Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems

In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.

Text Simplification Using Transformer and BERT

Reading and writing are the main interaction methods with web content.Text simplification tools are helpful for people with cognitive impairments,new language learners,and children as they might find difficulties in understanding the complex web content.Text simplification is the process of changing complex text intomore readable and understandable text.The recent approaches to text simplification adopted the machine translation concept to learn simplification rules from a parallel corpus of complex and simple sentences.In this paper,we propose two models based on the transformer which is an encoder-decoder structure that achieves state-of-the-art(SOTA)results in machine translation.The training process for our model includes three steps:preprocessing the data using a subword tokenizer,training the model and optimizing it using the Adam optimizer,then using the model to decode the output.The first model uses the transformer only and the second model uses and integrates the Bidirectional Encoder Representations from Transformer(BERT)as encoder to enhance the training time and results.The performance of the proposed model using the transformerwas evaluated using the Bilingual Evaluation Understudy score(BLEU)and recorded(53.78)on the WikiSmall dataset.On the other hand,the experiment on the second model which is integrated with BERT shows that the validation loss decreased very fast compared with the model without the BERT.However,the BLEU score was small(44.54),which could be due to the size of the dataset so the model was overfitting and unable to generalize well.Therefore,in the future,the second model could involve experimenting with a larger dataset such as the WikiLarge.In addition,more analysis has been done on the model’s results and the used dataset using different evaluation metrics to understand their performance.

Analysis of a simplification strategy in a nonhydrostatic model for surface and internal wave problems

This paper examines the simplification strategy of retaining only the nonhydrostatic effect of local acceleration in a three-dimensional fully nonhydrostatic model regarding the submesoscale wave phenomenon in the ocean.Elaborate scale analysis of the vertical component of the Reynold-averaged Navier-Stokes(RANS)equation was performed,confirming the rationalization of this simplification.Then,the simplification was implemented in a RANS equation-based nonhydrostatic model NHWAVE(nonhydrostatic WAVE)to make a simplified nonhydrostatic model.Numerical examples were taken to test its performance,including surface sinusoidal waves propagating on an idealized East China Sea topography,tidally induced internal lee waves and small-scale solitary waves.The results show that in a considerably wide range of nonlinear strengths,the simplified nonhydrostatic model can obtain similar results as those in the fully nonhydrostatic model,even for smaller-scale solitary waves.Nonlinearity influences the applicability of the simplification.The stronger the nonlinearity is,the worse the simplified model describes the nonhydrostatic phenomenon.In general,the simplified nonhydrostatic model can simulate surface waves better than internal waves.Improvement of computational efficiency in the simplified nonhydrostatic model is reasonable,reducing the central processing unit time duration in the fully nonhydrostatic model by 16.4%–20.6%.The specially designed algorithm based on the simplified nonhydrostatic equation can remarkably reduce the computational time.

Recognition of Hybrid PQ Disturbances Based on Multi-Resolution S-Transform and Decision Tree

Aiming at the problems of multiple types of power quality composite disturbances,strong feature correlation and high recognition error rate,a method of power quality composite disturbances identification based on multiresolution S-transform and decision tree was proposed.Firstly,according to IEEE standard,the signal models of seven single power quality disturbances and 17 combined power quality disturbances are given,and the disturbance waveform samples are generated in batches.Then,in order to improve the recognition accuracy,the adjustment factor is introduced to obtain the controllable time-frequency resolution through multi-resolution S-transform time-frequency domain analysis.On this basis,five disturbance time-frequency domain features are extracted,which quantitatively reflect the characteristics of the analyzed power quality disturbance signal,which is less than the traditional method based on S-transform.Finally,three classifiers such as K-nearest neighbor,support vector machine and decision tree algorithm are used to effectively complete the identification of power quality composite disturbances.Simulation results showthat the classification accuracy of decision tree algorithmis higher than that of K-nearest neighbor and support vector machine.Finally,the proposed method is compared with other commonly used recognition algorithms.Experimental results show that the proposedmethod is effective in terms of detection accuracy,especially for combined PQ interference.

