BTTB preconditioners for BTTB least squares problems

AbstractIn this paper, we consider solving the least squares problem minx‖b-Tx‖2 by using preconditioned conjugate gradient (PCG) methods, where T is a large rectangular matrix which consists of several square block-Toeplitz–Toeplitz-block (BTTB) matrices and b is a column vector. We propose a BTTB preconditioner to speed up the PCG method and prove that the BTTB preconditioner is a good preconditioner. We then discuss the construction of the BTTB preconditioner. Numerical examples, including image restoration problems, are given to illustrate the efficiency of our BTTB preconditioner. Numerical results show that our BTTB preconditioner is more efficient than the well-known Level-1 and Level-2 circulant preconditioners

Hamilton paths in Z-transformation graphs of perfect matchings of hexagonal systems

AbstractLet H be a hexagonal system. The Z-transformation graph Z(H) is the graph where the vertices are the perfect matchings of H and where two perfect matchings are joined by an edge provided their symmetric difference is a hexagon of H (Z. Fu-ji et al., 1988). In this paper we prove that Z(H) has a Hamilton path if H is a catacondensed hexagonal system

2-[(Adamantan-1-yl­amino)­meth­yl]phenol

The asymmetric unit of the title compound, C17H23NO, contains two independent mol­ecules. In both mol­ecules, the hy­droxy group is involved in the formation of an intra­molecular O—H⋯N hydrogen bond. In the crystal, there are two crystallographically independent chains of the mol­ecules propagating along the c axis and formed by weak inter­molecular N—H⋯O hydrogen bonds

Effects of online one-yuan Dutch auction on the seller’s revenue: Evidence from an online community for auctioning agricultural and subsidiary products in China

The traditional Dutch auction usually sets the starting price but does not set the final price. The effects and impact factors on the seller’s revenue have not been discussed if the final price of online Dutch auction is set to a teeny number (i.e., one RMB) which is termed as an one-RMB Dutch auction. Based on the regret theory and related literature, the effects of starting price, time pressure (one day and 15 minutes of time interval respectively) and product perishability on buyers\u27 choice behavior and the revenue of sellers were examined. The results showed that there is a negative effect coming from the starting price, time pressure and perishability of products and the overall discount rate of product auction; and buyers are more inclined to bid in the penultimate round of the price reduction cycle

Highly efficient and transferable interatomic potentials for {\alpha}-iron and {\alpha}-iron/hydrogen binary systems using deep neural networks

Artificial neural network potentials (NNPs) have emerged as effective tools for understanding atomic interactions at the atomic scale in various phenomena. Recently, we developed highly transferable NNPs for {\alpha}-iron and {\alpha}-iron/hydrogen binary systems (Physical Review Materials 5 (11), 113606, 2021). These potentials allowed us to investigate deformation and fracture in {\alpha}-iron under the influence of hydrogen. However, the computational cost of the NNP remains relatively high compared to empirical potentials, limiting their applicability in addressing practical issues related to hydrogen embrittlement. In this work, building upon our prior research on iron-hydrogen NNP, we developed a new NNP that not only maintains the excellent transferability but also significantly improves computational efficiency (more than 40 times faster). We applied this new NNP to study the impact of hydrogen on the cracking of iron and the deformation of polycrystalline iron. We employed large-scale through-thickness {110} crack models and large-scale polycrystalline {\alpha}-iron models. The results clearly show that hydrogen atoms segregated at crack tips promote brittle-cleavage failure followed by crack growth. Additionally, hydrogen atoms at grain boundaries facilitate the nucleation of intergranular nanovoids and subsequent intergranular fracture. We anticipate that this high-efficiency NNP will serve as a valuable tool for gaining atomic-scale insights into hydrogen embrittlement

The juxtamembrane and carboxy-terminal domains of Arabidopsis PRK2 are critical for ROP-induced growth in pollen tubes.

Polarized growth of pollen tubes is a critical step for successful reproduction in angiosperms and is controlled by ROP GTPases. Spatiotemporal activation of ROP (Rho GTPases of plants) necessitates a complex and sophisticated regulatory system, in which guanine nucleotide exchange factors (RopGEFs) are key components. It was previously shown that a leucine-rich repeat receptor-like kinase, Arabidopsis pollen receptor kinase 2 (AtPRK2), interacted with RopGEF12 for its membrane recruitment. However, the mechanisms underlying AtPRK2-mediated ROP activation in vivo are yet to be defined. It is reported here that over-expression of AtPRK2 induced tube bulging that was accompanied by the ectopic localization of ROP-GTP and the ectopic distribution of actin microfilaments. Tube depolarization was also induced by a potentially kinase-dead mutant, AtPRK2K366R, suggesting that the over-expression effect of AtPRK2 did not require its kinase activity. By contrast, deletions of non-catalytic domains in AtPRK2, i.e. the juxtamembrane (JM) and carboxy-terminal (CT) domains, abolished its ability to affect tube polarization. Notably, AtPRK2K366R retained the ability to interact with RopGEF12, whereas AtPRK2 truncations of these non-catalytic domains did not. Lastly, it has been shown that the JM and CT domains of AtPRK2 were not only critical for its interaction with RopGEF12 but also critical for its distribution at the plasma membrane. These results thus provide further insight into pollen receptor kinase-mediated ROP activation during pollen tube growth

Sequential Wnt Agonist then Antagonist Treatment Accelerates Tissue Repair and Minimizes Fibrosis

Tissue fibrosis compromises organ function and occurs as a potential long-term outcome in response to acute tissue injuries. Currently, lack of mechanistic understanding prevents effective prevention and treatment of the progression from acute injury to fibrosis. Here, we combined quantitative experimental studies with a mouse kidney injury model and a computational approach to determine how the physiological consequences are determined by the severity of ischemia injury, and to identify how to manipulate Wnt signaling to accelerate repair of ischemic tissue damage while minimizing fibrosis. The study reveals that Wnt-mediated memory of prior injury contributes to fibrosis progression, and ischemic preconditioning reduces the risk of death but increases the risk of fibrosis. Furthermore, we validated the prediction that sequential combination therapy of initial treatment with a Wnt agonist followed by treatment with a Wnt antagonist can reduce both the risk of death and fibrosis in response to acute injuries