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UNT College of Arts and Sciences
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Center for Nonlinear Science
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2010-2019
- 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/
- Dynamics of Electroencephalogram Entropy and Pitfalls of Scaling Detection
- This article discusses dynamics of electroencephalogram entropy and pitfalls of scaling detection. Abstract: In recent studies a number of research groups have determined that human electroencephalograms (EEG) have scaling properties. In particular, a crossover between two regions with different scaling exponents has been reported. Herein the authors study the time evolution of diffusion entropy to elucidate the scaling of EGG time series. For a cohort of 20 awake healthy volunteers with closed eyes, the authors find that the diffusion entropy of EEG increments (obtained from EEG waveforms by differencing) exhibits three features: short-time growth, an alpha wave related oscillation whose amplitude gradually decays in time, and asymptotic saturation which is achieved after approximately 1 s. This analysis suggests a linear, stochastic Ornstein-Uhlenbeck Langevin equation with a quasiperiodic forcing (whose frequency and/or amplitude may vary in time) as the model for the underlying dynamics. This model captures the salient properties of EEG dynamics. In particular, both the experimental and simulated EEG time series exhibit short-time scaling which is broken by a strong periodic component, such as alpha waves. The saturation of EEG diffusion entropy precludes the existence of asymptotic scaling. We find that the crossover between two scaling regions seen in detrended fluctuation analysis (DFA) of EEG increments does not originate from the underlying dynamics but is merely an artifact of the algorithm. This artifact is rooted in the failure of the "trend plus signal" paradigm of DFA. digital.library.unt.edu/ark:/67531/metadc40408/
- Memory Effects in Fractional Brownian Motion with Hurst Exponent H<1/3
- In this article, the authors study the regression to the origin of a walker driven by dynamically generated fractional Brownian motion (FBM) and the authors 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/
- Temporal Complexity of the Order Parameter at the Phase Transition
- In this article, the authors study a decision making model in a condition where it is equivalent to the two-dimensional Ising model, and the authors show that at the onset of phase transition it generates temporal complexity, namely, nonstationary and nonergodic fluctuations. The authors argue that this is a general property of criticality, thereby opening the door to the application of the recently discovered phenomenon of complexity matching: For an efficient transfer of information to occur, a perturbing complex network must share the same temporal complexity as the perturbed complex network. digital.library.unt.edu/ark:/67531/metadc40402/
- 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/
- 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/
- Criticality and Transmission of Information in a Swarm of Cooperative Units
- This article discusses criticality and transmission of information in a swarm of cooperative units. Abstract: We show that the intelligence of a swarm of cooperative units (birds) emerges at criticality, as an effect of the joint action of frequent organizational collapses and of spatial correlation as extended as the flock size. The organizational collapses make the birds become independent of one another, thereby allowing the flock to follow the direction of the lookout birds. Long-range correlation violates the principle of locality, making the lookout birds transmit information on either danger or resources with a time delay determined by the time distance between two consecutive collapses. digital.library.unt.edu/ark:/67531/metadc40392/
- Cooperation in neural systems: Bridging complexity and periodicity
- This article discusses cooperation in neural systems. Abstract: 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 paper 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 interactions into long-range interactions, thereby generating time complexity followed by time periodicity. Increasing the density of neuron firings reduces the influence of periodicity, thus creating a cooperation-induced renewal condition that is distinctly non-Poissonian. digital.library.unt.edu/ark:/67531/metadc132986/
- Probability flux as a method for detecting scaling
- In this article, the authors introduce a new method for detecting scaling in time series. The method uses the properties of the probability flux for stochastic self-affine processes and is called the 'probability flux analysis' (PFA). The advantages of this method are: 1) it is independent of the finiteness of the moments of the self-affine process; 2) it does not require a binning procedure for numerical evaluation of the probability density function. These properties make the method particularly efficient for heavy tailed distributions in which the variance is not finite, for example, in Lévy α-stable processes. This utility is established using a comparison with the 'diffusion entropy' (DE) method. digital.library.unt.edu/ark:/67531/metadc132978/
- Networking of psychophysics, psychology, and neurophysiology
- This article focuses on dynamic networking and dynamic networks in complex research on psychophysics, psychology, and neurophysiology. It states that new ways were suggested by dynamic networking and dynamic networks to transfer information utilizing the long-distance communication through local cooperative interaction. It says that the fluctuations in brain and social dynamics reveal the emergence of complex behavior when analyzed with advanced methods of fractal statistical analysis. digital.library.unt.edu/ark:/67531/metadc132991/
