Extremal problems and results related to Gallai-colorings

A Gallai-coloring (Gallai-$k$-coloring) is an edge-coloring (with colors from $\{1, 2, \ldots, k\}$) of a complete graph without rainbow triangles. Given a graph $H$ and a positive integer $k$, the $k$-colored Gallai-Ramsey number $GR_k(H)$ is the minimum integer $n$ such that every Gallai-$k$-coloring of the complete graph $K_n$ contains a monochromatic copy of $H$. In this paper, we prove that for any positive integers $d$ and $k$, there exists a constant $c$ such that if $H$ is an $n$-vertex graph with maximum degree $d$, then $GR_k(H)$ is at most $cn$. We also determine $GR_k(K_4+e)$ for the graph on 5 vertices consisting of a $K_4$ with a pendant edge. Furthermore, we consider two extremal problems related to Gallai-$k$-colorings. For $n\geq GR_k(K_3)$, we determine upper and lower bounds for the minimum number of monochromatic triangles in a Gallai-$k$-coloring of $K_{n}$, implying that this number is $O(n^3)$ and yielding the exact value for $k=3$. We also determine upper and lower bounds for the maximum number of edges that are not contained in any rainbow triangle or monochromatic triangle in a $k$-edge-coloring of $K_n$.Comment: 20 pages, 1 figur

Movement in High School: Proportion of Chinese Adolescents Meeting 24-Hour Movement Guidelines

The purposes of this study were (a) to examine the proportions of adolescents in China who partially or fully meet three 24-h movement guidelines on physical activity, screen-time, and sleep duration and (b) to examine whether there were gender differences in the proportion of boys and girls meeting these guidelines. The sample was made up of high school adolescents from an eastern province of China (N = 1338). The participants completed a self-reported survey on demographic variables and weekly health behaviors including physical activity, screen-time, and sleep duration. A frequency analysis was conducted to summarize the number of 24-h movement guidelines met of the total sample and by gender; chi-squared tests were used to examine the gender differences in the proportion of students meeting different guidelines, independently and jointly. A high proportion of adolescents did not meet physical activity (97.2%, 95% CI = 96.2–98.0%), or sleep (92.1%, 95% CI = 90.6–93.5%) guidelines, but met screen-time (93.6%, 95% CI = 92.4–94.7%) guidelines. Overall, only 0.3% (95%CI = 0.1–0.6%) of the sample met all three guidelines, 8.8% (95%CI = 7.5–10.2%) met two, 85.8%% (95%CI = 84.0–87.4%) met one, and 5.1% (95%CI = 4.0–6.4%) met none. There was no statistically significant percentage difference between female and male participants in meeting physical activity, screen-time viewing, or sleep duration guidelines, independently or jointly (p values \u3e 0.05). These figures of participants meeting all three guidelines or physical activity and sleep independently are much lower than many estimates in prior research internationally. Considerations to improve adherence to physical activity and sleep guidelines are critical in this population

Acute toxicity study of tilmicosin-loaded hydrogenated castor oil-solid lipid nanoparticles

<p>Abstract</p> <p>Background</p> <p>Our previous studies demonstrated that tilmicosin-loaded hydrogenated castor oil solid lipid nanoparticles (Til-HCO-SLN) are a promising formulation for enhanced pharmacological activity and therapeutic efficacy in veterinary use. The purpose of this work was to evaluate the acute toxicity of Til-HCO-SLN.</p> <p>Methods</p> <p>Two nanoparticle doses were used for the study in ICR mice. The low dose (766 mg/kg.bw) with tilmicosin 7.5 times of the clinic dosage and below the median lethal dose (LD₅₀) was subcutaneously administered twice on the first and 7th day. The single high dose (5 g/kg.bw) was the practical upper limit in an acute toxicity study and was administered subcutaneously on the first day. Blank HCO-SLN, native tilmicosin, and saline solution were included as controls. After medication, animals were monitored over 14 days, and then necropsied. Signs of toxicity were evaluated via mortality, symptoms of treatment effect, gross and microscopic pathology, and hematologic and biochemical parameters.</p> <p>Results</p> <p>After administration of native tilmicosin, all mice died within 2 h in the high dose group, in the low dose group 3 died after the first and 2 died after the second injections. The surviving mice in the tilmicosin low dose group showed hypoactivity, accelerated breath, gloomy spirit and lethargy. In contrast, all mice in Til-HCO-SLN and blank HCO-SLN groups survived at both low and high doses. The high nanoparticle dose induced transient clinical symptoms of treatment effect such as transient reversible action retardation, anorexy and gloomy spirit, increased spleen and liver coefficients and decreased heart coefficients, microscopic pathological changes of liver, spleen and heart, and minor changes in hematologic and biochemical parameters, but no adverse effects were observed in the nanoparticle low dose group.</p> <p>Conclusions</p> <p>The results revealed that the LD₅₀of Til-HCO-SLN and blank HCO-SLN exceeded 5 g/kg.bw and thus the nanoparticles are considered low toxic according to the toxicity categories of chemicals. Moreover, HCO-SLN significantly decreased the toxicity of tilmicosin. Normal clinic dosage of Til-HCO-SLN is safe as evaluated by acute toxicity.</p

Activin A and BMP4 Signaling Expands Potency of Mouse Embryonic Stem Cells in Serum-Free Media.

