Unusual structure-energy correlations in intramolecular Diels–Alder reaction transition states

Detailed analysis of calculated data from an experimental/computational study of intramolecular furan Diels–Alder reactions has led to the unusual discovery that the mean contraction of the newly forming C-C σ-bonds from the transition state to the product shows a linear correlation with both reaction Gibbs free energies and reverse energy barriers. There is evidence for a similar correlation in other intramolecular Diels–Alder reactions involving non-aromatic dienes. No such correlation is found for intermolecular Diels–Alder reactions

Distinct difference configurations: multihop paths and key predistribution in sensor networks

A distinct difference configuration is a set of points in Z2 with the property that the vectors (difference vectors) connecting any two of the points are all distinct. Many specific examples of these configurations have been previously studied: the class of distinct difference configurations includes both Costas arrays and sonar sequences, for example. Motivated by an application of these structures in key predistribution for wireless sensor networks, we define the k-hop coverage of a distinct difference configuration to be the number of distinct vectors that can be expressed as the sum of k or fewer difference vectors. This is an important parameter when distinct difference configurations are used in the wireless sensor application, as this parameter describes the density of nodes that can be reached by a short secure path in the network. We provide upper and lower bounds for the k-hop coverage of a distinct difference configuration with m points, and exploit a connection with Bh sequences to construct configurations with maximal k-hop coverage. We also construct distinct difference configurations that enable all small vectors to be expressed as the sum of two of the difference vectors of the configuration, an important task for local secure connectivity in the application