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2021 Report Open Access OPEN

SI-Lab Annual Research Report 2020
Leone G. R., Righi M., Carboni A., Caudai C., Colantonio S., Kuruoglu E. E., Leporini B., Magrini M., Paradisi P., Pascali M. A., Pieri G., Reggiannini M., Salerno E., Scozzari A., Tonazzini A., Fusco G., Galesi G., Martinelli M., Pardini F., Tampucci M., Buongiorno R., Bruno A., Germanese D., Matarese F., Coscetti S., Coltelli P., Jalil B., Benassi A., Bertini G., Salvetti O., Moroni D.
The Signal & Images Laboratory (http://si.isti.cnr.it/) is an interdisciplinary research group in computer vision, signal analysis, smart vision systems and multimedia data understanding. It is part of the Institute for Information Science and Technologies of the National Research Council of Italy. This report accounts for the research activities of the Signal and Images Laboratory of the Institute of Information Science and Technologies during the year 2020.Source: ISTI Technical Report, ISTI-2021-TR/009, pp.1–38, 2021
DOI: 10.32079/isti-tr-2021/009

See at: ISTI Repository Open Access | CNR ExploRA Open Access


2020 Contribution to conference Open Access OPEN

Augmented reality and intelligent systems in Industry 4.0
Benassi A., Carboni A., Colantonio S., Coscetti S., Germanese D., Jalil B., Leone R., Magnavacca J., Magrini M., Martinelli M., Matarese F., Moroni D., Paradisi P., Pardini F., Pascali M., Pieri G., Reggiannini M., Righi M., Salvetti O., Tampucci M.
Augmented reality and intelligent systems in Industry 4.0 - Presentazione ARTESSource: ARTES, 12/11/2020
DOI: 10.5281/zenodo.4277713
DOI: 10.5281/zenodo.4277712

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2020 Conference article Open Access OPEN

Pilot study on music-heart entrainment in a pianist during a live performance
Sebastiani L., Magrini M., Orsini P., Mastorci F., Pingitore A., Paradisi P.
Entrainment between music features and heart rhythms have been reported but, to date, evidence in support of music-heart synchronization are still inconsistent. We studied the possible music-heart entrainment in a skilled pianist during a live performance before an audience. We recorded ECG before and during the concert. We derived the beat-to-beat RR time series and analyzed heart rate variability in the time domain and with non linear analysis, to evaluate the autonomic changes associated with 4 different music pieces. Results indicated an autonomic modulation specific for each piece and the decrease and increase of parasympathetic and sympathetic tone across the whole session. Also, for each music piece, analysis of correlation between the music envelope and the RR series revealed a negative correlation which could be the expression of the entrainment of music on heart rhythm.Source: 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities (ESGCO 2020), pp. 1–2, Pisa, 15 July 2020
DOI: 10.1109/esgco49734.2020.9158149

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2019 Journal article Open Access OPEN

A Hypothesis about parallelism vs. seriality in dreams
Barcaro U., Paradisi P., Sebastiani L.
The process of dream building implies the construction of a complex network of closely interrelated sources. On the other hand, the dream experience develops as a succession of events. In this paper a hypothesis is advanced about how the psycho-physiological system of dream building, which is distributed, acts to provide a serial output. This hypothesis is basically connected with the property, enjoyed by the dream experience, of simultaneously representing a plurality of meanings.Source: Frontiers in Psychology 10 (2019): 2299-1–2299-4. doi:10.3389/fpsyg.2019.02299
DOI: 10.3389/fpsyg.2019.02299

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2019 Journal article Open Access OPEN

