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We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed light on the scenario, we perform a multifractal analysis, which allows highlighting the emergence of many poorly populated symbolic sequences generated by the stochastic fluctuations. We finally make use of this information to reconstruct the noiseless permutation entropy. While this approach works quite well for Hénon and tent maps, it is much less effective in the case of hyperchaos. We argue about the underlying motivations.

The amount of information exchanged per unit of time between two dynamic processes is an important concept for the analysis of complex systems. Theoretical formulations and data-efficient estimators have been recently introduced for this quantity, known as the mutual information rate (MIR), allowing its continuous-time computation for event-based data sets measured as realizations of coupled point processes. This work presents the implementation of MIR for point process applications in Network Physiology and cardiovascular variability, which typically feature short and noisy experimental time series. We assess the bias of MIR estimated for uncoupled point processes in the frame of surrogate data, and we compensate it by introducing a corrected MIR (cMIR) measure designed to return zero values when the two processes do not exchange information. The method is first tested extensively in synthetic point processes including a physiologically-based model of the heartbeat dynamics and the blood pressure propagation times, where we show the ability of cMIR to compensate the negative bias of MIR and return statistically significant values even for weakly coupled processes. The method is then assessed in real point-process data measured from healthy subjects during different physiological conditions, showing that cMIR between heartbeat and pressure propagation times increases significantly during postural stress, though not during mental stress. These results document that cMIR reflects physiological mechanisms of cardiovascular variability related to the joint neural autonomic modulation of heart rate and arterial compliance.

In the effort to communicate modern physics to a vast audience, the flux of cosmic ray muons is commonly mentioned as the most abundant, naturally available particle/radioactivity source. The detection of atmospheric muons can therefore make up a powerful workbench for educational purposes, allowing many laboratory experiences in different topics of modern physics like: special relativity, cosmic rays, statistics and particle detection. Unfortunately, a particle detector being suitable for cosmic ray muon identification is typically expensive, cumbersome and requires high voltage, thus preventing its widespread application in laboratory sessions based on cosmic ray muons, ex.gr. for undergraduate courses. Here we describe the project for a low-cost muon detector based on a plastic scintillator coupled with silicon photomultipliers, whose signals are acquired and preprocessed via a common FPGA evaluation board. Besides the detector, which was developed by supervised master students, we describe some possible physics measurements.

The on-site measurement of the thermal properties of existing building envelopes is of utmost importance to fairly accurately calculate the thermal loss by transmission to the outside environment and so to define the building overall energy performance. This paper presents a preliminary investigation concerning the use of a new indirect method for measuring the thermal characteristics of building materials throughout the year based on the analysis of the material electrical properties. The main goal is to identify a relationship between thermal transmittance, moisture content and electrical impedance through relative electrical permittivity measurements.

The statistical analysis of data stemming from dynamical systems, including, but not limited to, time series, routinely relies on the estimation of information theoretical quantities, most notably Shannon entropy. To this purpose, possibly the most widespread tool is provided by the so-called plug-in estimator, whose statistical properties in terms of bias and variance were investigated since the first decade after the publication of Shannon's seminal works. In the case of an underlying multinomial distribution, while the bias can be evaluated by knowing support and data set size, variance is far more elusive. The aim of the present work is to investigate, in the multinomial case, the statistical properties of an estimator of a parameter that describes the variance of the plug-in estimator of Shannon entropy. We then exactly determine the probability distributions that maximize that parameter. The results presented here allow to set upper limits to the uncertainty of entropy assessments under the hypothesis of memoryless underlying stochastic processes., 9 pages, 5 figures. Published in Physical Review E

The task of identifying and characterizing network structures out of experimentally observed time series is tackled by implementing different solutions, ranging from entropy-based techniques to the evaluation of the significance of observed correlation estimators. Among the metrics that belong to the first class, mutual information is of major importance due to the relative simplicity of implementation and its relying on the crucial concept of entropy. With regard to the second class, a method that allows us to assess the connectivity strength of a link in terms of a time scale of its observability via the significance estimate of measured cross correlation was recently shown to provide a reliable tool to study network structures. In this paper, we investigate the relationship between this last metric and mutual information by simultaneously assessing both metrics on large sets of data extracted from three experimental contexts, human brain magnetoencephalography, human brain electroencephalography, and surface wind measurements carried out on a small regional scale, as well as on simulated coupled, auto-regressive processes. We show that the relationship is well described by a power law and provide a theoretical explanation based on a simple noise and signal model. Besides further upholding the reliability of cross-correlation time scale of observability, the results show that the combined use of this metric and mutual information can be used as a valuable tool to identify and characterize connectivity links in a wide range of experimental contexts.

