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Partner: UNT College of Arts and Sciences
Department: Center for Nonlinear Science
Collection: UNT Scholarly Works
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In the search for the low-complexity sequences in prokaryotic and eukaryotic genomes: how to derive a coherent picture from global and local entropy measures
Paper discussing the search for the low-complexity sequences in prokaryotic and eukaryotic genomes and how to derive a coherent picture from global and local entropy measures. Abstract: We investigate on a possible way to connect the presence of Low-Complexity Sequences (LCS) in DNA genomes and the nonstationary properties of base correlations. Under the hypothesis that these variations signal a change in the DNA function, we use a new technique, called Non-Stationarity Entropic Index (NSEI) method, and we prove that this technique is an efficient way to detect functional changes with respect to a random baseline. The remarkable aspect is that NSEI does not imply any training data or fitting parameter, the only arbitrarity being the choice of a marker in the sequence. We make this choice on the basis of biological information about LCS distributions in genomes. We show that there exists a correlation between changing the amount in LCS and the ration of long-to short-range correlation. digital.library.unt.edu/ark:/67531/metadc174697/
Breakdown of the Onsager Principle as a Sign of Aging
Article discussing the breakdown of the Onsager principle as a sign of aging. Abstract: We discuss the problem of the equivalence between Continuous Time Random Walk (CTRW) and Generalized Master Equation (GME). The walker, making instantaneous jumps from one site of the lattice to another, resides in each site or extended time. The sojourn times have a distribution ψ (t) that is assumed to be an inverse power law with the power index μ. We assume that the Onsager principle is fulfilled, and we use this assumption to establish a complete equivalence between GME and the Montroll-Weiss CTRW. We prove that this equivalence is confined to the case when ψ (t) is an exponential. We argue that is so because the Montroll-Weiss CTRW, as recently proved by Barkai [E. Barkai, Phys. Rev. Lett. 90, 104101 (2003)], is non-stationary, thereby implying aging, while the Onsager principle, is valid only in the case of fully aged systems. The case of Poissonian distribution of sojourn times is the only one with no aging associated to it, and consequently with no need to establish special initial conditions to fulfill the Onsager principle. We consider the case of a dichotomous fluctuation, and we prove that the Onsager principle is fulfilled for any form of regression to equilibrium provided that the stationary condition hold true. We set the stationary condition on both the CTRW and the GME, thereby creating a condition of total equivalence, regardless the nature of the waiting time distribution. As a consequence of this procedure we create a GME that is a bona fide master equation, in spite of being non-Markovian. We note that the memory kernel of the GME affords information on the interaction between system of interest and its bath. The Poisson case yields a bath with infinitely fast fluctuations. We argue that departing from the Poisson form has the effect of creating a condition of infinite memory and that these results might be useful to shed light into the problem of how to unravel non-Markovian master equations. digital.library.unt.edu/ark:/67531/metadc174692/
Generalized Master Equation Via Aging Continuous-Time Random Walks
This article discusses the problem of the equivalence between continuous-time random walk (CTRW) and generalized master equation (GME). digital.library.unt.edu/ark:/67531/metadc67635/
Correlation Function and Generalized Master Equation of Arbitrary Age
This article discusses correlation function and generalized master equation of arbitrary age using non-Poisson, Markovian, and Liouville methods. digital.library.unt.edu/ark:/67531/metadc40401/
Renewal aging and linear response
Paper discussing renewal aging and linear response. Abstract: 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. digital.library.unt.edu/ark:/67531/metadc174702/
Long- and Short-Time Analysis of Heartbeat Sequences: Correlation with Mortality Risk in Congestive Heart Failure Patients
This paper discusses long- and short-time analysis of heartbeat sequences and the correlation with mortality risk in congestive heart failure patients. Abstract: We analyze RR heartbeat sequences with a dynamic model that satisfactorily reproduces both the long- and the short-time statistical properties of heart beating. These properties are expressed quantitatively by means of two significant parameters, the scaling δ concerning the asymptotic effects of long-range correlation, and the quantity 1 - π establishing the amount of uncorrelated fluctuations. We find a correlation between the position in the phase space (δ,π) of patients with congestive heart failure and their mortality risk. digital.library.unt.edu/ark:/67531/metadc67633/
Real event detection and the treatment of congestive heart failure: an efficient technique to help cardiologists to make crucial decisions
