Asymmetries arising from the space-filling nature of vascular networks

Cardiovascular networks span the body by branching across many generations of vessels. The resulting structure delivers blood over long distances to supply all cells with oxygen via the relatively short-range process of diffusion at the capillary level. The structural features of the network that accomplish this density and ubiquity of capillaries are often called space-filling. There are multiple strategies to fill a space, but some strategies do not lead to biologically adaptive structures by requiring too much construction material or space, delivering resources too slowly, or using too much power to move blood through the system. We empirically measure the structure of real networks (18 humans and 1 mouse) and compare these observations with predictions of model networks that are space-filling and constrained by a few guiding biological principles. We devise a numerical method that enables the investigation of space-filling strategies and determination of which biological principles influence network structure. Optimization for only a single principle creates unrealistic networks that represent an extreme limit of the possible structures that could be observed in nature. We first study these extreme limits for two competing principles, minimal total material and minimal path lengths. We combine these two principles and enforce various thresholds for balance in the network hierarchy, which provides a novel approach that highlights the trade-offs faced by biological networks and yields predictions that better match our empirical data.Comment: 17 pages, 15 figure

Electricity Transmission Pricing and Performance-Based Regulation

Performance-based regulation (PBR) is influenced by the Bayesian and non-Bayesian incentive mechanisms. While Bayesian incentives are impractical, the insights from their properties can be combined with practical non-Bayesian mechanisms for application to transmission pricing. This combination suggests an approach based on the distinction between ultra-short, short and long periods. Ultra-short periods are marked by real-time pricing of point-to-point transmission services. Pricing in short periods involves fixed fees and adjustments via price-cap formulas or profit sharing. Productivity-enhancing incentives have to be tempered by long-term commitment considerations, so that profit sharing may dominate pure price caps. Investment incentives require long-term adjustments based on rate-of-return regulation with a “used and useful” criterion.