scholarly journals Identifying Higher-Order Interactions in Wave Time-Series

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Kevin Ewans ◽  
Marios Christou ◽  
Suzana Ilic ◽  
Philip Jonathan
Keyword(s):  
Time Series ◽  
Offshore Structures ◽  
Higher Order ◽  
Wave Interactions ◽  
Third Order ◽  
Signal Process ◽  
Reliable Design ◽  
Frequency Relationship ◽  
Order Four

Abstract Reliable design and reanalysis of coastal and offshore structures require, among other things, characterization of extreme crest elevation corresponding to long return periods. Extreme crests typically correspond to focused wave events enhanced by wave–wave interactions of different orders—third-order, four-wave interactions dominating in deep water (Janssen, P. A. E. M., 2003, “Nonlinear Four-Wave Interactions and Freak Waves,” J. Phys. Oceanogr., 33(4), pp. 863–884). Higher-order spectral (HOS) analysis can be used to identify wave–wave interactions in time-series of water surface elevation; trispectral analysis is needed to detect third-order, four-wave interactions. Four-wave interactions between Fourier components can involve interactions of the type where f1 + f2 + f3 = f4 and where f1 + f2 = f3 + f4, resulting in two definitions of the trispectrum—the T- and V-trispectrum (with corresponding tricoherences), respectively. It is shown that the T-tricoherence is capable of detecting phase-locked four-wave interactions of the type f4 = f1 + f2 + f3 when these are simulated with simple sinusoids, but such interactions were not detected in HOS model simulations and field data. It is also found that high V-tricoherence levels are detected at frequencies at which four-wave interactions of the type f1 + f2 = f3 + f4 are expected, but these may simply indicate combinations of independent pairs of Fourier components that happen to satisfy the frequency relationship. Preliminary analysis shows that using a cumulant-based trispectrum (Kravtchenko-Berejnoi, V., Lefeuvre, F., Krasnosel'skikh, V. V., and Lagoutte, D., 1995, “On the Use of Tricoherent Analysis to Detect Nonlinear Wave–Wave Interactions,” Signal Process., 42(3), pp. 291–309) may improve identification of wave–wave interactions. These results highlight that caution needs to be exercised in interpreting trispectra in terms of specific four-wave interactions occurring in sea states and further research is needed to establish whether this is in fact possible in practice.

scholarly journals Identifying Higher-Order Interactions in Wave Time-Series

2019 ◽  
Author(s):  
Kevin Ewans ◽  
Marios Christou ◽  
Suzana Ilic ◽  
Philip Jonathan
Keyword(s):  
Time Series ◽  
Power Spectrum ◽  
Frequency Domain ◽  
Fourier Transforms ◽  
Offshore Structures ◽  
Higher Order ◽  
Wave Interactions ◽  
Third Order ◽  
Reliable Design ◽  
Original Time

Abstract Reliable design and reanalysis of coastal and offshore structures requires, amongst other things, characterisation of extreme crest elevation corresponding to long return periods, and of the evolution of a wave in space and time conditional on an extreme crest. Extreme crests typically correspond to focussed wave events enhanced by wave-wave interactions of different orders. Higher-order spectral analysis can be used to identify wave-wave interactions in time-series of water surface elevation. The bispectrum and its normalised form (the bicoherence) have been reported by numerous authors as a means to characterise three-wave interactions in laboratory, field and simulation experiments. The bispectrum corresponds to a frequency-domain representation of the third order cumulant of the time-series, and can be thought of as an extension of the power spectrum (itself the frequency-domain representation of the second order cumulant). The power spectrum and bispectrum can both be expressed in terms of the Fourier transforms of the original time-series. The Fast Fourier transform (FFT) therefore provides an efficient means of estimation. However, there are a number of important practical considerations to ensuring reasonable estimation. To detect four-wave interactions, we need to consider the trispectrum and its normalised form (the tricoherence). The trispectrum corresponds to a frequency-domain (Fourier) representation of the fourth-order cumulant of the time-series. Four-wave interactions between Fourier components can involve interactions of the type where f1 + f2 + f3 = f4 and where f1 + f2 = f3 + f4, resulting in two definitions of the trispectrum, depending on which of the two interactions is of interest. We consider both definitions in this paper. Both definitions can be estimated using the FFT, but it’s estimation is considerably more challenging than estimation of the bispectrum. Again, there are important practicalities to bear in mind. In this work, we consider the key practical steps required to correctly estimate the trispectrum and tricoherence. We demonstrate the usefulness of the trispectrum and tricoherence for identifying wave-wave interactions in synthetic (based on combinations of sinusoids and on the HOS model) and measured wave time-series.