Paper discussing the treatment of congestive heart failure. Abstract: Using a method of entropic analysis of time series we establish the correlation between heartbeat long-range memory and mortality risk in patients with congestive heart failure. digital.library.unt.edu/ark:/67531/metadc174688/
Short- and Long-Term Statistical Properties of Heartbeat Time-Series in Healthy and Pathological Subjects
Paper discussing short- and long-term statistical properties of heartbeat time-series in healthy and pathological subjects. Abstract: We analyze heartbeat time-series corresponding to several groups of individuals (healthy, heart transplanted, with congestive heart failure (CHF), after myocardial infarction (MI), hypertensive), looking for short- and long-time statistical behaviors. In particular we study the persistency patterns of interbeat times and interbeat-time variations. Long-range correlations are revealed using an information-based technique which makes a wise use of the available statistics. The presence of strong long-range time correlations seems to be a general feature for all subjects, with the exception of some CHF individuals. We also show that short time-properties detected in healthy subjects, and seen also in hypertensive and MI patients, and completely absent in the transplanted, are characterized by a general behavior when we apply a proper coarse-graining procedure for time series analysis. digital.library.unt.edu/ark:/67531/metadc174687/
Renewal, Modulation, and Superstatistics in Times Series
In this article, the authors consider two different approaches, to which the authors refer to as renewal and modulation, to generate time series with a nonexponential distribution of waiting times. digital.library.unt.edu/ark:/67531/metadc40400/
Dynamical model for DNA sequences
This article discusses a dynamical model for DNA sequences based on the assumption that the statistical properties of DNA paths are determined by the joint action of two processes, one deterministic with long-range correlations and the other random and δ-function correlated. digital.library.unt.edu/ark:/67531/metadc139499/
Scaling Breakdown: A Signature of Aging
In this article, the authors prove that the Lévy walk is characterized by bilinear scaling. This effect mirrors the existence of a form of aging that does not require the adoption of nonstationary conditions. digital.library.unt.edu/ark:/67531/metadc67630/
Compression and Diffusion: A Joint Approach to Detect Complexity
Article discussing a joint approach to detect complexity by combining the Compression Algorithm Sensitive To Regularity (CASToRe) and Complex Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA) procedures. digital.library.unt.edu/ark:/67531/metadc139462/
Experimental Quenching of Harmonic Stimuli: Universality of Linear Response Theory
This article discusses experimental quenching of harmonic stimuli. Abstract: We show that liquid crystals in the weak turbulence electroconvective regime respond to harmonic perturbations with oscillations whose intensity decay with an inverse power law of time. We use the results of this experiment to prove that this effect is the manifestation of a form of linear response theory (LRT) valid in the out-of-equilibrium case, as well as at thermodynamic equilibrium where it reduces to the ordinary LRT. We argue that this theory is a universal property, which is not confined to physical processes such as turbulent or excitable media, and that it holds true in all possible conditions, and for all possible systems, including a complex networks, thereby establishing a bridge between statistical physics and all the fields of research in complexity. digital.library.unt.edu/ark:/67531/metadc40394/
Fluctuation-Dissipation Theorem for Event-Dominated Processes
This article discusses fluctuation-dissipation theorem for event-dominated processes. Abstract: We study a system whose dynamics are driven by non-Poisson, renewal, and nonergodic events. We show that external perturbations influencing the times at which these events occur violate the standard fluctuation-dissipation prescription due to renewal aging. The fluctuation-dissipation relation of this Letter is shown to be the linear response limit of an exact expression that has been recently proposed to account for the luminescence decay in a Gibbs ensemble of semiconductor nanocrystals, with intermittent fluorescence. digital.library.unt.edu/ark:/67531/metadc40397/
Response of Complex Systems to Complex Perturbations: the Complexity Matching Effect
Paper discussing the complexity matching effect. Abstract: 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(T) for the time intervals between successfully recorded breakdowns. In the intermittent case ψ(t) ~ 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 μs perturbed by a signal with complexity index μp. The analysis focuses on the non-ergodic (non-stationary) case μ ≤ 2 showing that for μs ≥ μp, the system S statistically inherits the correlation function of the perturbation P. The condition μp = μs is a resonant maximum for correlation information exchange. digital.library.unt.edu/ark:/67531/metadc132965/
