criticality. In that work, the power-law distribution of neural avalanches was manifestation of supercriticality rather than criticality. Here, however, we show that continuous solution of the model and replacing the stochastic noise with a Gaussian zero-mean noise leads to the coincidence of power-law display of temporal complexity and spatiotemporal patterns of neural avalanches at the critical point. We conclude that the source of inconsistency may in fact be a numerical artifact originated by the discrete description of the model, which may imply slow numerical convergence of avalanche distribution compared to temporal complexity., Comment: 7 pages, 5 figures

This article examines how self-organizing criticality can assist in answering complex questions in health and health care systems.

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., 6 two-column pages, 1 figure; accepted for publication in Chaos, Solitons & Fractals [the special issue is available at http://www.sciencedirect.com/science/journal/09600779/56]

The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation of a fractional trajectory, that being an average over an ensemble of stochastic trajectories. Heretofore what has been interpreted as intrinsic friction, a form of non-Markovian dissipation that automatically arises from adopting the fractional calculus, is shown to be a manifestation of decorrelations between trajectories. We apply the general theory developed herein to the Lotka–Volterra ecological model, providing new insight into the final equilibrium state. The relaxation time to achieve this state is also considered.

Experimental work, both in vitro and in vivo, reveals the occurrence of neural avalanches with an inverse power law distribution in size and time duration. These properties are interpreted as an evident manifestation of criticality, thereby suggesting that the brain is an operating near criticality complex system: an attractive theoretical perspective that according to Gerhard Werner may help to shed light on the origin of consciousness. However, a recent experimental observation shows no clear evidence for power-law scaling in awake and sleeping brain of mammals, casting doubts on the assumption that the brain works at criticality. This article rests on a model proposed by our group in earlier publications to generate neural avalanches with the time duration and size distribution matching the experimental results on neural networks. We now refine the analysis of the time distance between consecutive firing bursts and observe the deviation of the corresponding distribution from the Poisson statistics, as the system moves from the non-cooperative to the cooperative regime. In other words, we make the assumption that the genuine signature of criticality may emerge from temporal complexity rather than from the size and time duration of avalanches. We argue that the Mittag–Leffler (ML) exponential function is a satisfactory indicator of temporal complexity, namely of the occurrence of non-Poisson and renewal events. The assumption that the onset of criticality corresponds to the birth of renewal non-Poisson events establishes a neat distinction between the ML function and the power law avalanches generating regime. We find that temporal complexity uncontaminated by periodicity occurs in a narrow range of values of the control parameter, in correspondence of which the information transfer from one network to another becomes maximal. We argue that if this enhancement of information transport is interpreted as a signature of criticality, then the power law avalanches are a manifestation of supercriticality rather than criticality. This leads us to conclude that the recent experiment showing no evidence of power-law avalanches in the brain of mammals would not conflict with the hypothesis that the brain works at criticality.

The dynamics of a two-state decision-making model (DMM) with a tunable control parameter K is described. On all-to-all (ATA) networks, the system undergoes a phase transition at a critical value of K c = 1 . Scale-free networks were also found to undergo phase transitions, but the value of K c increases as the scale-free exponent increases. Time to consensus is defined as a first passage time to a specified threshold of the global mean field, which represents a level of majority for the network. At criticality, the time to consensus for sparse networks with broad degree distributions (e.g., scale-free networks) approaches that of the ATA networks, although somewhat more cooperation (higher K c ) is required.

The evolution of cardiac disease after an acute ischemic event depends on a complex and dynamic network of mechanisms alternating from ischemic damage due to acute coronary occlusion to reperfusion injury due to the adverse effects of coronary revascularization till post-ischemic remodeling. Cardioprotection is a new purpose of the therapeutic interventions in cardiology with the goal to reduce infarct size and thus prevent the progression toward heart failure after an acute ischemic event. In a complex biological system such as the human one, an effective cardioprotective strategy should diachronically target the network of cross-talking pathways underlying the disease progression. Thyroid system is strictly interconnected with heart homeostasis, and recent studies highlighted its role in cardioprotection, in particular through the preservation of mitochondrial function and morphology, the antifibrotic and proangiogenetic effect and also to the potential induction of cell regeneration and growth. The objective of this review was to highlight the cardioprotective role of triiodothyronine in the complexity of post-ischemic disease evolution.

