Search

Wheat is one of the most important crops to ensure food production globally. Understanding the mechanism of leaf senescence in wheat plays a crucial role in improving its productivity and resilience under various stress scenarios. In this study, we investigated biochemical, functional, and ultrastructural changes during leaf senescence in wheat genotypes with contrasting drought tolerance. For this, key parameters such as chlorophyll and total protein content, membrane stability, malondialdehyde level, and the activity of antioxidant enzymes (superoxide dismutase, ascorbate peroxidase, guaiacol peroxidase, benzidine peroxidase, and catalase) were comparatively analyzed during both natural and drought-induced senescence. Additionally, the expression of superoxide dismutase isoform genes functioning in different cellular compartments was studied, alongside ultrastructural changes in flag leaves. The experiments involved genotypes of bread wheat (Triticum aestivum L.) and durum (Triticum durum Desf.) wheat. The plants were grown in controlled environment chambers under control and drought conditions using a completely randomized design. After the booting stage, irrigation was discontinued for drought-treated plants. Flag leaves were sampled at 7, 14, 21, 28, and 35 days after anthesis. Drought-tolerant genotypes exhibited slower chlorophyll degradation, lower lipid peroxidation, enhanced membrane stability, and stronger antioxidant responses, allowing them to maintain cellular function longer, whereas sensitive genotypes showed accelerated leaf senescence. Transcript levels of FeSOD increased significantly post-flowering but declined as senescence progressed, while MnSOD expression exhibited a rise towards the later stages of ontogenesis across all studied genotypes. Ultrastructural analysis revealed progressive damage to chloroplast membranes, thylakoid structures, and mesophyll cell walls under stress conditions, particularly in sensitive genotypes. These findings contribute to a deeper understanding of the physiological and molecular responses of wheat to drought stress, offering potential targets for improving crop performance in water-limited environments. [ABSTRACT FROM AUTHOR]

Osteoporosis is a metabolic skeletal disease characterized by lowered bone mineral density and quality, which lead to an increased risk of fracture. The aim of this study was to evaluate the anti-osteoporosis effects of a mixture (called BPX) of Cervus elaphus sibiricus and Glycine max (L.) Merrill and its underlying mechanisms using an ovariectomized (OVX) mouse model. BALB/c female mice (7 weeks old) were ovariectomized. From 12 weeks of ovariectomy, mice were administered BPX (600 mg/kg) mixed in a chow diet for 20 weeks. Changes in bone mineral density (BMD) and bone volume (BV), histological findings, osteogenic markers in serum, and bone formation-related molecules were analyzed. Ovariectomy notably decreased the BMD and BV scores, while these were significantly attenuated by BPX treatment in the whole body, femur, and tibia. These anti-osteoporosis effects of BPX were supported by the histological findings for bone microstructure from H&E staining, increased activity of alkaline phosphatase (ALP), but a lowered activity of tartrate-resistant acid phosphatase (TRAP) in the femur, along with other parameters in the serum, including TRAP, calcium (Ca), osteocalcin (OC), and ALP. These pharmacological actions of BPX were explained by the regulation of key molecules in the bone morphogenetic protein (BMP) and mitogen-activated protein kinase (MAPK) pathways. The present results provide experimental evidence for the clinical relevance and pharmaceutical potential of BPX as a candidate for anti-osteoporosis treatment, especially under postmenopausal conditions. [ABSTRACT FROM AUTHOR]

We introduce a family of implementations of low-order, additive, geometric multilevel solvers for systems of Helmholtz equations arising from Schrödinger equations. Both grid spacing and arithmetics may comprise complex numbers, and we thus can apply complex scaling to the indefinite Helmholtz operator. Our implementations are based on the notion of a spacetree and work exclusively with a finite number of precomputed local element matrices. They are globally matrix-free. Combining various relaxation factors with two grid transfer operators allows us to switch from additive multigrid over a hierarchical basis method into a Bramble-Pasciak-Xu (BPX)-type solver, with several multiscale smoothing variants within one code base. Pipelining allows us to realize full approximation storage (FAS) within the additive environment where, amortized, each grid vertex carrying degrees of freedom is read/written only once per iteration. The codes realize a single-touch policy. Among the features facilitated by matrix-free FAS is arbitrary dynamic mesh refinement (AMR) for all solver variants. AMR as an enabler for full multigrid (FMG) cycling—the grid unfolds throughout the computation—allows us to reduce the cost per unknown. The present work primary contributes toward software realization and design questions. Our experiments show that the consolidation of single-touch FAS, dynamic AMR, and vectorization-friendly, complex scaled, matrix-free FMG cycles delivers a mature implementation blueprint for solvers of Helmholtz equations in general. For this blueprint, we put particular emphasis on a strict implementation formalism as well as some implementation correctness proofs. [ABSTRACT FROM AUTHOR]

