A control oriented strategy of disruption prediction to avoid the configuration collapse of tokamak reactors.

The objective of thermonuclear fusion consists of producing electricity from the coalescence of light nuclei in high temperature plasmas. The most promising route to fusion envisages the confinement of such plasmas with magnetic fields, whose most studied configuration is the tokamak. Disruptions are catastrophic collapses affecting all tokamak devices and one of the main potential showstoppers on the route to a commercial reactor. In this work we report how, deploying innovative analysis methods on thousands of JET experiments covering the isotopic compositions from hydrogen to full tritium and including the major D-T campaign, the nature of the various forms of collapse is investigated in all phases of the discharges. An original approach to proximity detection has been developed, which allows determining both the probability of and the time interval remaining before an incoming disruption, with adaptive, from scratch, real time compatible techniques. The results indicate that physics based prediction and control tools can be developed, to deploy realistic strategies of disruption avoidance and prevention, meeting the requirements of the next generation of devices.

Effects of environmental conditions on COVID-19 morbidity as an example of multicausality: a multi-city case study in Italy.

The coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), broke out in December 2019 in Wuhan city, in the Hubei province of China. Since then, it has spread practically all over the world, disrupting many human activities. In temperate climates overwhelming evidence indicates that its incidence increases significantly during the cold season. Italy was one of the first nations, in which COVID-19 reached epidemic proportions, already at the beginning of 2020. There is therefore enough data to perform a systematic investigation of the correlation between the spread of the virus and the environmental conditions. The objective of this study is the investigation of the relationship between the virus diffusion and the weather, including temperature, wind, humidity and air quality, before the rollout of any vaccine and including rapid variation of the pollutants (not only their long term effects as reported in the literature). Regarding them methodology, given the complexity of the problem and the sparse data, robust statistical tools based on ranking (Spearman and Kendall correlation coefficients) and innovative dynamical system analysis techniques (recurrence plots) have been deployed to disentangle the different influences. In terms of results, the evidence indicates that, even if temperature plays a fundamental role, the morbidity of COVID-19 depends also on other factors. At the aggregate level of major cities, air pollution and the environmental quantities affecting it, particularly the wind intensity, have no negligible effect. This evidence should motivate a rethinking of the public policies related to the containment of this type of airborne infectious diseases, particularly information gathering and traffic management.

On the Potential of Relational Databases for the Detection of Clusters of Infection and Antibiotic Resistance Patterns.

In recent years, several bacterial strains have acquired significant antibiotic resistance and can, therefore, become difficult to contain. To counteract such trends, relational databases can be a powerful tool for supporting the decision-making process. The case of Klebsiella pneumoniae diffusion in a central region of Italy was analyzed as a case study. A specific relational database is shown to provide very detailed and timely information about the spatial-temporal diffusion of the contagion, together with a clear assessment of the multidrug resistance of the strains. The analysis is particularized for both internal and external patients. Tools such as the one proposed can, therefore, be considered important elements in the identification of infection hotspots, a key ingredient of any strategy to reduce the diffusion of an infectious disease at the community level and in hospitals. These types of tools are also very valuable in the decision-making process related to antibiotic prescription and to the management of stockpiles. The application of this processing technology to viral diseases such as COVID-19 is under investigation.

Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems.

Model selection criteria are widely used to identify the model that best represents the data among a set of potential candidates. Amidst the different model selection criteria, the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) are the most popular and better understood. In the derivation of these indicators, it was assumed that the model's dependent variables have already been properly identified and that the entries are not affected by significant uncertainties. These are issues that can become quite serious when investigating complex systems, especially when variables are highly correlated and the measurement uncertainties associated with them are not negligible. More sophisticated versions of this criteria, capable of better detecting spurious relations between variables when non-negligible noise is present, are proposed in this paper. Their derivation is obtained starting from a Bayesian statistics framework and adding an a priori Chi-squared probability distribution function of the model, dependent on a specifically defined information theoretic quantity that takes into account the redundancy between the dependent variables. The performances of the proposed versions of these criteria are assessed through a series of systematic simulations, using synthetic data for various classes of functions and noise levels. The results show that the upgraded formulation of the criteria clearly outperforms the traditional ones in most of the cases reported.

