BACKGROUND Stable-isotope ratios of carbon (¹³C/¹²C, expressed as δ¹³C) and nitrogen (¹⁵N/¹⁴N, or δ¹⁵N) have been proposed as potential nutritional biomarkers to distinguish between meat, fish, and plant-based foods. OBJECTIVE The objective was to investigate dietary correlates of δ¹³C and δ¹⁵N and examine the association of these biomarkers with incident type 2 diabetes in a prospective stud...

This paper reconsiders the problem of maintaining longest paths in directed graphs, which is at the core of many scheduling applications. It presents bounded incremental algorithms for arc insertion and deletion running in time O(‖δ‖ + |δ| log |δ|) on Cyclic< 0 graphs (i.e., graphs whose cycles have strictly negative lengths), where |δ| and ‖δ‖ are measures of the change in the input and output...

Animals incorporate local δ 2 H values from available water and dietary sources during tissue synthesis, which can provide evidence of elevational movements if multiple tissues with different turnover times are examined. Here we test the applicability of using δ 2 H as an indicator of altitudinal movements by examining multiple tissues (δ 2 Hbw (body water), δ 2 Hfeather, δ 2 Hfur, and δ 2 Hcla...

Appendix Proof of Lemma 1: We first provide the complete parameter regions and the corresponding consumer equilibrium outcome: (I) Unpatched On-premises only (0 < v u < 1): (A) δ ≤ 1 − c p (i) p ≤ p s (1 − c p)/δ and α ≤ α B ; (ii) p s (1 − c p)/δ < p ≤ p s /δ and α ≤ α A ; (B) δ > 1 − c p (i) p ≤ 1 − c p − δ + p s and α ≤ α B ; (ii) 1 − c p − δ + p s < p ≤ p s and α ≤ α C ; (iii) p s < p ≤ p s...

Graph-theoretic properties of certain proximity graphs defined on planar point sets are investigated. We first consider some of the most common proximity graphs of the family of the Delaunay graph, and study their number of edges, minimum and maximum degree, clique number, and chromatic number. In the second part of the paper we focus on the higher order versions of some of these graphs and giv...

Plummer and Toft conjectured in 1987 that the vertices of every 3-connected plane graph with maximum face size Δ⋆ can be colored using at most Δ⋆+2 colors such a way no is incident two same color. The conjecture has been proven for Δ⋆=3, Δ⋆=4 Δ⋆≥18. We prove Δ⋆=16 Δ⋆=17.

A vertex-colored graph is rainbow vertex-connected if any two vertices are connected by a path whose internal vertices have distinct colors. The rainbow vertex-connection of a connected graph G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainbow vertexconnected. It was proved that ifG is a graph of order n with minimum degree δ, then rvc(G) < 11n/δ. I...