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This paper is focused on kernel estimation of the gradient of a multivariate regression function. Despite the importance of this topic, the progress in this area is rather slow. Our aim is to construct a gradient estimator using the idea of local linear estimator for a regression function. The quality of this estimator is expressed in terms of the Mean Integrated Square Error. We focus on a choice of bandwidth matrix. Further, we present some data-driven methods for its choice and develop a new approach. The performance of presented methods is illustrated using a simulation study and real data example. [ABSTRACT FROM AUTHOR]

Abstract A top-priority task nowadays is to ensure quality, safety, and dependability of technical systems. As present systems are highly reliable, it is relatively unlikely for hard failure to occur frequently. One of the ways to avoid failures is by monitoring the conditions and degradation of the system using diagnostic signals. In this article, modern and nontrivial semiparametric approaches to analyze the statistically relevant set of field data are used. In particular, the generalized additive models (GAM) are applied. GAM reflect the current trends in statistics as they include both linear and spline-based modeling. We applied GAM to successfully obtain an appropriate description of the variability of the analyzed field data. The analyzed data come as diagnostic signals from an observed vehicle fleet. Based on the diagnostic signals and applied GAM, we present outcomes from investigating, studying and modeling the technical condition, degradation and failure occurrence of the observed system. Highlights • Contribution to system degradation and failure occurrence understanding based on diagnostics signals. • New modeling approach based on functional data analysis. • New application of general additive models. • Time dependent Ornstein-Uhlenbeck Process utilization. • Outcomes applicable as contribution to maintenance optimisation and operation rationalization. [ABSTRACT FROM AUTHOR]

Despite the abundance of available global climate model (GCM) and regional climate model (RCM) outputs, their use for evaluation of past and future climate change is often complicated by substantial differences between individual simulations and the resulting uncertainties. In this study, we present a methodological framework for the analysis of multi-model ensembles based on a functional data analysis approach. A set of two metrics that generalize the concept of similarity based on the behavior of entire simulated climatic time series, encompassing both past and future periods, is introduced. To our knowledge, our method is the first to quantitatively assess similarities between model simulations based on the temporal evolution of simulated values. To evaluate mutual distances of the time series, we used two semimetrics based on Euclidean distances between the simulated trajectories and based on differences in their first derivatives. Further, we introduce an innovative way of visualizing climate model similarities based on a network spatialization algorithm. Using the layout graphs, the data are ordered on a two-dimensional plane which enables an unambiguous interpretation of the results. The method is demonstrated using two illustrative cases of air temperature over the British Isles (BI) and precipitation in central Europe, simulated by an ensemble of EURO-CORDEX RCMs and their driving GCMs over the 1971–2098 period. In addition to the sample results, interpretational aspects of the applied methodology and its possible extensions are also discussed. [ABSTRACT FROM AUTHOR]

• Studies of long-term stored Li-ion cells based on tests, modelling, and simulation. • Application of modern principles on functional data analysis. • Developed models animate battery operational behaviour. • Obtaining very relevant generalized outcomes of Li-ion reliability measures. • Outcome comparison between long-term stored and new battery cells. Issues related to sources of electrical energy are not only currently relevant but are also increasing in number. A high-quality and stable source of electrical energy is an essential part and requirement in many technical systems of today. The power source is expected to meet quality, stability, and safety requirements crucial in systems whose operation is entirely dependent on the electrical energy source. It is even more important if the consequences of its failure have a catastrophic impact on the system, the operator, people, or the environment. This article is concerned with issues not yet addressed. The content of the article observes the properties and reliability indicators in Li-ion batteries that are the source of energy of an electric airplane and which have been stored for several years. The properties of these Li-ion cells are examined in several stages. The first one is based on i) extensive experiments, the next on ii) a study of the results, modelling, and simulations and, subsequently, on iii) a comparison of the results with new, non-stored batteries. The modelling is performed using modern and up to date methods of non-parametric functional analysis that have not yet been applied. In order to obtain useful time of safe operation, primary focus was directed at studying and modelling safe operating time of the battery. The achieved outcomes for long-term stored batteries are compared to new batteries outcomes. The results not only extend the knowledge of Li-ion batteries but are applicable far beyond the aviation industry. The obtained results show that operating aircraft when using batteries stored for several years ought to be safe. The stored batteries did not show a higher rate of quality or reliability degradation. [ABSTRACT FROM AUTHOR]

