On Eulerian subgraphs and hamiltonian line graphs

A graph {\color{black}$G$} is Hamilton-connected if for any pair of distinct vertices {\color{black}$u, v \in V(G)$}, {\color{black}$G$} has a spanning $(u,v)$-path; {\color{black}$G$} is 1-hamiltonian if for any vertex subset $S \subseteq {\color{black}V(G)}$ with $|S| \le 1$, $G - S$ has a spanning cycle. Let $\delta(G)$, $\alpha\u27(G)$ and $L(G)$ denote the minimum degree, the matching number and the line graph of a graph $G$, respectively. The following result is obtained. {\color{black} Let $G$ be a simple graph} with $|E(G)| \ge 3$. If $\delta(G) \geq \alpha\u27(G)$, then each of the following holds. \\ (i) $L(G)$ is Hamilton-connected if and only if $\kappa(L(G))\ge 3$. \\ (ii) $L(G)$ is 1-hamiltonian if and only if $\kappa(L(G))\ge 3$. %==========sp For a graph $G$, an integer $s \ge 0$ and distinct vertices $u, v \in V(G)$, an $(s; u, v)$-path-system of $G$ is a subgraph $H$ consisting of $s$ internally disjoint $(u,v)$-paths. The spanning connectivity $\kappa^*(G)$ is the largest integer $s$ such that for any $k$ with $0 \le k \le s$ and for any $u, v \in V(G)$ with $u \neq v$, $G$ has a spanning $(k; u,v)$-path-system. It is known that $\kappa^*(G) \le \kappa(G)$, and determining if $\kappa^*(G) \u3e 0$ is an NP-complete problem. A graph $G$ is maximally spanning connected if $\kappa^*(G) = \kappa(G)$. Let $msc(G)$ and $s_k(G)$ be the smallest integers $m$ and $m\u27$ such that $L^m(G)$ is maximally spanning connected and $\kappa^*(L^{m\u27}(G)) \ge k$, respectively. We show that every locally-connected line graph with connectivity at least 3 is maximally spanning connected, and that the spanning connectivity of a locally-connected line graph can be polynomially determined. As applications, we also determined best possible upper bounds for $msc(G)$ and $s_k(G)$, and characterized the extremal graphs reaching the upper bounds. %==============st For integers $s \ge 0$ and $t \ge 0$, a graph $G$ is $(s,t)$-supereulerian if for any disjoint edge sets $X, Y \subseteq E(G)$ with $|X|\le s$ and $|Y|\le t$, $G$ has a spanning closed trail that contains $X$ and avoids $Y$. Pulleyblank in [J. Graph Theory, 3 (1979) 309-310] showed that determining whether a graph is $(0,0)$-supereulerian, even when restricted to planar graphs, is NP-complete. Settling an open problem of Bauer, Catlin in [J. Graph Theory, 12 (1988) 29-45] showed that every simple graph $G$ on $n$ vertices with $\delta(G) \ge \frac{n}{5} -1$, when $n$ is sufficiently large, is $(0,0)$-supereulerian or is contractible to $K_{2,3}$. We prove the following for any nonnegative integers $s$ and $t$. \\ (i) For any real numbers $a$ and $b$ with $0 \u3c a \u3c 1$, there exists a family of finitely many graphs \F(a,b;s,t) such that if $G$ is a simple graph on $n$ vertices with $\kappa\u27(G) \ge t+2$ and $\delta(G) \ge an + b$, then either $G$ is $(s,t)$-supereulerian, or $G$ is contractible to a member in \F(a,b;s,t). \\ (ii) Let $\ell K_2$ denote the connected loopless graph with two vertices and $\ell$ parallel edges. If $G$ is a simple graph on $n$ vertices with $\kappa\u27(G) \ge t+2$ and $\delta(G) \ge \frac{n}{2}-1$, then when $n$ is sufficiently large, either $G$ is $(s,t)$-supereulerian, or for some integer $j$ with $t+2 \le j \le s+t$, $G$ is contractible to a $j K_2$. %==================index For a hamiltonian property \cp, Clark and Wormold introduced the problem of investigating the value \cp(a,b) = \max\{\min\{n: L^n(G) has property \cp\}: $\kappa\u27(G) \ge a$ and $\delta(G) \ge b\}$, and proposed a few problems to determine \cp(a,b) with $b \ge a \ge 4$ when \cp is being hamiltonian, edge-hamiltonian and hamiltonian-connected. Zhan in 1986 proved that the line graph of a 4-edge-connected graph is Hamilton-connected, which implies a solution to the unsettled cases of above-mentioned problem. We consider an extended version of the problem. Let $ess\u27(G)$ denote the essential edge-connectivity of a graph $G$, and define \cp\u27(a,b) = \max\{\min\{n: L^n(G) has property \cp\}: $ess\u27(G) \ge a$ and $\delta(G) \ge b\}$. We investigate the values of \cp\u27(a,b) when \cp is one of these hamiltonian properties. In particular, we show that for any values of $b \ge 1$, \cp\u27(4,b) \le 2 and \cp\u27(4,b) = 1 if and only if Thomassen\u27s conjecture that every 4-connected line graph is hamiltonian is valid