Quantifying Total Influence between Variables with Information Theoretic and Machine Learning Techniques.

The increasingly sophisticated investigations of complex systems require more robust estimates of the correlations between the measured quantities. The traditional Pearson correlation coefficient is easy to calculate but sensitive only to linear correlations. The total influence between quantities is, therefore, often expressed in terms of the mutual information, which also takes into account the nonlinear effects but is not normalized. To compare data from different experiments, the information quality ratio is, therefore, in many cases, of easier interpretation. On the other hand, both mutual information and information quality ratio are always positive and, therefore, cannot provide information about the sign of the influence between quantities. Moreover, they require an accurate determination of the probability distribution functions of the variables involved. As the quality and amount of data available are not always sufficient to grant an accurate estimation of the probability distribution functions, it has been investigated whether neural computational tools can help and complement the aforementioned indicators. Specific encoders and autoencoders have been developed for the task of determining the total correlation between quantities related by a functional dependence, including information about the sign of their mutual influence. Both their accuracy and computational efficiencies have been addressed in detail, with extensive numerical tests using synthetic data. A careful analysis of the robustness against noise has also been performed. The neural computational tools typically outperform the traditional indicators in practically every respect.

Upgrading Model Selection Criteria with Goodness of Fit Tests for Practical Applications.

The Bayesian information criterion (BIC), the Akaike information criterion (AIC), and some other indicators derived from them are widely used for model selection. In their original form, they contain the likelihood of the data given the models. Unfortunately, in many applications, it is practically impossible to calculate the likelihood, and, therefore, the criteria have been reformulated in terms of descriptive statistics of the residual distribution: the variance and the mean-squared error of the residuals. These alternative versions are strictly valid only in the presence of additive noise of Gaussian distribution, not a completely satisfactory assumption in many applications in science and engineering. Moreover, the variance and the mean-squared error are quite crude statistics of the residual distributions. More sophisticated statistical indicators, capable of better quantifying how close the residual distribution is to the noise, can be profitably used. In particular, specific goodness of fit tests have been included in the expressions of the traditional criteria and have proved to be very effective in improving their discriminating capability. These improved performances have been demonstrated with a systematic series of simulations using synthetic data for various classes of functions and different noise statistics.

On the Potential of Time Delay Neural Networks to Detect Indirect Coupling between Time Series.

Determining the coupling between systems remains a topic of active research in the field of complex science. Identifying the proper causal influences in time series can already be very challenging in the trivariate case, particularly when the interactions are non-linear. In this paper, the coupling between three Lorenz systems is investigated with the help of specifically designed artificial neural networks, called time delay neural networks (TDNNs). TDNNs can learn from their previous inputs and are therefore well suited to extract the causal relationship between time series. The performances of the TDNNs tested have always been very positive, showing an excellent capability to identify the correct causal relationships in absence of significant noise. The first tests on the time localization of the mutual influences and the effects of Gaussian noise have also provided very encouraging results. Even if further assessments are necessary, the networks of the proposed architecture have the potential to be a good complement to the other techniques available in the market for the investigation of mutual influences between time series.

Image-Based Methods to Investigate Synchronization between Time Series Relevant for Plasma Fusion Diagnostics.

