Vertices with the Second Neighborhood Property in Eulerian Digraphs

The Second Neighborhood Conjecture states that every simple digraph has a vertex whose second out-neighborhood is at least as large as its first out-neighborhood, i.e. a vertex with the Second Neighborhood Property. A cycle intersection graph of an even graph is a new graph whose vertices are the cycles in a cycle decomposition of the original graph and whose edges represent vertex intersections of the cycles. By using a digraph variant of this concept, we prove that Eulerian digraphs which admit a simple dicycle intersection graph have not only adhere to the Second Neighborhood Conjecture, but have a vertex of minimum outdegree that has the Second Neighborhood Property.Comment: fixed an error in an earlier version and made structural change

Climate-Driven Synchronized Growth of Alpine Trees in the Southeast Tibetan Plateau

<div><p>Knowledge about the spatiotemporal tree growth variability and its associations with climate provides key insights into forest dynamics under future scenarios of climate change. We synthesized 17 tree-ring width chronologies from four tree species at the high-elevation sites in the southeast Tibetan Plateau (SETP) to study the regional tree growth variability and climate-growth relationships. Despite of diverse habitats and different physiological characteristics of these species, these tree-ring chronologies shared a significant common variance in SETP. An unprecedented increase in the shared variance is found along the latter half of the 20th century, coinciding with the enhancement of the frequency of extreme rings among chronologies. It is found that minimum winter temperature tends to be the dominant climate for trees in this region. The site-specific responses in cold (1965–1980) and warm (1990–2005) intervals by means of Fuzzy Cmeans (FCM) clustering reveal that the remarkable enhancement of growth synchrony among trees mainly occur in warm conditions. This is different from previous findings indicating that increased consistence among temperature sensitive tree rings in cold periods. This may be related to the reduced temperature sensitivity of regional tree growth as winter minimum temperature is lower than a certain threshold, which is in agreement with the “principle of ecological amplitude”. In addition, it is worth noting that precipitation in June have started to restrain the tree growth since the beginning of the 1980s, which is possibly an important contributor for synchronized growth among trees in SETP.</p></div

Gene ontology (GO) and pathway enrichment analysis of differentially expressed mRNAs.

<p>(A) Category of cellular components; (B) Category of molecular functions; (C) Category of biological process.</p

Scatter plot of the principal component (PC) loadings of the tree-ring chronology network for the common period 1825–2005 Tree species symbols as in Fig 1.

<p>Scatter plot of the principal component (PC) loadings of the tree-ring chronology network for the common period 1825–2005 Tree species symbols as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0156126#pone.0156126.g001" target="_blank">Fig 1</a>.</p

Differentially expressed mRNAs in RSV-infected and mock-inoculated rice plants.

<p>(A) Total numbers of up- and down-regulated DEGs; (B) Differentially expressed mRNAs in RSV-infected (RI-1~RI-3) and mock-inoculated (CK-1~CK-2) rice plants. Every row shows a different gene. Green, black and red indicate expression levels of genes, respectively low, medium and high.</p

Map showing the sites of selected tree-ring chronologies, gridded climate records and major cities over SETP <i>Picea likiangensis (Franchet) Pritzel</i> chronologies are represented by green stars, <i>Abies forestii Rogers</i> chronologies by blue squares, <i>Juniperus tibetica Kom</i> chronologies by purple circles and <i>Tsuga dumosa Eichler</i> chronologies by red triangles.

<p>Map showing the sites of selected tree-ring chronologies, gridded climate records and major cities over SETP <i>Picea likiangensis (Franchet) Pritzel</i> chronologies are represented by green stars, <i>Abies forestii Rogers</i> chronologies by blue squares, <i>Juniperus tibetica Kom</i> chronologies by purple circles and <i>Tsuga dumosa Eichler</i> chronologies by red triangles.</p

a) temporal change of the variance explained by the PC1 using a running window of 50 years lagged by 10 years; b) frequency of chronologies with extreme wide >1.5 SD, blue bar and narrow <1.5 SD, red bar during the period 1825–2005.

<p>a) temporal change of the variance explained by the PC1 using a running window of 50 years lagged by 10 years; b) frequency of chronologies with extreme wide >1.5 SD, blue bar and narrow <1.5 SD, red bar during the period 1825–2005.</p

The relative levels of 8 differentially expressed disease resistance genes evaluated by qRT-PCR.

<p>These genes were identified as LRR receptor-like serine/threonine-protein kinase (LOC_Os11g40970) (target of Osa-miR159b), LRR receptor-like serine/threonine-protein kinase (LOC_Os02g40200) (target of Osa-miR444e), Glucan endo-1,3-beta-glucosidase (LOC_Os01g71340) (target of Osa-miR1320-5p), Cysteine-rich receptor-like protein kinase 8 (LOC_Os07g35680) (target of Osa-miR1429-5p and Osa-miR1432-3p), Brown planthopper-induced resistance protein 6 (LOC_Os02g57280) (target of Osa-miR1432-5p), heat shock protein DnaJ (LOC_Os01g53020) (target of Osa-miR172d-3p), Wall-associated receptor kinase 5 (LOC_Os04g21820) (target of Osa-miR396c-3p), and Putative disease resistance protein RGA4 (LOC_Os10g04570) (target of Osa-miR5072).</p

Artificial neural network (ANN) simulates tree-ring indices from January average temperature increasing from -11°C to -65°C associated with previous November-December average temperature increasing from -68°C to -4°C during the period 1951–2005.

<p>Artificial neural network (ANN) simulates tree-ring indices from January average temperature increasing from -11°C to -65°C associated with previous November-December average temperature increasing from -68°C to -4°C during the period 1951–2005.</p

The relative levels of 20 differentially expressed miRNAs as shown by stem-loop qRT-PCR.

<p>The relative levels of 20 differentially expressed miRNAs as shown by stem-loop qRT-PCR.</p