Site correlation, anomalous diffusion, and enhancement of the localization length
This article discusses site correlation, anomalous diffusion, and enhancement of localization length. Herein the authors study the effects on Anderson localizations of correlations in the energy distribution of the sites of a tight-binding Hamiltonian. The lattice correlations are introduced are introduced by means of classical maps generating anomalous diffusion, that have recently been found to account for the correlated disorder of "biological" lattices. The authors show that the enhancement of localization length takes place on a much wider band of energies than in the case of the random-dimer model if the random walk on the site energies of the tight-binding Hamiltonian is determined by the joint action of short- and long-range correlations. digital.library.unt.edu/ark:/67531/metadc139487/
Fractional Brownian motion as a nonstationary process: An alternative paradigm for DNA sequences
This article discusses fractional Brownian motion as a nonstationary process. The model adopted is compatible with the known biological and physical constraints, namely, it is shown to be consistent with the information of current biological literature on folding as well as with the statistical analyses of DNA sequences. digital.library.unt.edu/ark:/67531/metadc75416/
Non-Gaussian statistics of anomalous diffusion: The DNA sequences of prokaryotes
This article discusses non-Gaussian statistics of anomalous diffusion. Abstract: We adopt a non-Gaussian indicator to measure the deviation from Gaussian statistics of a diffusion process generated by dichotomous fluctuations with infinite memory. We also make analytical predictions on the transient behavior of the non-Gaussian indicator as well as on its stationary value. We then apply this non-Gaussian analysis to the DNA sequences of prokaryotes adopting a theoretical model where the "DNA dynamics" are assumed to be determined by the statistical superposition of two independent generators of fluctuations: a generator of fluctuations with no correlation and a generator of fluctuations with infinite correlation "time". We study also the influence that the finite length of the observed sequences has on the short-range fluctuation and sequence truncation. Nevertheless, under proper conditions, fulfilled by all the DNA sequences of prokaryotes that have been examined, a non-Gaussian signature remains to signal the correlated nature of the driving process. digital.library.unt.edu/ark:/67531/metadc75418/
Detection of invisible and crucial events: from seismic fluctuations to the war against terrorism
Paper discussing the detection of invisible and crucial events. Abstract: We argue that the recent discovery of the non-Poissonian statistics of the seismic main-shocks is a special case of a more general approach to the detection of the distribution of the time increments between one crucial but invisible event and the next. We make the conjecture that the proposed approach can be applied to the analysis of terrorist network with significant benefits for the Intelligence Community. digital.library.unt.edu/ark:/67531/metadc174695/
From Knowledge, Knowability and the Search for Objective Randomness to a New Vision of Complexity
Paper discussing knowledge, knowability, and the search for objective randomness to a new vision of complexity. Abstract: Herein we consider various concepts of entropy as measure 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. digital.library.unt.edu/ark:/67531/metadc174694/
Cognitive Scale-Free Networks as a Model for Intermittency in Human Natural Language
Paper discussing cognitive scale-free networks as a model for intermittency in human natural language. Abstract: We model certain features of human language complexity by means of advanced concepts borrowed from statistical mechanics. Using a time series approach, the diffusion entropy method (DE), we compute the complexity of an Italian corpus of newspapers and magazines. We find that the anomalous scaling index is compatible with a simple dynamical model, a random walk on a complex scale-free network, which is linguistically related to Saussurre's paradigms. The model yields the famous Zipf's law in terms of the generalized central limit theorem. digital.library.unt.edu/ark:/67531/metadc174698/
Intermittency and scale-free networks: a dynamical model for human language complexity
Article discussing intermittency, scale-free networks, and a dynamical model for human language complexity. Abstract: In this paper we try to model certain features of human language complexity by means of advanced concepts borrowed from statistical mechanics. We use a time series approach, the diffusion entropy method (DE), to compute the complexity of an Italian corpus of newspapers and magazines. We find that the anomalous scaling index is compatible with a simple dynamical model, a random walk on a complex scale-free network, which is linguistically related to Saussurre's paradigms. The network complexity is independently measured on the same corpus, looking at the co-occurrence of nouns and verbs. This connection of cognitive complexity with long-range time correlations also provides an explanation for the famous Zipf's law in terms of the generalized central limit theorem. digital.library.unt.edu/ark:/67531/metadc174696/