Multiscale Fractional Cumulative Residual Entropy of Higher-Order Moments for Estimating Uncertainty

2020 ◽  
Vol 19 (04) ◽  
pp. 2050038
Author(s):  
Keqiang Dong ◽  
Xiaofang Zhang
Keyword(s):  
Time Series ◽  
Logistic Map ◽  
Higher Order ◽  
Stationary Time Series ◽  
Residual Entropy ◽  
Third Order ◽  
Cumulative Residual Entropy ◽  
Cumulative Residual ◽  
Simulated Time ◽  
Analyze Time Series

The fractional cumulative residual entropy is not only a powerful tool for the analysis of complex system, but also a promising way to analyze time series. In this paper, we present an approach to measure the uncertainty of non-stationary time series named higher-order multiscale fractional cumulative residual entropy. We describe how fractional cumulative residual entropy may be calculated based on second-order, third-order, fourth-order statistical moments and multiscale method. The implementation of higher-order multiscale fractional cumulative residual entropy is illustrated with simulated time series generated by uniform distribution on [0, 1]. Finally, we present the application of higher-order multiscale fractional cumulative residual entropy in logistic map time series and stock markets time series, respectively.

scholarly journals Assessment of long-range cross-correlations in cardiorespiratory and cardiovascular interactions

2021 ◽  
Vol 379 (2212) ◽  
Author(s):  
Akio Nakata ◽  
Miki Kaneko ◽  
Chinami Taki ◽  
Naoko Evans ◽  
Taiki Shigematsu ◽  
...  
Keyword(s):  
Time Series ◽  
Long Range ◽  
Moving Average ◽  
Time Lag ◽  
Higher Order ◽  
Cross Correlation Analysis ◽  
Challenges And Opportunities ◽  
Cross Correlations ◽  
Different Order

We propose higher-order detrending moving-average cross-correlation analysis (DMCA) to assess the long-range cross-correlations in cardiorespiratory and cardiovascular interactions. Although the original (zeroth-order) DMCA employs a simple moving-average detrending filter to remove non-stationary trends embedded in the observed time series, our approach incorporates a Savitzky–Golay filter as a higher-order detrending method. Because the non-stationary trends can adversely affect the long-range correlation assessment, the higher-order detrending serves to improve accuracy. To achieve a more reliable characterization of the long-range cross-correlations, we demonstrate the importance of the following steps: correcting the time scale, confirming the consistency of different order DMCAs, and estimating the time lag between time series. We applied this methodological framework to cardiorespiratory and cardiovascular time series analysis. In the cardiorespiratory interaction, respiratory and heart rate variability (HRV) showed long-range auto-correlations; however, no factor was shared between them. In the cardiovascular interaction, beat-to-beat systolic blood pressure and HRV showed long-range auto-correlations and shared a common long-range, cross-correlated factor. This article is part of the theme issue ‘Advanced computation in cardiovascular physiology: new challenges and opportunities’.

scholarly journals A closed-loop optogenetic screen for neurons controlling feeding in Drosophila

2021 ◽  
Author(s):  
Celia K S Lau ◽  
Meghan Jelen ◽  
Michael D Gordon
Keyword(s):  
Drosophila Melanogaster ◽  
Expression Pattern ◽  
Sensory Neurons ◽  
Closed Loop ◽  
Higher Order ◽  
Taste Detection ◽  
Proof Of Principle ◽  
Feeding Circuits

