New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties

In this paper,we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations(PDEs)with uncertainties.The new approach is realized in the semi-discrete finite-volume framework and is based on fifth-order weighted essentially non-oscillatory(WENO)interpolations in(multidimensional)random space combined with second-order piecewise linear reconstruction in physical space.Compared with spectral approximations in the random space,the presented methods are essentially non-oscillatory as they do not suffer from the Gibbs phenomenon while still achieving high-order accuracy.The new methods are tested on a number of numerical examples for both the Euler equations of gas dynamics and the Saint-Venant system of shallow-water equations.In the latter case,the methods are also proven to be well-balanced and positivity-preserving.

GENERAL COUPLED MEAN-FIELD REFLECTED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations(BSDEs)under Lipschitz conditions,and for the one-dimensional case a comparison theorem is studied.With the help of this comparison result,we prove the existence of the solution for our mean-field reflected forward-backward stochastic differential equation under continuity assumptions.It should be mentioned that,under appropriate assumptions,we prove the uniqueness of this solution as well as that of a comparison theorem for mean-field reflected FBSDEs in a non-trivial manner.

A Fourth-Order Unstructured NURBS-Enhanced Finite Volume WENO Scheme for Steady Euler Equations in Curved Geometries

In Li and Ren(Int.J.Numer.Methods Fluids 70:742–763,2012),a high-order k-exact WENO finite volume scheme based on secondary reconstructions was proposed to solve the two-dimensional time-dependent Euler equations in a polygonal domain,in which the high-order numerical accuracy and the oscillations-free property can be achieved.In this paper,the method is extended to solve steady state problems imposed in a curved physical domain.The numerical framework consists of a Newton type finite volume method to linearize the nonlinear governing equations,and a geometrical multigrid method to solve the derived linear system.To achieve high-order non-oscillatory numerical solutions,the classical k-exact reconstruction with k=3 and the efficient secondary reconstructions are used to perform the WENO reconstruction for the conservative variables.The non-uniform rational B-splines(NURBS)curve is used to provide an exact or a high-order representation of the curved wall boundary.Furthermore,an enlarged reconstruction patch is constructed for every element of mesh to significantly improve the convergence to steady state.A variety of numerical examples are presented to show the effectiveness and robustness of the proposed method.

Quintessence anisotropic stellar models in quadratic and Born-Infeld modified teleparallel Rastall gravity

This study aims to discuss anisotropic solutions that are spherically symmetric in the quintessence field,which describe compact stellar objects in the modified Rastall teleparallel theory of gravity.To achieve this goal,the Krori and Barua arrangement for spherically symmetric components of the line element is incorporated.We explore the field equations by selecting appropriate off-diagonal tetrad fields.Born-Infeld function of torsion f(T)=β√λT+1-1 and power law form h(T)=δTn are used.The Born-Infeld gravity was the first modified teleparallel gravity to discuss inflation.We use the linear equation of state pr=ξρto separate the quintessence density.After obtaining the field equations,we investigate different physical parameters that demonstrate the stability and physical acceptability of the stellar models.We use observational data,such as the mass and radius of the compact star candidates PSRJ 1416-2230,Cen X-3,&4U 1820-30,to ensure the physical plausibility of our findings.

ON THE EMPTY BALLS OF A CRITICAL OR SUBCRITICAL BRANCHING RANDOM WALK

Let{Z_(n)}_(n)≥0 be a critical or subcritical d-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure on R^(d).Denote by R_(n):=sup{u>0:Z_(n)({x∈R^(d):∣x∣<u})=0}the radius of the largest empty ball centered at the origin of Z_(n).In this work,we prove that after suitable renormalization,Rn converges in law to some non-degenerate distribution as n→∞.Furthermore,our work shows that the renormalization scales depend on the offspring law and the dimension of the branching random walk.This completes the results of Révész[13]for the critical binary branching Wiener process.

