arXiv subjects
Publications and source records attributed to Nicola Scafetta.
This paper presents a wavelet multiresolution analysis of a time series dataset to study the correlation between the real temperature data and three temperature model reconstructions at different scales. We show that the Mann et.al. model reconstructs the temperature better at all temporal resolutions. We show and discuss the wavelet multiresolution analysis of the Mann's temperature reconstruction for the period from 1400 to 2000 A.D.E.
The methods currently used to determine the scaling exponent of a complex dynamic process described by a time series are based on the numerical evaluation of variance. This means that all of them can be safely applied only to the case where ordinary statistical properties hold true even if strange kinetics are involved. We illustrate a method of statistical analysis based on the Shannon entropy of the diffusion process generated by the time series, called Diffusion Entropy Analysis (DEA). We adopt artificial Gauss and Lévy time series, as prototypes of ordinary and anomalus statistics, respectively, and we analyse them with the DEA and four ordinary methods of analysis, some of which are very popular. We show that the DEA determines the correct scaling exponent even when the statistical properties, as well as the dynamic properties, are anomalous. The other four methods produce correct results in the Gauss case but fail to detect the correct scaling in the case of Lévy statistics.
We analyze the waiting time distribution of time distances $τ$ between two nearest-neighbor flares. This analysis is based on the joint use of two distinct techniques. The first is the direct evaluation of the distribution function $ψ(τ)$, or of the probability, $Ψ(tau)$, that no time distance smaller than a given $τ$ is found. We adopt the paradigm of the inverse power law behavior, and we focus on the determination of the inverse power index $μ$, without ruling out different asymptotic properties that might be revealed, at larger scales, with the help of richer statistics. The second technique, called Diffusion Entropy (DE) method, rests on the evaluation of the entropy of the diffusion process generated by the time series. The details of the diffusion process depend on three different walking rules, which determine the form and the time duration of the transition to the scaling regime, as well as the scaling parameter $δ$. With the first two rules the information contained in the time series is transmitted, to a great extent, to the transition, as well as to the scaling regime. The same information is essentially conveyed, by using the third rules, into the scaling regime, which, in fact, emerges very quickly after a fast transition process. We show that the significant information hidden within the time series concerns memory induced by the solar cycle, as well as the power index $μ$. The scaling parameter $δ$ becomes a simple function of $μ$, when memory is annihilated. Thus, the three walking rules yield a unique and precise value of $μ$ if the memory is wisely taken under control, or cancelled by shuffling the data. All this makes compelling the conclusion that $μ= 2.138 \pm 0.01$.
We propose a new method of statistical analysis of nucleotide sequences yielding the true scaling without requiring any form of de-trending. With the help of artificial sequences that are proved to be statistically equivalent to the real DNA sequences we find that power-law correlations are present in both coding and non-coding sequences, in accordance with the recent work of other authors. We also afford a compelling evidence that these long-range correlations generate Lévy statistics in both types of sequences.
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 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 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.
In the case of fully chaotic systems the distribution of the Poincare'recurrence times is an exponential whose decay rate is the Kolmogorov-Sinai(KS) entropy.We address the discussion of the same problem, the connection between dynamics and thermodynamics,in the case of sporadic randomness,using the Manneville map as a prototype of this class of processes. We explore the possibility of relating the distribution of Poincare' recurrence times to `thermodynamics',in the sense of the KS entropy,also in the case of an inverse power law. This is the dynamic property that Zaslavsly [Phys.Today(8), 39(1999)] finds to be responsible for a striking deviation from ordinary statistical mechanics under the form of Maxwell's Demon effect. We show that this way of estabi- lishing a connection between thermodynamics and dynamics is valid only in the case of strong chaos. In the case of sporadic randomness, resulting at long times in the Levy diffusion processes,the sensitivity to initial conditions is initially an inverse pow erlaw,but it becomes exponential in the long-time scale, whereas the distribution of Poincare times keeps its inverse power law forever. We show that a nonextensive thermodynamics would imply the Maxwell's Demon effect to be determined by memory and thus to be temporary,in conflict with the dynamic approach to Levy statistics. The adoption of heuristic arguments indicates that this effect,is possible, as a form of genuine equilibrium,after completion of the process of memory erasure.