Efficient Sparse-Grid Implementation of a Fifth-Order Multi-resolution WENO Scheme for Hyperbolic Equations

High-order accurate weighted essentially non-oscillatory(WENO)schemes are a class of broadly applied numerical methods for solving hyperbolic partial differential equations(PDEs).Due to highly nonlinear property of the WENO algorithm,large amount of computational costs are required for solving multidimensional problems.In our previous work(Lu et al.in Pure Appl Math Q 14:57–86,2018;Zhu and Zhang in J Sci Comput 87:44,2021),sparse-grid techniques were applied to the classical finite difference WENO schemes in solving multidimensional hyperbolic equations,and it was shown that significant CPU times were saved,while both accuracy and stability of the classical WENO schemes were maintained for computations on sparse grids.In this technical note,we apply the approach to recently developed finite difference multi-resolution WENO scheme specifically the fifth-order scheme,which has very interesting properties such as its simplicity in linear weights’construction over a classical WENO scheme.Numerical experiments on solving high dimensional hyperbolic equations including Vlasov based kinetic problems are performed to demonstrate that the sparse-grid computations achieve large savings of CPU times,and at the same time preserve comparable accuracy and resolution with those on corresponding regular single grids.

Numerical Simulation of the Settling Flux of Biodeposition in a Bay with Cage Culture Through Similarity Theory and a Simplified Pollution Source

The settling flux of biodeposition affects the environmental quality of cage culture areas and determines their environmental carrying capacity.Simple and effective simulation of the settling flux of biodeposition is extremely important for determining the spatial distribution of biodeposition.Theoretically,biodeposition in cage culture areas without specific emission rules can be simplified as point source pollution.Fluent is a fluid simulation software that can simulate the dispersion of particulate matter simply and efficiently.Based on the simplification of pollution sources and bays,the settling flux of biodeposition can be easily and effectively simulated by Fluent fluid software.In the present work,the feasibility of this method was evaluated by simulation of the settling flux of biodeposition in Maniao Bay,Hainan Province,China,and 20 sampling sites were selected for determining the settling fluxes.At sampling sites P1,P2,P3,P4,P5,Z1,Z2,Z3,Z4,A1,A2,A3,A4,B1,B2,C1,C2,C3 and C4,the measured settling fluxes of biodeposition were 26.02,15.78,10.77,58.16,6.57,72.17,12.37,12.11,106.64,150.96,22.59,11.41,18.03,7.90,19.23,7.06,11.84,5.19 and 2.57 g d^(−1)m^(−2),respectively.The simulated settling fluxes of biodeposition at the corresponding sites were 16.03,23.98,8.87,46.90,4.52,104.77,16.03,8.35,180.83,213.06,39.10,17.47,20.98,9.78,23.25,7.84,15.90,6.06 and 1.65 g d^(−1)m^(−2),respectively.There was a positive correlation between the simulated settling fluxes and measured ones(R=0.94,P=2.22×10^(−9)<0.05),which implies that the spatial differentiation of biodeposition flux was well simulated.Moreover,the posterior difference ratio of the simulation was 0.38,and the small error probability was 0.94,which means that the simulated results reached an acceptable level from the perspective of relative error.Thus,if nonpoint source pollution is simplified to point source pollution and open waters are simplified based on similarity theory,the setting flux of biodeposition in the open waters can be simply and effectively simulated by the fluid simulation software Fluent.

Multi-resolution graph-based clustering analysis for lithofacies identifi cation from well log data: Case study of intraplatform bank gas fi elds, Amu Darya Basin

In this study, we used the multi-resolution graph-based clustering （MRGC） method for determining the electrofacies （EF） and lithofacies （LF） from well log data obtained from the intraplatform bank gas fields located in the Amu Darya Basin. The MRGC could automatically determine the optimal number of clusters without prior knowledge about the structure or cluster numbers of the analyzed data set and allowed the users to control the level of detail actually needed to define the EF. Based on the LF identification and successful EF calibration using core data, an MRGC EF partition model including five clusters and a quantitative LF interpretation chart were constructed. The EF clusters 1 to 5 were interpreted as lagoon, anhydrite flat, interbank, low-energy bank, and high-energy bank, and the coincidence rate in the cored interval could reach 85%. We concluded that the MRGC could be accurately applied to predict the LF in non-cored but logged wells. Therefore, continuous EF clusters were partitioned and corresponding LF were characteristics ＆different LF were analyzed interpreted, and the distribution and petrophysical in the framework of sequence stratigraphy.

