A New Extrapolation Economy Cascadic Multigrid Method for Image Restoration Problems

In this paper, a new extrapolation economy cascadic multigrid method is proposed to solve the image restoration model. The new method combines the new extrapolation formula and quadratic interpolation to design a nonlinear prolongation operator, which provides more accurate initial values for the fine grid level. An edge preserving denoising operator is constructed to remove noise and preserve image edges. The local smoothing operator reduces the influence of staircase effect. The experiment results show that the new method not only improves the computational efficiency but also ensures good recovery quality.

Standard and Economical Cascadic Multigrid Methods for the Mortar Finite Element Methods

In this paper, standard and economical cascadic multigrid methods are considered for solving the algebraic systems resulting from the mortar finite element methods. Both cascadic multigrid methods do not need full elliptic regularity, so they can be used to tackle more general elliptic problems. Numerical experiments are reported to suonort our theorv.

L^2-ERROR OF EXTRAPOLATION CASCADIC MULTIGRID (EXCMG)

Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method （EXCMG） is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. In the case of multiple grids, both superconvergence error in H^1-norm and the optimal error in l2-norm are analyzed. The numerical experiment shows the advantage of EXCMG in comparison with CMG.

A Cascadic Multigrid Algorithm for the Mortar Element Method for Semiliner Ellptic Problems

In this paper a cascadic multigrid algorithm for the mortar finite element approximation of the semilinear elliptic problem is proposed,and corresponding theorems aregiven,which display the error estimate and the computational complexity of the method.

两阶具角点奇性椭圆问题的Mortar有限元方法的Cascadic解法

证明了具有角点奇性两阶椭圆问题的MortarP1元的存在唯一性和收敛性,给出了离散问题的Cascadic解法的收敛性.

基于改进Cascade R-CNN的安全帽检测算法

针对安全帽检测中,目标形状、尺度变化大,易出现漏检、误检等问题,提出了一种基于改进级联基于区域的卷积神经网络(Cascade R-CNN)的安全帽检测算法。首先,对ResNet50进行改进形成D-ResNet50,利用可变形卷积仅增加少量参数就可增大感受野的特性,对特征提取网络的C2~C5卷积层进行重塑,提高网络对目标几何变换的适应能力和特征提取能力。其次,将D-ResNet50作为主干网络引入Cascade R-CNN,形成级联目标检测器,在每个阶段对正负样本重采样,抑制误检问题。再次,对递归特征金字塔进行改进,更高效地进行多尺度特征融合,并且基于反馈信息对特征进行二次处理,增强特征表达,提高网络的分类和定位能力。最后,使用Soft-非极大值抑制(Soft-NMS)进行后处理,进一步解决漏检问题。提出的方法在Hard hat workers数据集上的AP值相比检测基线提高了3.5%,与Sparse R-CNN、TridentNet、VFnet等先进算法相比分别提升了4.7%、5.9%、2.3%等。

Pluggable multitask diffractive neural networks based on cascaded metasurfaces

Optical neural networks have significant advantages in terms of power consumption,parallelism,and high computing speed,which has intrigued extensive attention in both academic and engineering communities.It has been considered as one of the powerful tools in promoting the fields of imaging processing and object recognition.However,the existing optical system architecture cannot be reconstructed to the realization of multi-functional artificial intelligence systems simultaneously.To push the development of this issue,we propose the pluggable diffractive neural networks(P-DNN),a general paradigm resorting to the cascaded metasurfaces,which can be applied to recognize various tasks by switching internal plug-ins.As the proof-of-principle,the recognition functions of six types of handwritten digits and six types of fashions are numerical simulated and experimental demonstrated at near-infrared regimes.Encouragingly,the proposed paradigm not only improves the flexibility of the optical neural networks but paves the new route for achieving high-speed,low-power and versatile artificial intelligence systems.