Gaussian processes in complex media: new vistas on anomalous diffusion
Di Tullio F., Paradisi P., Spigler R., Pagnini G.
Normal or Brownian diffusion is historically identified by the linear growth in time of the variance and by a Gaussian shape of the displacement distribution. Processes departing from the at least one of the above conditions defines anomalous diffusion, thus a nonlinear growth in time of the variance and/or a non-Gaussian displacement distribution. Motivated by the idea that anomalous diffusion emerges from standard diffusion when it occurs in a complex medium, we discuss a number of anomalous diffusion models for strongly heterogeneous systems. These models are based on Gaussian processes and characterized by a population of scales, population that takes into account the medium heterogeneity. In particular, we discuss diffusion processes whose probability density function solves space- and time-fractional diffusion equations through a proper population of time-scales or a proper population of length-scales. The considered modeling approaches are: the continuous time random walk, the generalized gray Brownian motion, and the time-subordinated process. The results show that the same fractional diffusion follows from different populations when different Gaussian processes are considered. The different populations have the common feature of a large spreading in the scale values, related to power-law decay in the distribution of population itself. This suggests the key role of medium properties, embodied in the population of scales, in the determination of the proper stochastic process underlying the given heterogeneous medium.Source: Frontiers in Physics 7 (2019): 123-1–123-11. doi:10.3389/fphy.2019.00123
DOI: 10.3389/fphy.2019.00123

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2019 Journal article Open Access OPEN

Finite-energy Levy-type motion through heterogeneous ensemble of Brownian particles
Sliusarenko O. Y., Vitali S., Sposini V., Paradisi P., Chechkin A., Castellani G., Pagnini G.
Complex systems are known to display anomalous diffusion, whose signature is a space/time scaling x similar to t(delta) with delta not equal 1/2 in the probability density function (PDF). Anomalous diffusion can emerge jointly with both Gaussian, e.g. fractional Brownian motion, and power-law decaying distributions, e.g. Levy Flights or Levy Walks (LWs). Levy flights get anomalous scaling, but, being jumps of any size allowed even at short times, have infinite position variance, infinite energy and discontinuous paths. LWs, which are based on random trapping events, overcome these limitations: they resemble a Levy-type power-law distribution that is truncated in the large displacement range and have finite moments, finite energy and, even with discontinuous velocity, they are continuous. However, LWs do not take into account the role of strong heterogeneity in many complex systems, such as biological transport in the crowded cell environment. In this work we propose and discuss a model describing a heterogeneous ensemble of Brownian particles (HEBP). Velocity of each single particle obeys a standard underdamped Langevin equation for the velocity, with linear friction term and additive Gaussian noise. Each particle is characterized by its own relaxation time and velocity diffusivity. We show that, for proper distributions of relaxation time and velocity diffusivity, the HEBP resembles some LW statistical features, in particular power-law decaying PDF, long-range correlations and anomalous diffusion, at the same time keeping finite position moments and finite energy. The main differences between the HEBP model and two different LWs are investigated, finding that, even when both velocity and position PDFs are similar, they differ in four main aspects: (i) LWs are biscaling, while HEBP is monoscaling; (ii) a transition from anomalous (delta = 1/2) to normal (delta = 1/2) diffusion in the long-time regime is seen in the HEBP and not in LWs; (iii) the power-law index of the position PDF and the space/time diffusion scaling are independent in the HEBP, while they both depend on the scaling of the interevent time PDF in LWs; (iv) at variance with LWs, our HEBP model obeys a fluctuation-dissipation theorem.Source: Journal of physics. A, Mathematical and theoretical (Print) 52 (2019). doi:10.1088/1751-8121/aafe90
DOI: 10.1088/1751-8121/aafe90

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2018 Journal article Open Access OPEN

Langevin equation in complex media and anomalous diffusion
Vitali S., Sposini V., Sliusarenko O., Paradisi P., Castellani G., Pagnini G.
The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modelling approaches for the description of anomalous diffusion in biological systems, such as the very complex and heterogeneous cell environment. Nevertheless, many questions are still open, such as the joint manifestation of statistical features in agreement with different models that can also be somewhat alternative to each other, e.g. continuous time random walk and fractional Brownian motion. To overcome these limitations, we propose a stochastic diffusion model with additive noise and linear friction force (linear Langevin equation), thus involving the explicit modelling of velocity dynamics. The complexity of the medium is parametrized via a population of intensity parameters (relaxation time and diffusivity of velocity), thus introducing an additional randomness, in addition to white noise, in the particle's dynamics. We prove that, for proper distributions of these parameters, we can get both Gaussian anomalous diffusion, fractional diffusion and its generalizations.Source: Journal of the Royal Society interface (Print) 15 (2018). doi:10.1098/rsif.2018.0282
DOI: 10.1098/rsif.2018.0282