Despite the abundance of available global and regional climate model outputs, their use for evaluation of past and future climate changes is often complicated by substantial differences between individual simulations, and the resulting uncertainties. In this study, we present a methodology framework for the analysis of multi-model ensembles based on functional data analysis approach. A set of two metrics that generalize the concept of similarity based on the behaviour of entire simulated climatic time series, encompassing both past and future periods, is introduced. As far as our knowledge, our method is the first to quantitatively assess similarities between model simulations based on the temporal evolution of simulated values. To evaluate mutual distances of the time series we used two semimetrics based on Euclidean distances between the simulated trajectories and on differences in their first derivatives. Further, we introduce an innovative way of visualizing climate model similarities based on a network spatialization algorithm. Using the layout graphs the data are ordered on a 2-dimensional plane which enables an unambiguous interpretation of the results. The method is demonstrated using two illustrative cases of air temperature over the British Isles and precipitation in central Europe, simulated by an ensemble of EURO-CORDEX regional climate models and their driving global climate models over the 1971-2098 period. In addition to the sample results, interpretational aspects of the applied methodology and its possible extensions are also discussed. [ABSTRACT FROM AUTHOR]

Experience with the analysis and performance of 15 lightweight concrete footbridges is presented from the point of view of their dynamic response caused by moving people. The footbridges are formed either by a stress ribbon or by a slender deck supported by arches or suspended from pylons. The dynamic response was determined according to a procedure given in a 1998 draft of Eurocode 2: Design of Concrete Structures - Part 2: Concrete Bridges. Thirteen footbridges have been built and so far no complaints about their dynamic behaviour have been recorded. [ABSTRACT FROM AUTHOR]

The correlated density appears in many physical systems ranging from dense interacting gases up to Fermi liquids which develop a coherent state at low temperatures, the superconductivity. One consequence of the correlated density is the Bernoulli potential in superconductors which compensates forces from dielectric currents. This Bernoulli potential allows to access material parameters. Though within the surface potential these contributions are largely canceled, the bulk measurements with NMR can access this potential. Recent experiments are explained and new ones suggested. The underlying quantum statistical theory in nonequilibrium is the nonlocal kinetic theory developed earlier. [ABSTRACT FROM AUTHOR]

For more than four decades, mass of Abrikosov vortices defied experimental observations. We demonstrate a method of its detection in high-temperature superconductors. Similarly to electrons, fluxons circulate in the direction given by the magnetic field, causing circular dichroism. We report the magneto-transmittance of a nearly optimally doped thin YBa 2 Cu 3 O 7 - δ film, measured using circularly polarized submillimeter waves. The circular dichroism emerges in the superconducting state and increases with dropping temperature. Our results confirm the dominant role of quasiparticle states in the vortex core and yield the diagonal fluxon mass of 2.2 × 10 8 electron masses per centimeter at 45 K and zero-frequency limit, and even larger off-diagonal mass of 4.9 × 10 8 m e /cm. [ABSTRACT FROM AUTHOR]

Abstract: Superconducting Nb thin films with a spacing-graded array of holes were prepared by electron beam lithography. Two films with different hole gradients were fabricated. The ac-driven vortices were investigated in Nb superconductors with a spacing-graded array of holes. The measurements revealed pronounced rectified voltage when the vortex lattice is driven by an ac injected current. The rectified voltage is mainly caused by the strength of the vortex–vortex interaction. The rectified motion of a vortex is affected by the pinning potential of the spacing-graded array and the applied magnetic field. The vortex–vortex interaction strength changes the effective pinning landscape of the vortices and an asymmetric potential is formed. Vortices depin easily from high concentration to low concentration of pinning sites. In both samples, the ac-driven vortices exhibit a variety of dynamical responses and the rectified voltage is tunable with the applied magnetic field. [Copyright &y& Elsevier]

Evoked potentials (EPs) reflect neural processing and are widely used to study sensory perception. However, methods of analyzing EP have been limited mostly to the conventional ensemble averaging of EP response trials to a repeated stimulus, and less so to single-trials analysis. Here we applied a new approach - functional data analysis (FDA) - to study auditory EP in the rat model of tinnitus, in which overdoses of salicylate (SS) are known to alter sound perception characteristically, as the same way as in humans. Single-trial auditory EPs were analyzed, after being collected on a daily basis from an awake rat, which had been surgically implanted with intracranial electrodes over its auditory cortex. Single-trial EP integrals were generated with sound stimuli (tones and clicks) presented systematically over an intensity range. The results were approximated using the cubic spline to give sets of smoothed response-level functions in dependence on the sound intensity. These functional data were analyzed using the methods of FDA. Comparisons between daily intensity series for each sound type were done using cross-distance measures based on the response-level functions in both the original form and the first-derivative form. From the results of FDA, the first-derivative form was found to provide a clearer separation when EP data from control groups were compared to the data from SS groups. This is also true when the daily data were compared within the more variable SS-group itself. In addition, at the high-intensity region where SS-action is presumably strong, we also observed characteristic changes in two statistical parameters, mean and skewness, of the cross-distance representations. Results suggested that FDA is a sensitive approach for EP studies, and it can become a powerful tool for the research in neural science, particularly neuropharmacology., (Copyright © 2017 Elsevier B.V. All rights reserved.)