Biological factors driving colorectal cancer metastasis

Approximately 20%of colorectal cancer(CRC)patients present with metastasis at diagnosis.Among Stage I-III CRC patients who undergo surgical resection,18%typically suffer from distal metastasis within the first three years following initial treatment.The median survival duration after the diagnosis of metastatic CRC(mCRC)is only 9 mo.mCRC is traditionally considered to be an advanced stage malignancy or is thought to be caused by incomplete resection of tumor tissue,allowing cancer cells to spread from primary to distant organs;however,increa-sing evidence suggests that the mCRC process can begin early in tumor development.CRC patients present with high heterogeneity and diverse cancer phenotypes that are classified on the basis of molecular and morphological alterations.Different genomic and nongenomic events can induce subclone diversity,which leads to cancer and metastasis.Throughout the course of mCRC,metastatic cascades are associated with invasive cancer cell migration through the circulatory system,extravasation,distal seeding,dormancy,and reactivation,with each step requiring specific molecular functions.However,cancer cells presenting neoantigens can be recognized and eliminated by the immune system.In this review,we explain the biological factors that drive CRC metastasis,namely,genomic instability,epigenetic instability,the metastatic cascade,the cancer-immunity cycle,and external lifestyle factors.Despite remarkable progress in CRC research,the role of molecular classification in therapeutic intervention remains unclear.This review shows the driving factors of mCRC which may help in identifying potential candidate biomarkers that can improve the diagnosis and early detection of mCRC cases.

Economical cascadic multigrid method (ECMG)

In this paper, an economical cascadic multigrid method is proposed. Compared with the usual cascadic multigrid method developed by Bornemann and Deuflhard, the new one requires less iterations on each level, especially on the coarser grids. Many operations can be saved in the new cascadic multigrid algorithms. The main ingredient is the control of the iteration numbers on the each level to preserve the accuracy without over iterations. The theoretical justification is based on the observations that the error reduction rate of an iteration scheme in terms of the smoothing property is no longer accurate while the iteration number is big enough. A new formulae of the error reduction rate is employed in our new algorithm. Numerical experiments are reported to support our theory.

Analysis of extrapolation cascadic multigrid method(EXCMG)

Based on an asymptotic expansion of finite element,a new extrapolation formula and extrapolation cascadic multigrid method(EXCMG)are proposed,in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid.In the case of triple grids,the error of the new initial value is analyzed in detail.A larger scale computation is completed in PC.

Multi-dimensional multiplexing optical secret sharing framework with cascaded liquid crystal holograms

Secret sharing is a promising technology for information encryption by splitting the secret information into different shares.However,the traditional scheme suffers from information leakage in decryption process since the amount of available information channels is limited.Herein,we propose and demonstrate an optical secret sharing framework based on the multi-dimensional multiplexing liquid crystal(LC)holograms.The LC holograms are used as spatially separated shares to carry secret images.The polarization of the incident light and the distance between different shares are served as secret keys,which can significantly improve the information security and capacity.Besides,the decryption condition is also restricted by the applied external voltage due to the variant diffraction efficiency,which further increases the information security.In implementation,an artificial neural network(ANN)model is developed to carefully design the phase distribution of each LC hologram.With the advantage of high security,high capacity and simple configuration,our optical secret sharing framework has great potentials in optical encryption and dynamic holographic display.

ON EXTRAPOLATION CASCADIC MULTIGRID METHOD

Based on an asymptotic expansion of （bi）linear finite elements, a new extrapolation formula and extrapolation cascadic multigrid method （EXCMG） are proposed. The key ingredients of the proposed methods are some new extrapolations and quadratic interpolations, which are used to provide better initial values on the refined grid. In the case of triple grids, the errors of the new initial values are analyzed in detail. The numerical experiments show that EXCMG has higher accuracy and efficiency.

CASCADIC MULTIGRID FOR PARABOLIC PROBLEMS CASCADIC MULTIGRID FOR PARABOLIC PROBLEMS

In this paper, we develop the cascadic multigrid method for parabolic problems. The optimal convergence accuracy and computation complexity are obtained.

