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

Changes in N-Transforming Archaea and Bacteria in Soil during the Establishment of Bioenergy Crops

Widespread adaptation of biomass production for bioenergy may influence important biogeochemical functions in the landscape, which are mainly carried out by soil microbes. Here we explore the impact of four potential bioenergy feedstock crops (maize, switchgrass, Miscanthus X giganteus, and mixed tallgrass prairie) on nitrogen cycling microorganisms in the soil by monitoring the changes in the quantity (real-time PCR) and diversity (barcoded pyrosequencing) of key functional genes (nifH, bacterial/archaeal amoA and nosZ) and 16S rRNA genes over two years after bioenergy crop establishment. The quantities of these N-cycling genes were relatively stable in all four crops, except maize (the only fertilized crop), in which the population size of AOB doubled in less than 3 months. The nitrification rate was significantly correlated with the quantity of ammonia-oxidizing archaea (AOA) not bacteria (AOB), indicating that archaea were the major ammonia oxidizers. Deep sequencing revealed high diversity of nifH, archaeal amoA, bacterial amoA, nosZ and 16S rRNA genes, with 229, 309, 330, 331 and 8989 OTUs observed, respectively. Rarefaction analysis revealed the diversity of archaeal amoA in maize markedly decreased in the second year. Ordination analysis of T-RFLP and pyrosequencing results showed that the N-transforming microbial community structures in the soil under these crops gradually differentiated. Thus far, our two-year study has shown that specific N-transforming microbial communities develop in the soil in response to planting different bioenergy crops, and each functional group responded in a different way. Our results also suggest that cultivation of maize with N-fertilization increases the abundance of AOB and denitrifiers, reduces the diversity of AOA, and results in significant changes in the structure of denitrification community

Fault-Diagnosis Method for Rotating Machinery Based on SVMD Entropy and Machine Learning

Rolling bearings and gears are important components of rotating machinery. Their operating condition affects the operation of the equipment. Fault in the accessory directly leads to equipment downtime or a series of adverse reactions in the system, which brings enormous pecuniary loss to the institution. Hence, it is of great significance to detect the operating status of rolling bearings and gears for fault diagnosis. At present, the vibration method is considered to be the most common method for fault diagnosis, a method that analyzes the equipment by collecting vibration signals. However, rotating-machinery fault diagnosis is challenging due to the need to select effective fault feature vectors, use appropriate machine-learning classification methods, and achieve accurate fault diagnosis. To solve this problem, this paper illustrates a new fault-diagnosis method combining successive variational-mode decomposition (SVMD) entropy values and machine learning. First, the simulation signal and the real fault signal are used to analyze and compare the variational-mode decomposition (VMD) and SVMD methods. The comparison results prove that SVMD can be a useful method for fault diagnosis. Then, these two methods are utilized to extract the energy entropy and fuzzy entropy of the gearbox dataset of Southeast University (SEU), respectively. The feature vector and multiple machine-learning classification models are constructed for failure-mode identification. The experimental-analysis results successfully verify the effectiveness of the combined SVMD entropy and machine-learning approach for rotating-machinery fault diagnosis

A allele of ICAM-1 rs5498 and VCAM-1 rs3181092 is correlated with increased risk for periodontal disease

Periodontal disease (PD) is viewed today as multifactorial problems initiated and sustained by bacteria but significantly modified by the body’s response to bacterial plaque. Recent studies have suggested that gene polymorphisms could be involved in the pathophysiology of periodontitis. This study aimed to investigate a possible correlation of the polymorphisms of intercellular adhesion molecule-1 (ICAM-1) and vascular cell adhesion molecule-1 (VCAM-1) with PD