Star-critical Ramsey numbers and regular Ramsey numbers for stars

Let $G$ be a graph, $H$ be a subgraph of $G$, and let $G- H$ be the graph obtained from $G$ by removing a copy of $H$. Let $K_{1, n}$ be the star on $n+ 1$ vertices. Let $t\geq 2$ be an integer and $H_{1}, \dots, H_{t}$ and $H$ be graphs, and let $H\rightarrow (H_{1}, \dots, H_{t})$ denote that every $t$ coloring of $E(H)$ yields a monochromatic copy of $H_{i}$ in color $i$ for some $i\in [t]$. Ramsey number $r(H_{1}, \dots, H_{t})$ is the minimum integer $N$ such that $K_{N}\rightarrow (H_{1}, \dots, H_{t})$. Star-critical Ramsey number $r_{*}(H_{1}, \dots, H_{t})$ is the minimum integer $k$ such that $K_{N}- K_{1, N- 1- k}\rightarrow (H_{1}, \dots, H_{t})$ where $N= r(H_{1}, \dots, H_{t})$. Let $rr(H_{1}, \dots, H_{t})$ be the regular Ramsey number for $H_{1}, \dots, H_{t}$, which is the minimum integer $r$ such that if $G$ is an $r$-regular graph on $r(H_{1}, \dots, H_{t})$ vertices, then $G\rightarrow (H_{1}, \dots, H_{t})$. Let $m_{1}, \dots, m_{t}$ be integers larger than one, exactly $k$ of which are even. In this paper, we prove that if $k\geq 2$ is even, then $r_{*}(K_{1, m_{1}}, \dots, K_{1, m_{t}})= \sum_{i= 1}^{t} m_{i}- t+ 1- \frac{k}{2}$ which disproves a conjecture of Budden and DeJonge in 2022. Furthermore, we prove that if $k\geq 2$ is even, then $rr(K_{1, m_{1}}, \dots, K_{1, m_{t}})= \sum_{i= 1}^{t} m_{i}- t$. Otherwise, $rr(K_{1, m_{1}}, \dots, K_{1, m_{t}})= \sum_{i= 1}^{t} m_{i}- t+ 1$

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

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

Rosiglitazone Restores Endothelial Dysfunction in a Rat Model of Metabolic Syndrome through PPARγ- and PPARδ-Dependent Phosphorylation of Akt and eNOS

Vascular endothelial dysfunction has been demonstrated in metabolic syndrome (MS). Chronic administration of rosiglitazone ameliorates endothelial dysfunction through PPARγ-mediated metabolic improvements. Recently, studies suggested that single dose of rosiglitazone also has direct vascular effects, but the mechanisms remain uncertain. Here we established a diet-induced rat model of MS. The impaired vasorelaxation in MS rats was improved by incubating arteries with rosiglitazone for one hour. Importantly, this effect was blocked by either inhibition of PPARγ or PPARδ. In cultured endothelial cells, acute treatment with rosiglitazone increased the phosphorylation of Akt and eNOS and the production of NO. These effects were also abolished by inhibition of PPARγ, PPARδ, or PI3K. In conclusion, rosiglitazone improved endothelial function through both PPARγ- and PPARδ-mediated phosphorylation of Akt and eNOS, which might help to reconsider the complex effects and clinical applications of rosiglitazone

Pressure-Induced Confined Metal from the Mott Insulator Sr\u3csub\u3e3\u3c/sub\u3eIr\u3csub\u3e2\u3c/sub\u3eO\u3csub\u3e7\u3c/sub\u3e

The spin-orbit Mott insulator Sr3Ir2O7 provides a fascinating playground to explore insulator-metal transition driven by intertwined charge, spin, and lattice degrees of freedom. Here, we report high-pressure electric resistance and resonant inelastic x-ray scattering measurements on single-crystal Sr3Ir2O7 up to 63–65 GPa at 300 K. The material becomes a confined metal at 59.5 GPa, showing metallicity in the ab plane but an insulating behavior along the c axis. Such an unusual phenomenon resembles the strange metal phase in cuprate superconductors. Since there is no sign of the collapse of spin-orbit or Coulomb interactions in x-ray measurements, this novel insulator-metal transition is potentially driven by a first-order structural change at nearby pressures. Our discovery points to a new approach for synthesizing functional materials

Activation of TRPV1 by Dietary Capsaicin Improves Endothelium-Dependent Vasorelaxation and Prevents Hypertension

Some plant-based diets lower the cardiometabolic risks and prevalence of hypertension. New evidence implies a role for the transient receptor potential vanilloid 1 (TRPV1) cation channel in the pathogenesis of cardiometabolic diseases. Little is known about impact of chronic TRPV1 activation on the regulation of vascular function and blood pressure. Here we report that chronic TRPV1 activation by dietary capsaicin increases the phosphorylation of protein kinase A (PKA) and eNOS and thus production of nitric oxide (NO) in endothelial cells, which is calcium dependent. TRPV1 activation by capsaicin enhances endothelium-dependent relaxation in wild-type mice, an effect absent in TRPV1-deficient mice. Long-term stimulation of TRPV1 can activate PKA, which contributes to increased eNOS phosphorylation, improves vasorelaxation, and lowers blood pressure in genetically hypertensive rats. We conclude that TRPV1 activation by dietary capsaicin improves endothelial function. TRPV1-mediated increase in NO production may represent a promising target for therapeutic intervention of hypertension

Genomic monitoring of SARS-CoV-2 uncovers an Nsp1 deletion variant that modulates type I interferon response

The SARS-CoV-2 virus, the causative agent of COVID-19, is undergoing constant mutation. Here, we utilized an integrative approach combining epidemiology, virus genome sequencing, clinical phenotyping, and experimental validation to locate mutations of clinical importance. We identified 35 recurrent variants, some of which are associated with clinical phenotypes related to severity. One variant, containing a deletion in the Nsp1-coding region (D500-532), was found in more than 20% of our sequenced samples and associates with higher RT-PCR cycle thresholds and lower serum IFN-beta levels of infected patients. Deletion variants in this locus were found in 37 countries worldwide, and viruses isolated from clinical samples or engineered by reverse genetics with related deletions in Nsp1 also induce lower IFN-beta responses in infected Calu-3 cells. Taken together, our virologic surveillance characterizes recurrent genetic diversity and identified mutations in Nsp1 of biological and clinical importance, which collectively may aid molecular diagnostics and drug design.Peer reviewe

Interplay of Ecological Opportunities and Functional Traits Drives the Evolution and Diversification of Millettiod Legumes (Fabaceae)

Understanding the striking diversity of the angiosperms is a paramount issue in biology and of interest to biologists. The Millettiod legumes is one of the most hyper-diverse groups of the legume family, containing many economically important medicine, furniture and craft species. In the present study, we explore how the interplay of past climate change, ecological opportunities and functional traits&rsquo; evolution may have triggered diversification of the Millettiod legumes. Using a comprehensive species-level phylogeny from three plastid markers, we estimate divergence times, infer habit shifts, test the phylogenetic and temporal diversification heterogeneity, and reconstruct ancestral biogeographical ranges. We found that three dramatic accumulations of the Millettiod legumes occurred during the Miocene. The rapid diversification of the Millettiod legumes in the Miocene was driven by ecological opportunities created by the emergence of new niches and range expansion. Additionally, habit shifts and the switch between biomes might have facilitated the rapid diversification of the Millettiod legumes. The Millettiod legumes provide an excellent case for supporting the idea that the interplay of functional traits, biomes, and climatic and geographic factors drives evolutionary success