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Kernel functions play an important role in a wide range of scientific computing and machine learning problems. These functions lead to dense kernel matrices that impose great challenges in computational costs at large scale. In this paper, we develop a set of fast kernel matrix compressing algorithms, which can reduce computation cost of matrix operations in the related applications. The foundation of these algorithms is the polyharmonic spline interpolation, which includes a set of radial basis functions that allow flexible choices of interpolating nodes, and a set of polynomial basis functions that guarantee the solvability and convergence of the interpolation. With these properties, original data points in the interacting kernel function can be randomly sampled with great flexibility, so the proposed method is suitable for complicated data structures, such as high-dimensionality, random distribution, or manifold. To further boost the algorithm accuracy and efficiency, this scheme is equipped with a QR sampling strategy, and combined with a recently developed fast stochastic SVD to form a hybrid method. If the overall number of degree of freedom is N, then the compressing algorithm has complexity of O(N) for low-rank matrices, and O(NlogN) for general matrices with a hierarchical structure. Numerical results for data on various domains and different kernel functions validate the accuracy and efficiency of the proposed method.

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"Three straight and two flat" is the inevitable demand when realizing the intelligent mining of a fully mechanized mining face. To address the crucial technical issue of lacking accurate perception of the shape of the scraper conveyor during intelligent coal mining, a three-dimensional curvature sensor involving fiber Bragg grating (FBG) is used as a perceptive tool to conduct curve reconstruction research based on different local motion frames and to reconstruct the shape of the scraper conveyor. Firstly, the formation process of the 'S'-shaped bending section of the scraper conveyor during the pushing process is determined. Based on the FBG sensing principle, a mathematical model between the variation in the central wavelength and the strain and curvature is established, and the cubic B-spline interpolation method is employed to continuously process the obtained discrete curvature. Secondly, based on differential geometry, a spatial curve reconstruction algorithm based on the Frenet moving frame is derived, and the shape curve prediction interpolation model is built based on a gated recurrent unit (GRU) model, which reduces the impact of the decrease in curve reconstruction accuracy caused by damage to some grating measuring points. Finally, an experimental platform was designed and built, and sensors with curvature radii of 6 m, 7 m, and 8 m were tested. The experimental results showed that the reconstructed curve was essentially consistent with the actual shape, and the absolute error at the end was about 2 mm. The feasibility of this reconstruction algorithm in engineering has been proven, and this is of great significance in achieving shape curve perception and straightness control for scraper conveyors.

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Early detection and effective treatment of severe COVID-19 patients remain two major challenges during the current pandemic. Analysis of molecular changes in blood samples of severe patients is one of the promising approaches to this problem. From thousands of proteomic, metabolomic, lipidomic, and transcriptomic biomarkers selected in other research, we identify several pairs of biomarkers that after additional nonlinear spline transformation are highly effective in classifying and predicting severe COVID-19 cases. The performance of these pairs is evaluated in-sample, in a cross-validation exercise, and in an out-of-sample analysis on two independent datasets. We further improve our classifier by identifying complementary pairs using hierarchical clustering. In a result, we achieve 96-98% AUC on the validation data. Our findings can help medical experts to identify small groups of biomarkers that after nonlinear transformation can be used to construct a cost-effective test for patient screening and prediction of severity progression.

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This paper aims to address the obstacle avoidance problem of autonomous underwater vehicles (AUVs) in complex environments by proposing a trajectory planning method based on the Gauss pseudospectral method (GPM). According to the kinematics and dynamics constraints, and the obstacle avoidance requirement in AUV navigation, a multi-constraint trajectory planning model is established. The model takes energy consumption and sailing time as optimization objectives. The optimal control problem is transformed into a nonlinear programming problem by the GPM. The trajectory satisfying the optimization objective can be obtained by solving the problem with a sequential quadratic programming (SQP) algorithm. For the optimization of calculation parameters, the cubic spline interpolation method is proposed to generate initial value. Finally, through comparison with the linear fitting method, the rapidity of the solution of the cubic spline interpolation method is verified. The simulation results show that the cubic spline interpolation method improves the operation performance by 49.35% compared with the linear fitting method, which verifies the effectiveness of the cubic spline interpolation method in solving the optimal control problem.

