Multi and breather wave soliton solutions and the linear superposition principle for generalized Hietarinta equation

In this paper, we study the generalized ([Formula: see text])-dimensional Hietarinta equation which is investigated by utilizing Hirota’s bilinear method. Also, the bilinear form is obtained, and the N-soliton solutions are constructed. In addition, multi-wave and breather wave solutions of the addressed equation with specific coefficients are presented. Finally, under certain conditions, the asymptotic behavior of solutions is analyzed in both methods. Moreover, we employ the linear superposition principle to determine [Formula: see text]-soliton wave solutions for the generalized ([Formula: see text])-dimensional Hietarinta equation.

Intracranial Electric Field Recording During Multichannel Transcranial Electrical Stimulation

Background: Multichannel transcranial electrical stimulation (tES) modeling and optimization have been widely studied in recent years. Its theoretical bases include quasi-static assumption and linear superposition. However, there is still a lack of direct in vivo evidence to validate the simulation model and theoretical assumptions. Methods: We directly measured the multichannel tES-induced voltage changes with implanted stereotactic-electroencephalographic (sEEG) electrodes in 12 epilepsy subjects. By combining these measured data, we investigate the linear superposition and prediction accuracy of simulation models for multi-electrode stimulation and further compare the induced EF differences between transcranial direct current stimulation (tDCS) and transcranial alternating current stimulation (tACS). Results: Our in vivo measurements demonstrated that the multi-electrode tES-induced voltages were almost equal to the sum of the voltages generated independently by bipolar stimulation. Both measured voltages and electric fields obtained in vivo were highly correlated with the predicted values in our cohort (Voltages: r = 0.92, p < 0.001; electric fields: r = 0.74, p < 0.001). Under the same stimulation intensity, the tDCS-induced peak-zero voltages were highly correlated with the values of tACS (r = 0.99, p < 0.001; s = 0.99). Conclusions: The in vivo measurements provides confirmatory results for linear superposition and quasi-static assumption within the human brain. Furthermore, we found that the individualized simulation model reliably predicted the multi-electrode tES-induced electric fields.

Classifier Performance Evaluation in Wrist and Finger Movement Fitting Task Based on Forearm HD-sEMG

Background: The transmission of human body movements to other devices through wearable smart bracelets have attracted more and more attentions in the field of human-machine interface (HMI) applications. However, due to the limitation of the collection range of wearable bracelets, it is necessary to study the relationship between the superposition of wrist and finger motion and their cooperative motion to simplify the collection system of the device.Methods: The multi-channel high-density surface electromyogram (HD-sEMG) signal has high spatial resolution and can improve the accuracy of multi-channel fitting. In this study, we quantified the HD-sEMG forearm spatial activation features of 256 channels of hand movement, and performed a linear fitting of the quantified features of fingers and wrist movements to verify the linear superposition relationship between fingers and wrist cooperative movements and their independent movements. The most important thing is to classify and predict the results of the fitting and the actual measured fingers and wrist cooperative actions by four commonly used classifiers: Linear Discriminant Analysis (LDA) ,K-Nearest Neighbor (KNN) ,Support Vector Machine (SVM) and Random Forest (RF), and evaluate the performance of the four classifiers in gesture fitting in detail according to the classification results.Results: In a total of 12 kinds of synthetic gesture actions, in the three cases where the number of fitting channels was selected as 8, 32 and 64, four classifiers of LDA, SVM, RF and KNN are used for classification prediction. When the number of fitting channels was 8, the prediction accuracy of LDA classifier was 99.70%, the classification accuracy of KNN was 99.40%, the classification accuracy of SVM was 99.20%, and the classification accuracy of RF was 93.75%. When the number of fitting channels was 32, the accuracy of LDA was 98.51%, the classification accuracy of KNN was 97.92%, the accuracy of SVM is 96.73%, and the accuracy of RF was 86.61%. When the number of fitting channels is 64, the accuracy of LDA is 95.83%, the classification accuracy of KNN is 91.67%, the accuracy of SVM is 86.90%, and the accuracy of RF is 83.30%.Conclusion: It can be seen from the results that when the number of fitting channels is 8, the classification accuracy of the three classifiers of LDA, KNN and SVM is basically the same, but the time-consuming of SVM is very small. When the amount of data is large, the priority should be selected SVM as the classifier. When the number of fitting channels increases, the classification accuracy of the LDA classifier will be higher than the other three classifiers, so the LDA classifier should be more appropriate. The classification accuracy of the RF classifier in this type of problem has always been far lower than the other three classifiers, so it is not recommended to use the RF classifier as a classifier for gesture stacking related work.

Study on Slamming Pressure Characteristics of Platform under Freak Wave

Freak waves have great peak energy, short duration, great contingency, and strong nonlinear characteristics, and can cause severe damage to ships and marine structures. In this study, numerical simulations in conjunction with experimental tests are applied to study air gap response and wave slamming loads of a semi-submersible offshore platform under a freak wave. A three-dimensional wave tank, which is created based on the computational fluid dynamics (CFD) method, is applied to study the hydrodynamic responses of a semi-submersible platform. The numerical model of the tank and offshore platform system are checked according to the experimental results. A typical freak wave is modelled in numerical wave tanks by the linear superposition method, and its significant wave height is 13.03 m. It is found that the freak wave is closely associated with the wave slamming. The appearance of the freak wave gives rise to a negative air, gap which appears on the side of the back wave surface at the bottom of the deck box, and considerable slamming pressure is generated. Furthermore, the wave run up at the junction of the column and the buoyancy tank is also seen due to the freak wave.

