Is the Classic Convex Decomposition Optimal for Bound-Preserving Schemes in Multiple Dimensions?

Since proposed in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229: 3091--3120, 2010], the Zhang--Shu framework has attracted extensive attention and motivated many bound-preserving (BP) high-order discontinuous Galerkin and finite volume schemes for various hyperbolic equations. A key ingredient in the framework is the decomposition of the cell averages of the numerical solution into a convex combination of the solution values at certain quadrature points, which helps to rewrite high-order schemes as convex combinations of formally first-order schemes. The classic convex decomposition originally proposed by Zhang and Shu has been widely used over the past decade. It was verified, only for the 1D quadratic and cubic polynomial spaces, that the classic decomposition is optimal in the sense of achieving the mildest BP CFL condition. Yet, it remained unclear whether the classic decomposition is optimal in multiple dimensions. In this paper, we find that the classic multidimensional decomposition based on the tensor product of Gauss--Lobatto and Gauss quadratures is generally not optimal, and we discover a novel alternative decomposition for the 2D and 3D polynomial spaces of total degree up to 2 and 3, respectively, on Cartesian meshes. Our new decomposition allows a larger BP time step-size than the classic one, and moreover, it is rigorously proved to be optimal to attain the mildest BP CFL condition, yet requires much fewer nodes. The discovery of such an optimal convex decomposition is highly nontrivial yet meaningful, as it may lead to an improvement of high-order BP schemes for a large class of hyperbolic or convection-dominated equations, at the cost of only a slight and local modification to the implementation code. Several numerical examples are provided to further validate the advantages of using our optimal decomposition over the classic one in terms of efficiency

On Optimal Cell Average Decomposition for High-Order Bound-Preserving Schemes of Hyperbolic Conservation Laws

This paper presents the first systematic study on the fundamental problem of seeking optimal cell average decomposition (OCAD), which arises from constructing efficient high-order bound-preserving (BP) numerical methods within Zhang--Shu framework. Since proposed in 2010, Zhang--Shu framework has attracted extensive attention and been applied to developing many high-order BP discontinuous Galerkin and finite volume schemes for various hyperbolic equations. An essential ingredient in the framework is the decomposition of the cell averages of the numerical solution into a convex combination of the solution values at certain quadrature points. The classic CAD originally proposed by Zhang and Shu has been widely used in the past decade. However, the feasible CADs are not unique, and different CAD would affect the theoretical BP CFL condition and thus the computational costs. Zhang and Shu only checked, for the 1D $\mathbb P^2$ and $\mathbb P^3$ spaces, that their classic CAD based on the Gauss--Lobatto quadrature is optimal in the sense of achieving the mildest BP CFL conditions. In this paper, we establish the general theory for studying the OCAD problem on Cartesian meshes in 1D and 2D. We rigorously prove that the classic CAD is optimal for general 1D $\mathbb P^k$ spaces and general 2D $\mathbb Q^k$ spaces of arbitrary $k$. For the widely used 2D $\mathbb P^k$ spaces, the classic CAD is not optimal, and we establish the general approach to find out the genuine OCAD and propose a more practical quasi-optimal CAD, both of which provide much milder BP CFL conditions than the classic CAD. As a result, our OCAD and quasi-optimal CAD notably improve the efficiency of high-order BP schemes for a large class of hyperbolic or convection-dominated equations, at little cost of only a slight and local modification to the implementation code

Revealing the role of regulatory T cells in the tumor microenvironment of lung adenocarcinoma: a novel prognostic and immunotherapeutic signature