Detection of chaos in experimental data is a crucial issue in nonlinear science. Historically, one of the first evidences of a chaotic behavior in experimental recordings came from laser physics. In a recent work, a Minimal Universal Model of chaos was developed by revisiting the model of laser with feedback, and a first electronic implementation was discussed. Here, we propose an upgraded electronic implementation of the Minimal Universal Model, which allows for a precise and reproducible analysis of the model’s parameters space. As a marker of a possible chaotic behavior the variability of the spiking activity that characterizes one of the system’s coordinates was used. Relying on a numerical characterization of the relationship between spiking activity and maximum Lyapunov exponent at different parameter combinations, several potentially chaotic settings were selected. The analysis via divergence exponent method of experimental time series acquired by using those settings confirmed a robust chaotic behavior and provided values of the maximum Lyapunov exponent that are in very good agreement with the theoretical predictions. The results of this work further uphold the reliability of the Minimal Universal Model. In addition, the upgraded electronic implementation provides an easily controllable setup that allows for further developments aiming at coupling multiple chaotic systems and investigating synchronization processes.

The detection of an underlying chaotic behavior in experimental recordings is a longstanding issue in the field of nonlinear time series analysis. Conventional approaches require the assessment of a suitable dimension and lag pair to embed a given input sequence and, thereupon, the estimation of dynamical invariants to characterize the underlying source. In this work, we propose an alternative approach to the problem of identifying chaos, which is built upon an improved method for optimal embedding. The core of the new approach is the analysis of an input sequence on a lattice of embedding pairs whose results provide, if any, evidence of a finite-dimensional, chaotic source generating the sequence and, if such evidence is present, yield a set of equivalently suitable embedding pairs to embed the sequence. The application of this approach to two experimental case studies, namely, an electronic circuit and magnetoencephalographic recordings of the human brain, highlights how it can make up a powerful tool to detect chaos in complex systems.

The possibility of using microRNA (miRNA) levels as diagnostic and prognostic tools to detect different pathologies requires the implementation of reliable classifiers, whose training and use call for quality control of data corresponding to miRNA expression. In this work we present the MiRNA-QC-and-Diagnosis package. The package provides a set of functions for the R environment that implement the required quality control steps and thereupon allow to train, use and optimize a Bayesian classifier for diagnosis based on the measured miRNA expressions. The package thus makes up a complete and dedicated analytical toolbox for miRNA-based diagnosis.

The divergence rate method, which is used to determine the maximum Lyapunov exponent out of time series, is based on the evaluation of the time-dependent divergence exponent. For chaotic systems and in the small time regime, this exponent grows linearly in time. The asymptotic regime is instead characterized by a time-independent behavior due to the system eventually losing its memory of the starting conditions. The amplitude of this "plateau"-like divergence exponent depends both on the choice of the embedding dimension and lag and on the maximum distance of nearby starting trajectories in a way that is characteristic of the underlying dynamical system. In this paper, upon introducing the basic mathematical tools, we address the plateau evaluation for two classes of time series, those generated by a white noise source and those generated by a finite-dimensional chaotic system. The different behavior provides a novel tool to distinguish purely stochastic sources from deterministic ones, as well as to provide a precise estimate of the correlation dimension in the latter case. The method is also sensitive to correlated noise sources.