Advanced time series analysis and causality detection techniques have been successfully applied to the assessment of synchronization experiments in tokamaks, such as Edge Localized Modes (ELMs) and sawtooth pacing. Lag synchronization is a typical strategy for fusion plasma instability control by pace-making techniques. The major difficulty, in evaluating the efficiency of the pacing methods, is the coexistence of the causal effects with the periodic or quasi-periodic nature of the plasma instabilities. In the present work, a set of methods based on the image representation of time series, are investigated as tools for evaluating the efficiency of the pace-making techniques. The main options rely on the Gramian Angular Field (GAF), the Markov Transition Field (MTF), previously used for time series classification, and the Chaos Game Representation (CGR), employed for the visualization of large collections of long time series. The paper proposes an original variation of the Markov Transition Matrix, defined for a couple of time series. Additionally, a recently proposed method, based on the mapping of time series as cross-visibility networks and their representation as images, is included in this study. The performances of the method are evaluated on synthetic data and applied to JET measurements.

A Refinement of Recurrence Analysis to Determine the Time Delay of Causality in Presence of External Perturbations.

This article describes a refinement of recurrence analysis to determine the delay in the causal influence between a driver and a target, in the presence of additional perturbations affecting the time series of the response observable. The methodology is based on the definition of a new type of recurrence plots, the Conditional Joint Recurrence plot. The potential of the proposed approach resides in the great flexibility of recurrence plots themselves, which allows extending the technique to more than three quantities. Autoregressive time series, both linear and nonlinear, with different couplings and percentage of additive Gaussian noise have been investigated in detail, with and without outliers. The approach has also been applied to the case of synthetic periodic signals, representing realistic situations of synchronization experiments in thermonuclear fusion. The results obtained have been very positive; the proposed Conditional Joint Recurrence plots have always managed to identify the right interval of the causal influences and are very competitive with alternative techniques such as the Conditional Transfer Entropy.

A Model Falsification Approach to Learning in Non-Stationary Environments for Experimental Design.

The application of data driven machine learning and advanced statistical tools to complex physics experiments, such as Magnetic Confinement Nuclear Fusion, can be problematic, due the varying conditions of the systems to be studied. In particular, new experiments have to be planned in unexplored regions of the operational space. As a consequence, care must be taken because the input quantities used to train and test the performance of the analysis tools are not necessarily sampled by the same probability distribution as in the final applications. The regressors and dependent variables cannot therefore be assumed to verify the i.i.d. (independent and identical distribution) hypothesis and learning has therefore to take place under non stationary conditions. In the present paper, a new data driven methodology is proposed to guide planning of experiments, to explore the operational space and to optimise performance. The approach is based on the falsification of existing models. The deployment of Symbolic Regression via Genetic Programming to the available data is used to identify a set of candidate models, using the method of the Pareto Frontier. The confidence intervals for the predictions of such models are then used to find the best region of the parameter space for their falsification, where the next set of experiments can be most profitably carried out. Extensive numerical tests and applications to the scaling laws in Tokamaks prove the viability of the proposed methodology.

Causality Detection Methods Applied to the Investigation of Malaria Epidemics.

Malaria, a disease with major health and socio-economic impacts, is driven by multiple factors, including a complex interaction with various climatic variables. In this paper, five methods developed for inferring causal relations between dynamic processes based on the information encapsulated in time series are applied on cases previously studied in literature by means of statistical methods. The causality detection techniques investigated in the paper are: a version of the kernel Granger causality, transfer entropy, recurrence plot, causal decomposition and complex networks. The methods provide coherent results giving a quite good confidence in the conclusions.

On the Use of Entropy to Improve Model Selection Criteria.

The most widely used forms of model selection criteria, the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC), are expressed in terms of synthetic indicators of the residual distribution: the variance and the mean-squared error of the residuals respectively. In many applications in science, the noise affecting the data can be expected to have a Gaussian distribution. Therefore, at the same level of variance and mean-squared error, models, whose residuals are more uniformly distributed, should be favoured. The degree of uniformity of the residuals can be quantified by the Shannon entropy. Including the Shannon entropy in the BIC and AIC expressions improves significantly these criteria. The better performances have been demonstrated empirically with a series of simulations for various classes of functions and for different levels and statistics of the noise. In presence of outliers, a better treatment of the errors, using the Geodesic Distance, has proved essential.

