Independent paths and K5-subdivisions

A well known theorem of Kuratowski states that a graph is planar iff it contains no subdivision of K5 or K3,3. Seymour conjectured in 1977 that every 5-connected nonplanar graph contains a subdivision of K5. In this paper, we prove several results about independent paths (no vertex of a path is internal to another), which are then used to prove Seymour’s conjecture for two classes of graphs. These results will be used in a subsequent paper to prove Seymour’s conjecture for graphs containing K − 4, which is a step in a program to approach Seymour’s conjecture

QCD radiative correction to color-octet J/ψJ/\psi inclusive production at B Factories

In nonrelativistic Quantum Chromodynamics (NRQCD), we study the next-to-leading order (NLO) QCD radiative correction to the color-octet $J/\psi$ inclusive production at B Factories. Compared with the leading-order (LO) result, the NLO QCD corrections are found to enhance the short-distance coefficients in the color-octet $J/\psi$ production $e^+ e^-\to c \bar c (^3P_0^{(8)} {\rm or} ^3P_0^{(8)})g$ by a factor of about 1.9. Moreover, the peak at the endpoint in the $J/\psi$ energy distribution predicted at LO can be smeared by the NLO corrections, but the major color-octet contribution still comes from the large energy region of $J/\psi$. By fitting the latest data of $\sigma(e^{+}e^{-}\to J/\psi+X_{\mathrm{non-c\bar{c}}})$ observed by Belle, we find that the values of color-octet matrix elements are much smaller than expected earlier by using the naive velocity scaling rules or extracted from fitting experimental data with LO calculations. As the most stringent constraint by setting the color-singlet contribution to be zero in $e^{+}e^{-}\to J/\psi+X_{\mathrm{non-c\bar{c}}}$, we get an upper limit of the color-octet matrix element, $+ 4.0 <0| {\cal O}^{J/\psi} [{}^3P_0^{(8)}]|0>/m_c^2 <(2.0 \pm 0.6)\times 10^{-2} {\rm GeV}^3$ at NLO in $\alpha_s$.Comment: 18 pages, 8 figure

Position Analysis of a Hybrid Serial-Parallel Manipulator in Immersion Lithography

This paper proposes a novel hybrid serial-parallel mechanism with 6 degrees of freedom. The new mechanism combines two different parallel modules in a serial form. 3-P̲(PH) parallel module is architecture of 3 degrees of freedom based on higher joints and specializes in describing two planes’ relative pose. 3-P̲SP parallel module is typical architecture which has been widely investigated in recent researches. In this paper, the direct-inverse position problems of the 3-P̲SP parallel module in the couple mixed-type mode are analyzed in detail, and the solutions are obtained in an analytical form. Furthermore, the solutions for the direct and inverse position problems of the novel hybrid serial-parallel mechanism are also derived and obtained in the analytical form. The proposed hybrid serial-parallel mechanism is applied to regulate the immersion hood’s pose in an immersion lithography system. Through measuring and regulating the pose of the immersion hood with respect to the wafer surface simultaneously, the immersion hood can track the wafer surface’s pose in real-time and the gap status is stabilized. This is another exploration to hybrid serial-parallel mechanism’s application

Long non-coding RNA SNHG1 promotes bladder cancer progression by upregulating EZH2 and repressing KLF2 transcription

Objective: Long Non-Coding RNAs (LncRNAs) act as an indispensable role in cancer development. The study aimed to investigate the role and mechanism of lncRNA Small Nucleolar RNA Host Gene&nbsp;1 (SNHG1) in Bladder Cancer (BC) progression. Method: The expression, prognostic value, diagnostic value, and correlation of SNHG1, Enhancer of Zeste&nbsp;2 polycomb repressive complex&nbsp;2 subunit (EZH2), and Kruppel Like Factor&nbsp;2 (KLF2) were analyzed through bioinformatics analysis. The expression was also validated in BC tissues and cell lines. Besides, their regulation and binding were tested via qPCR, Western blot, Dual-Luciferase Reporter Assay (DLRA), Argonaute RISC catalytic component 2-RNA Immunoprecipitation (AGO2-RIP), and Chromatin Immunoprecipitation (ChIP). A xenograft model in nude mice was also established. Results: SNHG1 was significantly overexpressed in BC tissues and cells. Importantly, SNHG1 was associated with poor survival, and ROC curves revealed high diagnostic values. Moreover, by CCK8, wound healing, transwell, and Western blot analysis, SNHG1 knockdown significantly inhibited the proliferation, migration, invasion, and epithelial-mesenchymal transition of BC cells. Additionally, in vivo experiments showed that silencing SNHG1 hindered tumorigenesis and tumor growth. Regarding mechanism, the results of AGO2-RIP, ChIP or DLRA showed that SNHG1 played different roles at diverse subcellular sites. In the cytoplasm, SNHG1 acted as a competing endogenous RNA for miR-137-3p to promote EZH2 expression. In the nucleus, SNHG1 could interact with EZH2 to inhibit KLF2 transcription. Conclusion: Our study elucidated that SNHG1 formed a regulatory network and played an oncogenic role in BC, which provided a novel therapeutic target for BC treatment

Circumference of 3-connected claw-free graphs and large Eulerian subgraphs of 3-edge-connected graphs

AbstractThe circumference of a graph is the length of its longest cycles. Results of Jackson, and Jackson and Wormald, imply that the circumference of a 3-connected cubic n-vertex graph is Ω(n0.694), and the circumference of a 3-connected claw-free graph is Ω(n0.121). We generalize and improve the first result by showing that every 3-edge-connected graph with m edges has an Eulerian subgraph with Ω(m0.753) edges. We use this result together with the Ryjáček closure operation to improve the lower bound on the circumference of a 3-connected claw-free graph to Ω(n0.753). Our proofs imply polynomial time algorithms for finding large Eulerian subgraphs of 3-edge-connected graphs and long cycles in 3-connected claw-free graphs