The Existence of Exactlym-Coloured Complete Subgraphs

AbstractGiven a graphG, its edges are said to be exactlyx-coloured if we have a surjective map from the edges to some set of colours of sizex. Erickson considered the following statement which he denotedP(c,m): if the edges ofKω—the complete graph on vertex set N—are exactlyc-coloured, then there exists an infinite complete subgraph ofKωwhose edges are exactlym-coloured. Ramsey's Theorem states thatP(c,m) is true form=1 and allc⩾1, and can easily be used to show thatP(c,m) holds whenm=2 andc⩾2. Erickson conjectured thatP(c,m) is false wheneverc>m⩾3. We prove that givenm⩾3 there exists an integerC(m) such thatP(c,m) is false for allc⩾C(m)

Asphaltene detection using Surface Enhanced Raman Scattering (SERS)

Peer reviewedPostprin

Factors Affecting Asulam Activity on Sugarcane (Saccharum Sp.) Cultivars and Johnsongrass (Sorghum Halepense).

Studies were conducted to evaluate several factors that may account for the variability in johnsongrass (Sorghum halepense (L.) Pers.) control and sugarcane (Saccharum sp.) cultivar sensitivity observed with postemergence application of asulam, methyl ((4-aminophenyl)sulfonyl) carbamate, herbicide. Johnsongrass at boot stage to 70% seedhead emergence was exposed to simulated rainfall (1.3 cm of water in 15 min) 0, 3, 6, 12, 24, and 48 h after application of asulam at 3.7 kg/ha. Predicted critical rainfree period at which greatest johnsongrass control (65 to 80%) was obtained ranged from 8 to 20 h after treatment, dependent on johnsongrass growth stage and environmental conditions following application. Compared with the 48 h washoff treatment, fresh weight 42 d after treatment was reduced 58, 46, and 64% at the predicted critical rainfree periods of 3, 8, and 18 HAT, respectively. Asulam was applied at 3.7 kg/ha to rhizomatous johnsongrass 3 d before fertilization (DBF) or 0, 3, 7, 10, or 14 d after fertilization (DAF) to evaluate possible interactions. Liquid fertilizer was injected 15 cm deep with knives spaced 70 cm apart on each side of the row. Johnsongrass control based on biomass reduction was 60 to 78% when asulam was applied 3 DBF, which was greater than for applications 0, 3, 7, or 10 DAF. Reduced johnsongrass control appeared to be related to root pruning and subsequent stress associated with the fertilizer operation. In plant cane with seedling johnsongrass, highest control (75%) and lowest johnsongrass panicle counts were observed with asulam application May 15 compared with April 15 or May 1. Cane and sugar yields were 18% higher when asulam was applied May 15 rather than June 15, but were equivalent to application April 15 or May 1. With rhizome johnsongrass in plant cane, johnsongrass control and cane and sugar yields were equivalent with asulam application April 15, May 1, or May 15 and greater than for June 15. Sugarcane cultivars were most sensitive to asulam application in June and injury ranking was \u27CP 72-370\u27 $\u3e$ \u27LCP 82-89\u27 $\ge$ \u27CP 70-321\u27. Leaf uptake of \sp{14}C-asulam was greater for CP 72-370, but translocation within the plant was less than for CP 70-321, which may account for the differential sensitivity observed under field conditions. In none of the studies conducted was johnsongrass controlled more than 80%. Results of these studies help to explain the inconsistency in johnsongrass control with asulam and provide information applicable to its efficient use in a sugarcane production system

Groupoid symmetry and constraints in general relativity

When the vacuum Einstein equations are cast in the form of hamiltonian evolution equations, the initial data lie in the cotangent bundle of the manifold M\Sigma\ of riemannian metrics on a Cauchy hypersurface \Sigma. As in every lagrangian field theory with symmetries, the initial data must satisfy constraints. But, unlike those of gauge theories, the constraints of general relativity do not arise as momenta of any hamiltonian group action. In this paper, we show that the bracket relations among the constraints of general relativity are identical to the bracket relations in the Lie algebroid of a groupoid consisting of diffeomorphisms between space-like hypersurfaces in spacetimes. A direct connection is still missing between the constraints themselves, whose definition is closely related to the Einstein equations, and our groupoid, in which the Einstein equations play no role at all. We discuss some of the difficulties involved in making such a connection.Comment: 22 pages, major revisio

Life histories and niche dynamics in late Quaternary proboscideans from Midwestern North America: evidence from stable isotope analyses