Dynamical approach to Lévy processes
This article discusses a dynamical approach to Lévy processes, which makes it possible to derive all statistical properties of the diffusion process from the correlation function of the dichotomous fluctuating variable Φy(t). digital.library.unt.edu/ark:/67531/metadc139498/
Memory Beyond Memory in Heart Beating, a Sign of a Healthy Physiological Condition
This article discusses memory beyond memory in heart beating. Abstract: We describe two types of memory and illustrate each using artificial and actual heartbeat data sets. The first type of memory, yielding anomalous diffusion, implies the inverse power-law nature of the waiting time distribution and the second the correlation among distinct times, and consequently also the occurrence of many pseudoevents, namely, not genuinely random events. Using the method of diffusion entropy analysis, we establish the scaling that would be determined by the real events alone. We prove that the heart beating of healthy patients reveals the existence of many more pseudoevents than in the patients with congestive heart failure. digital.library.unt.edu/ark:/67531/metadc67628/
Conflict between trajectories and density description: the statistical source of disagreement
Paper discussing the statistical source of disagreement between trajectories and density description. Abstract: We study an idealized version of intermittent process leading the fluctuations of a stochastic dichotomous variable. It consists of an overdamped and symmetric potential well with a cusp-like minimum. The right-hand and left-hand portions of the potential corresponds to = W and = W, respectively. When the particle reaches this minimum is injected back to a different and randomly chosen position, still within the potential well. We build up the corresponding Frobenius-Perron equation and we evaluate the correlation function of the stochastic variable, called (t). We assign the potential well a form yielding (t) = (T = (t=T)), with > 0. Thanks to the symmetry of potential, there are no biases, and we limit ourselves to considering correlation functions with an even number of times, indicated for concision, by h12i, h1234i, and more, in general, by h1:::2ni. The adoption of a formal treatment, based on density, and thus of the operator driving the density time evolution, establishes a prescription for the evaluation of the correlation functions, yielding h1::2ni - h12i:::h(2n 1)2ni. We study the same dynamic problem using trajectories, and we establish that the resulting two-time correlation function coincides with that ordered by the density picture, as it should. We then study the four-times correlation function and we prove that in the non-Poisson case it departs from the density prescription, namely, from h1234i=h12ih34i. We conclude that this is the main reason why the two pictures yield two different diffusion processes, as noticed in an earlier work. [M. Bologna, P. Grigolini, B. J. West, Chem. Phys. 284, (1-2) 115-128 (2002)]. digital.library.unt.edu/ark:/67531/metadc174689/
Non-Poisson Dichotomous Noise: Higher-Order Correlation Functions and Aging
This article discusses non-Poisson dichotomous noise and higher-order correlation functions and aging. Abstract: We study a two-state symmetric noise, with a given waiting time distribution ψ(τ), and focus our attention on the connection between the four-time and two-time correlation functions. The transition of ψ(τ) from the exponential to the nonexponential condition yields the breakdown of the usual factorization condition of high-order correlation functions, as well as the birth of aging effects. We discuss the subtle connections between these two properties and establish the condition that the Liouville-like approach has to satisfy in order to produce a correct description of the resulting diffusion process. digital.library.unt.edu/ark:/67531/metadc40403/
Spontaneous Brain Activity as a Source of Ideal 1/f Noise
In this article, the authors study the electroencephalogram (EEG) of 30 closed-eye subjects with a technique of analysis recently proposed to detect punctual events signaling rapid transitions between different metastable states. After single-EEG-channel event detection, the authors study global properties of events simultaneously occurring among two or more electrodes termed coincidences. The authors convert the coincidences into a diffusion process with three distinct rules that can yield the same μ only in the case where the coincidences are driven by a renewal process. The authors establish that the time interval between two consecutive renewal events driving the coincidences has a waiting-time distribution with inverse power-law index μ≈2 corresponding to ideal 1/f noise. The authors argue that this discovery, shared by all subjects of our study, supports the conviction that 1/f noise is an optimal communication channel for complex networks as in art or language and may therefore be the channel through which the brain influences complex processes and is influenced by them. digital.library.unt.edu/ark:/67531/metadc40409/
