Is there long-range memory in solar activity on time scales shorter than the sunspot period?

The sunspot number (SSN), the total solar irradiance (TSI), a TSI reconstruction, and the solar flare index (SFI), are analyzed for long-range persistence (LRP). Standard Hurst analysis yields $H \approx 0.9$, which suggests strong LRP. However, solar activity time series are non-stationary due to the almost periodic 11 year smooth component, and the analysis does not give the correct $H$ for the stochastic component. Better estimates are obtained by detrended fluctuations analysis (DFA), but estimates are biased and errors are large due to the short time records. These time series can be modeled as a stochastic process of the form $x(t)=y(t)+\sigma \sqrt{y(t)}\, w_H(t)$, where $y(t)$ is the smooth component, and $w_H(t)$ is a stationary fractional noise with Hurst exponent $H$. From ensembles of numerical solutions to the stochastic model, and application of Bayes' theorem, we can obtain bias and error bars on $H$ and also a test of the hypothesis that a process is uncorrelated ($H=1/2$). The conclusions from the present data sets are that SSN, TSI and TSI reconstruction almost certainly are long-range persistent, but with most probable value $H\approx 0.7$. The SFI process, however, is either very weakly persistent ($H<0.6$) or completely uncorrelated. Some differences between stochastic properties of the TSI and its reconstruction indicate some error in the reconstruction scheme.Comment: 23 pages, 12 figure

Predictive biomarkers for checkpoint inhibitor-based immunotherapy: The Galectin-3 signature in NSCLCs

Checkpoint inhibitor-based immunotherapy is opening a promising scenario in oncology, with objective responses registered in multiple cancer types. However, reliable predictive markers of tumor responsiveness are still lacking. These markers need to be urgently identified for a better selection of patients that can be candidates for immunotherapy. In this pilot study, a cohort of 34 consecutive patients bearing programmed death-ligand 1 (PD-L1)-positive non-small cell lung carcinoma (NSCLC), treated with pembrolizumab, was considered. The retrospective immuno-phenotypic analysis performed on the original tumor biopsies allowed for the identification of a specific “galectin signature”, which strongly correlated with tumor responsiveness to anti PD-1 immunotherapy. We observed that the large majority of patients (about 90%) with high galectin-3 tumor expression (score 3+) showed an early and dramatic progression of the disease after three cycles of treatments. In contrast, all patients with negative or low/intermediate expression of galectin-3 in tumor cells showed an early and durable objective response to pembrolizumab, indicating galectin-3 as an interesting predictive marker of tumor responsiveness. The galectin-3 signature, at least in NSCLCs, promises a better selection of patient candidates for immunotherapy, reducing unnecessary treatment exposures and social costs. A large multicenter study is ongoing to validate this finding

Scaling detection in time series: diffusion entropy analysis

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 L\'{e}vy 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 L\'{e}vy statistics.Comment: 21 pages,10 figures, 1 tabl

Compression and diffusion: a joint approach to detect complexity

The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are a manifestation of system dynamics whose rules are either unknown or too complex for a mathematical treatment, is still a challenge since the KS entropy is not computable, in general, in that case. Here we present a plan of action based on the joint action of two procedures, both related to the KS entropy, but compatible with computer implementation through fast and efficient programs. The former procedure, called Compression Algorithm Sensitive To Regularity (CASToRe), establishes the amount of order by the numerical evaluation of algorithmic compressibility. The latter, called Complex Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA), establishes the complexity degree through the numerical evaluation of the strength of an anomalous effect. This is the departure, of the diffusion process generated by the observed fluctuations, from ordinary Brownian motion. The CASSANDRA algorithm shares with CASToRe a connection with the Kolmogorov complexity. This makes both algorithms especially suitable to study the transition from dynamics to thermodynamics, and the case of non-stationary time series as well. The benefit of the joint action of these two methods is proven by the analysis of artificial sequences with the same main properties as the real time series to which the joint use of these two methods will be applied in future research work.Comment: 27 pages, 9 figure

