Physics

This paper discusses change detection in SAR time-series. Firstly, several statistical properties of the coefficient of variation highlight its pertinence for change detection. Then several criteria are proposed. The coefficient of variation is suggested to detect any kind of change. Then other criteria based on ratios of coefficients of variations are proposed to detect long events such as construction test sites, or point-event such as vehicles. These detection methods are evaluated first on theoretical statistical simulations to determine the scenarios where they can deliver the best results. Then detection performance is assessed on real data for different types of scenes and sensors (Sentinel-1, UAVSAR). In particular, a quantitative evaluation is performed with a comparison of our solutions with state-of-the-art methods.

One of the most useful tools for distinguishing between chaotic and stochastic time series is the so-called complexity-entropy causality plane. This diagram involves two complexity measures: the Shannon entropy and the statistical complexity. Recently, this idea has been generalized by considering the Tsallis monoparametric generalization of the Shannon entropy, yielding complexity-entropy curves. These curves have proven to enhance the discrimination among different time series related to stochastic and chaotic processes of numerical and experimental nature. Here we further explore these complexity-entropy curves in the context of the Rényi entropy, which is another monoparametric generalization of the Shannon entropy. By combining the Rényi entropy with the proper generalization of the statistical complexity, we associate a parametric curve (the Rényi complexity-entropy curve) with a given time series. We explore this approach in a series of numerical and experimental applications, demonstrating the usefulness of this new technique for time series analysis. We show that the Rényi complexity-entropy curves enable the differentiation among time series of chaotic, stochastic, and periodic nature. In particular, time series of stochastic nature are associated with curves displaying positive curvature in a neighborhood of their initial points, whereas curves related to chaotic phenomena have a negative curvature; finally, periodic time series are represented by vertical straight lines.

Diffusion processes are important in several physical, chemical, biological and human phenomena. Examples include molecular encounters in reactions, cellular signalling, the foraging of animals, the spread of diseases, as well as trends in financial markets and climate records. Deviations from Brownian diffusion, known as anomalous diffusion, can often be observed in these processes, when the growth of the mean square displacement in time is not linear. An ever-increasing number of methods has thus appeared to characterize anomalous diffusion trajectories based on classical statistics or machine learning approaches. Yet, characterization of anomalous diffusion remains challenging to date as testified by the launch of the Anomalous Diffusion (AnDi) Challenge in March 2020 to assess and compare new and pre-existing methods on three different aspects of the problem: the inference of the anomalous diffusion exponent, the classification of the diffusion model, and the segmentation of trajectories. Here, we introduce a novel method (CONDOR) which combines feature engineering based on classical statistics with supervised deep learning to efficiently identify the underlying anomalous diffusion model with high accuracy and infer its exponent with a small mean absolute error in single 1D, 2D and 3D trajectories corrupted by localization noise. Finally, we extend our method to the segmentation of trajectories where the diffusion model and/or its anomalous exponent vary in time.

We present the Time of Flight Fixed by Energy Estimation (TOFFEE) as a measure of the fission chain dynamics in subcritical assemblies. TOFFEE is the time between correlated gamma rays and neutrons, subtracted by the estimated travel time of the incident neutron from its proton recoil. The measured subcritical assembly was the BeRP ball, a 4.482 kg sphere of alpha-phase weapons grade plutonium metal, which came in five configurations: bare, 0.5, 1, and 1.5 in iron, and 1 in nickel closed fitting shell reflectors. We extend the measurement with MCNPX-PoliMi simulations of shells ranging up to 6 inches in thickness, and two new reflector materials: aluminum and tungsten. We also simulated the BeRP ball with different masses ranging from 1 to 8 kg. A two-region and single-region point kinetics models were used to model the behavior of the positive side of the TOFFEE distribution from 0 to 100 ns. The single region model of the bare cases gave positive linear correlations between estimated and expected neutron decay constants and leakage multiplications. The two-region model provided a way to estimate neutron multiplication for the reflected cases, which correlated positively with expected multiplication, but the nature of the correlation (sub or super linear) changed between material types. Finally, we found that the areal density of the reflector shells had a linear correlation with the integral of the two-region model fit. Therefore, we expect that with knowledge of reflector composition, one could determine the shell thickness, or vice versa. Furthermore, up to a certain amount and thickness of the reflector, the two-region model provides a way of distinguishing bare and reflected plutonium assemblies.

