182 research outputs found
Cognitive scale-free networks as a model for intermittency in human natural language
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.Comment: Conference FRACTAL 200
Renewal, Modulation and Superstatistics
We consider two different proposals to generate a time series with the same
non-Poisson distribution of waiting times, to which we refer to as renewal and
modulation. We show that, in spite of the apparent statistical equivalence, the
two time series generate different physical effects. Renewal generates aging
and anomalous scaling, while modulation yields no aging and either ordinary or
anomalous diffusion, according to the prescription used for its generation. We
argue, in fact, that the physical realization of modulation involves critical
events, responsible for scaling. In conclusion, modulation rather than ruling
out the action of critical events, sets the challenge for their identification
From Knowledge, Knowability and the Search for Objective Randomness to a New Vision of Complexity
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.Comment: Phylosophica
Response of Complex Systems to Complex Perturbations: the Complexity Matching Effect
The dynamical emergence (and subsequent intermittent breakdown) of collective
behavior in complex systems is described as a non-Poisson renewal process,
characterized by a waiting-time distribution density for the time
intervals between successively recorded breakdowns. In the intermittent case
, with complexity index . We show that two systems
can exchange information through complexity matching and present theoretical
and numerical calculations describing a system with complexity index
perturbed by a signal with complexity index . The analysis focuses on
the non-ergodic (non-stationary) case showing that for
, the system statistically inherits the correlation
function of the perturbation . The condition is a resonant
maximum for correlation information exchange.Comment: 4 pages, 1 figur
Breakdown of the Onsager principle as a sign of aging
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 for
extended times. The sojourn times have a distribution psi(t) that is assumed to
be an inverse power law. 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 psi(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. 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 holds 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 it 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.Comment: one file .tex, revtex4 style, 11 page
Fractal Complexity in Spontaneous EEG Metastable-State Transitions: New Vistas on Integrated Neural Dynamics
Resting-state EEG signals undergo rapid transition processes (RTPs) that glue otherwise stationary epochs. We study the fractal properties of RTPs in space and time, supporting the hypothesis that the brain works at a critical state. We discuss how the global intermittent dynamics of collective excitations is linked to mentation, namely non-constrained non-task-oriented mental activity
Conflict between trajectories and density description: the statistical source of disagreement
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 and
, 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
. We assign to the potential well a form yielding , with . We limit ourselves to considering
correlation functions with an even number of times, indicated for concision, by
and, more, in general, by . The adoption of a
treatment based on density yields . We
study the same dynamic problem using trajectories, and we establish that the
resulting two-time correlation function coincides with that afforded 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 . 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.
{\bf 284}, (1-2) 115-128 (2002)].Comment: 8 pages, no figure
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
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
ratio of long- to short-range correlation
Cooperation-Induced Topological Complexity: A Promising Road to Fault Tolerance and Hebbian Learning
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. We 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. We focus on the critical condition that has been recently shown to maximize information transport and we 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 we focus on the correlation threshold generating a scale-free topology with power index ν ≈ 1 and we 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. We find that criticality in this case generates also a third state, corresponding to a total lack of consensus. However, we make a numerical analysis of the dynamically induced network, and we 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. We argue that these results are compatible with both Hebbian learning and fault tolerance
Aging in Financial Market
We analyze the data of the Italian and U.S. futures on the stock markets and
we test the validity of the Continuous Time Random Walk assumption for the
survival probability of the returns time series via a renewal aging experiment.
We also study the survival probability of returns sign and apply a coarse
graining procedure to reveal the renewal aspects of the process underlying its
dynamics.Comment: To appear in special issue of Chaos, Solitons and Fractal
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