Physics

Correlations in multifractal series have been investigated, extensively. Almost all approaches try to find scaling features of a given time series. However, the analysis of such scaling properties has some difficulties such as finding a proper scaling region. On the other hand, such correlation detection methods may be affected by the probability distribution function of the series. In this article, we apply the horizontal visibility graph algorithm to map stochastic time series into networks. By investigating the magnitude and sign of a multifractal time series, we show that one can detect linear as well as nonlinear correlations, even for situations that have been considered as uncorrelated noises by typical approaches like MFDFA. In this respect, we introduce a topological parameter that can well measure the strength of nonlinear correlations. This parameter is independent of the probability distribution function and calculated without the need to find any scaling region. Our findings may provide new insights about the multifractal analysis of time series in a variety of complex systems.

High-energy physics detectors, images, and point clouds share many similarities in terms of object detection. However, while detecting an unknown number of objects in an image is well established in computer vision, even machine learning assisted object reconstruction algorithms in particle physics almost exclusively predict properties on an object-by-object basis. Traditional approaches from computer vision either impose implicit constraints on the object size or density and are not well suited for sparse detector data or rely on objects being dense and solid. The object condensation method proposed here is independent of assumptions on object size, sorting or object density, and further generalises to non-image-like data structures, such as graphs and point clouds, which are more suitable to represent detector signals. The pixels or vertices themselves serve as representations of the entire object, and a combination of learnable local clustering in a latent space and confidence assignment allows one to collect condensates of the predicted object properties with a simple algorithm. As proof of concept, the object condensation method is applied to a simple object classification problem in images and used to reconstruct multiple particles from detector signals. The latter results are also compared to a classic particle flow approach.

In this paper, we apply multi-task Gaussian Process (MT-GP) to show that the adsorption energy of small adsorbates on transition metal surfaces can be modeled to a high level of fidelity using data from multiple sources, taking advantage of the relatively abundant ''low fidelity" data (such as from density functional theory computations) and small amounts of ''high fidelity" computational (e.g. using the random phase approximation) or experimental data. To fully explore the performance of MT-GP, we perform two case studies - one using purely computational datasets and the other using a combination of experimental and computational datasets. In both cases, the performance of MT-GPs is significantly better than single-task models built on a single data source. This method can be used to learn improved models from fused datasets, and thereby build accurate models under tight computational and experimental budget.

Machine learning has become a widely popular and successful paradigm, including in data-driven science and engineering. A major application problem is data-driven forecasting of future states from a complex dynamical. Artificial neural networks (ANN) have evolved as a clear leader amongst many machine learning approaches, and recurrent neural networks (RNN) are considered to be especially well suited for forecasting dynamical systems. In this setting, the echo state networks (ESN) or reservoir computer (RC) have emerged for their simplicity and computational complexity advantages. Instead of a fully trained network, an RC trains only read-out weights by a simple, efficient least squares method. What is perhaps quite surprising is that nonetheless an RC succeeds to make high quality forecasts, competitively with more intensively trained methods, even if not the leader. There remains an unanswered question as to why and how an RC works at all, despite randomly selected weights. We explicitly connect the RC with linear activation and linear read-out to well developed time-series literature on vector autoregressive averages (VAR) that includes theorems on representability through the WOLD theorem, which already perform reasonably for short term forecasts. In the case of a linear activation and now popular quadratic read-out RC, we explicitly connect to a nonlinear VAR (NVAR), which performs quite well. Further, we associate this paradigm to the now widely popular dynamic mode decomposition (DMD), and thus these three are in a sense different faces of the same thing. We illustrate our observations in terms of popular benchmark examples including Mackey-Glass differential delay equations and the Lorenz63 system.

Integrated Digital Image Correlation (IDIC) is nowadays a well established full-field experimental procedure for reliable and accurate identification of material parameters. It is based on the correlation of a series of images captured during a mechanical experiment, that are matched by displacement fields derived from an underlying mechanical model. In recent studies, it has been shown that when the applied boundary conditions lie outside the employed field of view, IDIC suffers from inaccuracies. A typical example is a micromechanical parameter identification inside a Microstructural Volume Element (MVE), whereby images are usually obtained by electron microscopy or other microscopy techniques but the loads are applied at a much larger scale. For any IDIC model, MVE boundary conditions still need to be specified, and any deviation or fluctuation in these boundary conditions may significantly influence the quality of identification. Prescribing proper boundary conditions is generally a challenging task, because the MVE has no free boundary, and the boundary displacements are typically highly heterogeneous due to the underlying microstructure. The aim of this paper is therefore first to quantify the effects of errors in the prescribed boundary conditions on the accuracy of the identification in a systematic way. To this end, three kinds of mechanical tests, each for various levels of material contrast ratios and levels of image noise, are carried out by means of virtual experiments. For simplicity, an elastic compressible Neo-Hookean constitutive model under plane strain assumption is adopted. It is shown that a high level of detail is required in the applied boundary conditions. This motivates an improved boundary condition application approach, which considers constitutive material parameters as well as kinematic variables at the boundary of the entire MVE as degrees of freedom in...