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2018 Journal article Open Access OPEN

Centre-of-mass like superposition of Ornstein-Uhlenbeck processes: A pathway to non-autonomous stochastic differential equations and to fractional diffusion
D'Ovidio M., Vitali S., Sposini V., Sliusarenko O., Paradisi P., Castellani G., Pagnini G.
We consider an ensemble of Ornstein-Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass like variable corresponding to this ensemble is statistically equivalent to a process driven by a non-autonomous stochastic differential equation with time-dependent drift and a white noise. In particular, the time scaling and the density function of such variable are driven by the population of timescales and of noise amplitudes, respectively. Moreover, we show that this variable is equivalent in distribution to a randomly-scaled Gaussian process, i.e., a process built by the product of a Gaussian process times a non-negative independent random variable. This last result establishes a connection with the so-called generalized grey Brownian motion and suggests application to model fractional anomalous diffusion in biological systems.Source: Fractional Calculus & Applied Analysis (Print) 21 (2018): 1420–1435. doi:10.1515/fca-2018-0074
DOI: 10.1515/fca-2018-0074

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2017 Contribution to book Open Access OPEN

A low cost, portable device for breath analysis and self-monitoring, the Wize sniffer
Germanese D., Righi M., Benassi A., D'Acunto M., Leone R., Magrini M., Paradisi P., Puppi D., Salvetti O.
Here we describe the implementation of the first prototype of the Wize Sniffer 1.x (WS 1.x), a low cost, portable electronic device for breath analysis. The device is being developed in the framework of the Collaborative European Project SEMEOTICONS (SEMEiotic Oriented Technology for Individuals CardiOmetabolic risk self-assessmeNt and Self-monitoring). In the frame of SEMEOTICONS project, the Wize Sniffer will help the user monitor his/her state of health, in particular giving feedbacks about those noxious habits for cardio-metabolic risk, such as alcohol intake and smoking. The low cost and compactness of the device allows for a daily screening that, even if without a real diagnostic meaning, could represent a pre-monitoring, useful for an optimal selection of more sophisticated and standard medical analysis.Source: Applications in Electronics Pervading Industry, Environment and Society, edited by Alessandro De Gloria, pp. 51–57. CH-6330 Cham (ZG): Springer International Publishing, 2017
DOI: 10.1007/978-3-319-47913-2_7
Project(s): SEMEOTICONS via OpenAIRE

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2017 Contribution to book Open Access OPEN

Intermittency-driven complexity in the brain: towards a general-purpose event detection algorithm
Paradisi P., Righi M., Barcaro U., Salvetti O., Virgillito A., Carboncini M. C., Sebastiani L.
In this work we first discuss a well-known theoretical framework for the analysis and modeling of self-organized structures in complex systems. These self-organized states are metastable and rapid transition events mark the passages between self-organization and background or between two different self-organized states. Thus, our approach focuses on characterizing and modeling the complex system as a intermittent point process describing the sequence of transition events. Complexity is usually associated with the emergence of a renewal point process with power-law distributed inter-event times, hence the term fractal intermittency. This point process drives the self-organizing behavior of the complex system, a condition denoted here as intermittency-driven complexity. In order to find the underlying intermittent birth-death process of selforganization, we introduce and discuss a preliminary version of an algorithm for the detection of transition events in human electroencephalograms. As the sequence of transition events is known, the complexity of the intermittent point process can be investigated by applying an algorithm for the scaling analysis of diffusion processes driven by the intermittent process itself. The method is briefly illustrated by discussing some preliminary analyses carried out on real electroencephalograms.Source: , pp. 108–118, 2017

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2017 Contribution to book Open Access OPEN