Building Better Li Metal Anodes in Liquid Electrolyte: Challenges and Progress

Li metal has been widely recognized as a promising anode candidate for high-energy-density batteries. However, the inherent limitations of Li metal, that is, the low Coulombic efficiency and dendrite issues, make it still far from practical applications. In short, the low Coulombic efficiency shortens the cycle life of Li metal batteries, while the dendrite issue raises safety concerns. Thanks to the great efforts of the research community, prolific fundamental understanding as well as approaches for mitigating Li metal anode safety have been extensively explored. In this Review, Li electrochemical deposition behaviors have been systematically summarized, and recent progress in electrode design and electrolyte system optimization is reviewed. Finally, we discuss the future directions, opportunities, and challenges of Li metal anodes

R&D and its Application to NPPs on Aging Management and Lifetime Assessment

ABSTRACT With more and more aged Nuclear Power Plants (NPPs) are still in operation in main nuclear industrial countries, aging and life management for operational NPPs becomes a worldwide concern. Many countries and international organizations, like IAEA, etc., have published a lot of regulatory requirements and guidelines to make the aging be well controlled by implementing effective aging management (AM) system in NPPs based on well understanding on aging mechanisms, assessment methodology and online monitoring technique. As a pioneering R&D institute in NPP design in China, Shanghai Nuclear Engineering research & Design Institute (SNERDI) initiated R&D on aging and life management for main components of NPP in the middle of 1990s, when Chinese first NPP, Qinshan-I (Q1), was very young. At present, China has a very ambitious NPP development plan in the following 15 years. Establishment of regulatory requirements and guidelines on aging management for operational NPPs gradually becomes an actual need, with more and more new NPPs being put into operation in the near future. This paper provides a schematic introduction on SNERDI's strategic consideration and R&D activities on aging management and lifetime assessment. As an example of application of R&D to operational NPPs, PSR for Qinshan-I (Q1) is briefly introduced. Finally, the paper provides some points of view on establishment of Chinese aging management (AM) regulatory system

14-Thienyl Methylene Matrine (YYJ18), the Derivative from Matrine, Induces Apoptosis of Human Nasopharyngeal Carcinoma Cells by Targeting MAPK and PI3K/Akt Pathways in Vitro