Fluctuation-dissipation process without a time scale
This article discusses fluctuation-dissipation process without a time scale. Abstract: We study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long-range correlations. We make the assumption that the perturbation process involved is of the same kind as those recently studied numerically and theoretically, with a good agreement between theory and numerical treatment. As a result of this assumption the equilibrium distribution departs from the ordinary canonical distribution. The distribution tails are truncated, the distribution border is signaled by sharp peaks, and, in the weak dissipation limit, the central distribution body becomes identical to a truncated Lévy distribution. digital.library.unt.edu/ark:/67531/metadc77161/
Canonical and noncanonical equilibrium distribution
This article discusses canonical and noncanonical equilibrium distribution. Abstract: We address the problem of the dynamical foundation of noncanonical equilibrium. We consider, as a source of divergence from ordinary statistical mechanics, the breakdown of the condition of time scale separation between microscopic and macroscopic dynamics. We show that this breakdown has the effect of producing a significant deviation from the canonical prescription. We also show that, while the canonical equilibrium can be reached with no apparent dependence on dynamics, the specific form of noncanonical equilibrium is, in fact, determined by dynamics. We consider the special case where the thermal reservoir driving the system of interest to equilibrium is a generator of intermittent fluctuations. We assess the form of the noncanonical equilibrium reached by the system in this case. Using both theoretical and numerical arguments we demonstrate that Lévy statistics are the best description of the dynamics and that the Lévy distribution is the correct basin of attraction. We show that the correct path to noncanonical equilibrium by means of strictly thermodynamic arguments has not yet been found, and that further research has to be done to establish a connection between dynamics and thermodynamics. digital.library.unt.edu/ark:/67531/metadc77164/
Aging and Rejuvenation with Fractional Derivatives
This article discusses aging rejuvenation with fractional derivatives. Abstract: We discuss a dynamic procedure that makes a fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment, and divergent second moment, namely, with the power index μ in the interval 2<μ<3, yield a generalized master equation equivalent to the sum of an ordinary Markov contribution and a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, o, is given by o=3-μ. A brand new system is characterized by the degree o=μ-2. If the system is prepared at time -tₐ<0 and the observation begins at time t=0, we derive the following scenario. For times 0<t«tₐ the system is satisfactorily described by the fractional derivative with o=3-μ. Upon time increase the system undergoes a rejuvenation process that in the time limit t⪢tₐ yields o=μ-2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative. digital.library.unt.edu/ark:/67531/metadc67638/
Aging and Rejuvenation with Fractional Derivatives
Paper discussing aging and rejuvenation with fractional derivatives. Abstract: We discuss a dynamic procedure that makes the fractional derivative emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment and divergent second moment, namely with the power index μ in the interval 2 < μ < 3, yields a generalized master equation equivalent to the sum of an ordinary Markov contribution and of a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, ord = μ - 2. If the system is prepared at time -tₐ < 0 and the observation begins at time t = 0, we derive the following scenario. For times 0 < t << tₐ the system is satisfactorily described by the fractional derivative with ord = 3 - μ. Upon time increase the system undergoes a rejuvenation process that in the time limit t >> tₐ yields ord = μ - 2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative. digital.library.unt.edu/ark:/67531/metadc174699/
Beyond the Death of Linear Response: 1/f Optimal Information Transport
This article discusses linear response and 1/f optimal information transport. Article: Nonergodic 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. The authors 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 nonergodic renewal processes, by taking as stimulus a similar nonergodic process. The ideal condition of 1/f noise corresponds to a singularity that is expected to be relevant in several experimental conditions. digital.library.unt.edu/ark:/67531/metadc40407/
Publisher's Note: Beyond the Death of Linear Response: 1/f Optimal Information Transport [Phys. Rev. Lett. 105,040601 (2010)]
This is a Publisher's Note for the article 'Beyond the Death of Linear Response: 1/f Optimal Information Transport' [Phys. Rev. Lett. 105, 040601 (2010)]. digital.library.unt.edu/ark:/67531/metadc40406/
Transmission of Information Between Complex Systems: 1/ f resonance