基于改进Cascade R-CNN算法的船舶目标检测方法

为了解决实际场景下船舶目标检测精度低的问题,本文在Cascade R-CNN算法的基础上,提出一种船舶目标检测方法 Boat R-CNN。Boat R-CNN使用带自注意力机制的Swin-Transformer Tiny网络提取图像特征,使用Soft-NMS非极大值抑制方法提升候选框过滤精度,使用Smooth_L1损失函数加速模型收敛并减少梯度爆炸情况,使用CIOU边界框回归损失提高候选框回归质量,并针对船舶目标的形状特征优化锚框的长宽比,提高锚框的生成质量。实验结果表明,Boat R-CNN算法的精度相比原版Cascade R-CNN算法提高了21.8%,相比主流Faster R-CNN算法提高了30.3%,有效提升了实际场景下的船舶目标检测精度。

Cascading multi-segment rupture process of the 2023 Turkish earthquake doublet on a complex fault system revealed by teleseismic P wave back projection method

In this study,the vertical components of broadband teleseismic P wave data recorded by China Earthquake Network are used to image the rupture processes of the February 6th,2023 Turkish earthquake doublet via back projection analysis.Data in two frequency bands(0.5-2 Hz and 1-3 Hz)are used in the imaging processes.The results show that the rupture of the first event extends about 200 km to the northeast and about 150 km to the southwest,lasting~90 s in total.The southwestern rupture is triggered by the northeastern rupture,demonstrating a sequential bidirectional unilateral rupture pattern.The rupture of the second event extends approximately 80 km in both northeast and west directions,lasting~35 s in total and demonstrates a typical bilateral rupture feature.The cascading ruptures on both sides also reflect the occurrence of selective rupture behaviors on bifurcated faults.In addition,we observe super-shear ruptures on certain fault sections with relatively straight fault structures and sparse aftershocks.

Cascadic multigrid methods for parabolic problems

In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the smoother.Using new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter,these conditions are verified for a number of popular smoothers.Optimal error bound sare derived for both smooth and non-smooth data.Iteration strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.

A CASCADIC MULTIGRID METHOD FOR EIGENVALUE PROBLEM

A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by linear smoothing steps on a series of multilevel finite element spaces and nonlinear correcting steps on special coarsest spaces. Once the sequence of finite element spaces and the number of smoothing steps are appropriately chosen, the optimal convergence rate with the optimal computational work can be obtained. Some numerical experiments are presented to validate our theoretical analysis.

P1-NONCONFORMING QUADRILATERAL FINITE VOLUME ELEMENT METHOD AND ITS CASCADIC MULTIGRID ALGORITHM FOR ELLIPTIC PROBLEMS

In this paper, we discuss the finite volume element method of P1-nonconforming quadrilateral element for elliptic problems and obtain optimal error estimates for general quadrilateral partition. An optimal cascadic multigrid algorithm is proposed to solve the non-symmetric large-scale system resulting from such discretization. Numerical experiments are reported to support our theoretical results.

CASCADIC MULTIGRID METHOD FOR THE MORTAR ELEMENT METHOD FOR P1 NONCONFORMING ELEMENT

In this paper, we consider the cascadic multigrid method for the mortar P1 nonconforming element which is used to solve the Poisson equation and prove that the cascadic conjugate gradient method is accurate with optimal complexity.

A CASCADIC MULTIGRID ALGORITHM FOR COMPUTING THE FIEDLER VECTOR OF GRAPH LAPLACIANS

In this paper, we develop a cascadic multigrid algorithm for fast computation of the Fiedler vector of a graph Laplacian, namely, the eigenvector corresponding to the second smallest eigenvalne. This vector has been found to have applications in fields such as graph partitioning and graph drawing. The algorithm is a purely algebraic approach based on a heavy edge coarsening scheme and pointwise smoothing for refinement. To gain theoretical insight, we also consider the related cascadic multigrid method in the geometric setting for elliptic eigenvalue problems and show its uniform convergence under certain assumptions. Numerical tests are presented for computing the Fiedler vector of several practical graphs, and numerical results show the efficiency and optimality of our proposed cascadic multigrid algorithm.