We discuss a route to intermittency based on the concept of reflexivity, namely on the interaction between observer and stochastic reality. A simple model mirroring the essential aspects of this interaction is shown to generate perennial out of equilibrium condition, intermittency and 1 / f -noise. In the absence of noise the model yields a symmetry-induced equilibrium manifold with two stable states. Noise makes this equilibrium manifold unstable, with an escape rate becoming lower and lower upon time increase, thereby generating an inverse power law distribution of waiting times. The distribution of the times of permanence in the basin of attraction of the equilibrium manifold are analytically predicted through the adoption of a first-passage time technique. Finally we discuss the possible extension of our approach to deal with the intermittency of complex systems in different fields.

a b s t r a c t We address the issue of the dynamical origin of scale-free link distributions. We study a two-dimensional lattice of cooperatively interacting units. Although the units interact only with the four nearest neighbors, a sufficiently large cooperation strength generates dynamically a scale-free network with the power law index ν approaching 1. We explain this result by using a new definition of network efficiency determined by the Euclidean distance between correlated units. According to this definition the link distribution favoring long-range connections makes efficiency increase. We embed an ad hoc scale-free network with power index ν ≥ 1 into a Euclidean two-dimensional space and show that the network efficiency becomes maximal as ν approaches 1. We therefore conclude that ν = 1 emerging from the cooperative interaction of units may be a consequence of the principle of network maximal efficiency.

Habituation is the reversible decrement in the behavior response to a novel and repeating stimulus without a corresponding change in the strength of the stimulus. Dishabituation is a complementary phenomenon in which a habituated process is revitalized by presenting a complex stimulus that is distinct from the original. Herein we propose a statistical habituation model (SHM); a phenomenological model based on a generalization of linear response theory and discrete events. The SHM suggests that the fundamental mechanism producing habituation in its myriad of forms, as well as the associated dishabituation, is the 1 / f -noise that is generically produced in complex neuronal networks.

summary It is hypothesized that the special way information is exchanged between living networks, the Living Matter Way (LMW), is determined by the Principle of Complexity Matching, which asserts that the relative complexity of two complex networks determines the transfer of information between them. The LMW explains the neurophysiology of habituation and why classical music persists in your head long after the music stops. Published by Elsevier Ltd.

Herein we develop a psychophysical model of decision making based on the difference between objective clock time and the human brain’s perception of time. In this model the utility function is given by the survival probability, which is shown to be a generalized hyperbolic distribution. The parameters of the utility function are fit to intertemporal choice model experimental data and decision making is determined to be a 1 / f -noise process.

The brain is probably the most interesting example of a complex network having 1 / f variability as determined through the analysis of EEG time series and magnetoencephalogram recordings. Herein we develop a theory of 1 / f noise of human cognition to explain the recent experimental observations that increasing the difficultly of cognitive tasks accelerates the transition from observed 1 / f noise to white noise in decision-making time series.