Lung cancer is still one of the leading cause of death worldwide. The clinical variability of lung cancer is high and drives treatment decision. In this context, correct discrimination of pulmonary neuroendocrine tumors is still of critical relevance. The spectrum of neuroendocrine tumors is various, and each type has molecular and phenotypical differences. In order to advance in the discrimination of neuroendocrine from non-neuroendocrine lung tumors, we tested a series of 95 surgically resected and formalin-fixed paraffin embedded lung cancer tissues, and we analyzed the expression of miR205-5p and miR375-3p via TaqMan RT-qPCR. Via a robust mathematical approach, we excluded technical outliers increasing the data reproducibility. We found that miR375-3p levels are higher in low-grade neuroendocrine lung tumor samples compared to non-neuroendocrine lung tumors. However, miR375-3p is not able to distinguish among different types of neuroendocrine lung tumors. In this work, we provide a new molecular marker for distinguishing non-neuroendocrine from low-grade neuroendocrine lung tumors samples establishing an easy miRNA score to be used in clinical settings, enabling the pathologist to classify more accurately lung tumors biopsies, which may be ambiguously cataloged in routine examination.

In any network, the dependence of connectivity on physical distance between nodes is a direct consequence of trade-off mechanisms between costs of establishing and sustaining links, processing rates, propagation speed of signals between nodes. Despite its universality, there are still few studies addressing this issue. Here we apply a recently–developed method to infer links between nodes, and possibly subnetwork structures, to determine connectivity strength as a function of physical distance between nodes. The model system we investigate is brain activity reconstructed on the cortex out of magnetoencephalography recordings sampled on a set of healthy subjects in resting state. We found that the dependence of the time scale of observability of a link on its geometric length follows a power–law characterized by an exponent whose extent is inversely proportional to connectivity. Our method provides a new tool to highlight and investigate networks in neuroscience.

The central limit theorem for Markov chains is widely used, in particular in its pristine univariate form. As far as the multivariate case is concerned, a few proofs exist, which depend on different assumptions and require advanced mathematical and statistical tools. Here a novel proof is presented that, starting from the standard condition of regularity only, relies on time-independent quantum-mechanical perturbation theory. The result, which is obtained by using techniques that are typical of physics, is expected to enhance the usability of this cornerstone theorem, especially in nonlinear dynamics and physics of complex systems.

The study of many dynamical systems relies on the analysis of experimentally-recorded sequences of events for which information is encoded in the sequence of interevent intervals. A correct interpretation of the results of the application of analytical techniques to these sequences requires the assessment of statistical significance. In most cases, the corresponding null-hypothesis distribution is unknown, thus forbidding an evaluation of the significance. An alternative solution, which is efficient in the case of continuous signals, is provided by the generation of surrogate data that share statistical and spectral properties with the original dataset. However, in the case of event sequences, the available algorithms for the generation of surrogate data can become cumbersome and computationally demanding. In this work, we present a new method for the generation of surrogate event sequences that relies on the joint distribution of successive interevent intervals. Our method, which was tested on both synthetic and experimental sequences, performs equally well or even better than conventional methods in terms of interevent interval distribution and autocorrelation while abating the computational time by at least one order of magnitude.

The purpose of this study was to develop an easy and minimally invasive assay to detect a plasma miRNA profile in frontotemporal dementia (FTD) patients, with the final aim of discriminating between FTD patients and healthy controls (HCs). After a global miRNA profiling, significant downregulation of miR-663a, miR-502-3p, and miR-206 (p = 0.0001, p = 0.0002, and p = 0.02 respectively) in FTD patients was confirmed when compared with HCs in a larger case-control sample. Moreover, miR-663a and miR-502-3p showed significant differences in both genders, whereas miR-206, only in male subjects. To obtain a discriminating measure between FTD patients and HCs, we calculated a combined score of the 3 miRNAs by applying a Bayesian approach and obtaining a classifier with an accuracy of 84.4%. Moreover, for men, combined miRNA levels showed an excellent sensitivity (100%) and a good specificity (87.5%) in distinguishing FTD patients from HCs. All these findings open new hypotheses in the pathophysiology and new perspectives in the diagnosis of a complex pathology as FTD.