Inhibitors of Mek1/2 and Gsk3β, known as 2i, and, together with leukemia inhibitory factor, enhance the derivation of embryonic stem cells (ESCs) and promote ground-state pluripotency (2i/L-ESCs). However, recent reports show that prolonged Mek1/2 suppression impairs developmental potential of ESCs, and is rescued by serum (S/L-ESCs). Here, we show that culturing ESCs in Activin A and BMP4, and in the absence of MEK1/2 inhibitor (ABC/L medium), establishes advanced stem cells derived from ESCs (esASCs). We demonstrate that esASCs contributed to germline lineages, full-term chimeras and generated esASC-derived mice by tetraploid complementation. We show that, in contrast to 2i/L-ESCs, esASCs display distinct molecular signatures and a stable hypermethylated epigenome, which is reversible and similar to serum-cultured ESCs. Importantly, we also derived novel ASCs (blASCs) from blastocysts in ABC/L medium. Our results provide insights into the derivation of novel ESCs with DNA hypermethylation from blastocysts in chemically defined medium

DNMTs Play an Important Role in Maintaining the Pluripotency of Leukemia Inhibitory Factor-Dependent Embryonic Stem Cells.

Naive pluripotency can be maintained in medium with two inhibitors plus leukemia inhibitory factor (2i/LIF) supplementation, which primarily affects canonical WNT, FGF/ERK, and JAK/STAT3 signaling. However, whether one of these three supplements alone is sufficient to maintain naive self-renewal remains unclear. Here we show that LIF alone in medium is sufficient for adaptation of 2i/L-ESCs to embryonic stem cells (ESCs) in a hypermethylated state (L-ESCs). Global transcriptomic analysis shows that L-ESCs are close to 2i/L-ESCs and in a stable state between naive and primed pluripotency. Notably, our results demonstrate that DNA methyltransferases (DNMTs) play an important role in LIF-dependent mouse ESC adaptation and self-renewal. LIF-dependent ESC adaptation efficiency is significantly increased in serum treatment and reduced in Dnmt3a or Dnmt3l knockout ESCs. Importantly, unlike epiblast stem cells, L-ESCs contribute to somatic tissues and germ cells in chimeras. L-ESCs cultured under such simple conditions as in this study would provide a more conducive platform to clarify the molecular mechanism of ESCs in in vitro culture

Derivation of hypermethylated pluripotent embryonic stem cells with high potency.

Naive hypomethylated embryonic pluripotent stem cells (ESCs) are developmentally closest to the preimplantation epiblast of blastocysts, with the potential to contribute to all embryonic tissues and the germline, excepting the extra-embryonic tissues in chimeric embryos. By contrast, epiblast stem cells (EpiSCs) resembling postimplantation epiblast are relatively more methylated and show a limited potential for chimerism. Here, for the first time, we reveal advanced pluripotent stem cells (ASCs), which are developmentally beyond the pluripotent cells in the inner cell mass but with higher potency than EpiSCs. Accordingly, a single ASC contributes very efficiently to the fetus, germline, yolk sac and the placental labyrinth in chimeras. Since they are developmentally more advanced, ASCs do not contribute to the trophoblast. ASCs were derived from blastocysts in two steps in a chemically defined medium supplemented with Activin A and basic fibroblast growth factor, followed by culturing in ABCL medium containing ActA, BMP4, CHIR99021 and leukemia inhibitory factor. Notably, ASCs exhibit a distinct transcriptome with the expression of both naive pluripotency genes, as well as mesodermal somatic genes; Eomes, Eras, Tdgf1, Evx1, hand1, Wnt5a and distinct repetitive elements. Conversion of established ESCs to ASCs is also achievable. Importantly, ASCs exhibit a stable hypermethylated epigenome and mostly intact imprints as compared to the hypomethylated inner cell mass of blastocysts and naive ESCs. Properties of ASCs suggest that they represent cells at an intermediate cellular state between the naive and primed states of pluripotency.This work was supported by grants from the Ministry of Science and Technology project of Inner Mongolia (N0. 20130216), the National Natural Science Foundation of China (No.31560335) and by Wellcome Trust Investigator Award to MAS, and by a core grant from the Wellcome Trust and CRUK to the Gurdon Institute