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There are many frequent landslide areas in China, which badly affect local people. Since the 1980s, there have been more than 200 landslides in China with a death toll of 30 or more people at a time, economic losses of more than CNY 10 million or significant social impact. Therefore, the study of landslide displacement prediction is very important. The traditional ARIMA and LSTM models are commonly used for forecasting time series data. In our study, a multivariable LSTM landslide displacement prediction model is proposed based on the traditional LSTM model, which integrates rainfall and reservoir water level data. Taking the Baijiabao landslide in the Three Gorges Reservoir area as an example, the data of displacement, rainfall and reservoir water level of monitoring point ZG323 from November 2006 to December 2012 were selected for this study. Our results show that the displacement prediction results of the multivariable LSTM model are more accurate than those of the ARIMA and the univariate LSTM models, and the mean square, root mean square and mean absolute errors are the smallest, which are 0.64223, 0.8014 and 0.50453 mm, respectively. Therefore, the multivariable LSTM model method has higher accuracy and better application prospects in the displacement prediction of the Baijiabao landslide, which can provide a certain reference for the displacement prediction of the same type of landslide.

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The hydrolysis time is directly related to the flavor of the Maillard reaction, but existing proxy models cannot simulate and model the variation curves of vital volatile components. This study developed a predictive model for modelling and simulating key volatile compounds of Maillard reaction products (MRPs) derived from beef tallow residue hydrolysate. Results showed the degree of hydrolysis increased with hydrolysis time, and the most significant improvement in the roast flavor and overall acceptance was when hydrolyzing 4 h. Based on flavor dilution value and the relative odor activity value, nine key volatile components were identified, and 2-ethyl-3,5-dimethylpyrazine with roast flavor was the highest. Compared with Polynomial Curve Fitting (PCF) and Cubic Spline Interpolation (CSI), key volatile compounds of MRPs could be better modeled and simulated by the Curve Prediction Model (CPM). All results suggested that CPM could predict the changes in key volatile components produced by MRPs.

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The demodulation algorithm based on 3 × 3 coupler in a fiber-optic hydrophone array has gained extensive attention in recent years. The traditional method uses a circulator to construct the normal path-match interferometry; however, the problem of increasing the asymmetry of the three-way signal to be demodulated is easily overlooked. To provide a solution, we report a pretreatment method for hydrophone array based on 3 × 3 coupler demodulation. We use cubic spline interpolation to perform nonlinear fitting to the reflected pulse train and calculate the peak-to-peak values of the single pulse to determine the light intensity compensation coefficient of the interference signal, so as to demodulate the corrected three-way interference signal. For experimental verification, ultra-weak fiber Bragg gratings (uwFBGs) with reflectivity of -50 dB are applied to construct a hydrophone array with 800 sensors, and a vibratory liquid column method is set up to generate a low-frequency hydroacoustic signal. Compared to the traditional demodulation algorithm based on a 3 × 3 coupler, the pretreatment method can improve the consistency of interference signals. The Lissajous figures show that cubic spline interpolation can improve the accuracy of monopulse peak seeking results by about 1 dB, and intensity compensation can further lead to a much lower noise density level for the interference pulse amplitude-specifically, more than 7 dB at 5~50 Hz-and the signal-to-noise ratio is improved by approximately 10 dB at 10 Hz. The distinct advantages of the proposed pretreatment method make it an excellent candidate for a hydrophone array system based on path-match interferometry.

