Long properly colored cycles in edge colored complete graphs

Let $K_{n}^{c}$ denote a complete graph on $n$ vertices whose edges are colored in an arbitrary way. Let $\Delta^{\mathrm{mon}} (K_{n}^{c})$ denote the maximum number of edges of the same color incident with a vertex of $K_{n}^{c}$. A properly colored cycle (path) in $K_{n}^{c}$ is a cycle (path) in which adjacent edges have distinct colors. B. Bollob\'{a}s and P. Erd\"{o}s (1976) proposed the following conjecture: if $\Delta^{\mathrm{mon}} (K_{n}^{c})<\lfloor \frac{n}{2} \rfloor$, then $K_{n}^{c}$ contains a properly colored Hamiltonian cycle. Li, Wang and Zhou proved that if $\Delta^{\mathrm{mon}} (K_{n}^{c})< \lfloor \frac{n}{2} \rfloor$, then $K_{n}^{c}$ contains a properly colored cycle of length at least $\lceil \frac{n+2}{3}\rceil+1$. In this paper, we improve the bound to $\lceil \frac{n}{2}\rceil + 2$.Comment: 8 page

List version of (pp,1)-total labellings

The ($p$,1)-total number $\lambda_p^T(G)$ of a graph $G$ is the width of the smallest range of integers that suffices to label the vertices and the edges of $G$ such that no two adjacent vertices have the same label, no two incident edges have the same label and the difference between the labels of a vertex and its incident edges is at least $p$. In this paper we consider the list version. Let $L(x)$ be a list of possible colors for all $x\in V(G)\cup E(G)$. Define $C_{p,1}^T(G)$ to be the smallest integer $k$ such that for every list assignment with $|L(x)|=k$ for all $x\in V(G)\cup E(G)$, $G$ has a ($p$,1)-total labelling $c$ such that $c(x)\in L(x)$ for all $x\in V(G)\cup E(G)$. We call $C_{p,1}^T(G)$ the ($p$,1)-total labelling choosability and $G$ is list $L$-($p$,1)-total labelable. In this paper, we present a conjecture on the upper bound of $C_{p,1}^T$. Furthermore, we study this parameter for paths and trees in Section 2. We also prove that $C_{p,1}^T(K_{1,n})\leq n+2p-1$ for star $K_{1,n}$ with $p\geq2, n\geq3$ in Section 3 and $C_{p,1}^T(G)\leq \Delta+2p-1$ for outerplanar graph with $\Delta\geq p+3$ in Section 4.Comment: 11 pages, 2 figure

Modification of wool fiber using steam explosion

Wool fiber was modified by steam explosion in this study. SEM results show that some scales on the fiber surface were cleaved and tiny grooves generated during the explosion. FTIR results suggest no evident changes in the chemical composition of the fiber after the explosion treatment. However, the crystallinity of the fiber decreased slightly as the steam pressure increased based on the X-ray results. In the thermal analysis, DSC results show that the temperature corresponding to vaporization of absorbed water and cleavage of disulfide bonds respectively decreased as the steam pressure increased. The reduction in thermal decomposition energy of the treated fiber indicates that steam explosion might have destroyed some crystals and crosslinks of macromolecular chains in the fiber. The treatment also led to some alterations of the fiber properties, including reduction in strength, moisture regain and solubility in caustic solution.<br /

Deformation and stress theory of surrounding rock of shallow circular tunnel based on complex variable function method

After reviewing many literature foundations, the thesis combines the basic methods of elastic mechanics with mathematical knowledge, sets the bipotential stress potential complex function and analyses the relationship between stress component, strain component and stress potential function, and applies the complex variable function. The expression of the relevant stress component is derived, and the displacement boundary conditions of the surrounding rock of shallow circular tunnel are obtained. Furthermore, the paper applies the basic theory of complex variable function to solve the boundary condition complex variable function for common tunnel sections, and obtains the analytical expression of the surrounding rock stress of shallow circular tunnel. The simulation is carried out by finite element method. The establishment of complex variable function has a good application value in solving the stress of surrounding rock of shallow tunnel