Intermittency-driven complexity in signal processing
Paradisi P., Allegrini P.
In this chapter, we rst discuss the main motivations that are causing an increasing interest of many research elds and the interdisciplinary eort of many research groups towards the new paradigm of complexity. Then, without claiming to include all possible complex systems, which is much beyond the cope of this review, we introduce a possible denition of complexity. Along this line, we also introduce our particular approach to the analysis and modeling of complex systems. This is based on the ubiquitous observation of metastability of self-organization, which triggers the emergence of intermittent events with fractal statistics. This condition, named fractal intermittency, is the signature of a particular class of complexity here referred to as Intermittency-Driven Complexity (IDC) . Limiting to the IDC framework, we give a survey of some recently developed statistical tools for the analysis of complex behavior in multi-component systems and we review recent applications to real data, especially in the eld of human physiology. Finally, we give a brief discussion about the role of complexity paradigm in human health and wellness.Source: Complexity and Nonlinearity in Cardiovascular Signals, edited by Barbieri R.; Scilingo E.; Valenza G., pp. 161–195. London: Springer, 2017
DOI: 10.1007/978-3-319-58709-7_6

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2016 Report Open Access OPEN

Criticality of human breath detection with a portable device II: data analysis
Germanese D., Righi M., D'Acunto M., Magrini M., Paradisi P., Guidi M.
Human breath is largely composed of oxygen, carbon dioxide, water vapor, nitric oxide, and numerous volatile organic compounds (VOCs) [1, 2]. Changes in the concentration of the molecules in VOCs could suggest various diseases or at least changes in the metabolism. Indeed, breath gases are recognized to be excellent indicators of the presence of diseases and clinical conditions. Such gases have been identified as biomarkers using accurate but expensive benchtop instrumentations such as gas chromatography (GC) or electronic nose (e-nose) [1]. As a consequence, in recent years, it has been stimulated the necessity to develop a portable device for breath analysis, easy to use, and feasible for patients living far from medical structures or physicians. In the framework of SEMEOTICONS (SEMEiotic Oriented Technology for Idividual's CardiOmetabolic risk self-assessmeNt and Self-monitoring) European Project, we developed a low cost, portable, easy-to- use device for the analysis of breath composition: the Wize Sniffer (WS). The WS captures breath samples, the chemical selective sensors sense the sample and accordingly form a sort of odor-print of healthy people or patients with known and specific diseases, in order to evaluate the well-being state of a human subject [3, 4]. It should be noted that does not exist a general definition of "well-being state", rather some indices for well-being that can be correlated to cardio-metabolic risk, which is representing the leading cause of worldwide mortality [3, 5]. The first prototype of such device is based on commercial, semiconductor-based gas sensors. This type of gas sensors is very robust and easy to integrate. Nevertheless, they are non- selective at all. This leads to several issues for data analysis. In this report we focus our attention on the different strategies for data analysis, evaluating also their performances and outcomes.Source: ISTI Technical reports, 2016
Project(s): SEMEOTICONS via OpenAIRE

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2016 Report Open Access OPEN