A Progressive Line Simplification Algorithm

An application of line simplification considering spatial knowledge is described.A method for identifying potential conflict regions,in order to avoid the self_intersection of generalized lines,is also discussed.Furthermore,a new progressive line simplification algorithm is presented.From the view point of spatial cognition,a spatial hierarchical structure is proposed,and its application to construction of spatial knowledge related to a line is explained.

Multi-resolution image segmentation based on Gaussian mixture model

Mixture model based image segmentation method, which assumes that image pixels are independent and do not consider the position relationship between pixels, is not robust to noise and usually leads to misclassification. A new segmentation method, called multi-resolution Ganssian mixture model method, is proposed. First, an image pyramid is constructed and son-father link relationship is built between each level of pyramid. Then the mixture model segmentation method is applied to the top level. The segmentation result on the top level is passed top-down to the bottom level according to the son-father link relationship between levels. The proposed method considers not only local but also global information of image, it overcomes the effect of noise and can obtain better segmentation result. Experimental result demonstrates its effectiveness.

Winter wheat identification by integrating spectral and temporal information derived from multi-resolution remote sensing data

Timely crop acreage and distribution information are the basic data which drive many agriculture related applications.For identifying crop types based on remote sensing,methods using only a single image type have significant limitations.Current research that integrates fine and coarser spatial resolution images,using techniques such as unmixing methods,regression models,and others,usually results in coarse resolution abundance without sufficient detail within pixels,and limited attention has been paid to the spatial relationship between the pixels from these two kinds of images.Here we propose a new solution to identify winter wheat by integrating spectral and temporal information derived from multi-resolution remote sensing data and determine the spatial distribution of sub-pixels within the coarse resolution pixels.Firstly,the membership of pixels which belong to winter wheat is calculated using a 25-m resolution resampled Landsat Thematic Mapper(TM)image based on the Bayesian equation.Then,the winter wheat abundance(acreage fraction in a pixel)is assessed by using a multiple regression model based on the unique temporal change features from moderate resolution imaging spectroradiometer(MODIS)time series data.Finally,winter wheat is identified by the proposed Abundance-Membership(AM)model based on the spatial relationship between the two types of pixels.Specifically,winter wheat is identified by comparing the spatially corresponding 10×10 membership pixels of each abundance pixel.In other words,this method takes advantage of the relative size of membership in a local space,rather than the absolute size in the entire study area.This method is tested in the major agricultural area of Yiluo Basin,China,and the results show that acreage accuracy(Aa)is 93.01%and sampling accuracy(As)is 91.40%.Confusion matrix shows that overall accuracy(OA)is 91.4%and the kappa coefficient(Kappa)is 0.755.These values are significantly improved compared to the traditional Maximum Likelihood classification(MLC)and Random Forest classification(RFC)which rely on spectral features.The results demonstrate that the identification accuracy can be improved by integrating spectral and temporal information.Since the identification of winter wheat is performed in the space corresponding to each MODIS pixel,the influence of differences of environmental conditions is greatly reduced.This advantage allows the proposed method to be effectively applied in other places.

Multi-sensor image registration using multi-resolution shape analysis

Multi-sensor image registration has been widely used in remote sensing and medical image field, but registration performance is degenerated when heterogeneous images are involved. An image registration method based on multi-resolution shape analysis is proposed in this paper, to deal with the problem that the shape of similar objects is always invariant. The contours of shapes are first detected as visual features using an extended contour search algorithm in order to reduce effects of noise, and the multi-resolution shape descriptor is constructed through Fourier curvature representation of the contour’s chain code. Then a minimum distance function is used to judge the similarity between two contours. To avoid the effect of different resolution and intensity distribution, suitable resolution of each image is selected by maximizing the consistency of its pyramid shapes. Finally, the transformation parameters are estimated based on the matched control-point pairs which are the centers of gravity of the closed contours. Multi-sensor Landsat TM imagery and infrared imagery have been used as experimental data for comparison with the classical contour-based registration. Our results have been shown to be superior to the classical ones.