In this article, the authors study the transport of information between two complex systems with similar properties. Both systems generate non-Poisson renewal fluctuations with a power-law spectrum 1/f 3-μ, the case μ=2 corresponding to ideal 1/f noise. The authors denote by μs and μp the power-law indexes of the system of interest S and the perturbing system P, respectively. By adopting a generalized fluctuation-dissipation theorem (FDT) the authors show that the ideal condition of 1/f noise for both systems corresponds to maximal information transport. The authors prove that to make the system S respond when μs < 2 the authors have to set the condition μp < 2. In the latter case, if μp < μs, the system S inherits the relaxation properties of the perturbing system. In the case where μp > 2, no response and no information transmission occurs in the long-time limit. The authors 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. digital.library.unt.edu/ark:/67531/metadc40404/
Absorption and Emission in the Non-Poissonian Case
This article discusses absorption and emission in the Non-Poissonian Case. Abstract: This Letter addresses the challenging problems posed to the Kubo-Anderson (KA) theory by the discovery of intermittent resonant fluorescence with a nonexponential distribution of waiting times. We show how to extend the KA theory from aged to aging systems, aging for a very extended time period or even forever, being a crucial consequence of non-Poisson statistics. digital.library.unt.edu/ark:/67531/metadc67641/
Linear Response to Perturbation of Nonexponential Renewal Processes
This article discusses the linear response to perturbation of nonexponential renewal processes. Abstract: We study the linear response of a two-state stochastic process, obeying the 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. digital.library.unt.edu/ark:/67531/metadc67626/
Vortex Dynamics in Evolutive Flows: A Weakly Chaotic Phenomenon
In this article, the authors make use of a wavelet method to extract, from experimental velocity signals obtained in an evolutive flow, the dominating velocity components generated by vortex dynamics. The authors characterize the resulting time series complexity by means of a joint use of data compression and of an entropy diffusion method. The authors assess that the time series emerging from the wavelet analysis of the vortex dynamics is a weakly chaotic process with a vanishing Kolmogorov-Sinai entropy and a power-law growth of the information content. To reproduce the Fourier spectrum of the experimental signal, the authors adopt a harmonic dependence on time with a fluctuating frequency, ruled by an inverse power-law distribution of random events. The complexity of these fluctuations is determined by studying the corresponding artificial sequences. The authors reproduce satisfactorily both spectral and complex properties of the experimental signal by locating the complexity of the fluctuating process at the border between the stationary and the nonstationary states. digital.library.unt.edu/ark:/67531/metadc67634/
Aging in financial market
Article discussing aging in the financial market. Abstract: 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. digital.library.unt.edu/ark:/67531/metadc174703/
Renewal Aging as Emerging Property of Phase Synchronization
Paper discussing renewal aging as emerging property of phase synchronization. Abstract: 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. digital.library.unt.edu/ark:/67531/metadc174704/
A fluctuating environment as a source of periodic modulation
Article discussing a fluctuating environment as a source of periodic modulation. Abstract: 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. digital.library.unt.edu/ark:/67531/metadc132981/
Fluorescence intermittency in blinking quantum dots: renewal or slow modulation?
Article discussing fluorescence intermittency in blinking quantum dots. Abstract: 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. digital.library.unt.edu/ark:/67531/metadc174701/
Brain, Music, and Non-Poisson Renewal Processes
This article is a reply to a comment by Massimo Falcioni and Angelo Vulpiani. In a previous letter, the authors have discussed the linear response theory (LRT) and shown that the breakdown of this theory occurring at intermediate times, observed in an earlier paper [2] as well as in [1], disappears upon an increase of the number of degrees of freedom. In a comment to [1] Falcioni and Vulpiani [3] claim that this breakdown is rather a consequence of the lack of mixing: according to them, regardless of the number of degrees of freedom, mixing is the key ingredient behind the LRT. digital.library.unt.edu/ark:/67531/metadc77166/
Linear Response of Hamiltonian Chaotic Systems as a Function of the Number of Degrees of Freedom
This article discusses the linear response of Hamiltonian chaotic systems as a function of the number of degrees of freedom. Abstract: Using numerical simulations we show that the response to weak perturbations of a variable of Hamiltonian chaotic systems depend on the number of degrees of freedom: When this is small (≈2) the response is not linear, in agreement with the well known objections to the Kubo linear response theory, while, for a larger number of degrees of freedom, the response becomes linear. This is due to the fact that increasing the number of degrees of freedom the shape of the distribution function, projected onto the subspace of the variable of interest, becomes fairly "regular." digital.library.unt.edu/ark:/67531/metadc139479/