Stable isotopes of mammoths and mastodons have the potential to illuminate ecological changes in late Pleistocene landscapes and megafaunal populations as these species approached extinction. The ecological factors at play in this extinction remain unresolved, but isotopes of bone collagen (δ13C, δ15N) and tooth enamel (δ13C, δ18O, 87Sr/86Sr) from the Midwest, USA are leveraged to examine ecological and behavioral changes that occurred during the last interglacial-glacial cycle. Both species had significant C3 contributions to their diets and experienced increasing levels of niche overlap as they approached extinction. A subset of mastodons after the last glacial maximum (LGM) exhibit low δ15N values that may represent expansion into a novel ecological niche, perhaps densely occupied by other herbivores. Stable isotopes from serial and micro-sampled enamel show increasing seasonality and decreasing temperatures as mammoths transitioned from Marine Isotope Stage (MIS) 5e to glacial conditions (MIS 4, MIS 3, MIS 2). Isotopic variability in enamel suggests mobility patterns and life histories have potentially large impacts on the interpretation of their stable isotope ecology. This study further refines the ecology of midwestern mammoths and mastodons demonstrating increasing seasonality and niche overlap as they responded to landscape changes in the final millennia before extinction

Dynamic telomerase gene suppression via network effects of GSK3 inhibition

<b>Background</b>: Telomerase controls telomere homeostasis and cell immortality and is a promising anti-cancer target, but few small molecule telomerase inhibitors have been developed. Reactivated transcription of the catalytic subunit hTERT in cancer cells controls telomerase expression. Better understanding of upstream pathways is critical for effective anti-telomerase therapeutics and may reveal new targets to inhibit hTERT expression. <b>Methodology/Principal Findings</b>: In a focused promoter screen, several GSK3 inhibitors suppressed hTERT reporter activity. GSK3 inhibition using 6-bromoindirubin-3′-oxime suppressed hTERT expression, telomerase activity and telomere length in several cancer cell lines and growth and hTERT expression in ovarian cancer xenografts. Microarray analysis, network modelling and oligonucleotide binding assays suggested that multiple transcription factors were affected. Extensive remodelling involving Sp1, STAT3, c-Myc, NFκB, and p53 occurred at the endogenous hTERT promoter. RNAi screening of the hTERT promoter revealed multiple kinase genes which affect the hTERT promoter, potentially acting through these factors. Prolonged inhibitor treatments caused dynamic expression both of hTERT and of c-Jun, p53, STAT3, AR and c-Myc. <b>Conclusions/Significance</b>: Our results indicate that GSK3 activates hTERT expression in cancer cells and contributes to telomere length homeostasis. GSK3 inhibition is a clinical strategy for several chronic diseases. These results imply that it may also be useful in cancer therapy. However, the complex network effects we show here have implications for either setting

Metabolomics reveals mouse plasma metabolite responses to acute exercise and effects of disrupting AMPK-glycogen interactions

Introduction: The AMP-activated protein kinase (AMPK) is a master regulator of energy homeostasis that becomes activated by exercise and binds glycogen, an important energy store required to meet exercise-induced energy demands. Disruption of AMPK-glycogen interactions in mice reduces exercise capacity and impairs whole-body metabolism. However, the mechanisms underlying these phenotypic effects at rest and following exercise are unknown. Furthermore, the plasma metabolite responses to an acute exercise challenge in mice remain largely uncharacterized. Methods: Plasma samples were collected from wild type (WT) and AMPK double knock-in (DKI) mice with disrupted AMPK-glycogen binding at rest and following 30-min submaximal treadmill running. An untargeted metabolomics approach was utilized to determine the breadth of plasma metabolite changes occurring in response to acute exercise and the effects of disrupting AMPK-glycogen binding. Results: Relative to WT mice, DKI mice had reduced maximal running speed (p < 0.0001) concomitant with increased body mass (p < 0.01) and adiposity (p < 0.001). A total of 83 plasma metabolites were identified/annotated, with 17 metabolites significantly different (p < 0.05; FDR<0.1) in exercised (↑6; ↓11) versus rested mice, including amino acids, acylcarnitines and steroid hormones. Pantothenic acid was reduced in DKI mice versus WT. Distinct plasma metabolite profiles were observed between the rest and exercise conditions and between WT and DKI mice at rest, while metabolite profiles of both genotypes converged following exercise. These differences in metabolite profiles were primarily explained by exercise-associated increases in acylcarnitines and steroid hormones as well as decreases in amino acids and derivatives following exercise. DKI plasma showed greater decreases in amino acids following exercise versus WT. Conclusion: This is the first study to map mouse plasma metabolomic changes following a bout of acute exercise in WT mice and the effects of disrupting AMPK-glycogen interactions in DKI mice. Untargeted metabolomics revealed alterations in metabolite profiles between rested and exercised mice in both genotypes, and between genotypes at rest. This study has uncovered known and previously unreported plasma metabolite responses to acute exercise in WT mice, as well as greater decreases in amino acids following exercise in DKI plasma. Reduced pantothenic acid levels may contribute to differences in fuel utilization in DKI mice