Centered Waves for the Two-dimensional Pseudo-Steady van der Waals Gas Satisfied Maxwell's Law Around a Sharp Corner

In this paper,the authors study the centered waves for the two-dimensional(2D for short)pseudo-steady supersonic flow with van der Waals gas satisfied Maxwell's law around a sharp corner.In view of the initial value of the specific volume and the properties of van der Waals gas,the centered waves at the sharp corner are constructed by classification.It is shown that the supersonic incoming flow turns the sharp corner by a centered simple wave or a centered simple wave with right-contact discontinuity or a composite wave(jump-fan,fan-jump or fan-jump-fan),or a combination of waves and constant state.Moreover,the critical angle of the sharp corner corresponding to the appearance of the vacuum phenomenon is obtained.

MODEL SELECTION METHOD BASED ON MAXIMAL INFORMATION COEFFICIENT OF RESIDUALS

The traditional model selection criterions try to make a balance between fitted error and model complexity. Assumptions on the distribution of the response or the noise, which may be misspecified, should be made before using the traditional ones. In this ar- ticle, we give a new model selection criterion, based on the assumption that noise term in the model is independent with explanatory variables, of minimizing the association strength between regression residuals and the response, with fewer assumptions. Maximal Information Coe^cient （MIC）, a recently proposed dependence measure, captures a wide range of associ- ations, and gives almost the same score to different type of relationships with equal noise, so MIC is used to measure the association strength. Furthermore, partial maximal information coefficient （PMIC） is introduced to capture the association between two variables removing a third controlling random variable. In addition, the definition of general partial relationship is given.

Moving-Water Equilibria Preserving HLL-Type Schemes for the Shallow Water Equations

We construct new HLL-type moving-water equilibria preserving upwind schemes for the one-dimensional Saint-Venant system of shallow water equations with nonflat bottom topography.The designed first-and secondorder schemes are tested on a number of numerical examples,in which we verify the well-balanced property as well as the ability of the proposed schemes to accurately capture small perturbations of moving-water steady states.

Adaptive Moving Mesh Central-Upwind Schemes for Hyperbolic System of PDEs:Applications to Compressible Euler Equations and Granular Hydrodynamics

We introduce adaptive moving mesh central-upwind schemes for one-and two-dimensional hyperbolic systems of conservation and balance laws.The proposed methods consist of three steps.First,the solution is evolved by solving the studied system by the second-order semi-discrete central-upwind scheme on either the one-dimensional nonuniform grid or the two-dimensional structured quadrilateral mesh.When the evolution step is complete,the grid points are redistributed according to the moving mesh differential equation.Finally,the evolved solution is projected onto the new mesh in a conservative manner.The resulting adaptive moving mesh methods are applied to the one-and two-dimensional Euler equations of gas dynamics and granular hydrodynamics systems.Our numerical results demonstrate that in both cases,the adaptive moving mesh central-upwind schemes outperform their uniform mesh counterparts.

Mathematical Model and Algorithm for Link Community Detection in Bipartite Networks

In the past ten years, community detection in complex networks has attracted more and more attention of researchers. Communities often correspond to functional subunits in the complex systems. In complex network, a node community can be defined as a subgraph induced by a set of nodes, while a link community is a subgraph induced by a set of links. Although most researches pay more attention to identifying node communities in both unipartite and bipartite networks, some researchers have investigated the link community detection problem in unipartite networks. But current research pays little attention to the link community detection problem in bipartite networks. In this paper, we investigate the link community detection problem in bipartite networks, and formulate it into an integer programming model. We proposed a genetic algorithm for partition the bipartite network into overlapping link communities. Simulations are done on both artificial networks and real-world networks. The results show that the bipartite network can be efficiently partitioned into overlapping link communities by the genetic algorithm.

Effect of the Tensor Force on Charge-Exchange Spin-Dependent Multipole Excitations

The charge-exchange spin-dipole （SD） and spin-quadrupole （SQ） strength functions of 90Zr are calculated with and without the tensor terms of the Skyrme interaction in self-consistent HF＋RPA approach. It is found that, in SD and SQ transitions, the RPA correlations associated with the tensor terms shin dramatically the strengths of （Ylσ）λ = l？1 and （Ylσ）λ = 1 modes upward and downward, respectively, and also shift the strengths of （Ylσ）λ = l ＋ 1 modes upward. The coupling between （Yl = λ ？ 1σ）λ and （Yl = λ ＋ 1σ）λ modes arising from the tensor correlation is noticeable. The RPA tensor correlations produce strengths of SD and SQ modes, which are distributed in a much wider energy range, and the （Ylσ）λ = l ？ 1 modes dominate the high energy part of the strength functions. These energy shifts and coupling effects of different modes can be understood qualitatively by expressing a finite range tensor force in a separable form.