Maximum likelihood bolometric tomography for the determination of the uncertainties in the radiation emission on JET TOKAMAK.

The total emission of radiation is a crucial quantity to calculate the power balances and to understand the physics of any Tokamak. Bolometric systems are the main tool to measure this important physical quantity through quite sophisticated tomographic inversion methods. On the Joint European Torus, the coverage of the bolometric diagnostic, due to the availability of basically only two projection angles, is quite limited, rendering the inversion a very ill-posed mathematical problem. A new approach, based on the maximum likelihood, has therefore been developed and implemented to alleviate one of the major weaknesses of traditional tomographic techniques: the difficulty to determine routinely the confidence intervals in the results. The method has been validated by numerical simulations with phantoms to assess the quality of the results and to optimise the configuration of the parameters for the main types of emissivity encountered experimentally. The typical levels of statistical errors, which may significantly influence the quality of the reconstructions, have been identified. The systematic tests with phantoms indicate that the errors in the reconstructions are quite limited and their effect on the total radiated power remains well below 10%. A comparison with other approaches to the inversion and to the regularization has also been performed.

On the Use of Transfer Entropy to Investigate the Time Horizon of Causal Influences between Signals.

Understanding the details of the correlation between time series is an essential step on the route to assessing the causal relation between systems. Traditional statistical indicators, such as the Pearson correlation coefficient and the mutual information, have some significant limitations. More recently, transfer entropy has been proposed as a powerful tool to understand the flow of information between signals. In this paper, the comparative advantages of transfer entropy, for determining the time horizon of causal influence, are illustrated with the help of synthetic data. The technique has been specifically revised for the analysis of synchronization experiments. The investigation of experimental data from thermonuclear plasma diagnostics proves the potential and limitations of the developed approach.

Improving Entropy Estimates of Complex Network Topology for the Characterization of Coupling in Dynamical Systems.

A new measure for the characterization of interconnected dynamical systems coupling is proposed. The method is based on the representation of time series as weighted cross-visibility networks. The weights are introduced as the metric distance between connected nodes. The structure of the networks, depending on the coupling strength, is quantified via the entropy of the weighted adjacency matrix. The method has been tested on several coupled model systems with different individual properties. The results show that the proposed measure is able to distinguish the degree of coupling of the studied dynamical systems. The original use of the geodesic distance on Gaussian manifolds as a metric distance, which is able to take into account the noise inherently superimposed on the experimental data, provides significantly better results in the calculation of the entropy, improving the reliability of the coupling estimates. The application to the interaction between the El Niño Southern Oscillation (ENSO) and the Indian Ocean Dipole and to the influence of ENSO on influenza pandemic occurrence illustrates the potential of the method for real-life problems.

Evaluation of reconstruction errors and identification of artefacts for JET gamma and neutron tomography.

The Joint European Torus (JET) neutron profile monitor ensures 2D coverage of the gamma and neutron emissive region that enables tomographic reconstruction. Due to the availability of only two projection angles and to the coarse sampling, tomographic inversion is a limited data set problem. Several techniques have been developed for tomographic reconstruction of the 2-D gamma and neutron emissivity on JET, but the problem of evaluating the errors associated with the reconstructed emissivity profile is still open. The reconstruction technique based on the maximum likelihood principle, that proved already to be a powerful tool for JET tomography, has been used to develop a method for the numerical evaluation of the statistical properties of the uncertainties in gamma and neutron emissivity reconstructions. The image covariance calculation takes into account the additional techniques introduced in the reconstruction process for tackling with the limited data set (projection resampling, smoothness regularization depending on magnetic field). The method has been validated by numerically simulations and applied to JET data. Different sources of artefacts that may significantly influence the quality of reconstructions and the accuracy of variance calculation have been identified.