Criticality of human breath detection with a portable device III: integration with other devices for health care and self-monitoring
Righi M., Germanese D., Magrini M., D'Acunto M., Paradisi P., Guidi M.
Human breath is largely composed of oxygen, carbon dioxide, water vapor, nitric oxide, and numerous volatile organic compounds (VOCs) [1, 2]. Changes in the concentration of the molecules in VOCs could suggest various diseases or at least changes in the metabolism. Indeed, breath gases are recognized to be excellent indicators of the presence of diseases and clinical conditions. Such gases have been identified as biomarkers using accurate but expensive benchtop instrumentations such as gas chromatography (GC) or electronic nose (e-nose) [1]. As a consequence, in recent years, it has been stimulated the necessity to develop a portable device for breath analysis, easy to use, and feasible for patients living far from medical structures or physicians. In the framework of SEMEOTICONS (SEMEiotic Oriented Technology for Idividual's CardiOmetabolic risk self-assessmeNt and Self-monitoring) European Project, we developed a low cost, portable, easy-to- use device for the analysis of breath composition: the Wize Sniffer (WS). The WS captures breath samples, the chemical selective sensors sense the sample and accordingly form a sort of odor-print of healthy people or patients with known and specific diseases, in order to evaluate the well-being state of a human subject [3, 4]. It should be noted that does not exist a general definition of "well-being state", rather some indices for well-being that can be correlated to cardio-metabolic risk, which is representing the leading cause of worldwide mortality [3, 5]. The breath molecules detected by the Wize Sniffer are the following, all related to those noxious habits for cardio-metabolic risk (alcohol intake, smoking, wrong diet): ï,· Carbon Monoxide (CO): CO is present in cigarette smoke (it is the major component, 75,95%). Mean carbon monoxide concentration in exhaled breath is about 3,5 ppm. Increasing levels of exhaled carbon monoxide can be detected in smoking subjects: 13.8 - 29 ppm. ï,· Carbon Dioxide (CO2) and Oxygen (O2): Exhaled air has a decreased amount of oxygen and an increased amount of CO2. These amounts show how much O2 is retained within the body for use by the cells and how much CO2 is produced as a by-product of cellular metabolism. CO2 is also one of constituents of tobacco smoke (13%). Exhaled O2 amount is about 13.6%-16% while mean CO2 concentration in exhaled breath is about 4% (= 40000ppm). Lower values may be due to respiration disorders. ï,· Ethanol: Exogenous Ethanol comes from alcoholic drink. It is important to note that it is recognized that ethanol breakdown leads to an accumulation of free radicals into the cells, a clear example of oxidative stress. Ethanol may cause arrhythmias and depresses the contractility of cardiac muscle. ï,· Nitrogen (di)Oxide (NOx): it is a vasodilator and it modulates inflammatory response (operating in combination with CO and Hydrogen Sulfide). It is also a good indicator for asthma diseases. ï,· Hydrogen Sulfide (H2S): it is a vascular relaxant agent, and has a therapeutic effect in various cardiovascular diseases (myocardial injury, hypertension). In general, H2S could have therapeutic effect against oxidative stress due to its capability to neutralize the action of free radicals. ï,· Ammonia (NH3): Mean baseline levels of ammonia in exhaled gas are about 0.42ppm. Elevated breath ammonia usually could be due to liver disease, such also to kidney disease. Ammonia is also one of the major compounds, together with CO, of tobacco fumes (approximately 22,15%). ï,· Hydrogen (H2): The production of hydrogen is a metabolic consequence of carbohydrate fermentation by anaerobic bacteria. This hydrogen traverses the gut wall, and is transported via the circulation to the lungs, where is execrated in exhaled breath. Not only, a certain amount of exhaled hydrogen is the result of fermentation by oropharingeal bacteria. As a consequence, increased values of breath hydrogen may be due to overweight problems, intestinal diseases, improper life-style. The baseline value is about 9.1ppm. In this report, we describe briefly the hardware/software architecture of the Wize Sniffer, and how it can be integrated in other multisensory platform for health care and self-monitoring.Source: ISTI Technical reports, 2016
Project(s): SEMEOTICONS via OpenAIRE

See at: ISTI Repository Open Access | CNR ExploRA Open Access


2016 Report Open Access OPEN

Criticality of human breath detection with a portable device I: nanotechniques for improving sensing materials
Germanese D., Righi M., D'Acunto M., Chiellini F., Guidi M., Magrini M., Paradisi P., Puppi D.
Human breath is largely composed of oxygen, carbon dioxide, water vapor, nitric oxide, and numerous volatile organic compounds (VOCs) [1, 2]. Changes in the concentration of the molecules in VOCs could suggest various diseases or at least changes in the metabolism. Indeed, breath gases are recognized to be excellent indicators of the presence of diseases and clinical conditions. Such gases have been identified as biomarkers using accurate but expensive benchtop instrumentations such as gas chromatography (GC) or electronic nose (e-nose) [1]. As a consequence, in recent years, it has been stimulated the necessity to develop a portable device for breath analysis, easy to use, and feasible for patients living far from medical structures or physicians. In the framework of SEMEOTICONS (SEMEiotic Oriented Technology for Idividual's CardiOmetabolic risk self-assessmeNt and Self-monitoring) European Project, we developed a low cost, portable, easy-to- use device for the analysis of breath composition: the Wize Sniffer (WS). The first prototype of such device is based on commercial, semiconductor-based gas sensors. This type of sensors is very robust and easy to be integrated. Nevertheless, they are not selective, thus impeding the discrimination of each type of molecule they are able to detect. In this report we describe a method to improve the sensitivity of semiconductor-based gas sensors. In particular, we focus our attention on the development of a hybrid, ad-hoc sensor, based on Polyaniline sol- gel nano-film, to detect Nitric Oxide. Why Nitric Oxide? NOx (Nitrogen (di)Oxide) is a VOC that plays an important role as an indicator of metabolic since it is related to endothelial function [8]. In addition, it is a vasodilator and it modulates inflammatory response (operating in combination with CO and Hydrogen Sulfide). It is also a good indicator for asthma diseases. Detection of NO presents some challenging problems, because low cost sensors are not available. As a consequence, the development of a sensor for NO to be used in a portable device for breath analysis and taking advantage by nano-scale sensing materials imposed us to work harmonizing existing commercial sensors with innovative sensing materials.Source: ISTI Technical reports, 2016
Project(s): SEMEOTICONS via OpenAIRE