Conical Statistical Optimal Near-Field Acoustic Holography with Combined Regularization

For the sound field reconstruction of large conical surfaces, current statistical optimal near-field acoustic holography (SONAH) methods have relatively poor applicability and low accuracy. To overcome this problem, conical SONAH based on cylindrical SONAH is proposed in this paper. Firstly, elementary cylindrical waves are transformed into those suitable for the radiated sound field of the conical surface through cylinder-cone coordinates transformation, which forms the matrix of characteristic elementary waves in the conical spatial domain. Secondly, the sound pressure is expressed as the superposition of those characteristic elementary waves, and the superposition coefficients are solved according to the principle of superposition of wave field. Finally, the reconstructed conical pressure is expressed as a linear superposition of the holographic conical pressure. Furthermore, to overcome ill-posed problems, a regularization method combining truncated singular value decomposition (TSVD) and Tikhonov regularization is proposed. Large singular values before the truncation point of TSVD are not processed and remaining small singular values representing high-frequency noise are modified by Tikhonov regularization. Numerical and experimental case studies are carried out to validate the effectiveness of the proposed conical SONAH and the combined regularization method, which can provide reliable evidence for noise monitoring and control of mechanical systems.

Special decompositions and linear superpositions of nonlinear systems: BKP and dispersionless BKP equations

The existence of decomposition solutions of the well-known nonlinear BKP hierarchy is analyzed. It is shown that these decompositions provide simple and interesting relationships between classical integrable systems and the BKP hierarchy. Further, some special decomposition solutions display a rare property: they can be linearly superposed. With the emphasis on the case of the fifth BKP equation, the structure characteristic having linear superposition solutions is analyzed. Finally, we obtain similar superposed solutions in the dispersionless BKP hierarchy.

Determination of lithium in human serum by isotope dilution atomic absorption spectrometry

The therapeutic dose of lithium (Li) compounds, which are widely used for the treatment of psychiatric and hematologic disorders, is close to its toxic level; therefore, drug monitoring protocols are mandatory. Herein, we propose a fast, simple, and low-cost analytical procedure for the traceable determination of Li concentration in human serum, based on the monitoring of the Li isotope dilution through the partially resolved isotope shift in its electronic transition around 670.80 nm using a commercially available high-resolution continuum source graphite furnace atomic absorption spectrometer. With this technique, serum samples only require acidic digestion before analysis. The procedure requires three measurements—an enriched 6Li spike, a mixture of a certified standard solution and spike, and a mixture of the sample and spike with a nominal 7Li/6Li ratio of 0.82. Lanthanum has been used as an internal spectral standard for wavelength correction. The spectra are described as the linear superposition of the contributions of the respective isotopes, each consisting of a spin-orbit doublet, which can be expressed as Gaussian components with constant spectral position and width and different relative intensity, reflecting the isotope ratio in the sample. Both the spectral constants and the correlation between isotope ratio and relative band intensity have been experimentally obtained using commercially available materials enriched with Li isotopes. The Li characteristic mass (mc) obtained corresponds to 0.6 pg. The procedure has been validated using five human serum certified reference materials. The results are metrologically comparable and compatible to the certified values. The measurement uncertainties are comparable to those obtained by the more complex and expensive technique, isotope dilution mass spectrometry. Graphical abstract

Linear superposition of responses evoked by individual glottal pulses explain over 80% of the frequency following response to human speech in the macaque monkey

The frequency-following response (FFR) is a scalp-recorded electrophysiological potential that closely follows the periodicity of complex sounds such as speech. It has been suggested that FFRs reflect the linear superposition of responses that are triggered by the glottal pulse in each cycle of the fundamental frequency (F0 responses) and sequentially propagate through auditory processing stages in brainstem, midbrain, and cortex. However, this conceptualization of the FFR is debated, and it remains unclear if and how well a simple linear superposition can capture the spectro-temporal complexity of FFRs that are generated within the highly recurrent and non-linear auditory system. To address this question, we used a deconvolution approach to compute the hypothetical F0 responses that best explain the FFRs in rhesus monkeys to human speech and click trains with time-varying pitch patterns. The linear superposition of F0 responses explained well over 90% of the variance of click train steady state FFRs and well over 80% of mandarin tone steady state FFRs. The F0 responses could be measured with high signal-to-noise ratio and featured several spectro-temporally and topographically distinct components that likely reflect the activation of brainstem (<5ms; 200-1000 Hz), midbrain (5-15 ms; 100-250 Hz) and cortex (15-35 ms; ~90 Hz). In summary, our results in the monkey support the notion that FFRs arise as the superposition of F0 responses by showing for the first time that they can capture the bulk of the variance and spectro-temporal complexity of FFRs to human speech with time-varying pitch. These findings identify F0 responses as a potential diagnostic tool that may be useful to reliably link altered FFRs in speech and language disorders to altered F0 responses and thus to specific latencies, frequency bands and ultimately processing stages.

Application of Two-Dimensional Compressive Sensing to Wavelet Method of Moments for Fast Analysis of Wide-Angle Electromagnetic Scattering Problems

To efficiently solve the electromagnetic scattering problems over a wide incident angle, a novel scheme by introducing the two-dimensional compressive sensing theory into the wavelet method of moments is proposed. In this scheme, a linear system of equations with multiple right-hand sides in wavelet domain is formed firstly, and one side of the bilateral sparse transform to the induced current matrix is simultaneously accomplished and then the bilateral measurement of the induced current matrix is operated by the linear superposition of the right-hand side vectors a few times and the extraction of rows from the impedance matrix. Finally, after completing the other side of the bilateral sparse transform, the wide-angle problems can be solved rapidly by two times of recovery algorithm with prior knowledge. The basic principle is elaborated in detail, and the effectiveness is demonstrated by numerical experiments.