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Although being a really active area of research, television super-resolution remains a difficult problem. Additionally, it is noted that the blur motion and computational crisis hinder the enhancement. As a result, the goal of this research is to present a brand-new smart SR framework for the camera shot. To create High Resolution (HR) videos, first frames in RGB format are converted to HSV and then the V-channel is enhanced. In order to create enriched video frames, a high - dimension grid with enhanced pixel intensity is then created. This paper introduces a particular progression to enable this: Motion estimation, Cubic Spline Interpolation, and Deblurring or Sharpening are the three methods. By carefully adjusting the parameters, the cubic spline interpolation is improved during operation. A brand-new hybrid technique dubbed Lion with Particle Swarm Velocity Update (LPSO-VU), which combines the principles of the Lion Algorithm (LA) and Particle Swarm Optimization (PSO) algorithms, is presented for this optimal tuning purpose. Finally, using the BRISQUE, SDME, and ESSIM metrics, the adequacy of the method is contrasted to other traditional models, and its superiority is demonstrated. Accordingly, the analysis shows that the suggested LPSO-VU model for video frame 1 is 16.6%, 25.56%, 26.2%, 26.2%, and 27.2% superior to the previous systems like PSO, GWO, WOA, ROA, MF-ROA, and LA, respectively, in terms of BRISQUE.

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Exploring the spatial distribution of the multi-fractal scaling behaviours in atmospheric CO2 concentration time series is useful for understanding the dynamic mechanisms of carbon emission and absorption. In this work, we utilise a well-established multi-fractal detrended fluctuation analysis to examine the multi-fractal scaling behaviour of a column-averaged dry-air mole fraction of carbon dioxide (XCO2) concentration time series over China, and portray the spatial distribution of the multi-fractal scaling behaviour. As XCO2 data values from the Greenhouse Gases Observing Satellite (GOSAT) are insufficient, a spatio-temporal thin plate spline interpolation method is applied. The results show that XCO2 concentration records over almost all of China exhibit a multi-fractal nature. Two types of multi-fractal sources are detected. One is long-range correlations, and the other is both long-range correlations and a broad probability density function; these are mainly distributed in southern and northern China, respectively. The atmospheric temperature and carbon emission/absorption are two possible external factors influencing the multi-fractality of the atmospheric XCO2 concentration. Highlight: (1) An XCO2 concentration interpolation is conducted using a spatio-temporal thin plate spline method. (2) The spatial distribution of the multi-fractality of XCO2 concentration over China is shown. (3) Multi-fractal sources and two external factors affecting multi-fractality are analysed.

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Smart wearable devices are occupying an increasingly important position in scientific research and people's life fields. As an indispensable component of smart wearable devices, sensors play a crucial role in their sensing and feedback capabilities. In this paper, we investigate the bending gesture sensing for the most dexterous part of human anatomy, the finger. Based on series-connected fiber Bragg gratings (FBGs), recognition of finger bending posture is achieved by MATLAB modeling and the cubic spline interpolation.

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The present paper deals with cubic B-spline approximation together with θ -weighted scheme to obtain numerical solution of the time fractional advection diffusion equation using Atangana-Baleanu derivative. To discretize the Atangana-Baleanu time derivative containing a non-singular kernel, finite difference scheme is utilized. The cubic basis functions are associated with spatial discretization. The current discretization scheme used in the present study is unconditionally stable and the convergence is of order O ( h 2 + Δ t 2 ) . The proposed scheme is validated through some numerical examples which reveal the current scheme is feasible and quite accurate.

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Using motion capture data as a part of mobile brain-body imaging (MoBI) recording has been increasing. With minimal linear algebra background, this paper explains how the rigid body transformation can be a useful preprocessing step for denoising and missing marker recovery. Such a transformation can provide insight and necessary-and-sufficient solutions requiring no assumption other than the minimum number of markers present. First, a simulation test using the empirical datasets from the AudioMaze project published from this journal's same volume demonstrates theoretical accuracy. The simulation results show that the rigid-body method perfectly recovers missing markers on a rigid body if a minimum of three marker positions is available. Second, the same transformation is applied to the empirical dataset. Before preprocessing, the raw data show that 15-80% of data frames had all markers present for rigid-body defined body parts. After using the rigid-body correction, most body parts recovered full markers in 90-95% of the data frames. The result also suggests the necessity for performing across-trial corrections for within-participant (42% missing detected in one of the body parts) and across-participants (11% missing). The discussion section introduces a solution and a performance summary for non-rigid-body marker correction using a neural network. Data support that the rigid body transformation is an intuitive and powerful correction method necessary for preprocessing motion capture data for neurocognitive experiments. The supporting information section contains a URL link to Matlab code and example data.