Approaches for mapping time series to networks have become essential tools for dealing with the increasing challenges of characterizing data from complex systems. Among the different algorithms, the recently proposed ordinal networks stand out due to its simplicity and computational efficiency. However, applications of ordinal networks have been mainly focused on time series arising from nonlinear dynamical systems, while basic properties of ordinal networks related to simple stochastic processes remain poorly understood. Here, we investigate several properties of ordinal networks emerging from random time series, noisy periodic signals, fractional Brownian motion, and earthquake magnitude series. For ordinal networks of random series, we present an approach for building the exact form of the adjacency matrix, which in turn is useful for detecting non-random behavior in time series and the existence of missing transitions among ordinal patterns. We find that the average value of a local entropy, estimated from transition probabilities among neighboring nodes of ordinal networks, is more robust against noise addition than the standard permutation entropy. We show that ordinal networks can be used for estimating the Hurst exponent of time series with accuracy comparable with state-of-the-art methods. Finally, we argue that ordinal networks can detect sudden changes in Earth seismic activity caused by large earthquakes.

We examine the χ 2 test for binned, Gaussian samples, including effects due to the fact that the experimentally available sample standard deviation and the unavailable true standard deviation have different statistical properties. For data formed by binning Gaussian samples with bin size n , we find that the expected value and standard deviation of the reduced χ 2 statistic is n−1 n−3 ± n−1 n−3 n−2 n−5 − − − − − √ 2 N−1 − − − − − − √ , where N is the total number of binned values. This is strictly larger in both mean and standard deviation than the value of 1±(2/(N−1) ) 1/2 reported in standard treatments, which ignore the distinction between true and sample standard deviation.

During a tokamak discharge, the plasma can vary between different confinement regimes: Low (L), High (H) and, in some cases, a temporary (intermediate state), called Dithering (D). In addition, while the plasma is in H mode, Edge Localized Modes (ELMs) can occur. The automatic detection of changes between these states, and of ELMs, is important for tokamak operation. Motivated by this, and by recent developments in Deep Learning (DL), we developed and compared two methods for automatic detection of the occurrence of L-D-H transitions and ELMs, applied on data from the TCV tokamak. These methods consist in a Convolutional Neural Network (CNN) and a Convolutional Long Short Term Memory Neural Network (Conv-LSTM). We measured our results with regards to ELMs using ROC curves and Youden's score index, and regarding state detection using Cohen's Kappa Index.

We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic modeling often assumes a low-dimensional subspace or manifold for the state. We liberate ourselves from this assumption by proposing cluster-based network modeling (CNM) bridging machine learning, network science, and statistical physics. CNM only assumes smoothness of the dynamics in the state space, robustly describes short- and long-term behavior and is fully automatable as it does not rely on application-specific knowledge. CNM is demonstrated for the Lorenz attractor, ECG heartbeat signals, Kolmogorov flow, and a high-dimensional actuated turbulent boundary layer. Even the notoriously difficult modeling benchmark of rare events in the Kolmogorov flow is solved. This automatable universal data-driven representation of complex nonlinear dynamics complements and expands network connectivity science and promises new fast-track avenues to understand, estimate, predict and control complex systems in all scientific fields.

We describe an approximation to the widely-used Poisson-likelihood chi-square using a linear combination of Neyman's and Pearson's chi-squares, namely "combined Neyman-Pearson chi-square" ( χ 2 CNP ). Through analytical derivations and toy model simulations, we show that χ 2 CNP leads to a significantly smaller bias on the best-fit model parameters compared to those using either Neyman's or Pearson's chi-square. When the computational cost of using the Poisson-likelihood chi-square is high, χ 2 CNP provides a good alternative given its natural connection to the covariance matrix formalism.

In their recent paper [Phys. Rev. E 99 (2019) 032134], T. Oikinomou and B. Bagci have argued that Rényi entropy is ill-suited for inference purposes because it is not consistent with the Shore{ Johnson axioms of statistical estimation theory. In this Comment we seek to clarify the latter statement by showing that there are several issues in Oikinomou{Bagci reasonings which lead to erroneous conclusions. When all these issues are properly accounted for, no violation of Shore- Johnson axioms is found.