Visual Analytics Law Enforcement Toolkit

VALET, visual analytics law enforcement toolkit, is an interactive toolkit developed for law enforcement agencies to explore concerned crime information and make police resource allocation strategies. As a visual analytics toolkit, VALET is coupled with data collection, data analytics and data prediction. The objective of VALET is to assist law enforcement agencies to reduce crime rate by wisely allocating police resource based on the analytics of historical crime records. The program incorporates three steps to generate police patrol route and policeman allocation. The first step is to generate crime hotspots and crime contours of collected crime data. The next step is to analyze historical crime information and predict potential defects. Finally, the program is to compute police patrol routes and allocate police resource based on schedule and specialty. The results from the program allow us to generate risky area for different type of crimes, and evaluate policemen’s performance in dealing with different type of crimes. Thus, police department is able to assign police officers to designed patrol routes that suggested by prediction tool based on policemen’s specialty. This would take advantage of crime prediction and decrease the time of handling criminal activities. With VALET, law enforcement agencies are able to explore concerned crime information intelligently. At the same time, police department is prompted to allocate police resource wisely

Simultaneous profiling of transcriptome and DNA methylome from a single cell.

BackgroundSingle-cell transcriptome and single-cell methylome technologies have become powerful tools to study RNA and DNA methylation profiles of single cells at a genome-wide scale. A major challenge has been to understand the direct correlation of DNA methylation and gene expression within single-cells. Due to large cell-to-cell variability and the lack of direct measurements of transcriptome and methylome of the same cell, the association is still unclear.ResultsHere, we describe a novel method (scMT-seq) that simultaneously profiles both DNA methylome and transcriptome from the same cell. In sensory neurons, we consistently identify transcriptome and methylome heterogeneity among single cells but the majority of the expression variance is not explained by proximal promoter methylation, with the exception of genes that do not contain CpG islands. By contrast, gene body methylation is positively associated with gene expression for only those genes that contain a CpG island promoter. Furthermore, using single nucleotide polymorphism patterns from our hybrid mouse model, we also find positive correlation of allelic gene body methylation with allelic expression.ConclusionsOur method can be used to detect transcriptome, methylome, and single nucleotide polymorphism information within single cells to dissect the mechanisms of epigenetic gene regulation

Baicalin Weakens Staphylococcus aureus Pathogenicity by Targeting Sortase B

Staphylococcus aureus (S. aureus) is a human and other animal pathogen that contributes to the primary etiology of nosocomial pneumonia, a disease with high mortality rates and costs. Treatment of multidrug-resistant S. aureus infection is extremely challenging, and new therapeutic strategies beyond antibiotic treatment are needed. Anti-virulence agents that specifically target the molecular determinants of virulence may be a novel method for treating drug-resistant nosocomial infections. Sortase B (SrtB) is a crucial virulence factor in S. aureus and plays an important role during infection. In this study, we find that baicalin suppresses the activity of SrtB. Minimum inhibitory concentration and growth curve assays confirmed that baicalin has no anti-S. aureus properties. We performed live/dead, lactate dehydrogenase (LDH), adherence, and enzyme-linked immunosorbent assays to confirm that baicalin reduced human alveolar epithelial A549 cell injury caused by S. aureus, reduced the adherence of S. aureus to A549 cells, and significantly attenuated the inflammatory response of mouse macrophage J774 cells to S. aureus. Additionally, we were able to elucidate the binding mechanics and identify the interacting sites of baicalin and SrtB via a molecular dynamics simulation, site-directed mutagenesis, and fluorescence spectroscopy quenching. Finally, we confirmed that baicalin directly binds to the active center of SrtB, and the residues Asn92 and Tyr128 perform an important function in the interaction of SrtB and baicalin. Taken together, these data indicate that baicalin is a promising candidate to combat S. aureus infections