Triadic Synchrony: Application of Multiple Wavelet Coherence to a Small Group Conversation

By applying multiple wavelet coherence (MWC) to data from human body movements in triadic interaction, this study quantified triadic synchrony, rhythmic similarity among three interactants. Thirty-nine Japanese undergraduates were randomly assigned in a triad, and engaged in a brain-storming task. Triadic synchrony was quantified by calculating MWC to the time-series movement data collected by Kinect v2 sensor. The existence of synchrony was statistically tested by using a pseudo-synchrony paradigm. Results showed that the averaged value of MWC was higher in the experimental participant trio than in those of the pseudo trio in the frequency band of 0.5 - 1 Hz. The result supports the possible utility of applying multiple wavelet coherence to evaluate triadic synchrony in a small group interaction.

Biorthogonal multiple wavelets generated by vector refinement equation

Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis. In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form $$\varphi (x) = \sum\limits_{\alpha \in \mathbb{Z}^s } {a(\alpha )\varphi (Mx - \alpha ), x \in \mathbb{R}^s } ,$$ where the vector of functions ? = (? 1, …, ? r)T is in $(L_2 (\mathbb{R}^s ))^r ,a = :(a(\alpha ))_{\alpha \in \mathbb{Z}^s } $ is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim n→∞ M ?n = 0. Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results.

The Biorthogonality of Multiple Vector-valued Bivariate Wavelet Packets

The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.

Synergistic effects of multiple driving factors on the runoff variations in the Yellow River Basin,China

River runoff plays an important role in watershed ecosystems and human survival,and it is controlled by multiple environmental factors.However,the synergistic effects of various large-scale circulation factors and meteorological factors on the runoff on different time-frequency scales have rarely been explored.In light of this,the underlying mechanism of the synergistic effects of the different environmental factors on the runoff variations was investigated in the Yellow River Basin of China during the period 1950-2019 using the bivariate wavelet coherence(WTC)and multiple wavelet coherence(MWC)methods.First,the continuous wavelet transform(CWT)method was used to analyze the multiscale characteristics of the runoff.The results of the CWT indicate that the runoff exhibited significant continuous or discontinuous annual and semiannual oscillations during the study period.Scattered inter-annual time scales were also observed for the runoff in the Yellow River Basin.The meteorological factors better explained the runoff variations on seasonal and annual time scales.The average wavelet coherence(AWC)and the percent area of the significant coherence(PASC)between the runoff and individual meteorological factors were 0.454 and 19.89%,respectively.The circulation factors mainly regulated the runoff on the inter-annual and decadal time scales with more complicated phase relationships due to their indirect effects on the runoff.The AWC and PASC between the runoff and individual circulation factors were 0.359 and 7.31%,respectively.The MWC analysis revealed that the synergistic effects of multiple factors should be taken into consideration to explain the multiscale characteristic variations of the runoff.The AWC or MWC ranges were 0.320-0.560,0.617-0.755,and 0.819-0.884 for the combinations of one,two,and three circulation and meteorological factors,respectively.The PASC ranges were 3.53%-33.77%,12.93%-36.90%,and 20.67%-39.34%for the combinations one,two,and three driving factors,respectively.The combinations of precipitation,evapotranspiration(or the number of rainy days),and the Arctic Oscillation performed well in explaining the variability in the runoff on all time scales,and the average MWC and PASC were 0.847 and 28.79%,respectively.These findings are of great significance for improving our understanding of hydro-climate interactions and water resources prediction in the Yellow River Basin.

Adaptive waveform design based on Morlet wavelet for ultra-wideband MIMO radar

For the issue of deterioration in detection performance caused by dynamically changing environment in ultra-wideband（UWB） multiple input multiple output（MIMO） radar, this paper proposes a novel adaptive waveform design which is aimed to improve the ability of discriminating target and clutter from the radar scene. Firstly, a sequence of Morlet wavelet pulses with frequency hopping and pulse position modulation by Welch-Costas array is designed. Then a waveform optimization solution is proposed which is achieved by applying the minimization mutual-information（MI） strategy. After that, with subsequent iterations of the algorithm, simulation results demonstrate that the optimal waveform design method brings an improvement in the target detection ability in the presence of noise and clutter.

Orthogonal Multiple Vector-Valued Wavelet Packets

The multiple vector-valued wavelet packets are defined and investigated. A procedure for constructing the multiple vector-valued wavelet packets is presented. The properties of multiple vector-valued wavelet packets are discussed by using integral transformation and operator theory. Finally, new orthogonal bases of L^2（R, C^s×s） is constructed from the orthogonal multiple vector-valued wavelet packets.

Modeling and forecasting time series of precious metals:a new approach to multifractal data

We introduce a novel approach to multifractal data in order to achieve transcended modeling and forecasting performances by extracting time series out of local Hurst exponent calculations at a specified scale.First,the long range and co-movement dependencies of the time series are scrutinized on time-frequency space using multiple wavelet coherence analysis.Then,the multifractal behaviors of the series are verified by multifractal de-trended fluctuation analysis and its local Hurst exponents are calculated.Additionally,root mean squares of residuals at the specified scale are procured from an intermediate step during local Hurst exponent calculations.These internally calculated series have been used to estimate the process with vector autoregressive fractionally integrated moving average(VARFIMA)model and forecasted accordingly.In our study,the daily prices of gold,silver and platinum are used for assessment.The results have shown that all metals do behave in phase movement on long term periods and possess multifractal features.Furthermore,the intermediate time series obtained during local Hurst exponent calculations still appertain the co-movement as well as multifractal characteristics of the raw data and may be successfully re-scaled,modeled and forecasted by using VARFIMA model.Conclusively,VARFIMA model have notably surpassed its univariate counterpart(ARFIMA)in all efficacious trials while re-emphasizing the importance of comovement procurement in modeling.Our study’s novelty lies in using a multifractal de-trended fluctuation analysis,along with multiple wavelet coherence analysis,for forecasting purposes to an extent not seen before.The results will be of particular significance to finance researchers and practitioners.

Linking the utilization of mineral resources and climate change:A novel approach with frequency domain analysis

Natural resources,climate change,and sustainable development are critical and simultaneously interrelated issues.This study investigates the interdependence between raw minerals material and sea level rise,considering the role of economic performance and material footprint employing wavelet locale multiple correlations from 1970 to 2019.The results provide strong evidence for cross-correlation of climate change with mineral resources,economic output,and domestic material consumption(biomass-fossil,metal,and non-metal)localized at the high frequency-time domain.However,the outcomes provide weak evidence for the association between bivariate time series at low frequency,which is a limitation in the short term.Based on the results,policymakers should implement effective environmental taxes and invest in cutting-edge technologies to optimize clean energy and mineral resources in a sustainable manner.