We study the subordination to a process that is periodic in the natural time scale, and equivalent to a clock with N states. The rationale for this investigation is given by a set of many interacting clocks with N states. The natural time scale representation corresponds to the dynamics of an individual clock with no interaction with the other clocks of this set. We argue that the cooperation among the clocks of this set has the effect of generating a global clock, whose times of sojourn in each of its N states are described by a distribution density with an inverse power law form and power index μ 2 . This is equivalent to extending the widely used subordination method from fluctuation–dissipation processes to periodic processes, thereby raising the question of whether special conditions exist of perfect synchronization, signaled by regular oscillations, and especially by oscillations with no damping. We study first the case of a Poisson subordination function. We show that in spite of the random nature of the subordination method the procedure has the effect of creating damped oscillations, whose damping vanishes in the limiting case of N ≫ 1 , thereby suggesting a condition of perfect synchronization in this limit. The Bateman’s mathematical arguments [H. Bateman, Higher Transcendental Functions, vol. III, Robert K Krieger, Publishing Company, Inc. Krim.Fr. Drive Malabar, FL; Copyright 1953 by McGraw-Hill Book Company Inc.] indicate that the condition of perfect synchronization is possible also in the non-Poisson case, with μ 2 , although it may lie beyond the range of computer simulation. To make the theoretical predictions accessible to numerical simulation, we use a subordination function whose survival probability is a Mittag–Leffler exponential function. This method prevents us from directly establishing the macroscopic coherence emerging from μ = 2 , which generates a perfect form of 1 / f noise. However, it affords indirect evidence that perfect synchronization signaled by undamped regular oscillations may be produced in this case. Furthermore, we explore a condition characterized by an excellent agreement between theory and numerical simulation, where the long-time region relaxation, with a perfect inverse power law decay, emerging from the subordination to ordinary fluctuation–dissipation processes, is replaced by exponentially damped regular oscillations.

In the ergodic regime, several methods efficiently estimate the temporal scaling of time series characterized by longrange power-law correlations by converting them into diffusion processes. However, in the condition of ergodicity breakdown, the same methods give ambiguous results. We show that in such regime, two different scaling behaviors emerge depending on the age of the windows used for the estimation. We explain the ambiguity of the estimation methods by the different influence of the two scaling behaviors on each method. Our results suggest that aging drastically alters the scaling properties of non-ergodic processes. 2007 Elsevier Ltd. All rights reserved.

Science is not merely the smooth progressive interaction of hypothesis, experiment and theory, although it sometimes has that form. More realistically the scientific study of any given complex phenomenon generates a number of explanations, from a variety of perspectives, that eventually requires synthesis to achieve a deep level of insight and understanding. One such synthesis has created the field of out-of-equilibrium statistical physics as applied to the understanding of complex dynamic networks. Over the past forty years the concept of complexity has undergone a metamorphosis. Complexity was originally seen as a consequence of memory in individual particle trajectories, in full agreement with a Hamiltonian picture of microscopic dynamics and, in principle, macroscopic dynamics could be derived from the microscopic Hamiltonian picture. The main difficulty in deriving macroscopic dynamics from microscopic dynamics is the need to take into account the actions of a very large number of components. The existence of events such as abrupt jumps, considered by the conventional continuous time random walk approach to describing complexity was never perceived as conflicting with the Hamiltonian view. Herein we review many of the reasons why this traditional Hamiltonian view of complexity is unsatisfactory. We show that as a result of technological advances, which make the observation of single elementary events possible, the definition of complexity has shifted from the conventional memory concept towards the action of non-Poisson renewal events. We show that the observation of crucial processes, such as the intermittent fluorescence of blinking quantum dots as well as the brain’s response to music, as monitored by a set of electrodes attached to the scalp, has forced investigators to go beyond the traditional concept of complexity and to establish closer contact with the nascent field of complex networks. Complex networks form one of the most challenging areas of modern research overarching all of the traditional scientific disciplines. The transportation networks of planes, highways and railroads; the economic networks of global finance and stock markets; the social networks of terrorism, governments, businesses and churches; the physical networks of telephones, the Internet, earthquakes and global warming and the biological networks of gene regulation, the human body, clusters of neurons and food webs, share a number of apparently universal properties as the networks become increasingly complex. Ubiquitous aspects of such complex networks are the appearance of non-stationary and non-ergodic statistical processes and inverse power-law statistical distributions. Herein we review the traditional dynamical and phase–space methods for modeling such networks as their complexity increases and focus on the limitations of these procedures in explaining complex networks. Of course we will not be able to review the entire nascent field of network science, so we limit ourselves to a review of how certain complexity barriers have been surmounted using newly applied theoretical concepts such as aging, renewal, non-ergodic statistics and the fractional calculus. One emphasis of this review is information transport between complex networks, which requires a fundamental change in perception that we express as a transition from the familiar stochastic resonance to the new concept of complexity matching.