Finding the Maximal Eigenpair for a Large, Dense, Symmetric Matrix based on Mufa Chen's Algorithm

A hybrid method is presented for determining maximal eigenvalue and its eigenvector(called eigenpair)of a large,dense,symmetric matrix.Many problems require finding only a small part of the eigenpairs,and some require only the maximal one.In a series of papers,efficient algorithms have been developed by Mufa Chen for computing the maximal eigenpairs of tridiagonal matrices with positive off-diagonal elements.The key idea is to explicitly construet effective initial guess of the maximal eigenpair and then to employ a self-closed iterative algorithm.In this paper we will extend Mufa Chen's algorithm to find maximal eigenpair for a large scale,dense,symmetric matrix.Our strategy is to first convert the underlying matrix into the tridiagonal form by using similarity transformations.We then handle the cases that prevent us from applying Chen's algorithm directly,e.g.,the cases with zero or negative super-or sub-diagonal elements.Serval numerical experiments are carried out to demonstrate the efficiency of the proposed hybrid method.

Improvements in continuum modeling for biomolecular systems

Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the Poisson- Boltzmann （PB）/Poisson-Nernst-Planck （PNP） equations has made great contributions towards simulation of these pro- cesses. However, the model has shortcomings in its commonly used form and cannot capture （or cannot accurately capture） some important physical properties of the biological systems. Considerable efforts have been made to improve the con- tinuum model to account for discrete particle interactions and to make progress in numerical methods to provide accurate and efficient simulations. This review will summarize recent main improvements in continuum modeling for biomolecu- lar systems, with focus on the size-modified models, the coupling of the classical density functional theory and the PNP equations, the coupling of polar and nonpolar interactions, and numerical progress.

Generating barcodes for nanopore sequencing data with PRO

DNA barcodes,short and unique DNA sequences,play a crucial role in sample identification when processing many samples simultaneously,which helps reduce experimental costs.Nevertheless,the low quality of long-read sequencing makes it difficult to identify barcodes accurately,which poses significant challenges for the design of barcodes for large numbers of samples in a single sequencing run.Here,we present a comprehensive study of the generation of barcodes and develop a tool,PRO,that can be used for selecting optimal barcode sets and demultiplexing.We formulate the barcode design problem as a combinatorial problem and prove that finding the optimal largest barcode set in a given DNA sequence space in which all sequences have the same length is theoretically NP-complete.For practical applications,we developed the novel method PRO by introducing the probability divergence between two DNA sequences to expand the capacity of barcode kits while ensuring demultiplexing accuracy.Specifically,the maximum size of the barcode kits designed by PRO is 2,292,which keeps the length of barcodes the same as that of the official ones used by Oxford Nanopore Technologies(ONT).We validated the performance of PRO on a simulated nanopore dataset with high error rates.The demultiplexing accuracy of PRO reached 98.29%for a barcode kit of size 2,922,4.31%higher than that of Guppy,the official demultiplexing tool.When the size of the barcode kit generated by PRO is the same as the official size provided by ONT,both tools show superior and comparable demultiplexing accuracy.

IMPROVED REGULARITY OF HARMONIC DIFFEOMORPHIC EXTENSIONS ON QUASIHYPERBOLIC DOMAINS

Let X be a Jordan domain satisfying certain hyperbolic growth conditions.Assume that φ is a homeomorphism from the boundary ?X of X onto the unit circle.Denote by h the harmonic diffeomorphic extension of φ from X onto the unit disk.We establish the optimal Orlicz-Sobolev regularity and weighted Sobolev estimate of h.These generalize the Sobolev regularity of h in [A.Koski,J.Onninen,Sobolev homeomorphic extensions,J.Eur.Math.Soc.23(2021) 4065-4089,Theorem 3.1].

