Smoothing analysis of two-color distributive relaxation for solving 2D Stokes flow by multigrid method

Smoothing properties of two-color distributive relaxation for solving a two-dimensional (2D) Stokes flow by multigrid method are theoretically investigated by using the local Fourier analysis (LFA) method. The governing equation of the 2D Stokes flow in consideration is discretized with the non-staggered grid and an added pressure stabilization term with stabilized parameters to be determined is introduced into the discretization system in order to enhance the smoothing effectiveness in the analysis. So, an important problem caused by the added pressure stabilization term is how to determine a suitable zone of parameters in the added term. To that end, theoretically, a two-color distributive relaxation, developed on the two-color Jacobi point relaxation, is established for the 2D Stokes flow. Firstly, a mathematical constitution based on the Fourier modes with various frequency components is constructed as a base of the two-color smoothing analysis, in which the related Fourier representation is presented by the form of two-color Jacobi point relaxation. Then, an optimal one-stage relaxation parameter and related smoothing factor for the two-color distributive relaxation are applied to the discretization system, and an analytical expression of the parameter zone on the added pressure stabilization term is established by LFA. The obtained analytical results show that numerical schemes for solving 2D Stokes flow by multigrid method on the two-color distributive relaxation have a specific convergence zone on the parameters of the added pressure stabilization term, and the property of convergence is independent of mesh size, but depends on the parameters of the pressure stabilization term

A Smoothing Process of Multicolor Relaxation for Solving Partial Differential Equation by Multigrid Method

This paper is concerned with a novel methodology of smoothing analysis process of multicolor point relaxation by multigrid method for solving elliptically partial differential equations (PDEs). The objective was firstly focused on the two-color relaxation technique on the local Fourier analysis (LFA) and then generalized to the multicolor problem. As a key starting point of the problems under consideration, the mathematical constitutions among Fourier modes with various frequencies were constructed as a base to expand two-color to multicolor smoothing analyses. Two different invariant subspaces based on the 2h-harmonics for the two-color relaxation with two and four Fourier modes were constructed and successfully used in smoothing analysis process of Poisson’s equation for the two-color point Jacobi relaxation. Finally, the two-color smoothing analysis was generalized to the multicolor smoothing analysis problems by multigrid method based on the invariant subspaces constructed

A Deep Neural Network/Meshfree Method for Solving Dynamic Two-phase Interface Problems

In this paper, a meshfree method using the deep neural network (DNN) approach is developed for solving two kinds of dynamic two-phase interface problems governed by different dynamic partial differential equations on either side of the stationary interface with the jump and high-contrast coefficients. The first type of two-phase interface problem to be studied is the fluid-fluid (two-phase flow) interface problem modeled by Navier-Stokes equations with high-contrast physical parameters across the interface. The second one belongs to fluid-structure interaction (FSI) problems modeled by Navier-Stokes equations on one side of the interface and the structural equation on the other side of the interface, both the fluid and the structure interact with each other via the kinematic- and the dynamic interface conditions across the interface. The DNN/meshfree method is respectively developed for the above two-phase interface problems by representing solutions of PDEs using the DNNs' structure and reformulating the dynamic interface problem as a least-squares minimization problem based upon a space-time sampling point set. Approximation error analyses are also carried out for each kind of interface problem, which reveals an intrinsic strategy about how to efficiently build a sampling-point training dataset to obtain a more accurate DNNs' approximation. In addition, compared with traditional discretization approaches, the proposed DNN/meshfree method and its error analysis technique can be smoothly extended to many other dynamic interface problems with fixed interfaces. Numerical experiments are conducted to illustrate the accuracies of the proposed DNN/meshfree method for the presented two-phase interface problems. Theoretical results are validated to some extent through three numerical examples

Over 300-km Transmission of 25 Gb/s Optical SSB NPAM-4 Signal with Electronic Dispersion Pre-compensation and Interference Mitigation

We experimentally demonstrate the interference mitigation in direct-detection of optical SSB signals with Nyquist-PAM-4. At 25 Gb/s, we achieve over 300-km and 500-km SSMF with an average BER of 2.7×10-3 (<HD-FEC) and 9.4×10-3 (<SD-FEC), respectively