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2016 Report Open Access OPEN

Towards the wize sniffer 1.1: a functional gas sensor for breath analysis
Germanese D., Righi M., D'Acunto M., Magrini M., Paradisi P., Guidi M.
In this report, we describe the manufacturing of a device for breath analysis. Breath analysis offers a relatively inexpensive, rapid, and non-invasive method for detecting a variety of life habits and possible diseases. Our activity was focused on the design and functionality of the Wize Sniffer (WS), a new portable device for breath analysis limited to an effective number of substances. Within the European SEMEOTICONS (SEMEiotic Oriented Technology for Idividual's CardiOmetabolic risk self-assessmeNt and Self-monitoring) Project by the WS, we intend a hardware/software tool for both the analysis of volatile organic compounds of breath and a platform for data mining and data integration. The WS should be able to provide useful information about the "breathprint", i.e., the analog of fingerprint for the state of health of an individual, to be used in the Virtual Individual Map. In this first period of activity, the WS has been designed in two main configurations. One configuration to work with commercial sensors (that is going to be operative) and the other one configuration to work with customized sensors made using electrospun nanofibers as sensing material. This last configuration is still work in progress. The efforts for the design of the WS involved also statistical data processing.Source: ISTI Technical reports, 2016
Project(s): SEMEOTICONS via OpenAIRE

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2016 Conference article Open Access OPEN

The challenge of brain complexity - A brief discussion about a fractal intermittency-based approach
Paradisi P., Righi M., Barcaro U.
In the last years, the complexity paradigm is gaining momentum in many research fields where large multidimensional datasets are made available by the advancements in instrumental technology. A complex system is a multi-component system with a large number of units characterized by cooperative behavior and, consequently, emergence of well-defined self-organized structures, such as communities in a complex network. The self-organizing behavior of the brain neural network is probably the most important prototype of complexity and is studied by means of physiological signals such as the ElectroEncephaloGram (EEG). Physiological signals are typically intermittent, i.e., display non-smooth rapid variations or crucial events (e.g., cusps or abrupt jumps) that occur randomly in time, or whose frequency changes randomly. In this work, we introduce a complexity-based approach to the analysis and modeling of physiological data that is focused on the characterization of intermittent events. Recent findings about self-similar or fractal intermittency in human EEG are reviewed. The definition of brain event is a crucial aspect of this approach that is discussed in the last part of the paper, where we also propose and discuss a first version of a general-purpose event detection algorithm for EEG signals.Source: PhyCS 2016 - International Conference on Physiological Computing Systems 2016, pp. 123–129, Lisbona, Portugal, 27-28 June 2016
DOI: 10.5220/0005998601230129

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2016 Conference article Open Access OPEN

Complexity measures based on intermittent events in brain EEG data
Paradisi P., Righi M., Magrini M., Carbonicini M. C., Virgillito A., Salvetti O.
In this work we discuss the application of the complexity approach to the study of physiological signals. In particular, a theoretical framework based on the ubiquitous emergence of fractal intermittency in complex signals is introduced. This approach is based on the ability of complex systems' cooperative micro-dynamics of triggering metastable, macroscopic, self-organized states. The metastability is strictly connected with the emergence of a intermittent point process displaying anomalous non-Poisson statistics and driving the fast transition events between successive metastable states. As a consequence, the estimation of features related to intermittent events can be used to characterize the ability of the complex system to trigger self-organized structures. We introduce an algorithm for the processing of complex signals that is based on the fractal intermittency paradigm, thus focusing on the detection and scaling analysis of intermittent events in human ElectroEncephaloGram (EEG). We finally discuss the application of this approach to real EEG recordings and introduce the preliminary findings.Source: BELBI2016 - Belgrade Bioinformatics Conference 2016, pp. 88–92, Belgrado, Serbia, 20-24 June 2016