Diffusion entropy and waiting time statistics of hard x-ray solar flares

We analyze the waiting time distribution of time distances $\tau$ 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 $\psi(\tau)$, or of the probability, $\Psi(tau)$, that no time distance smaller than a given $\tau$ is found. We adopt the paradigm of the inverse power law behavior, and we focus on the determination of the inverse power index $\mu$, 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 $\delta$. 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 $\mu$. The scaling parameter $\delta$ becomes a simple function of $\mu$, when memory is annihilated. Thus, the three walking rules yield a unique and precise value of $\mu$ if the memory is wisely taken under control, or cancelled by shuffling the data. All this makes compelling the conclusion that $\mu = 2.138 \pm 0.01$.Comment: 23 pages, 13 figure

L\'{e}vy scaling: the Diffusion Entropy Analysis applied to DNA sequences

We address the problem of the statistical analysis of a time series generated by complex dynamics with a new method: the Diffusion Entropy Analysis (DEA) (Fractals, {\bf 9}, 193 (2001)). This method is based on the evaluation of the Shannon entropy of the diffusion process generated by the time series imagined as a physical source of fluctuations, rather than on the measurement of the variance of this diffusion process, as done with the traditional methods. We compare the DEA to the traditional methods of scaling detection and we prove that the DEA is the only method that always yields the correct scaling value, if the scaling condition applies. Furthermore, DEA detects the real scaling of a time series without requiring any form of de-trending. We show that the joint use of DEA and variance method allows to assess whether a time series is characterized by L\'{e}vy or Gauss statistics. We apply the DEA to the study of DNA sequences, and we prove that their large-time scales are characterized by L\'{e}vy statistics, regardless of whether they are coding or non-coding sequences. We show that the DEA is a reliable technique and, at the same time, we use it to confirm the validity of the dynamic approach to the DNA sequences, proposed in earlier work.Comment: 24 pages, 9 figure

Peribiliary glands as a niche of extra-pancreatic precursors yielding insulin-producing cells in experimental and human diabetes

Peribiliary glands (PBGs) are niches in the biliary tree and containing heterogeneous endodermal stem/progenitors cells that can differentiate, in vitro and in vivo, towards pancreatic islets. The aim of this study was to evaluate, in experimental and human diabetes, proliferation of cells in PBGs and differentiation of the biliary tree stem/progenitor cells (BTSCs) towards insulin-producing cells. Diabetes was generated in mice by intraperitoneal injection of a single dose of 200 mg/kg (N=12) or 120 mg/kg (N=12) of streptozotocin. Liver, pancreas and extrahepatic biliary trees were en bloc dissected and examined. Cells in PBGs proliferated in experimental diabetes, and their proliferation was greatest in the PBGs of the hepato-pancreatic ampulla, and inversely correlated with the pancreatic islet area. In rodents, the cell proliferation in PBGs was characterized by the expansion of Sox9-positive stem/progenitor cells that gave rise to insulin-producing cells. Insulin-producing cells were located mostly in PBGs in the portion of the biliary tree closest to the duodenum, and their appearance was associated with up-regulation of MafA and Gli1 gene expression. In patients with type 2 diabetes, PBGs at the level of the hepato-pancreatic ampulla contained cells showing signs of proliferation and pancreatic fate commitment. In vitro, high glucose concentrations induced the differentiation of human BTSCs cultures towards pancreatic beta cell fates. The cells in PBGs respond to diabetes with proliferation and differentiation towards insulin-producing cells indicating that PBG niches may rescue pancreatic islet impairment in diabetes. These findings offer important implications for the patho-physiology and complications of this disease. This article is protected by copyright. All rights reserved

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

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

Solar Flare Intermittency and the Earth's Temperature Anomalies

We argue that earth's short-term temperature anomalies and the solar flare intermittency are linked. The analysis is based upon the study of the scaling of both the spreading and the entropy of the diffusion generated by the fluctuations of the temperature time series. The joint use of these two methods evidences the presence of a L\'{e}vy component in the temporal persistence of the temperature data sets that corresponds to the one that would be induced by the solar flare intermittency. The mean monthly temperature datasets cover the period from 1856 to 2002.Comment: 4 pages, 5 figure