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BACKGROUND: Speckle tracking has always been a challenging issue in echocardiography images due to the lowcontrast and noisy nature of ultrasonic imaging modality. While in ultrasound imaging, framerate is limited by image size and sound speed in tissue, speckle tracking results get worse inthree-dimensional imaging due to its lower frame rate. Therefore, numerous techniques have beenreported to overcome this limitation and enhance tracking accuracy. METHODS: In this work, we have proposedto increase the frame rate temporally for a sequence of three-dimensional (3D) echocardiographyframes to make tracking more accurate. To increase the number of frames, cubic B-spline is usedto interpolate between intensity variation time curves extracted from every single voxel in theimage during the cardiac cycle. We have shown that the frame rate increase will result in trackingaccuracy improvement. RESULTS: To prove the efficiency of the proposed method, numerical evaluation metricsfor tracking are reported to make a comparison between high temporal resolution sequences andlow temporal resolution sequences. Anatomical affine optical flow is selected as the state-of-the-artspeckle tracking method, and a 3D echocardiography dataset is used to evaluate the proposedmethod. CONCLUSION: Results show that it is beneficial for speckle tracking to perform on temporally condensedframes rather than ordinary clinical 3D echocardiography images. Normalized mean enhancementvalues for mean absolute error, Hausdorff distance, and Dice index for all cases and all frames are0.44 ± 0.09, 0.42± 0.09, and 0.36 ± 0.06, respectively.

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Finding a proper balance between video quality and the required bandwidth is an important issue, especially in networks of limited capacity. The problem of comparing the efficiency of video codecs and choosing the most suitable one in a specific situation has become very important. This paper proposes a method of comparing video codecs while also taking into account objective quality assessment metrics. The author shows the process of preparing video footage, assessing its quality, determining the rate-distortion curves, and calculating the bitrate saving for pairs of examined codecs. Thanks to the use of the spline interpolation method, the obtained results are better than those previously presented in the literature, and more resistant to the quality metric used.

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In the signal processing of real subway vehicles, impacts between wheelsets and rail joint gaps have significant negative effects on the spectrum. This introduces great difficulties for the fault diagnosis of gearboxes. To solve this problem, this paper proposes an adaptive time-domain signal segmentation method that envelopes the original signal using a cubic spline interpolation. The peak values of the rail joint gap impacts are extracted to realize the adaptive segmentation of gearbox fault signals when the vehicle was moving at a uniform speed. A long-time and unsteady signal affected by wheel-rail impacts is segmented into multiple short-term, steady-state signals, which can suppress the high amplitude of the shock response signal. Finally, on this basis, multiple short-term sample signals are analyzed by time- and frequency-domain analyses and compared with the nonfaulty results. The results showed that the method can efficiently suppress the high-amplitude components of subway gearbox vibration signals and effectively extract the characteristics of weak faults due to uniform wear of the gearbox in the time and frequency domains. This provides reference value for the gearbox fault diagnosis in engineering practice.

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Oxygen saturation and respiratory signals are important physiological signals of human body, respiratory monitoring plays an important role in clinical and daily life. A system was established to extract respiratory signals from photoplethysmography in this study. Including the collection of pulse wave signal, the extraction of respiratory signal, and the calculation of respiratory rate and pulse rate transmitted from the slave computer to the host computer in real time.