MULTI-RESOLUTION MOTION ESTIMATION AND COMPENSATION BASED ON ADJACENT PREDICTION OF FRAME DIFFERENCE IN WAVELET DOMAIN

Aiming at the higher bit-rate occupation of motion vector encoding and more time load of full-searching strategies, a multi-resolution motion estimation and compensation algorithm based on adjacent prediction of frame difference was proposed.Differential motion detection was employed to image sequences and proper threshold was adopted to identify the connected region.Then the motion region was extracted to carry out motion estimation and motion compensation on it.The experiment results show that the encoding efficiency of motion vector is promoted, the complexity of motion estimation is reduced and the quality of the reconstruction image at the same bit-rate as Multi-Resolution Motion Estimation(MRME) is improved.

Simplification and Experimental Verification for Temperature and Humidity Field Coupling Model of Conservatory Soil

Based on the surface energy balance model which is widely used abroad, a temperature and humidity field coupling model of conservatory soil without crop vegetation in full illumination was established. Considering the relatively closed environment in conservatory, weak solar radiation and little surface evaporation of soil, the daily variation of water content in different soil layers may be neglected, then the temperature and humidity field coupling model was simplified to a one-dimensional thermal diffusion model. The simplified model and the temperature and humidity field coupling model adopted the same computational method of soil physical parameters and discrete format of heat diffusion differential equations, and were applied to the continuous simulation of temperature field in conservatory soil without crop vegetation in full illumination. Through the comparison between simulation results and experimental data, the precision of the simplified model was verified. The typical rule of soil heat flux variation in a 24 h cycle was also obtained.

Automatic target tracking on multi-resolution terrain

We propose a high-performance path planning algorithm for automatic target tracking in the applications of real-time simulation and visualization of large-scale terrain datasets, with a large number of moving objects （such as vehicles） tracking multiple moving targets. By using a modified Dijkstra＇s algorithm, an optimal path between each vehicle-target pair over a weighted grid-presented terrain is computed and updated to eliminate the problem of local minima and losing of tracking. Then, a dynamic path re-planning strategy using multi-resolution representation of a dynamic updating region is proposed to achieve high-performance by trading-off precision for efficiency, while guaranteeing accuracy. Primary experimental results showed that our algorithm successfully achieved l0 to 96 frames per second interactive path-replanning rates during a terrain simulation scenario with 10 to 100 vehicles and multiple moving targets.

Application of multi-resolution analysis in sonar image denoising

Sonar images have complex background, low contrast, and deteriorative edges; these characteristics make it difficult for researchers to dispose the sonar objects. The multi-resolution analysis represents the signals in different scales efficiently, which is widely used in image processing. Wavelets are successful in disposing point discontinuities in one dimension, but not in two dimensions. The finite Ridgelet transform （FRIT） deals efficiently with the singularity in high dimension. It presents three improved denoising approaches, which are based on FRIT and used in the sonar image disposal technique. By experiment and comparison with traditional methods, these approaches not only suppress the artifacts, but also obtain good effect in edge keeping and SNR of the sonar image denoising.

Multi-resolution EMD and classscatter matrix extracting of tank sound

The acoustic vibration signal of tank is disassembled into the sum of intrinsic mode function （IMF） by multi-resolution empirical mode decomposition （EMD） method. The instantaneous frequency is obtained, and feature transformation matrix is figured out by class scatter matrix. Multi- dimensional scale energy vector is mapped into low-dimensional eigenvector, and classification extraction is realized. This method sufficiently separates of different sound target features. The test result indicates that it is effective.