From power law intermittence to macroscopic coherent regime
This article offers discussions from power law intermittence to macroscopic coherent regime. The authors address the problem of establishing which is the proper form of quantum master equation generating a survival probability identical to that corresponding to the nonergodic sequence of "light on" and "light off" fluorescence fluctuations in blinking quantum dots. digital.library.unt.edu/ark:/67531/metadc132992/
Lévy diffusion as an effect of sporadic randomness
This article discusses Lévy diffusion as an effect of sporadic randomness. Abstract: The Lévy diffusion processes are a form of nonordinary statistical mechanics resting, however, on the conventional Markov property. As a consequence of this, their dynamic derivation is possible provided that (i) a source of randomness is present in the corresponding microscopic dynamics and (ii) the consequent process of memory erasure is properly taken into account by the theoretical treatment. digital.library.unt.edu/ark:/67531/metadc77160/
Trajectory versus probability density entropy
In this article, the authors show that the widely accepted conviction that a connection can be established between the probability density entropy and the Kolmogorov-Sinai (KS) entropy is questionable. The authors adopt the definition of density entropy as a functional of a distribution density whose time evolution is determined by a transport equation, conceived as the only prescription to use for the calculation. Although the transport equation is built up for the purpose of affording a picture equivalent to that stemming from a trajectory dynamics, no direct use of trajectory time evolution is allowed, once the transport equation is defined. With this definition in mind the authors prove that the detection of a time regime of increase of the density entropy with a rate identical to the KS entropy is possible only in a limited number of cases. The proposals made by some authors to establish a connection between the two entropies in general, violate the authors' definition of density entropy and imply the concept of trajectory, which is foreign to that of density entropy. digital.library.unt.edu/ark:/67531/metadc77165/
Decoherence, wave function collapses and non-ordinary statistical mechanics
Article discussing decoherence, wave function collapses, and non-ordinary statistical mechanics. Abstract: We consider a toy model of pointer interacting with a 1/2-spin system, whose $\sigma_{x}$ variable is \emph{measured} by the environment, according to the prescription of decoherence theory. If the environment measuring the variable $\sigma_{x}$ yields ordinary statistical mechanics, the pointer sensitive to the 1/2-spin system undergoes the same, exponential, relaxation regardless of whether real collapses or an entanglement with the environment, mimicking the effect of real collapses, occur. In the case of non-ordinary statistical mechanics the occurrence of real collapses make the pointer still relax exponentially in time, while the equivalent picture in terms of reduced density matrix generates an inverse power law relaxation. digital.library.unt.edu/ark:/67531/metadc174684/
Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions
This article discusses anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation. Abstract: We consider the d=1 nonlinear Fokker-Planck-like equation with fractional derivatives (∂/∂t)P(x,t) = D(∂ƴ/∂xƴ)[P(x,t]v. Exact time-dependent solutions are found for v = (2 - y)/(1 + y)(-∞ < y ⩽ 2). By considering the long-distance asymptotic behavior of these solutions, a connection is established, namely, q = (y + 3)/(Y + 1)(0 < y ⩽ 2), with the solutions optimizing the nonextensive entropy characterized by index q. Interestingly enough, this relation coincides with the only already known for Lévy-like superdiffusion (i.e., v = 1 and 0 < y ⩽ 2). Finally, for (y,v) = (2,0) the authors obtain q=5/3, which differs from the value q = 2 corresponding to the y = 2 solutions available in the literature (v < 1 porous medium equation), thus exhibiting nonuniform convergence. digital.library.unt.edu/ark:/67531/metadc77162/
Memory Effects in Fractional Brownian Motion with Hurst Exponent H<1/3
This article discusses memory effects in fractional Brownian motion with Hurst exponent H<1/3. Abstract: We study the regression to the origin of a walker driven by dynamically generated fractional Brownian motion (FBM) and we prove that when the FBM scaling, i.e., the Hurst exponent H<1/3, the emerging inverse power law is characterized by a power index that is a compelling signature of the infinitely extended memory of the system. Strong memory effects leads to the relation H=θ/2 between the Hurst exponent and the persistent exponent θ, which is different from the widely used relation H=1 - θ. The latter is valid for 1/3<H<1 and is known to be compatible with the renewal assumption. digital.library.unt.edu/ark:/67531/metadc40405/
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