Fifth-Order A-WENO Schemes Based on the Adaptive Diffusion Central-Upwind Rankine-Hugoniot Fluxes

We construct new fifth-order alternative WENO(A-WENO)schemes for the Euler equations of gas dynamics.The new scheme is based on a new adaptive diffusion centralupwind Rankine-Hugoniot(CURH)numerical flux.The CURH numerical fluxes have been recently proposed in[Garg et al.J Comput Phys 428,2021]in the context of secondorder semi-discrete finite-volume methods.The proposed adaptive diffusion CURH flux contains a smaller amount of numerical dissipation compared with the adaptive diffusion central numerical flux,which was also developed with the help of the discrete RankineHugoniot conditions and used in the fifth-order A-WENO scheme recently introduced in[Wang et al.SIAM J Sci Comput 42,2020].As in that work,we here use the fifth-order characteristic-wise WENO-Z interpolations to evaluate the fifth-order point values required by the numerical fluxes.The resulting one-and two-dimensional schemes are tested on a number of numerical examples,which clearly demonstrate that the new schemes outperform the existing fifth-order A-WENO schemes without compromising the robustness.

Transcranial Direct Current Stimulation Combined with Peripheral Neuromuscular Stimulation Improves Quality of Life, Fatigue, and Pain in a Patient with Rheumatoid Arthritis and Refractory Radicular Pain Related to Spinal Stenosis

Background: Transcranial direct current stimulation (tDCS) has emerged as an adjuvant noninvasive neuromodulation tool to control fatigue and pain. To date, no studies have assessed the safety and efficiency of tDCS in patients with rheumatoid arthritis and with fatigue, poor quality of life, and refractory radicular pain associated with spinal stenosis. Case Presentation: An 85-year-old woman patient presented with rheumatoid arthritis in remission, refractory radicular pain-associated spinal stenosis, fatigue, and impaired quality of life. The patient underwent 16 daily sessions of tDCS intervention (2 mA, 20 min, positively and negatively charged electrodes were positioned at C1 and Fp2, respectively), in addition to simultaneous peripheral neuromuscular electrical stimulation (frequency of 100 Hz and amplitude of 500 μs). After the intervention, neither disease relapse nor clinical intercurrence occurred. Moreover, there was a significant and sustained improvement in her health-related quality of life, with a reduction in the level of pain and chronic fatigue. Conclusion: The present case report shows that tDCS is safe and may be an adjuvant tool for the treatment of pain and fatigue in patients with systemic autoimmune disease, as well as for improving quality of life. Further studies are required to corroborate this case report.

Q-BioLiP:A Comprehensive Resource for Quaternary Structure-based Protein-ligand Interactions

Since its establishment in 2013,BioLiP has become one of the widely used resources for protein-ligand interactions.Nevertheless,several known issues occurred with it over the past decade.For example,the protein-ligand interactions are represented in the form of single chain-based tertiary structures,which may be inappropriate as many interactions involve multiple protein chains(known as quaternary structures).We sought to address these issues,resulting in Q-BioLiP,a comprehensive resource for quaternary structure-based protein-ligand interactions.The major features of Q-BioLiP include:(1)representing protein structures in the form of quaternary structures rather than single chain-based tertiary structures;(2)pairing DNA/RNA chains properly rather than separation;(3)providing both experimental and predicted binding affinities;(4)retaining both biologically relevant and irrelevant interactions to alleviate the wrong justification of ligands’biological relevance;and(5)developing a new quaternary structure-based algorithm for the modelling of protein-ligand complex structure.With these new features,Q-BioLiP is expected to be a valuable resource for studying biomolecule interactions,including protein-small molecule interaction,protein-metal ion interaction,protein-peptide interaction,protein-protein interaction,protein-DNA/RNA interaction,and RNA-small molecule interaction.Q-BioLiP is freely available at https://yanglab.qd.sdu.edu.cn/Q-BioLiP/.