The statistical properties of sequences of Waiting Times generated by Non-Homogeneous Poisson Processes are investigated by means of Renewal Aging, i.e. a statistical analysis being able to detect the presence of genuine renewal events with non-Poisson statistics. The Renewal Aging features of two non-homogeneous Poisson models with different prescriptions of the rate modulation are compared. Both prescriptions are essentially periodic. In the first model, the rate is a totally deterministic and smooth harmonic function. In the second model, the rate modulation is deterministic and smooth almost everywhere, except in some singular points occurring with a periodicity affected by weak random fluctuations. The main parameter of both models is the modulation speed, defined as the ratio between the modulation period and the average Waiting Time. This allows to distinguish between slow, intermediate and fast modulation of the rate. As expected, in the very slow modulation case both models have a strongly reduced Renewal Aging, practically zero, because the analysis is affected by local clusters of Waiting Times with the same Poisson rate. In the intermediate range of modulation speeds, both models show non-zero Renewal Aging and the behavior of the two models tends to be more different as the modulation speed decreases. Going towards the fast modulation regime, the behavior of the two models becomes completely different from one another. Model I does not show a definite global Renewal Aging. On the time scale of the modulation period, local oscillations arise in the Probability Density Function and an apparent oscillating aging is also observed. However, this form of aging is not the manifestation of genuine renewal non-Poisson events, but it is related to the local oscillations. On the contrary, Model II displays Renewal Aging features in agreement with a homogeneous Renewal non-Poisson Process. It is argued that this is related to the singular points in the rate modulation of Model II, which, due to their random occurrence, could be identified with genuine critical non-Poisson events. The approach presented here could have interesting applications in problems involving dichotomous noise and, in particular, in the statistical characterization of ON–OFF fluorescence intermittency experimentally observed in complex systems, such as nano-crystals and single bio-molecules stimulated by laser fields.

We propose a dynamical model generating the same non-Poisson renewal events as those currently found in complex systems as the blinking quantum dots and the human brain. Our results suggest that these complex systems can be interpreted as a set of synchronized neurons.

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., 10 pages, 5 figures

This paper is an outgrowth of the discussions held during the 2005 Denton Workshop, In Search of a Theory of Complexity. The workshop title captures the intent of the scientists who had come from Europe, the middle east and the United States to discuss the possibility that recent advances in statistical physics might provide a perspective that could guide us in constructing a theory of complexity. In this first paper of the proceedings we attempt to summarize the concepts introduced in the various debates and to draw some conclusions. But we caution the reader that these conclusions are our own and are not necessarily shared by the other participants of the workshop.

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., To appear in special issue of Chaos, Solitons and Fractals

In this paper we discuss the connection between trajectory and density memory. The first form of memory is a property of a stochastic trajectory, whose stationary correlation function shows that the fluctuation at a given time depends on the earlier fluctuations. The density memory is a property of a collection of trajectories, whose density time evolution is described by a time convoluted equation showing that the density time evolution depends on its past history. We show that the trajectory memory does not necessarily yields density memory, and that density memory might be compatible with the existence of abrupt jumps resetting to zero the system’s memory. We focus our attention on a time-convoluted diffusion equation, when the memory kernel is an inverse power law with (i) negative and (ii) positive tail. In case (i) there exist both renewal trajectories and trajectories with memory, compatible with this equation. Case (ii), which has eluded so far a convincing interpretation in terms of trajectories, is shown to be compatible only with trajectory memory.

