The (k,ℓ)(k,\ell)-rainbow index of random graphs

A tree in an edge colored graph is said to be a rainbow tree if no two edges on the tree share the same color. Given two positive integers $k$, $\ell$ with $k\geq 3$, the \emph{$(k,\ell)$-rainbow index} $rx_{k,\ell}(G)$ of $G$ is the minimum number of colors needed in an edge-coloring of $G$ such that for any set $S$ of $k$ vertices of $G$, there exist $\ell$ internally disjoint rainbow trees connecting $S$. This concept was introduced by Chartrand et. al., and there have been very few related results about it. In this paper, We establish a sharp threshold function for $rx_{k,\ell}(G_{n,p})\leq k$ and $rx_{k,\ell}(G_{n,M})\leq k,$ respectively, where $G_{n,p}$ and $G_{n,M}$ are the usually defined random graphs.Comment: 7 pages. arXiv admin note: substantial text overlap with arXiv:1212.6845, arXiv:1310.278

Design and synthesis of non-peptidic thiosemicarbazone derivatives as inhibitors of cathepsins L and K.

Cathepsin L, a member of the lysosome cysteine proteases, is ubiquitously expressed in tissue and is responsible for protein turnover. An overexpression of cathepsin L by certain tumor types is associated with enhanced tumor expansion through degradation of the extracellular matrix and the invasion and migration of cancer cells. Therefore, the inhibition of cathepsin L has emerged as a therapeutic strategy against metastatic cancer. Cathepsin K is involved in osteoclastic bone resorption because it is selectively expressed in osteoclasts and is capable of degrading bone matrix. In this project, a small library of thiosemicarbazone derivatives containing thiochromanone, 2,3-dihydroquinoline-4-one, and dibenzoylbenzene scaffolds has been successfully designed and synthesized as potential inhibitors of cathepsin L and other homologous cathepsins (B and K). Through a collaborative study, ten compounds from this library were found to be potent inhibitors (IC50 < 300 nM) of cathepsin L, and nine compounds were potent inhibitors of cathepsin K. None of these inhibitors showed activity against cathepsin B. For example, 6,7-difluorothiochromanone thiosemicarbazone 4 (IC50 = 46 nM) was the most potent inhibitor against cathepsin L from this group, while the 6-trifluoromethyl derivative 28 (IC50 = 21 nM) was the most potent inhibitor against cathepsin K. Structure activity relationship (SAR) studies centered on the thiochromanone thiosemicarbazone scaffold demonstrated that electron-withdrawing functionalities, incorporated primarily at the 6-position of the thiochromanone scaffold, showed good inhibition against cathepsin L in comparison to related analogues bearing electron-donating groups. Collectively, these results expand the known SAR regarding molecular structures and their inhibitory activity against cathepsins L and K.Ph.D

New skew Laplacian energy of simple digraphs

For a simple digraph $G$ of order $n$ with vertex set${v_1,v_2,ldots, v_n}$, let $d_i^+$ and $d_i^-$ denote theout-degree and in-degree of a vertex $v_i$ in $G$, respectively. Let$D^+(G)=diag(d_1^+,d_2^+,ldots,d_n^+)$ and$D^-(G)=diag(d_1^-,d_2^-,ldots,d_n^-)$. In this paper we introduce$widetilde{SL}(G)=widetilde{D}(G)-S(G)$ to be a new kind of skewLaplacian matrix of $G$, where $widetilde{D}(G)=D^+(G)-D^-(G)$ and$S(G)$ is the skew-adjacency matrix of $G$, and from which we definethe skew Laplacian energy $SLE(G)$ of $G$ as the sum of the norms ofall the eigenvalues of $widetilde{SL}(G)$. Some lower and upperbounds of the new skew Laplacian energy are derived and the digraphsattaining these bounds are also determined

Preparation of the Carbonized Zif&minus;8@PAN Nanofiber Membrane for Cadmium Ion Adsorption

The zeolitic imidazolate framework (ZIF&minus;8)@polyacrylonitrile (PAN) nanofiber membrane was prepared and carbonized for heavy metal cadmium ion (Cd2+) adsorption in aqueous medium. Zinc oxide (ZnO) was first sputtered onto the surface of the PAN electrospun nanofiber membrane to provide a metal ion source. Then, the ZIF&minus;8@PAN nanofiber membrane was prepared via in situ solvothermal reaction and carbonized in a tube furnace at 900 &deg;C under a N2 atmosphere to enhance adsorption performance. The synthesized ZIF&minus;8 particles with polyhedral structure were uniformly immobilized on the surface of the PAN electrospun nanofiber membrane. After being heated at 900 &deg;C, the polygonal ZIF&minus;8 shrank, and the carbonized ZIF&minus;8@PAN nanofiber membrane was obtained. Compared with the nanofiber membrane without being carbonized, the adsorption capacity of the carbonized ZIF&minus;8@PAN nanofiber membrane reached 102 mg L&minus;1, and its Cd2+ adsorption efficiency could be more than 90% under the adsorption temperature of 35 &deg;C and solution of pH = 7.5 conditions. According to the adsorption thermodynamics analysis, the Cd2+ adsorption process of the carbonized ZIF&minus;8@PAN nanofiber membrane was spontaneous. The whole Cd2+ adsorption process was more suitably described by the pseudo second-order adsorption kinetics model, indicating that there exists a chemical adsorption mechanism besides physical adsorption

Oral Administration of a Seed-based Bivalent Rotavirus Vaccine Containing VP6 and NSP4 Induces Specific Immune Responses in Mice

Rotavirus is the leading cause of severe diarrheal disease among newborns. Plant-based rotavirus vaccines have been developed in recent years and have been proven to be effective in animal models. In the present study, we report a bivalent vaccine candidate expressing rotavirus subunits VP6 and NSP4 fused with the adjuvant subunit B of E. coli heat-labile enterotoxin (LTB) in maize seeds. The RT-PCR and Western blot results showed that VP6 and LTB-NSP4 antigens were expressed and accumulated in maize seeds. The expression levels were as high as 0.35 and 0.20% of the total soluble protein for VP6 and LTB-NSP4, respectively. Oral administration of transgenic maize seeds successfully stimulated systemic and mucosal responses, with high titers of serum IgG and mucosal IgA antibodies, even after long-term storage. This study is the first to use maize seeds as efficient generators for the development of a bivalent vaccine against rotavirus