On the determinant of the QQ-walk matrix of rooted product with a path

Let $G$ be an $n$-vertex graph and $Q(G)$ be its signless Laplacian matrix. The $Q$-walk matrix of $G$, denoted by $W_Q(G)$, is $[e,Q(G)e,\ldots,Q^{n-1}(G)e]$, where $e$ is the all-one vector. Let $G\circ P_m$ be the graph obtained from $G$ and $n$ copies of the path $P_m$ by identifying the $i$-th vertex of $G$ with an endvertex of the $i$-th copy of $P_m$ for each $i$. We prove that, $$\det W_Q(G\circ P_m)=\pm (\det Q(G))^{m-1}(\det W_Q(G))^m$$ holds for any $m\ge 2$. This gives a signless Laplacian counterpart of the following recently established identity [17]: $$\det W_A(G\circ P_m)=\pm (\det A(G))^{\lfloor\frac{m}{2}\rfloor}(\det W_A(G))^m,$$ where $A(G)$ is the adjacency matrix of $G$ and $W_A(G)=[e,A(G)e,\ldots,A^{n-1}(G)e]$. We also propose a conjecture to unify the above two equalities.Comment: 16 pages, 1 figur

The evolution of BIR domain and its containing proteins

AbstractBIR domain and its containing proteins play critical roles in cell apoptosis and cell division. Here several lines of novelty were revealed based on a comprehensive evolutionary analysis of BIR domains in 11 representative organisms. First, the type II BIR domains in Survivin and Bruce showed more conservation compared with the type I BIR domains in the inhibitors of apoptosis proteins (IAPs). Second, cIAP was derived from a XIAP duplicate and emerged just after the divergence of invertebrates and vertebrates. Third, the three BIR domains of NAIP displayed significantly elevated evolutionary rates compared with the BIR domains in other IAPs

Heat stress exposure cause alterations in intestinal microbiota, transcriptome, and metabolome of broilers

IntroductionHeat stress can affect the production of poultry through complex interactions between genes, metabolites and microorganisms. At present, it is unclear how heat stress affects genetic, metabolic and microbial changes in poultry, as well as the complex interactions between them.MethodsThus, at 28  days of age a total of 200 Arbor Acres broilers with similar body weights were randomly divided into the control (CON) and heat stress treatment (HS). There were 5 replicates in CON and HS, respectively, 20 per replication. From the 28–42  days, the HS was kept at 31 ± 1°C (9:00–17:00, 8 h) and other time was maintained at 21 ± 1°C as in the CON. At the 42nd day experiment, we calculated the growth performance (n = 8) of broilers and collected 3 and 6 cecal tissues for transcriptomic and metabolomic investigation and 4 cecal contents for metagenomic investigation of each treatment.Results and discussionThe results indicate that heat stress significantly reduced the average daily gain and body weight of broilers (value of p < 0.05). Transcriptome KEGG enrichment showed that the differential genes were mainly enriched in the NF-kB signaling pathway. Metabolomics results showed that KEGG enrichment showed that the differential metabolites were mainly enriched in the mTOR signaling pathway. 16S rDNA amplicon sequencing results indicated that heat stress increased the relative abundance of Proteobacteria decreased the relative abundance of Firmicutes. Multi-omics analysis showed that the co-participating pathway of differential genes, metabolites and microorganisms KEGG enrichment was purine metabolism. Pearson correlation analysis found that ornithine was positively correlated with SULT1C3, GSTT1L and g_Lactobacillus, and negatively correlated with CALB1. PE was negatively correlated with CALB1 and CHAC1, and positively with g_Alistipes. In conclusion, heat stress can generate large amounts of reactive oxygen and increase the types of harmful bacteria, reduce intestinal nutrient absorption and antioxidant capacity, and thereby damage intestinal health and immune function, and reduce growth performance indicators. This biological process is manifested in the complex regulation, providing a foundational theoretical basis for solving the problem of heat stress

Customers’ Mode Choice Behaviors of Express Service Based on Latent Class Analysis and Logit Model

As the parcel delivery service is booming in China, the competition among express companies intensifies. This paper employed multinomial logit model (MNL) and latent class model (LCM) to investigate customers’ express service choice behavior, using data from a SP survey. The attributes and attribute levels that matter most to express customers are identified. Meanwhile, the customers are divided into two segments (penny pincher segment and high-end segment) characterized by their taste heterogeneity. The results indicate that the LCM performs statistically better than MNL in our sample. Therefore, more attention should be paid to the taste heterogeneity, especially for further academic and policy research in freight choice behavior

Determining spin-orbit coupling in graphene by quasiparticle interference imaging

Inducing and controlling spin-orbit coupling (SOC) in graphene is key to create topological states of matter, and for the realization of spintronic devices. Placing graphene onto a transition metal dichalcogenide is currently the most successful strategy to achieve this goal, but there is no consensus as to the nature and the magnitude of the induced SOC. Here, we show that the presence of backscattering in graphene-on-WSe$_2$ heterostructures can be used to probe SOC and to determine its strength quantitatively, by imaging quasiparticle interference with a scanning tunneling microscope. A detailed theoretical analysis of the Fourier transform of quasiparticle interference images reveals that the induced SOC consists of a valley-Zeeman ($\lambda_{\text{vZ}}\approx 2$ meV) and a Rashba ($\lambda_\text{R}\approx 15$ meV) term, one order of magnitude larger than what theory predicts, but in excellent agreement with earlier transport experiments. The validity of our analysis is confirmed by measurements on a 30 degree twist angle heterostructure that exhibits no backscattering, as expected from symmetry considerations. Our results demonstrate a viable strategy to determine SOC quantitatively by imaging quasiparticle interference

On-water surface synthesis of charged two-dimensional polymer single crystals via the irreversible Katritzky reaction

Two-dimensional polymers (2DPs) and their layer-stacked 2D covalent organic frameworks (2D COFs) are classes of structurally defined crystalline polymeric materials with exotic physical and chemical properties. Yet, synthesizing 2DP and 2D COF single crystals via irreversible reactions remains challenging. Here we report the synthesis of charged 2DP (C2DP) single crystals through an irreversible Katritzky reaction, under pH control, on a water surface. The periodically ordered 2DPs comprise aromatic pyridinium cations and counter BF4− anions. The C2DP crystals, which are composed of linked porphyrin and pyrylium monomers (C2DP-Por), have a tunable thickness of 2–30 nm and a lateral domain size up to 120 μm2. Single crystals with a square lattice (a = b = 30.5 Å) are resolved by imaging and diffraction methods with near-atomic precision. Furthermore, the integration of C2DP-Por crystals in an osmotic power generator device shows an excellent chloride ion selectivity with a coefficient value reaching ~0.9 and an output power density of 4 W m−2, superior to those of graphene and boron nitride

A survey of parametric modelling methods for designing the head of a high-speed train

With the continuous increase of the running speed, the head shape of the high-speed train (HST) turns out to be a critical factor for further speed boost. In order to cut down the time used in the HST head design and improve the modelling efficiency, various parametric modelling methods have been widely applied in the optimization design of the HST head to obtain an optimal head shape so that the aerodynamic effect acting on the head of HSTs can be reduced and more energy can be saved. This paper reviews these parametric modelling methods and classifies them into four categories: 2D, 3D, CATIA-based, and mesh deformation-based parametric modelling methods. Each of the methods is introduced, and the advantages and disadvantages of these methods are identified. The simulation results are presented to demonstrate that the aerodynamic performance of the optimal models constructed by these parametric modelling methods has been improved when compared with numerical calculation results of the original models or the prototype models of running trains. Since different parametric modelling methods used different original models and optimization methods, few publications could be found which compare the simulation results of the aerodynamic performance among different parametric modelling methods. In spite of this, these parametric modelling methods indicate more local shape details will lead to more accurate simulation results, and fewer design variables will result in higher computational efficiency. Therefore, the ability of describing more local shape details with fewer design variables could serve as a main specification to assess the performance of various parametric modelling methods. The future research directions may concentrate on how to improve such ability

A genome-wide association study of coat color in Chinese Rex rabbits

Coat color is an important phenotypic characteristic of the domestic rabbit (Oryctolagus cuniculus) and has specific economic importance in the Rex rabbit industry. Coat color varies considerably among different populations of rabbits, and several causal genes for this variation have been thoroughly studied. Nevertheless, the candidate genes affecting coat color variation in Chinese Rex rabbits remained to be investigated. In this study, we collected blood samples from 250 Chinese Rex rabbits with six different coat colors. We performed genome sequencing using a restriction site-associated DNA sequencing approach. A total of 91,546 single nucleotide polymorphisms (SNPs), evenly distributed among 21 autosomes, were identified. Genome-wide association studies (GWAS) were performed using a mixed linear model, in which the individual polygenic effect was fitted as a random effect. We detected a total of 24 significant SNPs that were located within a genomic region on chromosome 4 (OCU4). After re-fitting the most significant SNP (OCU4:13,434,448, p = 1.31e-12) as a covariate, another near-significant SNP (OCU4:11,344,946, p = 7.03e-07) was still present. Hence, we conclude that the 2.1-Mb genomic region located between these two significant SNPs is significantly associated with coat color in Chinese Rex rabbits. The well-studied coat-color-associated agouti signaling protein (ASIP) gene is located within this region. Furthermore, low genetic differentiation was also observed among the six coat color varieties. In conclusion, our results confirmed that ASIP is a putative causal gene affecting coat color variation in Chinese Rex rabbits