The recent article \cite{hebbian} discusses the emergence of intelligence via criticality as a consequence of locality breakdown. Herein, we use criticality for the foundation of a novel generation of game theory making the local interaction between players yield long-range effects. We first establish that criticality is not confined to the Ising-like structure of the sociological model of \cite{hebbian}, called the decision making model (DMM), through the study of the emergence of altruism using the altruism-selfishness model (ASM). Both models generate criticality, one by imitation of opinion (DMM) the other by imitation of behavior (ASM). The dynamics of a sociological network $\mathcal{S}$ influences the behavioral network $\mathcal{F}$ through two game theoretic paradigms: (i) \emph{the value of altruism} ; (ii) \emph{the benefit of rapid consensus}. In (i) the network $\mathcal{S}$ debates the moral issue of altruism by means of the DMM, while at the level $\mathcal{F}$ the individuals operate according to the ASM. The individuals of the level $\mathcal{S}$, through a weak influence on the individuals of the level $\mathcal{F}$, exert a societal control on $\mathcal{F}$, fitting the principle of complexity management and complexity matching. In (ii) the benefit to society is the rapid attainment of consensus in the $\mathcal{S}$ level. The agents of the level $\mathcal{F}$ operate according to the prisoner's dilemma prescription, with the defectors acting as DMM contrarians at the level $\mathcal{S}$. The contrarians, acting as the inhibitory links of neural networks, exert on society the same beneficial effect of maintaining the criticality-induced resilience that they generate in neural networks. The conflict between personal and social benefit makes the networks evolve toward criticality. Finally, we show that the theory of this article is compatible with recent discoveries in the burgeoning field of social neuroscience.

We study the response to perturbation of non-Poisson dichotomous fluctuations that generate super-diffusion. We adopt the Liouville perspective and with it a quantum-like approach based on splitting the density distribution into a symmetric and an anti-symmetric component. To accomodate the equilibrium condition behind the stationary correlation function, we study the time evolution of the anti-symmetric component, while keeping the symmetric component at equilibrium. For any realistic form of the perturbed distribution density we expect a breakdown of the Onsager principle, namely, of the property that the subsequent regression of the perturbation to equilibrium is identical to the corresponding equilibrium correlation function. We find the directions to follow for the calculation of higher-order correlation functions, an unsettled problem, which has been addressed in the past by means of approximations yielding quite different physical effects., 30 pages

This paper is devoted to the problem of statistical mechanics raised by the analysis of an issue of sociological interest: the teen birth phenomenon. It is expected that these data are characterized by correlated fluctuations, reflecting the cooperative properties of the process. However, the assessment of the anomalous scaling generated by these correlations is made difficult, and ambiguous as well, by the non-stationary nature of the data that show a clear dependence on seasonal periodicity (periodic component) and an average changing slowly in time (slow component), as well. We use the detrending techniques described in the companion paper \cite{paper1}, to safely remove all the biases and to derive the genuine scaling of the teen birth phenomenon., 23 pages, 13 figures

Herein we consider various concepts of entropy as measures of the complexity of phenomena and in so doing encounter a fundamental problem in physics that affects how we understand the nature of reality. In essence the difficulty has to do with our understanding of randomness, irreversibility and unpredictability using physical theory, and these in turn undermine our certainty regarding what we can and what we cannot know about complex phenomena in general. The sources of complexity examined herein appear to be channels for the amplification of naturally occurring randomness in the physical world. Our analysis suggests that when the conditions for the renormalization group apply, this spontaneous randomness, which is not a reflection of our limited knowledge, but a genuine property of nature, does not realize the conventional thermodynamic state, and a new condition, intermediate between the dynamic and the thermodynamic state, emerges. We argue that with this vision of complexity, life, which with ordinary statistical mechanics seems to be foreign to physics, becomes a natural consequence of dynamical processes., Phylosophical