Oncolytic Virus M1 Functions as a Bifunctional Checkpoint Inhibitor To Enhance the Antitumor Activity of DC Vaccine

Although promising, dendritic cell (DC) vaccines still provide limited clinical benefits, mainly due to the immunosuppressive tumor microenvironment (TME) and the lack of tumor-associated antigens (TAAs). Oncolytic virus therapy is an ideal strategy to overcome immunosuppression and expose TAAs; therefore, they may work synergistically with DC vaccines. In this study, we demonstrate that oncolytic virus M1 (OVM) can enhance the antitumor effects of DC vaccines across diverse syngeneic mouse tumor models by increasing the infiltration of CD8+ effector T cells in the TME. Mechanically, we show that tumor cells counteract DC vaccines through the SIRPα-CD47 immune checkpoint, while OVM can downregulate SIRPα in DCs and CD47 in tumor cells. Since OVM upregulates PD-L1 in DCs, combining PD-L1 blockade with DC vaccines and OVM further enhances antitumor activity. Overall, OVM strengthens the antitumor efficacy of DC vaccines by targeting the SIRPα-CD47 axis, which exerts dominant immunosuppressive effects on DC vaccines

Computational Pathology: A Survey Review and The Way Forward

Computational Pathology CPath is an interdisciplinary science that augments developments of computational approaches to analyze and model medical histopathology images. The main objective for CPath is to develop infrastructure and workflows of digital diagnostics as an assistive CAD system for clinical pathology, facilitating transformational changes in the diagnosis and treatment of cancer that are mainly address by CPath tools. With evergrowing developments in deep learning and computer vision algorithms, and the ease of the data flow from digital pathology, currently CPath is witnessing a paradigm shift. Despite the sheer volume of engineering and scientific works being introduced for cancer image analysis, there is still a considerable gap of adopting and integrating these algorithms in clinical practice. This raises a significant question regarding the direction and trends that are undertaken in CPath. In this article we provide a comprehensive review of more than 800 papers to address the challenges faced in problem design all-the-way to the application and implementation viewpoints. We have catalogued each paper into a model-card by examining the key works and challenges faced to layout the current landscape in CPath. We hope this helps the community to locate relevant works and facilitate understanding of the field's future directions. In a nutshell, we oversee the CPath developments in cycle of stages which are required to be cohesively linked together to address the challenges associated with such multidisciplinary science. We overview this cycle from different perspectives of data-centric, model-centric, and application-centric problems. We finally sketch remaining challenges and provide directions for future technical developments and clinical integration of CPath (https://github.com/AtlasAnalyticsLab/CPath_Survey).Comment: Accepted in Elsevier Journal of Pathology Informatics (JPI) 202

Smoothing Analysis of Distributive Red-Black Jacobi Relaxation for Solving 2D Stokes Flow by Multigrid Method

Smoothing analysis process of distributive red-black Jacobi relaxation in multigrid method for solving 2D Stokes flow is mainly investigated on the nonstaggered grid by using local Fourier analysis (LFA). For multigrid relaxation, the nonstaggered discretizing scheme of Stokes flow is generally stabilized by adding an artificial pressure term. Therefore, an important problem is how to determine the zone of parameter in adding artificial pressure term in order to make stabilization of the algorithm for multigrid relaxation. To end that, a distributive red-black Jacobi relaxation technique for the 2D Stokes flow is established. According to the 2h-harmonics invariant subspaces in LFA, the Fourier representation of the distributive red-black Jacobi relaxation for discretizing Stokes flow is given by the form of square matrix, whose eigenvalues are meanwhile analytically computed. Based on optimal onestage relaxation, a mathematical relation of the parameter in artificial pressure term between the optimal relaxation parameter and related smoothing factor is well yielded. The analysis results show that the numerical schemes for solving 2D Stokes flow by multigrid method on the distributive red-black Jacobi relaxation have a specified convergence parameter zone of the added artificial pressure term