Inducing Effect on the Percolation Transition in Complex Networks

Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the percolating cluster. Here we study this inducing effect on the classical site percolation and K-core percolation, showing that the inducing effect always causes a discontinuous percolation transition. We precisely predict the percolation threshold and core size for uncorrelated random networks with arbitrary degree distributions. For low-dimensional lattices the percolation threshold fluctuates considerably over realizations, yet we can still predict the core size once the percolation occurs. The core sizes of real-world networks can also be well predicted using degree distribution as the only input. Our work therefore provides a theoretical framework for quantitatively understanding discontinuous breakdown phenomena in various complex systems.Comment: Main text and appendices. Title has been change

2, 9-diphenylamino-1, 10-phenanthroline

[[abstract]]2,9-Dichloro-1,10-phenanthroline was prepared by a previously published method [1]. 2,9-Dichloro-1,10-phenanthroline (50 mg) was placed in a flask where the temperature was raised 150 °C with oil-bath, and aniline was introduced under N2 gas. The temperature was raised to 250 °C and maintained for 5 hours. The mixture was purified by recrystalization from methanol, to give 2,9-diphenylamino-1,10 phenanthroline as a dark brown crystal (30 mg, yield: 30.0%).[[notice]]補正完畢[[booktype]]紙本[[countrycodes]]CH

Pareto-improving and revenue-neutral congestion pricing schemes in two-mode traffic networks

This paper studies a Pareto-improving and revenue-neutral congestion pricing scheme on a simple two-mode (highway and transit) network: this scheme aims at simultaneously improving system performance, making every individual user better off, and having zero total revenue. Different Pareto-improving situations are explored when a two-mode transportation system serves for travel groups with different value-of-time (VOT) distributions. Since the congestion pricing scheme suggested here charges transit users negative tolls and automobile users positive tolls, it can be considered as a proper way to implement congestion pricing and transit subsidy in one step, while offsetting the inequity for the poor. For a general VOT distribution of commuters, the condition of Pareto-improving is established, and the impact of the VOT distribution on solving the inequity issue is explored. For a uniform VOT distribution, we show that a Pareto-improving and revenue-neutral pricing scheme always exists for any target modal split pattern that reduces the total system travel time