BackgroundRegulatory T cells (Tregs), are a key class of cell types in the immune system. In the tumor microenvironment (TME), the presence of Tregs has important implications for immune response and tumor development. Relatively little is known about the role of Tregs in lung adenocarcinoma (LUAD).MethodsTregs were identified using but single-cell RNA sequencing (scRNA-seq) analysis and interactions between Tregs and other cells in the TME were investigated. Next, we used multiple bulk RNA-seq datasets to construct risk models based on marker genes of Tregs and explored differences in prognosis, mutational landscape, immune cell infiltration and immunotherapy between high- and low-risk groups, and finally, qRT-PCR and cell function experiments were performed to validate the model genes.ResultsThe cellchat analysis showed that MIF-(CD74+CXCR4) pairs play a key role in the interaction of Tregs with other cell subpopulations, and the Tregs-associated signatures (TRAS) could well classify multiple LUAD cohorts into high- and low-risk groups. Immunotherapy may offer greater potential benefits to the low-risk group, as indicated by their superior survival, increased infiltration of immune cells, and heightened expression of immune checkpoints. Finally, the experiment verified that the model genes LTB and PTTG1 were relatively highly expressed in cancer tissues, while PTPRC was relatively highly expressed in paracancerous tissues. Colony Formation assay confirmed that knockdown of PTTG1 reduced the proliferation ability of LUAD cellsConclusionTRAS were constructed using scRNA-seq and bulk RNA-seq to distinguish patient risk subgroups, which may provide assistance in the clinical management of LUAD patients

Early Mechanical and Microstructure Evolution Characteristics of Concrete in Steam Curing Condition

In order to study the effect of steam curing on early mechanical properties of concrete, the strength, dynamic elastic modulus, and microstructure characteristics of concrete under different curing methods were tested. The results show that the early strength growth rate of steam curing concrete is obviously higher than that of standard curing. The strength development of concrete during steam curing can be divided into three stages. Stage I and stage II (0 h-30 h) are critical periods for concrete strength growth. The dynamic elastic modulus of steam-curing concrete is mainly formed in the early stage and shows a linear rapid growth characteristic. The growth rate of the dynamic elastic modulus of concrete under standard curing condition is relatively slow, but in the later curing period (30 h-48 h), the growth rate of dynamic elastic modulus of concrete is significantly higher than that of steam curing concrete. Steam curing can accelerate the production of cement hydration products which rapidly increases the early strength of concrete. Under the standard curing condition, the hydration product structure of concrete is more compact, which is conducive to the growth of dynamic elastic modulus in a later period. This study provides a theoretical reference for the application of steam curing in engineering, which is important to ensure the production efficiency and quality of concrete in engineering

Effects of Forchlorfenuron on the Morphology, Metabolite Accumulation, and Transcriptional Responses of Siraitia grosvenorii Fruit

Siraitia grosvenorii fruit, called luo-han-guo (LHG), have been used as a traditional Chinese medicine (TCM) and dietary supplements for many years. Mogrosides, the main bioactive ingredients in LHG, are commercially available worldwide as a non-sugar-based and noncaloric sweetener. However, the production cannot meet the increasing market demand because of the low content of mogrosides and the small size of LHG. Therefore, some advanced technologies have been applied for improving the quality of LHG. Forchlorfenuron (CPPU), a plant growth regulator, is widely applied to promote plant yield and the secondary metabolite synthesis. Here, the content of nine mogrosides and three intermediates in LHG that were treated with three different concentrations of CPPU were determined by LC-MS/MS and GC-MS, respectively. The total content of mogrosides in LHG treated with CPPU was not enhanced, and the proportion of some main bioactive ingredients, including mogroside V (MV), were decreased relative to that of the control treatment. Morphological and cytological observations showed CPPU could make an early lignification in fruit epidermal cells, and 5 or 25 mg L−1 CPPU could inhibit LHG growth. The expression levels of 24 key genes in the mogroside biosynthesis pathway were measured and revealed that genes downregulated in upstream, and different expressions of SgUGTs would affect the accumulations and proportions of mogrosides in LHG induced by CPPU. This was the first study that applied CPPU individually on LHG, and assessed effects of CPPU on the morphology, the accumulation of metabolites, and expression profiles of 24 structural genes. The CPPU effects on LHG were undesirable, including development inhibition and the decrease of main mogroside content. These will provide guidance for the rational application of CPPU

New Technology of Pressure Relief Control in Soft Coal Roadways with Deep, Violent Mining and Large Deformation: A Key Study