Background/Aims: Nasopharyngeal carcinoma (NPC) is a distinctive type of head and neck cancer with the highest incidence in South China. Previous studies have proved that matrine, a main alkaloid isolated from Sophora flavescens Ait, has antitumor activity against NPC. However, the effect is not so pronounced and the underlying mechanism remains largely unclear. Here we investigated whether 14-thienyl methylene matrine (YYJ18) that was derived from matrine could exert more effective suppression activity on NPC, along with the underlying mechanism. Methods: NPC cell lines CNE1, CNE2 and HONE1 were treated with YYJ18. Cell proliferation and apoptosis were determined by MTT assay and flow cytometry. Activation of mitogen-activated protein kinases (MAPK) and phosphatidylinositol 3-kinase/protein kinase B (PI3K/Akt) pathways were determined by Western blotting and quantitative RT-PCR. Results: YYJ18 remarkably inhibited proliferation and induced apoptosis of all three NPC cell lines in a dose-dependent manner, especially in CNE2 cells. Furthermore, YYJ18 treatment significantly suppressed phosphorylation of p38 in CNE2 cells, but upregulated phosphorylation of extracellular signal-regulated kinase1/2 (ERK1/2) and Akt. Next, alterations in downstream signaling were found, including activation of BCL2-associated X protein (Bax), caspase-3 and inactivation of B-cell CLL/lymphoma 2 (Bcl-2). Conclusion: We demonstrate the potent inhibitory effects of 14-thienyl methylene matrine on NPC cells for the first time, which could be mediated by modulation of MAPK and PI3K/Akt pathways

Targeted mutagenesis by homologous recombination in D. melanogaster

We used a recently developed method to produce mutant alleles of five endogenous Drosophila genes, including the homolog of the p53 tumor suppressor. Transgenic expression of the FLP site-specific recombinase and the I-SceI endonuclease generates extrachromosomal linear DNA molecules in vivo. These molecules undergo homologous recombination with the corresponding chromosomal locus to generate targeted alterations of the host genome. The results address several questions about the general utility of this technique. We show that genes not near telomeres can be efficiently targeted; that no knowledge of the mutant phenotype is needed for targeting; and that insertional mutations and allelic substitutions can be easily produced

Image_2_Comparison of cytokine/chemokine profiles between dermatomyositis and anti-synthetase syndrome.TIF

ObjectivesDermatomyositis (DM) and anti-synthetase syndrome (ASS) are autoimmune diseases with multisystem involvement. Despite sharing some clinical and myopathological features, these are two diseases with different pathogeneses and prognoses. We aimed to clarify and compare cytokine/chemokine profiles in both disorders, which may help in the differential diagnosis.Materials and methodsWe collected clinical data and serum samples of consecutive patients with DM and ASS. Quantibody® Human Inflammation Array 3 for cytokines/chemokines was performed in the serum of all participants. Receiver operating characteristic analysis with the area under the curve and Youden's index were performed.ResultsEight newly diagnosed and treatment-naïve patients with DM, nine newly diagnosed and treatment-naïve patients with ASS, and 14 healthy controls were enrolled. Serum C-C motif chemokine ligand (CCL) 2, CCL4, C-X-C motif chemokine ligand (CXCL) 13, and tumor necrosis factor receptor 2 (TNFR2) were increased in patients with both DM and ASS. Serum interleukin (IL)-1 receptor type 1 (IL-1ra), IL-1b, CCL1, CXCL11, and CCL3 were modulated in patients with DM only, and IL-8, CXCL9, and tissue inhibitors of metalloproteinases-1 (TIMP-1) in patients with ASS only. Serum CCL2, CXCL13, and TNFR2 accurately distinguished patients with DM and ASS from healthy controls, as shown by the area under the curve >0.80. Moreover, receiver operating characteristic analysis showed that, as biomarkers for discrimination between DM and ASS, the combination of IL-1ra and TIMP-1, had an area under the curve of 0.944, a sensitivity of 87.5%, and a specificity of 88.9%.ConclusionOur study demonstrated that serum levels of cytokines/chemokines showed a different pattern in newly diagnosed patients with DM and ASS, in which serum IL-1ra and TIMP-1 could be used to distinguish between the two diseases.</p

Table_1_Comparison of cytokine/chemokine profiles between dermatomyositis and anti-synthetase syndrome.DOCX

