Monochromatic cycles in 2-edge-colored bipartite graphs with large minimum degree

For graphs $G_0$, $G_1$ and $G_2$, write $G_0\longmapsto(G_1, G_2)$ if each red-blue-edge-coloring of $G_0$ yields a red $G_1$ or a blue $G_2$. The Ramsey number $r(G_1, G_2)$ is the minimum number $n$ such that the complete graph $K_n\longmapsto(G_1, G_2)$. In [Discrete Math. 312(2012)], Schelp formulated the following question: for which graphs $H$ there is a constant $0<c<1$ such that for any graph $G$ of order at least $r(H, H)$ with $\delta(G)>c|V(G)|$, $G\longmapsto(H, H)$. In this paper, we prove that for any $m>n$, if $G$ is a balanced bipartite graph of order $2(m+n-1)$ with $\delta(G)>\frac{3}{4}(m+n-1)$, then $G\longmapsto(CM_m, CM_n)$, where $CM_i$ is a matching with $i$ edges contained in a connected component. By Szem\'{e}redi's Regularity Lemma, using a similar idea as introduced by [J. Combin. Theory Ser. B 75(1999)], we show that for every $\eta>0$, there is an integer $N_0>0$ such that for any $N>N_0$ the following holds: Let $\alpha_1>\alpha_2>0$ such that $\alpha_1+\alpha_2=1$. Let $G[X, Y]$ be a balanced bipartite graph on $2(N-1)$ vertices with $\delta(G)\geq(\frac{3}{4}+3\eta)(N-1)$. Then for each red-blue-edge-coloring of $G$, either there exist red even cycles of each length in $\{4, 6, 8, \ldots, (2-3\eta^2)\alpha_1N\}$, or there exist blue even cycles of each length in $\{4, 6, 8, \ldots, (2-3\eta^2)\alpha_2N\}$. Furthermore, the bound $\delta(G)\geq(\frac{3}{4}+3\eta)(N-1)$ is asymptotically tight. Previous studies on Schelp's question on cycles are on diagonal case, we obtain an asymptotic result of Schelp's question for all non-diagonal cases

Shoshonitic enclaves in the high Sr/Y Nyemo pluton, southern Tibet: Implications for Oligocene magma mixing and the onset of extension of the southern Lhasa terrane

Post-collisional potassic and high Sr/Y magmatism in the Lhasa terrane provides critical constraints on the timing and mechanism of subduction of Indian lithosphere and its role in the uplift of the Tibetan Plateau. Here, we report whole-rock geochemistry, mineral geochemistry, zircon U Pb ages, and in situ zircon Hf isotope ratios for the Nyemo pluton, a representative example of such magmatism. The Nyemo pluton is composed of high Sr/Y host rocks and coeval shoshonitic mafic microgranular enclaves (MMEs). Whole-rock compositions of the host rocks and MMEs form linear trends in Harker diagrams, consistent with modification of both end-members by magma mixing. Although the main high Sr/Y phase of the pluton formed by partial melting of the lower crust of the thickened Lhasa terrane, the MMEs display abnormally enriched light rare earth elements, low whole-rock ε_(Nd)(t) and low zircon ε_(Hf)(t) that suggest derivation from low degree melting of hydrous and enriched mantle. Based on the occurrence of shoshonitic magma and high La/Yb and high Sr/Y with adakitic affinity host rocks around 30 Ma, the Nyemo pluton is best explained as a record of onset of extension that resulted from convective removal of the mantle lithosphere beneath Tibet in the Oligocene

Study on pharmacokinetics of Amygdalin after oral administration of semen persicae extraction in rat plasma by HPLC

Semen Persicae was a traditional Chinese medicine for the treatment of diseases such as inflammation and hyperlipemia. Amygdalin was one of the main active ingredients of this traditional Chinese medicine. In this paper, pharmacokinetic study was conducted to obtain pharmacokinetic parameters of amygadalin after oral administration of Semen Persicae extraction in rat plasma. HPLC-UV was used to determine the concentration of amygdalin in rat plasma at different time points after administration. The main pharmacokinetic parameters of amygdalin in rat were obtained based on the analysis of the plasma sample. The pharmacokinetics of amygdalin was fitted with a one-compartment model and it eliminated relative slowly in rats.Colegio de Farmacéuticos de la Provincia de Buenos Aire

Metabolic regulation of forkhead box P3 alternative splicing isoforms and their impact on health and disease

Forkhead Box P3 (FOXP3) is crucial for the development and suppressive function of human regulatory T cells (Tregs). There are two predominant FOXP3 splicing isoforms in healthy humans, the full-length isoform and the isoform lacking exon 2, with different functions and regulation mechanisms. FOXP3 splicing isoforms show distinct abilities in the cofactor interaction and the nuclear translocation, resulting in different effects on the differentiation, cytokine secretion, suppressive function, linage stability, and environmental adaptation of Tregs. The balance of FOXP3 splicing isoforms is related to autoimmune diseases, inflammatory diseases, and cancers. In response to environmental challenges, FOXP3 transcription and splicing can be finely regulated by T cell antigen receptor stimulation, glycolysis, fatty acid oxidation, and reactive oxygen species, with various signaling pathways involved. Strategies targeting energy metabolism and FOXP3 splicing isoforms in Tregs may provide potential new approaches for the treatment of autoimmune diseases, inflammatory diseases, and cancers. In this review, we summarize recent discoveries about the FOXP3 splicing isoforms and address the metabolic regulation and specific functions of FOXP3 splicing isoforms in Tregs

Pressure-induced non-monotonic crossover of steady relaxation dynamics in a metallic glass

Relaxation dynamics, as a key to understand glass formation and glassy properties, remains an elusive and challenging issue in condensed matter physics. In this work, in situ high-pressure synchrotron high-energy x-ray photon correlation spectroscopy has been developed to probe the atomic-scale relaxation dynamics of a cerium-based metallic glass during compression. Although the sample density continuously increases, the collective atomic motion initially slows down as generally expected and then counter-intuitively accelerates with further compression (density increase), showing an unusual non-monotonic pressure-induced steady relaxation dynamics crossover at ~3 GPa. Furthermore, by combining in situ high-pressure synchrotron x-ray diffraction, the relaxation dynamics anomaly is evidenced to closely correlate with the dramatic changes in local atomic structures during compression, rather than monotonically scaling with either sample density or overall stress level. These findings could provide new insight into relaxation dynamics and their relationship with local atomic structures of glasses.Comment: 21 pages, 4 figure