Previous studies have shown that the influence of deep dynamic pressure on the surrounding rock control of a coal roadway is one of the difficulties in mine roadway support. Based on the investigation of the headgate 11231 in a coal mine, this study analyzes the damage characteristics of coal roadway surrounding rock affected by deep dynamic pressure, expounds on the difficulties of controlling the roadway surrounding rock, and creatively proposes a cooperative control technology of external anchor–internal unloading for regulating large deformation of roadways. The vertical stress distribution and transfer law of surrounding rock with different hole-making depths, spacing, and lengths after roadway excavation were simulated and studied, and an appropriate parameter range of hole-making space in the stage without dynamic pressure influence was obtained. Considering the influence of mining dynamic pressure, the surrounding rock pressure relief effect of each optimized hole-making parameter was analyzed. In addition, the optimal hole-making parameters (the hole-making depth, spacing, and length were 8 m, 3.2 m, and 3 m, respectively) that can effectively reduce the high stress of roadway shallow surrounding rock in two stages (without and with dynamic pressure) and ensure integrity of the shallow surrounding rock were obtained. The actual field application shows that the new technology can reduce the higher rib deformation by approximately 850 mm and achieve a good surrounding rock control effect. The research and practice show that the pressure relief control for soft coal roadways with deep, violent mining and large deformation has achieved success, providing technical support for the maintenance of the same type of roadway

Study on the Influence of the Strain-Softening of the Surrounding Rock with Buried Depth on Gas Extraction Boreholes

The buried depth of coal seams in China gradually increases as shallow resources decrease. The purpose of this article is to reveal the effect of buried depth on gas extraction boreholes. Firstly, we analyzed the shortcomings of the Mohr–Coulomb (M-C) constitutive model for simulating excavation problems and introduced the strain-softening (S-S) model and its advantages. Subsequently, we constructed the gas extraction models with different buried depths based on the S-S model and combined them with the evolution equations for permeability and the equations for gas migration. Then, we studied the difference between the M-C and S-S models using numerical simulations. We found that the influence of the S-S phenomenon in the surrounding rock of boreholes is more significant as the buried depth increases—that is, the strain-softening has a significant buried depth effect. When the buried depths were 300, 500, and 700 m, the maximum ratios of permeability to the initial permeability obtained from the Mohr–Coulomb model were 1.37, 6.88, and 97.56, respectively; the maximum ratios of permeability to the initial permeability obtained from the strain-softening model were 2.06, 291.23, and 3629.66. The differences in the increase zone of permeability from the two models also increased with the increase in the buried depth. The distribution curves of gas pressure in the surrounding rock of boreholes obtained from the S-S model were below those of the M-C constitutive model at the same buried depth, and the zones with slowly increasing gas pressure with the increase in buried depth were more obvious in the S-S model compared with the M-C constitutive model. The differences in borehole effective extraction radius also increased gradually between the S-S and M-C models as the buried depth increased. Through the analysis of the research results, we found that S-S of the surrounding rock has a lesser influence on the gas extraction boreholes, and the S-S phenomenon in the surrounding rock of boreholes can be ignored when the buried depth is relatively shallow. It is increasingly necessary to consider the S-S phenomenon in the surrounding rock of boreholes with the gradual increase in the buried depth

Molecular Identification and Targeted Quantitative Analysis of Medicinal Materials from Uncaria Species by DNA Barcoding and LC-MS/MS

The genus Uncaria is an important source of traditional Chinese medicines with multiple therapeutic effects. The identification of the correct species and accurate determination of the contents of bioactive constituents are important for quality control of Uncaria medicinal materials. Here, an integrated evaluation system based on DNA barcoding for species identification and quantitative analysis by LC-MS/MS has been established. DNA barcoding based on the ITS2 barcode region showed sufficient discriminatory power to precisely identify 24 samples from seven Uncaria species. The length of the 24 ITS2 sequences of Uncaria samples is 227 bp, and 17 variation sites were detected. Additionally, the results of qualitative and quantitative chemical analyses by LC-MS/MS indicated that the chemical compositions of all Uncaria samples were similar; while their contents of targeted alkaloids in samples from different species and origin areas were different. The contents of rhynchophylline (RC) and isorhynchophylline (IRC) were 2.9–1612 mg/kg and 2.60–1299 mg/kg in all tested samples, respectively. This study concludes that DNA barcoding should be used as the first screening step for Uncaria medicinal materials. Then, integration of DNA barcoding with chemical analyses should be applied in quality control of Uncaria medicinal materials in the medicinal industry