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Let P(k) denote the largest size of a non-collinear point set in the plane admitting at most k distinct angles. We prove P(2) = P(3) = 5, and we characterize the optimal sets. We also leverage results from Fleischmann et al. [Disc. Comput. Geom. (2023)] to provide the general bounds k+2 ≤ P(k) ≤ 6k, although the upper bound may be improved pending progress toward the Strong Dirac Conjecture. We conjecture that the lower bound is tight, providing infinite families of configurations meeting the bound and ruling out several classes of potential counterexamples. 

Abstract We consider the simultaneous propagation of two contagions over a social network. We assume a threshold model for the propagation of the two contagions and use the formal framework of discrete dynamical systems. In particular, we study an optimization problem where the goal is to minimize the total number of new infections subject to a budget constraint on the total number of available vaccinations for the contagions. While this problem has been considered in the literature for a single contagion, our work considers the simultaneous propagation of two contagions. This optimization problem is NP-hard. We present two main solution approaches for the problem, namely an integer linear programming (ILP) formulation to obtain optimal solutions and a heuristic based on a generalization of the set cover problem. We carry out a comprehensive experimental evaluation of our solution approaches using many real-world networks. The experimental results show that our heuristic algorithm produces solutions that are close to the optimal solution and runs several orders of magnitude faster than the ILP-based approach for obtaining optimal solutions. We also carry out sensitivity studies of our heuristic algorithm. 

We consider the simultaneous propagation of two contagions over a social network. We assume a threshold model for the propagation of the two contagions and use the formal framework of discrete dynamical systems. In particular, we study an optimization problem where the goal is to minimize the total number of new infections subject to a budget constraint on the total number of available vaccinations for the contagions. While this problem has been considered in the literature for a single contagion, our work considers the simultaneous propagation of two contagions. This optimization problem is NP-hard. We present two main solution approaches for the problem, namely an integer linear programming (ILP) formulation to obtain optimal solutions and a heuristic based on a generalization of the set cover problem. We carry out a comprehensive experimental evaluation of our solution approaches using many real-world networks. The experimental results show that our heuristic algorithm produces solutions that are close to the optimal solution and runs several orders of magnitude faster than the ILP-based approach for obtaining optimal solutions. We also carry out sensitivity studies of our heuristic algorithm. 

Spatially synthesizing stiff and elastic domains from a single monomer forms robust synthetic plastics. 

Networkrepresentationsofsocio-physicalsystemsareubiquitous,examplesbeingsocial(media)networks and infrastructurenetworkslikepowertransmissionandwatersystems.Themanysoftwaretoolsthatanalyze and visualizenetworks,andcarryoutsimulationsonthem,requiredifferentgraphformats.Consequently, it isimportanttodevelopsoftwareforconvertinggraphsthatarerepresentedinagivensourceformatintoa required representationinadestinationformat.Fornetwork-basedcomputations,graphconversionisakey capability thatfacilitatesinteroperabilityamongsoftwaretools.Thispaperdescribessuchasystemcalled GraphTrans to convertgraphsamongdifferentformats.Thissystemispartofanewcyberinfrastructure for networksciencecalled net.science. Wepresentthe GraphTrans system designandimplementation, results fromaperformanceevaluation,andacasestudytodemonstrateitsutility. 

Biodiversity collections are experiencing a renaissance fueled by the intersection of informatics, emerging technologies, and the extended use and interpretation of specimens and archived databases. In this article, we explore the potential for transformative research in ecology integrating biodiversity collections, stable isotope analysis (SIA), and environmental informatics. Like genomic DNA, SIA provides a common currency interpreted in the context of biogeochemical principles. Integration of SIA data across collections allows for evaluation of long-term ecological change at local to continental scales. Challenges including the analysis of sparse samples, a lack of information about baseline isotopic composition, and the effects of preservation remain, but none of these challenges is insurmountable. The proposed research framework interfaces with existing databases and observatories to provide benchmarks for retrospective studies and ecological forecasting. Collections and SIA add historical context to fundamental questions in freshwater ecological research, reference points for ecosystem monitoring, and a means of quantitative assessment for ecosystem restoration.