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2016 Journal article Open Access OPEN

A stochastic solution with Gaussian stationary increments of the symmetric space-time fractional diffusion equation
Pagnini G., Paradisi P.
The stochastic solution with Gaussian stationary increments is established for the symmetric space-time fractional diffusion equation when 0 < ? < ? <= 2, where 0 < ? <= 1 and 0 < ? <= 2 are the fractional derivation orders in time and space, respectively. This solution is provided by imposing the identity between two probability density functions resulting (i) from a new integral representation formula of the fundamental solution of the symmetric space-time fractional diffusion equation and (ii) from the product of two independent random variables. This is an alternative method with respect to previous approaches such as the scaling limit of the continuous time random walk, the parametric subordination and the subordinated Langevin equation. A new integral representation formula for the fundamental solution of the space-time fractional diffusion equation is firstly derived. It is then shown that, in the symmetric case, a stochastic solution can be obtained by a Gaussian process with stationary increments and with a random wideness scale variable distributed according to an arrangement of two extremal Lévy stable densities. This stochastic solution is self-similar with stationary increments and uniquely defined in a statistical sense by the mean and the covariance structure. Numerical simulations are carried out by choosing as Gaussian process the fractional Brownian motion. Sample paths and probability densities functions are shown to be in agreement with the fundamental solution of the symmetric space-time fractional diffusion equation.Source: Fractional Calculus & Applied Analysis (Online) 19 (2016): 408–440. doi:10.1515/fca-2016-0022
DOI: 10.1515/fca-2016-0022

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2016 Journal article Open Access OPEN

Fractional kinetics emerging from ergodicity breaking in random media
Molina-garcía D., Pham T. M., Paradisi P., Manzo C., Pagnini G.
We present a modeling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single-particle tracking experiments in living cells, such as ergodicity breaking, p variation, and aging. In particular, this approach recapitulates characteristic features previously described in part by the fractional Brownian motion and in part by the continuous-time random walk. Moreover, for a proper distribution of the length scale, a single parameter controls the ergodic-to-nonergodic transition and, remarkably, also drives the transition of the diffusion equation of the process from nonfractional to fractional, thus demonstrating that fractional kinetics emerges from ergodicity breaking.Source: Physical review. E (Print) 94 (2016). doi:10.1103/PhysRevE.94.052147
DOI: 10.1103/physreve.94.052147

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2016 Report Restricted

Mid-term report of project "Anomalous transport in complex systems: stochastic modeling and statistical data analysis"
Paradisi P.
Anomalous diffusion is defined by the nonlinear growth of the fluctuations' variance with time and it is often related to long-range memory. Many complex systems are supposed to trigger long-range memory dynamical structures, as long-range correlations are usually observed. However, apparent long-range correlations can arise non only as a consequence of long-range memory dynamics, but also due to inhomogeneities in the set of interacting units/particles in the system. Fractional diffusion equation (FDE) is a evolution equation for the 1-point 1-time probability density function of a fluctuating/diffusing variable and is a ubiquitously used model for anomalous diffusion. Following the alternative assumption that long-range memory could be related to heterogeneity of the complex medium, we derive a class of stochastic models, based of Gaussian processes, that are compatible with the fractional diffusion equation (FDE). Thus, we prove that FDE can emerge also as a consequence of heterogeneity and is not only due to long-range memory in the system, such as in the Continuous Time Random Walk (CTRW) model. In fact, even if CTRW is driven by renewal events, destroying memory at some crucial time points, it is also characterized by inter-event long-life coherent structures determining the emergence of long-range correlations in the system.Source: Project report, Anomalous transport in complex systems:stochastic modeling and statistical data analysis, pp.1–7, 2016

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