The goal of this paper is to design optimal multilevel solvers for the finite element approximation of second order linear elliptic problems with piecewise constant coefficients on bisection grids. Local multigrid and BPX preconditioners are constructed based on local smoothing only at the newest vertices and their immediate neighbors. The analysis of eigenvalue distributions for these local multilevel preconditioned systems shows that there are only a fixed number of eigenvalues which are deteriorated by the large jump. The remaining eigenvalues are bounded uniformly with respect to the coefficients and the meshsize. Therefore, the resulting preconditioned conjugate gradient algorithm will converge with an asymptotic rate independent of the coefficients and logarithmically with respect to the meshsize. As a result, the overall computational complexity is nearly optimal. [ABSTRACT FROM AUTHOR]

We consider an automatic construction of locally optimal preconditioners for positive definite linear systems. To achieve this goal, we introduce a differentiable loss function that does not explicitly include the estimation of minimal eigenvalue. Nevertheless, the resulting optimization problem is equivalent to a direct minimization of the condition number. To demonstrate our approach, we construct a parametric family of modified BPX preconditioners. Namely, we define a set of empirical basis functions for coarse finite element spaces and tune them to achieve better condition number. For considered model equations (that includes Poisson, Helmholtz, Convection–diffusion, Biharmonic, and others), we achieve from two to twenty times smaller condition numbers for symmetric positive definite linear systems. [ABSTRACT FROM AUTHOR]

In this article, we establish optimality of the Bramble-Pasciak-Xu (BPX) norm equivalence and optimality of the wavelet modified (or stabilized) hierarchical basis (WHB) preconditioner in the setting of local 3D mesh refinement. In the analysis of WHB methods, a critical first step is to establish the optimality of BPX norm equivalence for the refinement procedures under consideration. While the available optimality results for the BPX norm have been constructed primarily in the setting of uniformly refined meshes, a notable exception is the local 2D red-green result due to Dahmen and Kunoth. The purpose of this article is to extend this original 2D optimality result to the local 3D red-green refinement procedure introduced by Bornemann, Erdmann, and Kornhuber, and then to use this result to extend the WHB optimality results from the quasi-uniform setting to local 2D and 3D red-green refinement scenarios. The BPX extension is reduced to establishing that locally enriched finite element subspaces allow for the construction of a scaled basis which is formally Riesz stable. This construction turns out to rest not only on the shape regularity of the refined elements, but also critically on a number of geometrical properties we establish between neighboring simplices produced by the Bornemann-Erdmann-Kornhuber (BEK) refinement procedure. It is possible to show that the number of degrees of freedom used for smoothing is bounded by a constant times the number of degrees of freedom introduced at that level of refinement, indicating that a practical, implementable version of the resulting BPX preconditioner for the BEK refinement setting has provably optimal (linear) computational complexity per iteration. An interesting implication of the optimality of the WHB preconditioner is the a priori H¹-stability of the L²-projection. The existing a posteriori approaches in the literature dictate a reconstruction of the mesh if such conditions cannot be satisfied. The theoretical framework employed supports arbitrary spatial dimension d ≥ 1 and requires no coefficient smoothness assumptions beyond those required for well-posedness in H¹. [ABSTRACT FROM AUTHOR]

In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform refinement-based discretizations of elliptic equations, they tend to be less effective for algebraic systems, which arise from discretizations on locally refined meshes, losing their optimal behavior in both storage and computational complexity. Our primary focus here is on Bramble, Pasciak, and Xu (BPX)-style additive and multiplicative multilevel preconditioners, and on various stabilizations of the additive and multiplicative hierarchical basis (HB) method, and their use in the local mesh refinement setting. In parts I and II of this trilogy, it was shown that both BPX and wavelet stabilizations of HB have uniformly bounded condition numbers on several classes of locally refined two- and three-dimensional meshes based on fairly standard (and easily implementable) red and red-green mesh refinement algorithms. In this third part of the trilogy, we describe in detail the implementation of these types of algorithms, including detailed discussions of the data structures and traversal algorithms we employ for obtaining optimal storage and computational complexity in our implementations. We show how each of the algorithms can be implemented using standard data types, available in languages such as C and FORTRAN, so that the resulting algorithms have optimal (linear) storage requirements, and so that the resulting multilevel method or preconditioner can be applied with optimal (linear) computational costs. We have successfully used these data structure ideas for both MATLAB and C implementations using the FEtk, an open source finite element software package. We finish the paper with a sequence of numerical experiments illustrating the effectiveness of a number of BPX and stabilized HB variants for several examples requiring local refinement. [ABSTRACT FROM AUTHOR]