亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

In this paper, we develop a domain-decomposition method for the generalized Poisson-Boltzmann equation based on a solvent-excluded surface which is widely used in computational chemistry. The solver requires to solve a generalized screened Poisson (GSP) equation defined in $\mathbb{R}^3$ with a space-dependent dielectric permittivity and an ion-exclusion function that accounts for Steric effects. Potential theory arguments transform the GSP equation into two-coupled equations defined in a bounded domain. Then, the Schwarz decomposition method is used to formulate local problems by decomposing the cavity into overlapping balls and only solving a set of coupled sub-equations in each ball in which, the spherical harmonics and the Legendre polynomials are used as basis functions in the angular and radial directions. A series of numerical experiments are presented to test the method.

Modern high-throughput sequencing assays efficiently capture not only gene expression and different levels of gene regulation but also a multitude of genome variants. Focused analysis of alternative alleles of variable sites at homologous chromosomes of the human genome reveals allele-specific gene expression and allele-specific gene regulation by assessing allelic imbalance of read counts at individual sites. Here we formally describe an advanced statistical framework for detecting the allelic imbalance in allelic read counts at single-nucleotide variants detected in diverse omics studies (ChIP-Seq, ATAC-Seq, DNase-Seq, CAGE-Seq, and others). MIXALIME accounts for copy-number variants and aneuploidy, reference read mapping bias, and provides several scoring models to balance between sensitivity and specificity when scoring data with varying levels of experimental noise-caused overdispersion.

This paper presents a novel approach to construct regularizing operators for severely ill-posed Fredholm integral equations of the first kind by introducing parametrized discretization. The optimal values of discretization and regularization parameters are computed simultaneously by solving a minimization problem formulated based on a regularization parameter search criterion. The effectiveness of the proposed approach is demonstrated through examples of noisy Laplace transform inversions and the deconvolution of nuclear magnetic resonance relaxation data.

We consider {\it local} balances of momentum and angular momentum for the incompressible Navier-Stokes equations. First, we formulate new weak forms of the physical balances (conservation laws) of these quantities, and prove they are equivalent to the usual conservation law formulations. We then show that continuous Galerkin discretizations of the Navier-Stokes equations using the EMAC form of the nonlinearity preserve discrete analogues of the weak form conservation laws, both in the Eulerian formulation and the Lagrangian formulation (which are not equivalent after discretizations). Numerical tests illustrate the new theory.

The 3D reconstruction of simultaneous localization and mapping (SLAM) is an important topic in the field for transport systems such as drones, service robots and mobile AR/VR devices. Compared to a point cloud representation, the 3D reconstruction based on meshes and voxels is particularly useful for high-level functions, like obstacle avoidance or interaction with the physical environment. This article reviews the implementation of a visual-based 3D scene reconstruction pipeline on resource-constrained hardware platforms. Real-time performances, memory management and low power consumption are critical for embedded systems. A conventional SLAM pipeline from sensors to 3D reconstruction is described, including the potential use of deep learning. The implementation of advanced functions with limited resources is detailed. Recent systems propose the embedded implementation of 3D reconstruction methods with different granularities. The trade-off between required accuracy and resource consumption for real-time localization and reconstruction is one of the open research questions identified and discussed in this paper.

We give a short survey of recent results on sparse-grid linear algorithms of approximate recovery and integration of functions possessing a unweighted or weighted Sobolev mixed smoothness based on their sampled values at a certain finite set. Some of them are extended to more general cases.

Machine-learning (ML) based discretization has been developed to simulate complex partial differential equations (PDEs) with tremendous success across various fields. These learned PDE solvers can effectively resolve the underlying solution structures of interest and achieve a level of accuracy which often requires an order-of-magnitude finer grid for a conventional numerical method using polynomial-based approximations. In a previous work in [13], we introduced a learned finite volume discretization that further incorporates the semi-Lagrangian (SL) mechanism, enabling larger CFL numbers for stability. However, the efficiency and effectiveness of such methodology heavily rely on the availability of abundant high-resolution training data, which can be prohibitively expensive to obtain. To address this challenge, in this paper, we propose a novel multi-fidelity ML-based SL method for transport equations. This method leverages a combination of a small amount of high-fidelity data and sufficient but cheaper low-fidelity data. The approach is designed based on a composite convolutional neural network architecture that explore the inherent correlation between high-fidelity and low-fidelity data. The proposed method demonstrates the capability to achieve a reasonable level of accuracy, particularly in scenarios where a single-fidelity model fails to generalize effectively. We further extend the method to the nonlinear Vlasov-Poisson system by employing high order Runge-Kutta exponential integrators. A collection of numerical tests are provided to validate the efficiency and accuracy of the proposed method.

Very recently, Qi and Cui extended the Perron-Frobenius theory to dual number matrices with primitive and irreducible nonnegative standard parts and proved that they have Perron eigenpair and Perron-Frobenius eigenpair. The Collatz method was also extended to find Perron eigenpair. Qi and Cui proposed two conjectures. One is the k-order power of a dual number matrix tends to zero if and only if the spectral radius of its standard part less than one, and another is the linear convergence of the Collatz method. In this paper, we confirm these conjectures and provide theoretical proof. The main contribution is to show that the Collatz method R-linearly converges with an explicit rate.

Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step algorithm coupled with a solid dynamic relaxation scheme. The explicit scheme simplifies the equation system in contrast to the implicit scheme, while the multi-time step algorithm allows the equations of different physical processes to be solved under different time step sizes. Furthermore, an implicit viscous damping relaxation technique is applied to significantly reduce computational iterations required to achieve equilibrium in the comparatively fast solid response process. To validate the accuracy and efficiency of the proposed algorithm, two distinct scenarios, i.e., a nonlinear hardening bar stretching and a fluid diffusion coupled with Nafion membrane flexure, are simulated. The results show good agreement with experimental data and results from other numerical methods, and the simulation time is reduced firstly by independently addressing different processes with the multi-time step algorithm and secondly decreasing solid dynamic relaxation time through the incorporation of damping techniques.

For a singular integral equation on an interval of the real line, we study the behavior of the error of a delta-delta discretization. We show that the convergence is non-uniform, between order $O(h^{2})$ in the interior of the interval and a boundary layer where the consistency error does not tend to zero.