- Cooperation-induced topological complexity: a promising road to fault tolerance and Hebbian learning
- This article discusses cooperation-induced topological complexity. Abstract: According to an increasing number of researchers intelligence emerges from criticality as a consequence of locality breakdown and long-range correlation, well known properties of phase transition processes. The authors study a model of interacting units, as an idealization of real cooperative systems such as the brain or a flock of birds, for the purpose of discussing the emergence of long-range correlation from the coupling of any unit with its nearest neighbors. The authors focus on the critical condition that has been recently shown to maximize information transport and the authors study the topological structure of the network of dynamically linked nodes. Although the topology of this network depends on the arbitrary choice of correlation threshold, namely the correlation intensity selected to establish a link between two nodes; the numerical calculations of this paper afford some important indications on the dynamically induced topology. The first important property is the emergence of a perception length as large as the flock size, thanks to some nodes with a large number of links, thus playing the leadership role. All the units are equivalent and leadership moves in time from one to another set of nodes, thereby insuring fault tolerance. Then the authors focus on the correlation threshold generating a scale-free topology with power index v ≈ 1 and the authors find that if this topological structure is selected to establish consensus through the linked nodes, the control parameter necessary to generate criticality is close to the critical value corresponding to the all-to-all coupling condition. The authors find that criticality in this case generates also a third state, corresponding to a total lack of consensus. However, the authors make a numerical analysis of the dynamically induced network, and the authors find that it consists of two almost independent structures, each of which is equivalent to a network in the all-to-all coupling condition. This observation confirms that cooperation makes the system evolve toward favoring consensus topological structures. The authors argue that these results are compatible with both Hebbian learning and fault tolerance. digital.library.unt.edu/ark:/67531/metadc132972/
- From self-organized to extended criticality
- This article includes discussions from self-organized to extended criticality. Abstract: We address the issue of criticality that is attracting the attention of an increasing number of neurophysiologists. Our main purpose is to establish the specific nature of some dynamical processes that although physically different, are usually termed as "critical," and we focus on those characterized by the cooperative interaction of many units. We notice that the term "criticality" has been adopted to denote both noise-induced phase transitions and Self-Organized Criticality (SOC) with no clear connection with the traditional phase transitions, namely the transformation of a thermodynamic system from one state of matter to another. We notice the recent attractive proposal of extended criticality advocated by Bailly and Longo, which is realized through a wide set of critical points rather than emerging as a singularity from a unique value of the control parameter. We study a set of cooperatively firing neurons and we show that for an extended set of interaction couplings the system exhibits a form of temporal complexity similar to that emerging at criticality from ordinary phase transitions. This extended criticality regime is characterized by three main properties: (i) In the ideal limiting case of infinitely large time period, temporal complexity corresponds to Mittag-Leffler complexity; (ii) For large values of the interaction coupling the periodic nature of the process becomes a predominant while maintaining to some extent, in the intermediate time asymptotic region, the signature of complexity; (iii) Focusing their attention on firing neuron avalanches, We find two of the popular SOC properties, namely the power indexes 2 and 1.5 respectively for time length and for the intensity of the avalanches. We derive the main conclusion that SOC emerges from extended criticality, thereby explaining the experimental observation of Plenz and Beggs: avalanches occur in time with surprisingly regularity, in apparent conflict with the temporal complexity of physical critical points. digital.library.unt.edu/ark:/67531/metadc132990/
- Linear response at criticality
- This article discusses a linear response to criticality. Abstract: We study a set of cooperatively interacting units at criticality, and we prove with analytical and numerical arguments that they generate the same renewal non-Poisson intermittency as that produced by blinking quantum dots, thereby giving a stronger support to the results of earlier investigation. By analyzing how this out-of-equilibrium system responds to harmonic perturbations, we find that the response can be described only using only a new form of linear response theory that accounts for aging and the nonergodic behavior of the underlying process. We connect the undamped response of the system at criticality to the decaying response predicted by the recently established nonergodic fluctuation-dissipation theorem for dichotomous processes using information about the second moment of the fluctuations. We demonstrate that over a wide range of perturbation frequencies the response of the cooperative system is greatest when at criticality. digital.library.unt.edu/ark:/67531/metadc132985/