Abstract Feeding is an essential part of animal life that is greatly impacted by the sense of taste. Although the characterization of taste-detection at the periphery has been extensive, higher order taste and feeding circuits are still being elucidated. Here, we use an automated closed-loop optogenetic activation screen to detect novel taste and feeding neurons in Drosophila melanogaster. Out of 122 Janelia FlyLight Project GAL4 lines preselected based on expression pattern, we identify six lines that acutely promote feeding and 35 lines that inhibit it. As proof of principle, we follow up on R70C07-GAL4, which labels neurons that strongly inhibit feeding. Using split-GAL4 lines to isolate subsets of the R70C07-GAL4 population, we find both appetitive and aversive neurons. Furthermore, we show that R70C07-GAL4 labels putative second-order taste interneurons that contact both sweet and bitter sensory neurons. These results serve as a resource for further functional dissection of fly feeding circuits.

scholarly journals On the similarity to nonnegative and Metzler Hessenberg forms

2021 ◽  
Vol 10 (1) ◽  
pp. 1-8
Author(s):  
Christian Grussler ◽  
Anders Rantzer
Keyword(s):  
Standard Form ◽  
Complete Characterization ◽  
Nonnegative Matrices ◽  
Positive Systems ◽  
Third Order ◽  
Hessenberg Form ◽  
Hessenberg Matrices ◽  
Open Question ◽  
Order Continuous

Abstract We address the issue of establishing standard forms for nonnegative and Metzler matrices by considering their similarity to nonnegative and Metzler Hessenberg matrices. It is shown that for dimensions n 3, there always exists a subset of nonnegative matrices that are not similar to a nonnegative Hessenberg form, which in case of n = 3 also provides a complete characterization of all such matrices. For Metzler matrices, we further establish that they are similar to Metzler Hessenberg matrices if n 4. In particular, this provides the first standard form for controllable third order continuous-time positive systems via a positive controller-Hessenberg form. Finally, we present an example which illustrates why this result is not easily transferred to discrete-time positive systems. While many of our supplementary results are proven in general, it remains an open question if Metzler matrices of dimensions n 5 remain similar to Metzler Hessenberg matrices.

Near‐Field Characterization of Higher‐Order Topological Photonic States at Optical Frequencies

2021 ◽  
pp. 2004376
Author(s):  
Anton Vakulenko ◽  
Svetlana Kiriushechkina ◽  
Mingsong Wang ◽  
Mengyao Li ◽  
Dmitry Zhirihin ◽  
...  
Keyword(s):  
Near Field ◽  
Higher Order ◽  
Photonic States

scholarly journals Numerical Characterization of Cohesive and Non-Cohesive ‘Sediments’ under Different Consolidation States Using 3D DEM Triaxial Experiments

Processes ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1252
Author(s):  
Hadar Elyashiv ◽  
Revital Bookman ◽  
Lennart Siemann ◽  
Uri ten Brink ◽  
Katrin Huhn
Keyword(s):  
Mechanical Response ◽  
Burial Depth ◽  
Cohesive Sediments ◽  
Third Order ◽  
First Order ◽  
Numerical Characterization ◽  
Response To Stress ◽  
Bond Strengths ◽  
Individual Bond

The Discrete Element Method has been widely used to simulate geo-materials due to time and scale limitations met in the field and laboratories. While cohesionless geo-materials were the focus of many previous studies, the deformation of cohesive geo-materials in 3D remained poorly characterized. Here, we aimed to generate a range of numerical ‘sediments’, assess their mechanical response to stress and compare their response with laboratory tests, focusing on differences between the micro- and macro-material properties. We simulated two endmembers—clay (cohesive) and sand (cohesionless). The materials were tested in a 3D triaxial numerical setup, under different simulated burial stresses and consolidation states. Variations in particle contact or individual bond strengths generate first order influence on the stress–strain response, i.e., a different deformation style of the numerical sand or clay. Increased burial depth generates a second order influence, elevating peak shear strength. Loose and dense consolidation states generate a third order influence of the endmember level. The results replicate a range of sediment compositions, empirical behaviors and conditions. We propose a procedure to characterize sediments numerically. The numerical ‘sediments’ can be applied to simulate processes in sediments exhibiting variations in strength due to post-seismic consolidation, bioturbation or variations in sedimentation rates.

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