ObjectivesDermatomyositis (DM) and anti-synthetase syndrome (ASS) are autoimmune diseases with multisystem involvement. Despite sharing some clinical and myopathological features, these are two diseases with different pathogeneses and prognoses. We aimed to clarify and compare cytokine/chemokine profiles in both disorders, which may help in the differential diagnosis.Materials and methodsWe collected clinical data and serum samples of consecutive patients with DM and ASS. Quantibody® Human Inflammation Array 3 for cytokines/chemokines was performed in the serum of all participants. Receiver operating characteristic analysis with the area under the curve and Youden's index were performed.ResultsEight newly diagnosed and treatment-naïve patients with DM, nine newly diagnosed and treatment-naïve patients with ASS, and 14 healthy controls were enrolled. Serum C-C motif chemokine ligand (CCL) 2, CCL4, C-X-C motif chemokine ligand (CXCL) 13, and tumor necrosis factor receptor 2 (TNFR2) were increased in patients with both DM and ASS. Serum interleukin (IL)-1 receptor type 1 (IL-1ra), IL-1b, CCL1, CXCL11, and CCL3 were modulated in patients with DM only, and IL-8, CXCL9, and tissue inhibitors of metalloproteinases-1 (TIMP-1) in patients with ASS only. Serum CCL2, CXCL13, and TNFR2 accurately distinguished patients with DM and ASS from healthy controls, as shown by the area under the curve >0.80. Moreover, receiver operating characteristic analysis showed that, as biomarkers for discrimination between DM and ASS, the combination of IL-1ra and TIMP-1, had an area under the curve of 0.944, a sensitivity of 87.5%, and a specificity of 88.9%.ConclusionOur study demonstrated that serum levels of cytokines/chemokines showed a different pattern in newly diagnosed patients with DM and ASS, in which serum IL-1ra and TIMP-1 could be used to distinguish between the two diseases.</p

Image_1_Comparison of cytokine/chemokine profiles between dermatomyositis and anti-synthetase syndrome.TIF

ObjectivesDermatomyositis (DM) and anti-synthetase syndrome (ASS) are autoimmune diseases with multisystem involvement. Despite sharing some clinical and myopathological features, these are two diseases with different pathogeneses and prognoses. We aimed to clarify and compare cytokine/chemokine profiles in both disorders, which may help in the differential diagnosis.Materials and methodsWe collected clinical data and serum samples of consecutive patients with DM and ASS. Quantibody® Human Inflammation Array 3 for cytokines/chemokines was performed in the serum of all participants. Receiver operating characteristic analysis with the area under the curve and Youden's index were performed.ResultsEight newly diagnosed and treatment-naïve patients with DM, nine newly diagnosed and treatment-naïve patients with ASS, and 14 healthy controls were enrolled. Serum C-C motif chemokine ligand (CCL) 2, CCL4, C-X-C motif chemokine ligand (CXCL) 13, and tumor necrosis factor receptor 2 (TNFR2) were increased in patients with both DM and ASS. Serum interleukin (IL)-1 receptor type 1 (IL-1ra), IL-1b, CCL1, CXCL11, and CCL3 were modulated in patients with DM only, and IL-8, CXCL9, and tissue inhibitors of metalloproteinases-1 (TIMP-1) in patients with ASS only. Serum CCL2, CXCL13, and TNFR2 accurately distinguished patients with DM and ASS from healthy controls, as shown by the area under the curve >0.80. Moreover, receiver operating characteristic analysis showed that, as biomarkers for discrimination between DM and ASS, the combination of IL-1ra and TIMP-1, had an area under the curve of 0.944, a sensitivity of 87.5%, and a specificity of 88.9%.ConclusionOur study demonstrated that serum levels of cytokines/chemokines showed a different pattern in newly diagnosed patients with DM and ASS, in which serum IL-1ra and TIMP-1 could be used to distinguish between the two diseases.</p