3,168 research outputs found
Scaling in Non-stationary time series I
Most data processing techniques, applied to biomedical and sociological time
series, are only valid for random fluctuations that are stationary in time.
Unfortunately, these data are often non stationary and the use of techniques of
analysis resting on the stationary assumption can produce a wrong information
on the scaling, and so on the complexity of the process under study. Herein, we
test and compare two techniques for removing the non-stationary influences from
computer generated time series, consisting of the superposition of a slow
signal and a random fluctuation. The former is based on the method of wavelet
decomposition, and the latter is a proposal of this paper, denoted by us as
step detrending technique. We focus our attention on two cases, when the slow
signal is a periodic function mimicking the influence of seasons, and when it
is an aperiodic signal mimicking the influence of a population change (increase
or decrease). For the purpose of computational simplicity the random
fluctuation is taken to be uncorrelated. However, the detrending techniques
here illustrated work also in the case when the random component is correlated.
This expectation is fully confirmed by the sociological applications made in
the companion paper. We also illustrate a new procedure to assess the existence
of a genuine scaling, based on the adoption of diffusion entropy, multiscaling
analysis and the direct assessment of scaling. Using artificial sequences, we
show that the joint use of all these techniques yield the detection of the real
scaling, and that this is independent of the technique used to detrend the
original signal.Comment: 39 pages, 13 figure
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
Heat transfer simulation of evacuated tube collectors (ETC): An application to a prototype
Since fossil fuels shortages are predicted for the forthcoming generations, the use of renewable energy sources is playing a key role and is strongly recommended worldwide by national and international regulations. In this scenario, solar collectors for hot water preparation, space heating and cooling are becoming an increasingly interesting alternative, especially in the building sector because of population growth. Thus, the present paper is addressed to numerically investigate the thermal behaviour of a prototypal evacuated tube by solving the heat transfer differential equations using the Finite Element Method. This is to reproduce the heat transfer process occurring within the real system, helping the industry improve the prototype
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
Non-Poisson dichotomous noise: higher-order correlation functions and aging
We study a two-state symmetric noise, with a given waiting time distribution
, and focus our attention on the connection between the four-time
and the two-time correlation functions. The transition of from
the exponential to the non-exponential 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
Non-Poisson dichotomous noise: higher-order correlation functions and aging
We study a two-state symmetric noise, with a given waiting time distribution
, and focus our attention on the connection between the four-time
and the two-time correlation functions. The transition of from
the exponential to the non-exponential 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
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
Activity autocorrelation in financial markets. A comparative study between several models
We study the activity, i.e., the number of transactions per unit time, of
financial markets. Using the diffusion entropy technique we show that the
autocorrelation of the activity is caused by the presence of peaks whose time
distances are distributed following an asymptotic power law which ultimately
recovers the Poissonian behavior. We discuss these results in comparison with
ARCH models, stochastic volatility models and multi-agent models showing that
ARCH and stochastic volatility models better describe the observed experimental
evidences.Comment: 15 pages, 4 figure
- …