Laplacian eigenvalue distribution, diameter and domination number of trees

For a graph $G$ with domination number $\gamma$, Hedetniemi, Jacobs and Trevisan [European Journal of Combinatorics 53 (2016) 66-71] proved that $m_{G}[0,1)\leq \gamma$, where $m_{G}[0,1)$ means the number of Laplacian eigenvalues of $G$ in the interval $[0,1)$. Let $T$ be a tree with diameter $d$. In this paper, we show that $m_{T}[0,1)\geq (d+1)/3$. However, such a lower bound is false for general graphs. All trees achieving the lower bound are completely characterized. Moreover, for a tree $T$, we establish a relation between the Laplacian eigenvalues, the diameter and the domination number by showing that the domination number of $T$ is equal to $(d+1)/3$ if and only if it has exactly $(d+1)/3$ Laplacian eigenvalues less than one. As an application, it also provides a new type of trees, which show the sharpness of an inequality due to Hedetniemi, Jacobs and Trevisan

Expression of the chemokine receptor CXCR4 in human hepatocellular carcinoma and its role in portal vein tumor thrombus

<p>Abstract</p> <p>Background</p> <p>This study was conducted to investigate the expression of CXCR4 in portal vein tumor thrombus (PVTT) tissue and its possible role in the invasiveness of tumor thrombus cells.</p> <p>Methods</p> <p>We detected differential expression of CXCR4 between PVTT and hepatocellular carcinoma (HCC) by an immunohistochemical assay. Lentivirus-mediated RNA interference and a migration assay were performed on human primary cells derived from PVTT to study the impact of CXCR4 on the invasiveness of HCC.</p> <p>Results</p> <p>The expression of CXCR4 in tumor thrombus tissue was higher than that in HCC tissue. The invasion ratio of PVTT cells was significantly decreased (P < 0.05) after being infected with a CXCR4-targeting siRNA lentivirus, indicating that downregulation of CXCR4 by lentivirus-mediated RNA interference significantly impaired the invasive potential of PVTT.</p> <p>Conclusions</p> <p>These results indicate that CXCR4 is an effective curative target for hepatocellular carcinomas with PVTT.</p

China collection 2.1: Aerosol Optical Depth dataset for mainland China at 1km resolution

A wide range of data products have been published since the operation of the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor on NASA's TERRA and AQUA satellites. Based on DarkTarget and DeepBlue method, NASA has published Aerosol Optical Depth (AOD) products Collection 6.0 with spatial resolution of 3km. Although validated globally, regional and systematic errors are still found in the MODIS-retrieved AOD products. This is especially remarkable for bright heterogeneous land surface, such as mainland China. In order to solve the aerosol retrieval problem over heterogeneous bright land surface, the Synergetic Retrieval of Aerosol Properties algorithm (SRAP) has been developed based on the synergetic use of the MODIS data of TERRA and AQUA satellites. Using the SRAP algorithm, we produced AOD dataset-China Collection 2.1 at 1km spatial resolution, dated from August 2002 to 2012. We compared the China Collection 2.1 AOD datasets for 2010 with AERONET data. From those 2460 collocations, representing mutually cloud-free conditions, we find that 62% of China Collection 2.1 AOD values comparing with AERONET-observed values within an expected error envelop of 20% and 55% within an expected error envelop of 15%. Compared with MODIS Level 2 aerosol products, China Collection 2.1 AOD datasets have a more complete coverage with fewer data gaps over the study region