Magnetic-resonance image segmentation based on improved variable weight multi-resolution Markov random field in undecimated complex wavelet domain

To solve the problem that the magnetic resonance(MR)image has weak boundaries,large amount of information,and low signal-to-noise ratio,we propose an image segmentation method based on the multi-resolution Markov random field(MRMRF)model.The algorithm uses undecimated dual-tree complex wavelet transformation to transform the image into multiple scales.The transformed low-frequency scale histogram is used to improve the initial clustering center of the K-means algorithm,and then other cluster centers are selected according to the maximum distance rule to obtain the coarse-scale segmentation.The results are then segmented by the improved MRMRF model.In order to solve the problem of fuzzy edge segmentation caused by the gray level inhomogeneity of MR image segmentation under the MRMRF model,it is proposed to introduce variable weight parameters in the segmentation process of each scale.Furthermore,the final segmentation results are optimized.We name this algorithm the variable-weight multi-resolution Markov random field(VWMRMRF).The simulation and clinical MR image segmentation verification show that the VWMRMRF algorithm has high segmentation accuracy and robustness,and can accurately and stably achieve low signal-to-noise ratio,weak boundary MR image segmentation.

Fast image super-resolution algorithm based on multi-resolution dictionary learning and sparse representation

Sparse representation has attracted extensive attention and performed well on image super-resolution（SR） in the last decade. However, many current image SR methods face the contradiction of detail recovery and artifact suppression. We propose a multi-resolution dictionary learning（MRDL） model to solve this contradiction, and give a fast single image SR method based on the MRDL model. To obtain the MRDL model, we first extract multi-scale patches by using our proposed adaptive patch partition method（APPM）. The APPM divides images into patches of different sizes according to their detail richness. Then, the multiresolution dictionary pairs, which contain structural primitives of various resolutions, can be trained from these multi-scale patches.Owing to the MRDL strategy, our SR algorithm not only recovers details well, with less jag and noise, but also significantly improves the computational efficiency. Experimental results validate that our algorithm performs better than other SR methods in evaluation metrics and visual perception.

Convergence to Steady-State Solutions of the New Type of High-Order Multi-resolution WENO Schemes: a Numerical Study

A new type of high-order multi-resolution weighted essentially non-oscillatory(WENO)schemes(Zhu and Shu in J Comput Phys,375:659-683,2018)is applied to solve for steady-state problems on structured meshes.Since the classical WENO schemes(Jiang and Shu in J Comput Phys,126:202-228,1996)might suffer from slight post-shock oscillations(which are responsible for the residue to hang at a truncation error level),this new type of high-order finite-difference and finite-volume multi-resolution WENO schemes is applied to control the slight post-shock oscillations and push the residue to settle down to machine zero in steady-state simulations.This new type of multi-resolution WENO schemes uses the same large stencils as that of the same order classical WENO schemes,could obtain fifth-order,seventh-order,and ninth-order in smooth regions,and could gradually degrade to first-order so as to suppress spurious oscillations near strong discontinuities.The linear weights of such new multi-resolution WENO schemes can be any positive numbers on the condition that their sum is one.This is the first time that a series of unequal-sized hierarchical central spatial stencils are used in designing high-order finitedifference and finite-volume WENO schemes for solving steady-state problems.In comparison with the classical fifth-order finite-difference and finite-volume WENO schemes,the residue of these new high-order multi-resolution WENO schemes can converge to a tiny number close to machine zero for some benchmark steady-state problems.

A Collaborative Simplification Method for Multiple Coastlines Based on the Hierarchical Triangulation Network Partition

For the current automatic coastline generalization method,only one-line element is considered separately,but the relationship between the nearby elements is not effectively considered.A synergistic simplification method for multiple coastlines based on the hierarchical triangulation network partition(HTNP)is proposed in this paper.Firstly,the constrained Delaunay triangulation is constructed to partition the regions that can be simplified.Then,a hierarchical binary tree model to structure the morphological characteristics of the above several coastlines and the spatial proximity between different coastlines is constructed.Finally,the small curved and curved invisible parts of the coastline are deleted according to the visual constraints,and the narrow part between the coastline itself or the different coastlines is exaggerated appropriately,and the automatic simplification of the coastline is realized.The experimental results show that:①Relationships between the different coastlines are considered,and the shortcomings of considering the coastline separately are overcome;②Under the condition of the multiple coastlines in complex sea areas,the problem of collaborative simplification is solved,the quality of the coastlines are improved obviously,and the proposed method can be applied into more types of coastlines.