We address the problem of enhancing the sensitivity of biosensors to the influence of toxicants, with an entropy method of analysis, denoted as CASSANDRA, recently invented for the specific purpose of studying non-stationary time series. We study the specific case where the toxicant is tetrodotoxin. This is a very poisonous substance that yields an abrupt drop of the rate of spike production at t approximatively 170 minutes when the concentration of toxicant is 4 nanomoles. The CASSANDRA algorithm reveals the influence of toxicants thirty minutes prior to the drop in rate at a concentration of toxicant equal to 2 nanomoles. We argue that the success of this method of analysis rests on the adoption of a new perspective of complexity, interpreted as a condition intermediate between the dynamic and the thermodynamic state., 6 pages and 3 figures. Accepted for publication in the special issue of Chaos Solitons and Fractal dedicated to the conference "Non-stationary Time Series: A Theoretical, Computational and Practical Challenge", Center for Nonlinear Science at University of North Texas, from October 13 to October 19, 2002, Denton, TX (USA)

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., Comment: 5 pages, 2 figures

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., Comment: 5 pages, 3 figures, 1 supplement

We study a nonlinear Langevin equation describing the dynamic variable X(t), the mean field (order parameter) of a finite size complex network at criticality. The conditions under which the autocorrelation function of X shows any direct connection with criticality are discussed. We find that if the network is prepared in a state far from equilibrium, X(0)=1, the autocorrelation function is characterized by evident signs of critical slowing down as well as by significant aging effects, while the preparation X(0)=0 does not generate evident signs of criticality on X(t), in spite of the fact that the same initial state makes the fluctuating variable η(t)≡sgn(X(t)) yield significant aging effects. These latter effects arise because the dynamics of η(t) are directly dependent on crucial events, namely the re-crossings of the origin, which undergo a significant aging process with the preparation X(0)=0. The time scale dominated by temporal complexity, aging, and ergodicity breakdown of η(t) is properly evaluated by adopting the method of stochastic linearization which is used to explain the exponential-like behavior of the equilibrium autocorrelation function of X(t).

Book chapter discussing neural dynamics and the criticality, cooperation, avalanches and entrainment between complex networks.

We study the time evolution of a quantum system without classical counterpart, undergoing a process of entropy increase due to the environment influence. We show that if the environment-induced decoherence is interpreted in terms of wave-function collapses, a symbolic sequence can be generated. We prove that the Kolmogorov-Sinai entropy of this sequence coincides with rate of von Neumann entropy increase., 5 pages, 2 figures

We argue that a process of social interest is a balance of order and randomness, thereby producing a departure from a stationary diffusion process. The strength of this departure effect vanishes if the order to randomness intensity ratio vanishes, and this property allows us to reveal, although in an indirect way, the existence of a finite order to randomness intensity ratio. We aim at detecting this effect. We introduce a method of statistical analysis alternative to the compression procedures, with which the limitations of the traditional Kolmogorov-Sinai (KS) approach are bypassed. We prove that this method makes it possible for us to build up a memory detector, which signals the presence of even very weak memory, provided that this is persistent over large time intervals. We apply the analysis to the study of the teen birth phenomenon and we find that the unmarried teen births are a manifestation of a social process with a memory more intense than that of the married teens. We attempt to give a social interpretation of this effect.

We focus our attention on dynamical processes characterized by an entropic index Q, 7 pages, 4 figures

We consider the $d=1$ nonlinear Fokker-Planck-like equation with fractional derivatives $\frac{\partial}{\partial t}P(x,t)=D \frac{\partial^{\gamma}}{\partial x^{\gamma}}[P(x,t) ]^{\nu}$. Exact time-dependent solutions are found for $ \nu = \frac{2-\gamma}{1+ \gamma}$ ($-\infty, Comment: 3 figures

The √ n-rule of Schrodinger in his discussion of DNA is based onnormal statistics and equilibrium physics. Herein the kurtosis is used tomeasure the deviation from normality of the stistics of non-equilibrium DNAsequences. A pattern for this deviation from normality is identified andthis signature is found in prokaryotes. The signature is explained by atheory of DNA sequences that involves finite length DNA walks withdynamically generated long-range correlations.