Deep unfolding multi-scale regularizer network for image denoising

Existing deep unfolding methods unroll an optimization algorithm with a fixed number of steps,and utilize convolutional neural networks(CNNs)to learn data-driven priors.However,their performance is limited for two main reasons.Firstly,priors learned in deep feature space need to be converted to the image space at each iteration step,which limits the depth of CNNs and prevents CNNs from exploiting contextual information.Secondly,existing methods only learn deep priors at the single full-resolution scale,so ignore the benefits of multi-scale context in dealing with high level noise.To address these issues,we explicitly consider the image denoising process in the deep feature space and propose the deep unfolding multi-scale regularizer network(DUMRN)for image denoising.The core of DUMRN is the feature-based denoising module(FDM)that directly removes noise in the deep feature space.In each FDM,we construct a multi-scale regularizer block to learn deep prior information from multi-resolution features.We build the DUMRN by stacking a sequence of FDMs and train it in an end-to-end manner.Experimental results on synthetic and real-world benchmarks demonstrate that DUMRN performs favorably compared to state-of-theart methods.

Distributed Optimal Formation Control for Unmanned Surface Vessels by a Regularized Game-Based Approach

Dear Editor,This letter explores optimal formation control for a network of unmanned surface vessels(USVs).By designing an individual objective function for each USV,the optimal formation problem is transformed into a noncooperative game.Under this game theoretic framework,the optimal formation is achieved by seeking the Nash equilibrium of the regularized game.A modular structure consisting of a distributed Nash equilibrium seeker and a regulator is proposed.

A pruning algorithm with L_(1/2) regularizer for extreme learning machine

Compared with traditional learning methods such as the back propagation(BP)method,extreme learning machine provides much faster learning speed and needs less human intervention,and thus has been widely used.In this paper we combine the L1/2regularization method with extreme learning machine to prune extreme learning machine.A variable learning coefcient is employed to prevent too large a learning increment.A numerical experiment demonstrates that a network pruned by L1/2regularization has fewer hidden nodes but provides better performance than both the original network and the network pruned by L2regularization.

Analytical Method for the Wave Diffraction of Asymmetrically Arranged Breakwaters

The layout forms of several breakwater structures can be generalized as asymmetrical arrangements in actual engineering.However,the problem of wave diffraction around asymmetrically arranged breakwaters has not been adequately investigated.In this study,we propose an analytical method of wave diffraction for regular waves passing through asymmetrically arranged breakwaters,and we use the Nyström method to obtain the analytical solution numerically.We compared the results of this method with those of previous analytical solutions and with numerical results to demonstrate the validity of our approach.We also provided diffraction coefficient diagrams of breakwaters with different layout forms.Moreover,we described the analytical expression for the problem of diffraction through long-wave incident breakwaters and presented an analysis of the relationship between the diffraction coefficients and the widths of breakwater gates.The analytical method presented in this study contributes to the limited literature on the theory of wave diffraction through asymmetrically arranged breakwaters.

Insufficient Physical Activity among Students Aged 6-17 Years in China,2016-2017

Regular physical activity of sufficient duration and intensity can provide health benefits such as improved physical fitness,which promotes bone health,prevents hypertension,improves mental health,and reduces adiposity^([1]).Furthermore,the benefits of regular physical exercise during youth may persist into adulthood^([2]).

THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small initial data.In addition,we also obtain the Gevrey class regularity and the temporal decay rate of the solution.

THE SMOOTHING EFFECT IN SHARP GEVREY SPACE FOR THE SPATIALLY HOMOGENEOUS NON-CUTOFF BOLTZMANN EQUATIONS WITH A HARDPOTENTIAL

In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.

ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS

We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.

Thrust estimate method of an on-orbit Hall thruster using Hall drift current

In order to realize the thrust estimation of the Hall thruster during its flight mission,this study establishes an estimation method based on measurement of the Hall drift current.In this method,the Hall drift current is calculated from an inverse magnetostatic problem,which is formulated according to its induced magnetic flux density detected by sensors,and then the thrust is estimated by multiplying the Hall drift current with the characteristic magnetic flux density of the thruster itself.In addition,a three-wire torsion pendulum micro-thrust measurement system is utilized to verify the estimate values obtained from the proposed method.The errors were found to be less than 8%when the discharge voltage ranged from 250 V to 350 V and the anode flow rate ranged from 30 sccm to 50 sccm,indicating the possibility that the proposed thrust estimate method could be practically applied.Moreover,the measurement accuracy of the magnetic flux density is suggested to be lower than 0.015 mT and improvement on the inverse problem solution is required in the future.

SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION

This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.

A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS

In this article,we consider the diffusion equation with multi-term time-fractional derivatives.We first derive,by a subordination principle for the solution,that the solution is positive when the initial value is non-negative.As an application,we prove the uniqueness of solution to an inverse problem of determination of the temporally varying source term by integral type information in a subdomain.Finally,several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

A novel algorithm for evaluating cement azimuthal density based on perturbation theory in horizontal well

Cement density monitoring plays a vital role in evaluating the quality of cementing projects,which is of great significance to the development of oil and gas.However,the presence of inhomogeneous cement distribution and casing eccentricity in horizontal wells often complicates the accurate evaluation of cement azimuthal density.In this regard,this paper proposes an algorithm to calculate the cement azimuthal density in horizontal wells using a multi-detector gamma-ray detection system.The spatial dynamic response functions are simulated to obtain the influence of cement density on gamma-ray counts by the perturbation theory,and the contribution of cement density in six sectors to the gamma-ray recorded by different detectors is obtained by integrating the spatial dynamic response functions.Combined with the relationship between gamma-ray counts and cement density,a multi-parameter calculation equation system is established,and the regularized Newton iteration method is employed to invert casing eccentricity and cement azimuthal density.This approach ensures the stability of the inversion process while simultaneously achieving an accuracy of 0.05 g/cm^(3) for the cement azimuthal density.This accuracy level is ten times higher compared to density accuracy calculated using calibration equations.Overall,this algorithm enhances the accuracy of cement azimuthal density evaluation,provides valuable technical support for the monitoring of cement azimuthal density in the oil and gas industry.

A Recurrent Neural Network for Multimodal Anomaly Detection by Using Spatio-Temporal Audio-Visual Data

In video surveillance,anomaly detection requires training machine learning models on spatio-temporal video sequences.However,sometimes the video-only data is not sufficient to accurately detect all the abnormal activities.Therefore,we propose a novel audio-visual spatiotemporal autoencoder specifically designed to detect anomalies for video surveillance by utilizing audio data along with video data.This paper presents a competitive approach to a multi-modal recurrent neural network for anomaly detection that combines separate spatial and temporal autoencoders to leverage both spatial and temporal features in audio-visual data.The proposed model is trained to produce low reconstruction error for normal data and high error for abnormal data,effectively distinguishing between the two and assigning an anomaly score.Training is conducted on normal datasets,while testing is performed on both normal and anomalous datasets.The anomaly scores from the models are combined using a late fusion technique,and a deep dense layer model is trained to produce decisive scores indicating whether a sequence is normal or anomalous.The model’s performance is evaluated on the University of California,San Diego Pedestrian 2(UCSD PED 2),University of Minnesota(UMN),and Tampere University of Technology(TUT)Rare Sound Events datasets using six evaluation metrics.It is compared with state-of-the-art methods depicting a high Area Under Curve(AUC)and a low Equal Error Rate(EER),achieving an(AUC)of 93.1 and an(EER)of 8.1 for the(UCSD)dataset,and an(AUC)of 94.9 and an(EER)of 5.9 for the UMN dataset.The evaluations demonstrate that the joint results from the combined audio-visual model outperform those from separate models,highlighting the competitive advantage of the proposed multi-modal approach.

Impact Force Localization and Reconstruction via ADMM-based Sparse Regularization Method

In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although l_(1) regularization can be used to obtain sparse solutions,it tends to underestimate solution amplitudes as a biased estimator.To address this issue,a novel impact force identification method with l_(p) regularization is proposed in this paper,using the alternating direction method of multipliers(ADMM).By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators,ADMM can address the challenge effectively.To mitigate the sensitivity to regularization parameters,an adaptive regularization parameter is derived based on the K-sparsity strategy.Then,an ADMM-based sparse regularization method is developed,which is capable of handling l_(p) regularization with arbitrary p values using adaptively-updated parameters.The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure.Additionally,an investigation into the optimal p value for achieving high-accuracy solutions via l_(p) regularization is conducted.It turns out that l_(0.6)regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic l_(1) regularization method.The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.