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BACKGROUND: In clinical practice, EEGs are assessed visually. For practical reasons, recordings often need to be performed with a reduced number of electrodes and artifacts make assessment difficult. To circumvent these obstacles, different interpolation techniques can be utilized. These techniques usually perform better for higher electrode densities and values interpolated at areas far from electrodes can be unreliable. Using a method that learns the statistical distribution of the cortical electrical fields and predicts values may yield better results. NEW METHOD: Generative networks based on convolutional layers were trained to upsample from 4 or 14 channels or to dynamically restore single missing channels to recreate 21-channel EEGs. 5,144 h of data from 1,385 subjects of the Temple University Hospital EEG database were used for training and evaluating the networks. COMPARISON WITH EXISTING METHOD: The results were compared to spherical spline interpolation. Several statistical measures were used as well as a visual evaluation by board certified clinical neurophysiologists. Overall, the generative networks performed significantly better. There was no difference between real and network generated data in the number of examples assessed as artificial by experienced EEG interpreters whereas for data generated by interpolation, the number was significantly higher. In addition, network performance improved with increasing number of included subjects, with the greatest effect seen in the range 5-100 subjects. CONCLUSIONS: Using neural networks to restore or upsample EEG signals is a viable alternative to spherical spline interpolation.

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Respiratory activity is an important vital sign of life that can indicate health status. Diseases such as bronchitis, emphysema, pneumonia and coronavirus cause respiratory disorders that affect the respiratory systems. Typically, the diagnosis of these diseases is facilitated by pulmonary auscultation using a stethoscope. We present a new attempt to develop a lightweight, comprehensive wearable sensor system to monitor respiration using a multi-sensor approach. We employed new wearable sensor technology using a novel integration of acoustics and biopotentials to monitor various vital signs on two volunteers. In this study, a new method to monitor lung function, such as respiration rate and tidal volume, is presented using the multi-sensor approach. Using the new sensor, we obtained lung sound, electrocardiogram (ECG), and electromyogram (EMG) measurements at the external intercostal muscles (EIM) and at the diaphragm during breathing cycles with 500 mL, 625 mL, 750 mL, 875 mL, and 1000 mL tidal volume. The tidal volumes were controlled with a spirometer. The duration of each breathing cycle was 8 s and was timed using a metronome. For each of the different tidal volumes, the EMG data was plotted against time and the area under the curve (AUC) was calculated. The AUC calculated from EMG data obtained at the diaphragm and EIM represent the expansion of the diaphragm and EIM respectively. AUC obtained from EMG data collected at the diaphragm had a lower variance between samples per tidal volume compared to those monitored at the EIM. Using cubic spline interpolation, we built a model for computing tidal volume from EMG data at the diaphragm. Our findings show that the new sensor can be used to measure respiration rate and variations thereof and holds potential to estimate tidal lung volume from EMG measurements obtained from the diaphragm.

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A high-speed numerical potential delivering computational performance comparable with complex coarse-grained analytic potentials makes available models that have greater degrees of physical and chemical accuracy. This opens the possibility of increased accuracy in classical molecular dynamics simulations of anisotropic systems. In this work, we report the development of a high-speed lookup table (LUT) of four-dimensional gridded data, that uses cubic B-spline interpolations to derive off grid values and their associated partial derivatives that are located between the known grid data points. The accuracy of the coarse-grained numerical potential using a LUT from uniaxial Gay-Berne (GB) potential produced array of values is within a 3% and a 5% margin of error respectively for the interpolation of the uniaxial GB potential and its partial derivatives. The numerical potential model and partial derivatives speedup is made competitive with the analytical potential by exploiting graphics processing units on board functionality. The capability of the numerical potential is demonstrated by comparing minimizations of a box of 500 naphthalene molecules. The minimizations using a full atomistic (NAMD/CHARMM force field), a biaxial GB and a numerical potential from a LUT using data from the CHARMM pair potential was done. The numerical potential model is significantly more accurate in its approximation of the atomistic local minimum configuration than is the biaxial GB analytical potential function. This demonstrates that using a numerical potential founded on a direct lookup of the atomistic potential landscape significantly improves coarse grain (CG) modeling of complex molecules, possibly paving the way for accurate anisotropic system CG modeling.

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Oxygen saturation and respiratory signals are important physiological signals of human body, respiratory monitoring plays an important role in clinical and daily life. A system was established to extract respiratory signals from photoplethysmography in this study. Including the collection of pulse wave signal, the extraction of respiratory signal, and the calculation of respiratory rate and pulse rate transmitted from the slave computer to the host computer in real time.

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