Fractal structures pervade nature and are receiving increasing engineering attention towards the realization of broadband resonators and antennas. We show that fractal resonators can support the emergence of high-dimensional chaotic dynamics even in the context of an elementary, single-transistor oscillator circuit. Sierpi\'nski gaskets of variable depth are constructed using discrete capacitors and inductors, whose values are scaled according to a simple sequence. It is found that in regular fractals of this kind each iteration effectively adds a conjugate pole/zero pair, yielding gradually more complex and broader frequency responses, which can also be implemented as much smaller Foster equivalent networks. The resonators are instanced in the circuit as one-port devices, replacing the inductors found in the initial version of the oscillator. By means of a highly simplified numerical model, it is shown that increasing the fractal depth elevates the dimension of the chaotic dynamics, leading to high-order hyperchaos. This result is overall confirmed by SPICE simulations and experiments, which however also reveal that the non-ideal behavior of physical components hinders obtaining high-dimensional dynamics. The issue could be practically mitigated by building the Foster equivalent networks rather than the verbatim fractals. Furthermore, it is shown that considerably more complex resonances, and consequently richer dynamics, can be obtained by rendering the fractal resonators irregular through reshuffling the inductors, or even by inserting a limited number of focal imperfections. The present results draw attention to the potential usefulness of fractal resonators for generating high-dimensional chaotic dynamics, and underline the importance of irregularities and component non-idealities.

Alzheimer’s disease (AD) is a neurodegenerative disease. It is a growing concern, demanding the attention of families, scientists, and pharmaceutical companies due to its devastating impacts on patients. The disease is believed to be triggered by pathogenic amyloid beta protein (Aβ) formations in the brain. In order to understand the protein production and the plaque formation in the AD brain, we specifically focused on the ‘Amyloid Cascade Hypothesis,’ which explains the biological pathways and the players in the disease. Focusing on the macro-side, we modelled the progression of AD from neurodevelopment (healthy brain) to neurodegeneration (the disease state) by using the agent based computer simulation program called COBWEB. Our model begins with healthy, developing neurons thriving in the hippocampus and cerebrospinal fluid (CSF) working efficiently. The brain ages throughout the adulthood phase. The onset of the disease and its progression is modelled with plaque formation, a decline in neuron counts, and an inefficient cleaning mechanism close to the end of the experiment. We conclude that our model fulfills its purpose: to provide a visual contrast between health and disease through the slow progression of AD in real time, increasing one’s understanding of this illness. Its accuracy is attributed to Aβ plaque formation, neuronal death, and CSF deterioration. Future projects include testing, designing, and refining new treatments using this model, diminishing the barrier to entry for new ideas, and providing a new tool for teaching AD.La maladie d’Alzheimer (MA) est une maladie neurodégénérative. Elle est un souci croissant, exigeant l’attention des familles, des scientifiques et des sociétés pharmaceutiques en raison de ses effets dévastateurs sur les patients. Nous pensons que la maladie est provoquée par la formation pathogénique de la protéine bêta amyloïde (Aß) dans le cerveau. Afin de comprendre la production de la protéine et la formation de plaques dans le cerveaud’un patient atteint de MA, nous avons mis l’accent spécifiquement sur l’hypothèse de la cascade amyloïde, ce qui explique les voies biologiques et les acteurs impliqués dans la maladie. En nous concentrant sur la macroscopie, nous avons modélisé la progression de la MA du début du neurodéveloppement (le cerveau en bonne santé) à la neurodégénérescence (l’état de la maladie) en utilisant le programme de simulation numérique basé sur un agent appelé COBWEB. Notre modèle commence avec des neurones qui se développent normalement, grandissant dans l’hippocampe et le liquide céphalo-rachidien (LCR) et travaillant efficacement. Le cerveau vieillit tout au long de la phase adulte. L’apparition de la maladie et de sa progression est modélisée avec la formation des plaques, une diminution du nombre neurones, et un mécanisme de nettoyage inefficace près de la fin. Nous concluons que notre modèle répond à son but de fournir un contraste visuel entre la santé et la maladie à travers la lente progression de la MA en temps réel, ce qui augmente notre compréhension de la MA. Sa précision est attribuée à la formation de plaques Aß, la mort neuronale et la détérioration du LCR. Les projets futurs incluent des tests, la conception et le raffinage de nouveaux traitements en utilisant ce modèle, ce qui diminue la barrière à l’entrée pour de nouvelles idées, et de fournir un nouvel outil pour enseigner la MA.