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

Facing Non-Stationary Conditions with a New Indicator of Entropy Increase: The Cassandra Algorithm

We address the problem of detecting non-stationary effects in time series (in particular fractal time series) by means of the Diffusion Entropy Method (DEM). This means that the experimental sequence under study, of size $N$, is explored with a window of size $L << N$. The DEM makes a wise use of the statistical information available and, consequently, in spite of the modest size of the window used, does succeed in revealing local statistical properties, and it shows how they change upon moving the windows along the experimental sequence. The method is expected to work also to predict catastrophic events before their occurrence.Comment: FRACTAL 2002 (Spain

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

Memory beyond memory in heart beating: an efficient way to detect pathological conditions

We study the long-range correlations of heartbeat fluctuations with the method of diffusion entropy. We show that this method of analysis yields a scaling parameter $\delta$ that apparently conflicts with the direct evaluation of the distribution of times of sojourn in states with a given heartbeat frequency. The strength of the memory responsible for this discrepancy is given by a parameter $\epsilon^{2}$, which is derived from real data. The distribution of patients in the ($\delta$, $\epsilon^{2}$)-plane yields a neat separation of the healthy from the congestive heart failure subjects.Comment: submitted to Physical Review Letters, 5 figure

Survey of hyperfine structure measurements in alkali atoms

The spectroscopic hyperfine constants for all the alkali atoms are reported. For atoms from lithium to cesium, only the long lived atomic isotopes are examined. For francium, the measured data for nuclear ground states of all available isotopes are listed. All results obtained since the beginning of laser investigations are presented, while for previous works the data of Arimondo {\it et. al.} Rev. Mod. Phys. 49, 31 (1977) are recalled. Global analyses based on the scaling laws and on the hyperfine anomalies are performed.Comment: 41 pages, 5 figure

Down-Hole Heat Exchangers: Modelling of a Low-Enthalpy Geothermal System for District Heating

In order to face the growing energy demands, renewable energy sources can provide an alternative to fossil fuels. Thus, low-enthalpy geothermal plants may play a fundamental role in those areas—such as the Province of Viterbo—where shallow groundwater basins occur and conventional geothermal plants cannot be developed. This may lead to being fuelled by locally available sources. The aim of the present paper is to exploit the heat coming from a low-enthalpy geothermal system. The experimental plant consists in a down-hole heat exchanger for civil purposes and can supply thermal needs by district heating. An implementation in MATLAB environment is provided in order to develop a mathematical model. As a consequence, the amount of withdrawable heat can be successfully calculated

Purine-metabolising enzymes and apoptosis in cancer

The enzymes of both de novo and salvage pathways for purine nucleotide synthesis are regulated to meet the demand of nucleic acid precursors during proliferation. Among them, the salvage pathway enzymes seem to play the key role in replenishing the purine pool in dividing and tumour cells that require a greater amount of nucleotides. An imbalance in the purine pools is fundamental not only for preventing cell proliferation, but also, in many cases, to promote apoptosis. It is known that tumour cells harbour several mutations that might lead to defective apoptosis-inducing pathways, and this is probably at the basis of the initial expansion of the population of neoplastic cells. Therefore, knowledge of the molecular mechanisms that lead to apoptosis of tumoural cells is key to predicting the possible success of a drug treatment and planning more effective and focused therapies. In this review, we describe how the modulation of enzymes involved in purine metabolism in tumour cells may affect the apoptotic programme. The enzymes discussed are: ectosolic and cytosolic 5′-nucleotidases, purine nucleoside phosphorylase, adenosine deaminase, hypoxanthine-guanine phosphoribosyltransferase, and inosine-5′-monophosphate dehydrogenase, as well as recently described enzymes particularly expressed in tumour cells, such as deoxynucleoside triphosphate triphosphohydrolase and 7,8-dihydro-8-oxoguanine triphosphatase