A Comparison between the Zero Forcing Number and the Strong Metric Dimension of Graphs

The \emph{zero forcing number}, $Z(G)$, of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G)-S$ are colored white) such that $V(G)$ is turned black after finitely many applications of "the color-change rule": a white vertex is converted black if it is the only white neighbor of a black vertex. The \emph{strong metric dimension}, $sdim(G)$, of a graph $G$ is the minimum among cardinalities of all strong resolving sets: $W \subseteq V(G)$ is a \emph{strong resolving set} of $G$ if for any $u, v \in V(G)$, there exists an $x \in W$ such that either $u$ lies on an $x-v$ geodesic or $v$ lies on an $x-u$ geodesic. In this paper, we prove that $Z(G) \le sdim(G)+3r(G)$ for a connected graph $G$, where $r(G)$ is the cycle rank of $G$. Further, we prove the sharp bound $Z(G) \leq sdim(G)$ when $G$ is a tree or a unicyclic graph, and we characterize trees $T$ attaining $Z(T)=sdim(T)$. It is easy to see that $sdim(T+e)-sdim(T)$ can be arbitrarily large for a tree $T$; we prove that $sdim(T+e) \ge sdim(T)-2$ and show that the bound is sharp.Comment: 8 pages, 5 figure

Evolution of a Simulation Testbed into an Operational Tool

This paper describes the evolution over a 20-year period of the Future ATM (Air Traffic Management) Concepts Evaluation Tool (FACET) from a National Airspace System (NAS) based simulation testbed into an operational tool. FACET was developed as a testbed for assessing futuristic ATM concepts, e.g., automated conflict detection and resolution. NAS Constraint Evaluation and Notification Tool (NASCENT) is an application, within FACET, for alerting airspace users of inefficiencies in flight operations and advising time- and fuel-saving reroutes.It is currently in use at American Airlines Integrated Operations Center in Fort Worth, TX. The concepts assessed,research conducted, and the operational capability developed, along with the NASA support and achievements are presented in this paper

Contract Farming, Ecological Change and the Transformations of Reciprocal Gendered Social Relations in Eastern India

Debates on gender and the commodification of land highlight the loss of land rights, intensification of demands on women’s labour, and decline in their decision-making control. Supported by ‘extra-economic forces’ of religious nationalism (Hindutva), such neoliberal interventions are producing new gender ideologies involving a subtle shift from relations of reciprocity to those of subordination. Using data from fine grained fieldwork in Koraput district, Odisha, we analyse the tensions and transformations created jointly by corporate interventions (contract farming of eucalyptus by the paper industry) and religious nationalism in the local landscape. We examine how these phenomena are reshaping relations of asymmetric mutuality between nature and society, and between men and women

Absolute Single-Molecule Entropies from Quasi-Harmonic Analysis of Microsecond Molecular Dynamics: Correction Terms and Convergence Properties

The convergence properties of the absolute single-molecule configurational entropy and the correction terms used to estimate it are investigated using microsecond molecular dynamics simulation of a peptide test system and an improved methodology. The results are compared with previous applications for systems of diverse chemical nature. It is shown that (i) the effect of anharmonicity is small, (ii) the effect of pairwise correlation is typically large, and (iii) the latter affects to a larger extent the entropy estimate of thermodynamic states characterized by a higher motional correlation. The causes of such deviations from a quasi-harmonic behavior are explained. This improved approach provides entropies also for molecular systems undergoing conformational transitions and characterized by highly frustrated energy surfaces, thus not limited to systems sampling a single quasi-harmonic basin. Overall, this study emphasizes the need for extensive phase-space sampling in order to obtain a reliable estimation of entropic contributions