Supported Ziegler-Natta catalysts from MgCl_(2)·nROH precursors and its catalytic behaviors for diene copolymerization

Heterogeneous TiCl4/MgCl_(2) type Ziegler-Natta(Z-N)catalysts with unique advantages like low cost,high activity,high stereoregularity and pretty particle morphology,contribute to more than 130 Mt polyolefin large-scale production.However,most researches related with heterogeneous Z-N catalysts focused onα-olefin polymerizations like ethylene,propylene,etc.

Uncertainty-Aware Physical Simulation of Neural Radiance Fields for Fluids

This paper presents a novel framework aimed at quantifying uncertainties associated with the 3D reconstruction of smoke from2Dimages.This approach reconstructs color and density fields from 2D images using Neural Radiance Field(NeRF)and improves image quality using frequency regularization.The NeRF model is obtained via joint training ofmultiple artificial neural networks,whereby the expectation and standard deviation of density fields and RGB values can be evaluated for each pixel.In addition,customized physics-informed neural network(PINN)with residual blocks and two-layer activation functions are utilized to input the density fields of the NeRF into Navier-Stokes equations and convection-diffusion equations to reconstruct the velocity field.The velocity uncertainties are also evaluated through ensemble learning.The effectiveness of the proposed algorithm is demonstrated through numerical examples.The presentmethod is an important step towards downstream tasks such as reliability analysis and robust optimization in engineering design.

Convergent Data-Driven Regularizations for CT Reconstruction

The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography(CT).As the(naive)solution does not depend on the measured data continuously,regularization is needed to reestablish a continuous dependence.In this work,we investigate simple,but yet still provably convergent approaches to learning linear regularization methods from data.More specifically,we analyze two approaches:one generic linear regularization that learns how to manipulate the singular values of the linear operator in an extension of our previous work,and one tailored approach in the Fourier domain that is specific to CT-reconstruction.We prove that such approaches become convergent regularization methods as well as the fact that the reconstructions they provide are typically much smoother than the training data they were trained on.Finally,we compare the spectral as well as the Fourier-based approaches for CT-reconstruction numerically,discuss their advantages and disadvantages and investigate the effect of discretization errors at differentresolutions.

Investigation of the Film Formation in Dynamic Air Spray Painting

To accurately predict the film thickness distribution during dynamic spraying performed with air guns and support accordingly the development of intelligent spray painting,the spray problem was analyzed numerically.In particular,the Eulerian-Eulerian approach was employed to calculate the paint atomization and film deposition process.Different spray heights,spray angles,spray gun movement speeds,spray trajectory curvature radii,and air pressure values were considered.Numerical simulation results indicate that the angle of spray painting significantly affects the velocity of droplets near the spray surface.With an increase in the spraying angle,spraying height and spray gun movement speed,the maximum film thickness decreases to varying degrees,and the uniformity of the film thickness also continuously worsens.When the spray gun moves along an arc trajectory,at smaller arc radii,the film thickness on the inside of the arc is slightly greater than that on the outside,but the impact on the maximum film thickness is minimal.Increasing air pressure expands the coating coverage area,results in finer atomization of paint droplets,and leads to a thinner and a more uniform paint film.However,if the pressure is too high,it can cause paint splattering.Using the orthogonal experimental method,multiple sets of simulation calculations were conducted,and the combined effects of spraying height,spray angle,and spray gun movement speed on the film thickness distribution were comprehensively analyzed to determine optimal configurations.Finally,the reliability of the numerical simulations was validated through dynamic spray painting experiments.

Conditions for the enrichment of karst hydrothermal resources in Bohai Bay Basin

Drilling for karst hydrothermal resources in eastern China has posed challenges,including disparities between the temperature and yield of geothermal water.It is evident that relying solely on geothermal anomalies or indications of karst reservoirs is inadequate for the exploration of karst hydrothermal resources.This study seeks to elucidate the cause of geothermal sweet spots by analyzing the interplay between geothermal anomalies and karst reservoirs and the underlying geological conditions for karst hydrothermal enrichment.Key findings include:(1)the Bohai Bay Basin has been geologically favorable for the development of karst hydrothermal resources since the Mesozoic era;(2)the karst hydrothermal enrichment varies significantly between the basin’s margin and its interior.On the basin margin,the enrichment is largely driven by groundwater activity and faults,particularly where faults facilitate the upwelling of geothermal water.In contrast,within the basin’s interior,karst hydrothermal resources are predominantly influenced by buried hills and are especially enriched in areas facilitating the discharge of deep geothermal waters.

Enhanced Differentiable Architecture Search Based on Asymptotic Regularization

In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach.