Spectral radius, fractional [a,b][a,b]-factor and ID-factor-critical graphs

Let $G$ be a graph and $h: E(G)\rightarrow [0,1]$ be a function. For any two positive integers $a$ and $b$ with $a\leq b$, a fractional $[a,b]$-factor of $G$ with the indicator function $h$ is a spanning subgraph with vertex set $V(G)$ and edge set $E_h$ such that $a\leq\sum_{e\in E_{G}(v)}h(e)\leq b$ for any vertex $v\in V(G)$, where $E_h = \{e\in E(G)|h(e)>0\}$ and E_{G}(v)=\{e\in E(G)| e~\mbox{is incident with}~v~\mbox{in}~G\}. A graph $G$ is ID-factor-critical if for every independent set $I$ of $G$ whose size has the same parity as $|V(G)|$, $G-I$ has a perfect matching. In this paper, we present a tight sufficient condition based on the spectral radius for a graph to contain a fractional $[a,b]$-factor, which extends the result of Wei and Zhang [Discrete Math. 346 (2023) 113269]. Furthermore, we also prove a tight sufficient condition in terms of the spectral radius for a graph with minimum degree $\delta$ to be ID-factor-critical.Comment: 14 pages, 2 figure

Spectral radius and spanning trees of graphs

For integer $k\geq2,$ a spanning $k$-ended-tree is a spanning tree with at most $k$ leaves. Motivated by the closure theorem of Broersma and Tuinstra [Independence trees and Hamilton cycles, J. Graph Theory 29 (1998) 227--237], we provide tight spectral conditions to guarantee the existence of a spanning $k$-ended-tree in a connected graph of order $n$ with extremal graphs being characterized. Moreover, by adopting Kaneko's theorem [Spanning trees with constraints on the leaf degree, Discrete Appl. Math. 115 (2001) 73--76], we also present tight spectral conditions for the existence of a spanning tree with leaf degree at most $k$ in a connected graph of order $n$ with extremal graphs being determined, where $k\geq1$ is an integer

An improvement of sufficient condition for kk-leaf-connected graphs

For integer $k\geq2,$ a graph $G$ is called $k$-leaf-connected if $|V(G)|\geq k+1$ and given any subset $S\subseteq V(G)$ with $|S|=k,$ $G$ always has a spanning tree $T$ such that $S$ is precisely the set of leaves of $T.$ Thus a graph is $2$-leaf-connected if and only if it is Hamilton-connected. In this paper, we present a best possible condition based upon the size to guarantee a graph to be $k$-leaf-connected, which not only improves the results of Gurgel and Wakabayashi [On $k$-leaf-connected graphs, J. Combin. Theory Ser. B 41 (1986) 1-16] and Ao, Liu, Yuan and Li [Improved sufficient conditions for $k$-leaf-connected graphs, Discrete Appl. Math. 314 (2022) 17-30], but also extends the result of Xu, Zhai and Wang [An improvement of spectral conditions for Hamilton-connected graphs, Linear Multilinear Algebra, 2021]. Our key approach is showing that an $(n+k-1)$-closed non-$k$-leaf-connected graph must contain a large clique if its size is large enough. As applications, sufficient conditions for a graph to be $k$-leaf-connected in terms of the (signless Laplacian) spectral radius of $G$ or its complement are also presented.Comment: 15 pages, 2 figure

Exploring research hotspots and future directions in neural tube defects field by bibliometric and bioinformatics analysis

BackgroundNeural tube defects (NTDs) is the most common birth defect of the central nervous system (CNS) which causes the death of almost 88,000 people every year around the world. Much efforts have been made to investigate the reasons that contribute to NTD and explore new ways to for prevention. We trawl the past decade (2013–2022) published records in order to get a worldwide view about NTDs research field.Methods7,437 records about NTDs were retrieved from the Web of Science (WOS) database. Tools such as shell scripts, VOSviewer, SCImago Graphica, CiteSpace and PubTator were used for data analysis and visualization.ResultsOver the past decade, the number of publications has maintained an upward trend, except for 2022. The United States is the country with the highest number of publications and also with the closest collaboration with other countries. Baylor College of Medicine has the closest collaboration with other institutions worldwide and also was the most prolific institution. In the field of NTDs, research focuses on molecular mechanisms such as genes and signaling pathways related to folate metabolism, neurogenic diseases caused by neural tube closure disorders such as myelomeningocele and spina bifida, and prevention and treatment such as folate supplementation and surgical procedures. Most NTDs related genes are related to development, cell projection parts, and molecular binding. These genes are mainly concentrated in cancer, Wnt, MAPK, PI3K-Akt and other signaling pathways. The distribution of NTDs related SNPs on chromosomes 1, 3, 5, 11, 14, and 17 are relatively concentrated, which may be associated with high-risk of NTDs.ConclusionBibliometric analysis of the literature on NTDs field provided the current status, hotspots and future directions to some extant. Further bioinformatics analysis expanded our understanding of NTDs-related genes function and revealed some important SNP clusters and loci. This study provided some guidance for further studies. More extensive cooperation and further research are needed to overcome the ongoing challenge in pathogenesis, prevention and treatment of NTDs

Table_1_Exploring research hotspots and future directions in neural tube defects field by bibliometric and bioinformatics analysis.XLSX

BackgroundNeural tube defects (NTDs) is the most common birth defect of the central nervous system (CNS) which causes the death of almost 88,000 people every year around the world. Much efforts have been made to investigate the reasons that contribute to NTD and explore new ways to for prevention. We trawl the past decade (2013–2022) published records in order to get a worldwide view about NTDs research field.Methods7,437 records about NTDs were retrieved from the Web of Science (WOS) database. Tools such as shell scripts, VOSviewer, SCImago Graphica, CiteSpace and PubTator were used for data analysis and visualization.ResultsOver the past decade, the number of publications has maintained an upward trend, except for 2022. The United States is the country with the highest number of publications and also with the closest collaboration with other countries. Baylor College of Medicine has the closest collaboration with other institutions worldwide and also was the most prolific institution. In the field of NTDs, research focuses on molecular mechanisms such as genes and signaling pathways related to folate metabolism, neurogenic diseases caused by neural tube closure disorders such as myelomeningocele and spina bifida, and prevention and treatment such as folate supplementation and surgical procedures. Most NTDs related genes are related to development, cell projection parts, and molecular binding. These genes are mainly concentrated in cancer, Wnt, MAPK, PI3K-Akt and other signaling pathways. The distribution of NTDs related SNPs on chromosomes 1, 3, 5, 11, 14, and 17 are relatively concentrated, which may be associated with high-risk of NTDs.ConclusionBibliometric analysis of the literature on NTDs field provided the current status, hotspots and future directions to some extant. Further bioinformatics analysis expanded our understanding of NTDs-related genes function and revealed some important SNP clusters and loci. This study provided some guidance for further studies. More extensive cooperation and further research are needed to overcome the ongoing challenge in pathogenesis, prevention and treatment of NTDs.</p

Comparative transcriptome profiling analysis provides insight into the mechanisms for sugar change in Chinese jujube (Ziziphus jujuba Mill.) under rain‐proof cultivation

Abstract Chinese jujube (Ziziphus jujuba Mill.) is a globally popular and economically important fruit that is rich in bioactive compounds with strong anti‐cancer effects. Rain‐proof cultivation is widely used to cultivate Chinese jujube, as it helps avoid rainfall damage during fruit harvest. Although the sugar content of jujube fruits differs between rain‐proof and open‐field cultivation, the underlying molecular mechanisms are unknown. Here, we analyzed the levels of sugar content, sugar accumulation pattern, and transcriptome profiles of jujube fruits at five developmental stages grown under rain‐proof and open‐field cultivation modes. The sugar content of jujube fruits was significantly higher under rain‐proof cultivation than under open‐field cultivation, although the sugar composition and sugar accumulation patterns were comparable. Comparative analysis of transcriptomic profiles showed that rain‐proof cultivation enhanced the intrinsic metabolic activity of fruit development. Gene expression and correlation analyses suggested that ZjSPS, ZjSS, ZjHXK, and ZjINV regulate the development‐related changes in sugar content in jujube fruits grown under rain‐proof cultivation. Temperature, humidity, and moisture conditions were key climatic factors affecting sugar accumulation. Our results provide insights into the molecular mechanisms regulating sugar content and sugar accumulation in Chinese jujube fruits grown under rain‐proof cultivation, and we provide genetic resources for studying the development mechanism of Chinese jujube fruit

The Roles of Morphology on the Relaxation Rates of Magnetic Nanoparticles

The shape of magnetic nanoparticles is of great importance in determining their contrast abilities for magnetic resonance imaging. Various magnetic nanoparticles have been developed to achieve high <i>T</i>₁ or <i>T</i>₂ relaxivities, but the mechanism on how morphology influences the water proton relaxation process is still unrevealed. Herein we synthesize manganese-doped iron oxide (MnIO) nanoparticles of the same volume with six different shapes and reveal the relationship between morphologies and <i>T</i>₁/<i>T</i>₂ relaxation rates. The morphology of magnetic nanoparticles largely determines the effective radius and the gradient of stray field, which in turn affects the transverse relaxation rate. The longitudinal relaxivity has positive correlation with the surface-area-to-volume ratio and the occupancy rate of effective metal ions on exposed surfaces of magnetic nanoparticles. These findings together with the summary of <i>r</i>₂/<i>r</i>₁ ratios could help to guide the screening for the optimal shapes of promising <i>T</i>₁ or <i>T</i>₂ contrast agents. Varying effective radii could be utilized to change negative contrast abilities. The surface-area-to-volume ratio and the amount of effective metal ions on exposed surface are instrumental for tuning positive contrast abilities. These principles could serve as guidelines for design and development of high-performance nanoparticle-based contrast agents

Melatonin alleviates valproic acid-induced neural tube defects by modulating Src/PI3K/ERK signaling and oxidative stress

Neural tube defects (NTDs) represent a developmental disorder of the nervous system that can lead to significant disability in children and impose substantial social burdens. Valproic acid (VPA), a widely prescribed first-line antiepileptic drug for epilepsy and various neurological conditions, has been associated with a 4-fold increase in the risk of NTDs when used during pregnancy. Consequently, urgent efforts are required to identify innovative prevention and treatment approaches for VPA-induced NTDs. Studies have demonstrated that the disruption in the delicate balance between cell proliferation and apoptosis is a crucial factor contributing to NTDs induced by VPA. Encouragingly, our current data reveal that melatonin (MT) significantly inhibits apoptosis while promoting the restoration of neuroepithelial cell proliferation impaired by VPA. Moreover, further investigations demonstrate that MT substantially reduces the incidence of neural tube malformations resulted from VPA exposure, primarily by suppressing apoptosis through the modulation of intracellular reactive oxygen species levels. In addition, the Src/PI3K/ERK signaling pathway appears to play a pivotal role in VPA-induced NTDs, with significant inhibition observed in the affected samples. Notably, MT treatment successfully reinstates Src/PI3K/ERK signaling, thereby offering a potential underlying mechanism for the protective effects of MT against VPA-induced NTDs. In summary, our current study substantiates the considerable protective potential of MT in mitigating VPA-triggered NTDs, thereby offering valuable strategies for the clinical management of VPA-related birth defects