The extremal spectral radii of kk-uniform supertrees

In this paper, we study some extremal problems of three kinds of spectral radii of $k$-uniform hypergraphs (the adjacency spectral radius, the signless Laplacian spectral radius and the incidence $Q$-spectral radius). We call a connected and acyclic $k$-uniform hypergraph a supertree. We introduce the operation of "moving edges" for hypergraphs, together with the two special cases of this operation: the edge-releasing operation and the total grafting operation. By studying the perturbation of these kinds of spectral radii of hypergraphs under these operations, we prove that for all these three kinds of spectral radii, the hyperstar $\mathcal{S}_{n,k}$ attains uniquely the maximum spectral radius among all $k$-uniform supertrees on $n$ vertices. We also determine the unique $k$-uniform supertree on $n$ vertices with the second largest spectral radius (for these three kinds of spectral radii). We also prove that for all these three kinds of spectral radii, the loose path $\mathcal{P}_{n,k}$ attains uniquely the minimum spectral radius among all $k$-th power hypertrees of $n$ vertices. Some bounds on the incidence $Q$-spectral radius are given. The relation between the incidence $Q$-spectral radius and the spectral radius of the matrix product of the incidence matrix and its transpose is discussed

The proof of a conjecture on largest Laplacian and signless Laplacian H-eigenvalues of uniform hypergraphs

Let $\mathcal{A(}G\mathcal{)},\mathcal{L(}G\mathcal{)}$ and $\mathcal{Q(}G\mathcal{)}$ be the adjacency tensor, Laplacian tensor and signless Laplacian tensor of uniform hypergraph $G$, respectively. Denote by $\lambda (\mathcal{T})$ the largest H-eigenvalue of tensor $\mathcal{T}$. Let $H$ be a uniform hypergraph, and $H^{\prime}$ be obtained from $H$ by inserting a new vertex with degree one in each edge. We prove that $\lambda(\mathcal{Q(}H^{\prime}\mathcal{)})\leq\lambda(\mathcal{Q(}H\mathcal{)}).$ Denote by $G^{k}$ the $k$th power hypergraph of an ordinary graph $G$ with maximum degree $\Delta\geq2$. We will prove that $\{\lambda(\mathcal{Q(}$ is a strictly decreasing sequence, which imply Conjectrue 4.1 of Hu, Qi and Shao in \cite{HuQiShao2013}. We also prove that $\lambda(\mathcal{Q(}G^{k}\mathcal{)})$ converges to $\Delta$ when $k$ goes to infinity. The definiton of $k$th power hypergraph $G^{k}$ has been generalized as $G^{k,s}.$ We also prove some eigenvalues properties about $\mathcal{A(}G^{k,s}\mathcal{)},$ which generalize some known results. Some related results about $\mathcal{L(}G\mathcal{)}$ are also mentioned

Knockdown of TNFAIP1 mitigates sevoflurane-induced cognitive dysfunction by activating CREB/Nrf2 pathway

Purpose: To investigate the role of tumor necrosis factor-induced protein 1 (TNFAIP1) and cAMPresponsive element binding protein (CREB)/nuclear factor-erythroid factor 2-related factor 2 (Nrf2) pathway in sevoflurane (SEV)-induced cognitive dysfunction. Methods: A SEV-induced cognitive dysfunction rat model was developed. Bcl-2, Bax, heme oxygenase-1, Nrf2, p-CREB, and CREB protein levels in rat hippocampal tissue were assessed by western blot. Learning and long-term memory were evaluated using Morris water maze test. Glutathione peroxidase, malondialdehyde, and superoxide dismutase levels in hippocampal tissue were measured by enzyme-linked immunosorbent assay (ELISA). The 2,7-dichlorodihydro-fluorescein diacetate fluorescent assay was used to measure reactive oxygen species, while TUNEL staining was used to assess neuronal cell apoptosis. Results: Knockdown of TNFAIP1 attenuated SEV-induced learning and long-term memory dysfunction (p < 0.005), oxidative stress (p < 0.005), apoptosis (p < 0.005), and inhibition of the CREB/Nrf2 signaling pathway. Conclusion: This study demonstrates that knockdown of TNFAIP1 alleviates SEV-induced cognitive dysfunction by reversing inhibition of the CREB/Nrf2 signaling pathway. Keywords: TNFAIP1; Postoperative cognitive dysfunction; Sevoflurane; cAMP-responsive element binding protein (CREB); Nuclear factor-erythroid factor 2-related factor 2 (Nrf2

Genome-wide analysis of the nucleotide binding site leucine-rich repeat genes of four orchids revealed extremely low numbers of disease resistance genes

Orchids are one of the most diverse flowering plant families, yet possibly maintain the smallest number of the nucleotide-binding site-leucine-rich repeat (NBS-LRR) type plant resistance (R) genes among the angiosperms. In this study, a genome-wide search in four orchid taxa identified 186 NBS-LRR genes. Furthermore, 214 NBS-LRR genes were identified from seven orchid transcriptomes. A phylogenetic analysis recovered 30 ancestral lineages (29 CNL and one RNL), far fewer than other angiosperm families. From the genetics aspect, the relatively low number of ancestral R genes is unlikely to explain the low number of R genes in orchids alone, as historical gene loss and scarce gene duplication has continuously occurred, which also contributes to the low number of R genes. Due to recent sharp expansions, Phalaenopsis equestris and Dendrobium catenatum having 52 and 115 genes, respectively, and exhibited an "early shrinking to recent expanding" evolutionary pattern, while Gastrodia elata and Apostasia shenzhenica both exhibit a "consistently shrinking" evolutionary pattern and have retained only five and 14 NBS-LRR genes, respectively. RNL genes remain in extremely low numbers with only one or two copies per genome. Notably, all of the orchid RNL genes belong to the ADR1 lineage. A separate lineage, NRG1, was entirely absent and was likely lost in the common ancestor of all monocots. All of the TNL genes were absent as well, coincident with the RNL NRG1 lineage, which supports the previously proposed notion that a potential functional association between the TNL and RNL NRG1 genes

Distinct Topological Surface States on the Two Terminations of MnBi4_4Te7_7

The recent discovered intrinsic magnetic topological insulator MnBi2Te4 have been met with unusual success in hosting emergent phenomena such as the quantum anomalous Hall effect and the axion insulator states. However, the surface-bulk correspondence of the Mn-Bi-Te family, composed by the superlattice-like MnBi2Te4/(Bi2Te3)n (n = 0, 1, 2, 3 ...) layered structure, remains intriguing but elusive. Here, by using scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES) techniques, we unambiguously assign the two distinct surface states of MnBi4Te7 (n = 1) to the quintuple-layer (QL) Bi2Te3 termination and the septuple-layer (SL) MnBi2Te4 termination, respectively. A comparison of the experimental observations with theoretical calculations reveals the diverging topological behaviors, especially the hybridization effect between magnetic and nonmagnetic layers, on the two terminations: a gap on the QL termination originating from the topological surface states of the QL hybridizing with the bands of the beneath SL, and a gapless Dirac-cone band structure on the SL termination with time-reversal symmetry. The quasi-particle interference patterns further confirm the topological nature of the surface states for both terminations, continuing far above the Fermi energy. The QL termination carries a spin-helical Dirac state with hexagonal warping, while at the SL termination, a strongly canted helical state from the surface lies between a pair of Rashba-split states from its neighboring layer. Our work elucidates an unprecedented hybridization effect between the building blocks of the topological surface states, and also reveals the termination-dependent time-reversal symmetry breaking in a magnetic topological insulator, rendering an ideal platform to realize the half-integer quantum Hall effect and relevant quantum phenomena.Comment: 22 Pages, 4 Figure