As it is well known, the standard deviation of a weighted average depends only on the individual standard deviations, but not on the dispersion of the values around the mean. This property leads sometimes to the embarrassing situation in which the combined result 'looks' somehow at odds with the individual ones. A practical way to cure the problem is to enlarge the resulting standard deviation by the χ 2 /ν − − − − √ scaling, a prescription employed with arbitrary criteria on when to apply it and which individual results to use in the combination. But the `apparent' discrepancy between the combined result and the individual ones often remains. Moreover this rule does not affect the resulting `best value', even if the pattern of the individual results is highly skewed. In addition to these reasons of dissatisfaction, shared by many practitioners, the method causes another issue, recently noted on the published measurements of the charged kaon mass. It happens in fact that, if the prescription is applied twice, i.e. first to a sub-sample of the individual results and subsequently to the entire sample, then a bias on the result of the overall combination is introduced. The reason is that the prescription does not guaranty statistical sufficiency, whose importance is reminded in this script, written with a didactic spirit, with some historical notes and with a language to which most physicists are accustomed. The conclusion contains general remarks on the effective presentation of the experimental findings and a pertinent puzzle is proposed in the Appendix.

Permutation Entropy (PE) has been shown to be a useful tool for time series analysis due to its low computational cost and noise robustness. This has drawn for its successful application in many fields. Some of these include damage detection, disease forecasting, and financial volatility analysis. However, to successfully use PE, an accurate selection of two parameters is needed: the permutation dimension n and embedding delay τ . These parameters are often suggested by experts based on a heuristic or by a trial and error approach. unfortunately, both of these methods can be time-consuming and lead to inaccurate results. To help combat this issue, in this paper we investigate multiple schemes for automatically selecting these parameters with only the corresponding time series as the input. Specifically, we develop a frequency-domain approach based on the least median of squares and the Fourier spectrum, as well as extend two existing methods: Permutation Auto-Mutual Information (PAMI) and Multi-scale Permutation Entropy (MPE) for determining τ . We then compare our methods as well as current methods in the literature for obtaining both τ and n against expert-suggested values in published works. We show that the success of any method in automatically generating the correct PE parameters depends on the category of the studied system. Specifically, for the delay parameter τ , we show that our frequency approach provides accurate suggestions for periodic systems, nonlinear difference equations, and ECG/EEG data, while the mutual information function computed using adaptive partitions provides the most accurate results for chaotic differential equations. For the permutation dimension n , both False Nearest Neighbors and MPE provide accurate values for n for most of the systems with n=5 being suitable in most cases.

In this paper, it is shown an enhancement of a previous model on the measurement standard uncertainty (MU) of the insertion loss (IL) in a reverberation chamber (RC) including frequency stirring (FS). Differently from the previous model, the enhanced does not require specific conditions on the parameter to be measured. Such an enhancement is applicable for all usable measurement conditions in RCs. Moreover, a useful majorant is also shown; it is obtained under a weak condition on the coefficient of variation (CV) of the parameter to be measured. Results by measurements support the validity of the proposed enhancement and of the majorant.

In this paper we focus on the estimation of mutual information from finite samples (X×Y) . The main concern with estimations of mutual information is their robustness under the class of transformations for which it remains invariant: i.e. type I (coordinate transformations), III (marginalizations) and special cases of type IV (embeddings, products). Estimators which fail to meet these standards are not \textit{robust} in their general applicability. Since most machine learning tasks employ transformations which belong to the classes referenced in part I, the mutual information can tell us which transformations are most optimal\cite{Carrara_Ernst}. There are several classes of estimation methods in the literature, such as non-parametric estimators like the one developed by Kraskov et. al\cite{KSG}, and its improved versions\cite{LNC}. These estimators are extremely useful, since they rely only on the geometry of the underlying sample, and circumvent estimating the probability distribution itself. We explore the robustness of this family of estimators in the context of our design criteria.

The Feynman-alpha method is a neutron noise technique that is used to estimate the prompt neutron period of fissile assemblies. The method and quantity are of widespread interest including in applications such as nuclear criticality safety, safeguards and nonproliferation, and stockpile stewardship; the prompt neutron period may also be used to infer the k eff multiplication factor. The Feynman-alpha method is predicated on time-correlated neutron detections that deviate from a Poisson random variable due to multiplication. Traditionally, such measurements are diagnosed with one-region point kinetics, but two-region models are required when the fissile assembly is reflected. This paper presents a derivation of the two-region point kinetics Feynman-alpha equations based on a double integration of the Rossi-alpha equations, develops novel propagation of measurement uncertainty, and validates the theory. Validation is achieved with organic scintillator measurements of weapons-grade plutonium reflected by various amounts of copper to achieve k eff values of 0.83-0.94 and prompt periods of 5-75 ns. The results demonstrate that Feynman-alpha measurements should use the two-region model instead of the one-region model. The simplified one-region model deviates from the validated two-region models by as much as 10\% in the estimate of the prompt neutron period, and the two-region model reduces to the one-region model for small amounts of reflector. The Feynman-alpha estimates of the prompt neutron period are compared to those of the Rossi-alpha approach. The comparative results demonstrate that the Feynman-alpha method is more precise than the Rossi-alpha method and more accurate for k eff <0.92 , whereas the Rossi-alpha method is generally more accurate for higher multiplications.