Reliability of rank order in sampled networks

In complex scale-free networks, ranking the individual nodes based upon their importance has useful applications, such as the identification of hubs for epidemic control, or bottlenecks for controlling traffic congestion. However, in most real situations, only limited sub-structures of entire networks are available, and therefore the reliability of the order relationships in sampled networks requires investigation. With a set of randomly sampled nodes from the underlying original networks, we rank individual nodes by three centrality measures: degree, betweenness, and closeness. The higher-ranking nodes from the sampled networks provide a relatively better characterisation of their ranks in the original networks than the lower-ranking nodes. A closeness-based order relationship is more reliable than any other quantity, due to the global nature of the closeness measure. In addition, we show that if access to hubs is limited during the sampling process, an increase in the sampling fraction can in fact decrease the sampling accuracy. Finally, an estimation method for assessing sampling accuracy is suggested

Dynamic Asset Allocation With Event Risk

Major events often trigger abrupt changes in stock prices and volatility. We study the implications of jumps in prices and volatility on investment strategies. Using the event-risk framework of Duffie, Pan, and Singleton (2000), we provide analytical solutions to the optimal portfolio problem. Event risk dramatically affects the optimal strategy. An investor facing event risk is less willing to take leveraged or short positions. The investor acts as if some portion of his wealth may become illiquid and the optimal strategy blends both dynamic and buy-and-hold strategies. Jumps in prices and volatility both have important effects.

Macroscopic Kinetic Effect of Cell-to-Cell Variation in Biochemical Reactions

Genetically identical cells under the same environmental conditions can show strong variations in protein copy numbers due to inherently stochastic events in individual cells. We here develop a theoretical framework to address how variations in enzyme abundance affect the collective kinetics of metabolic reactions observed within a population of cells. Kinetic parameters measured at the cell population level are shown to be systematically deviated from those of single cells, even within populations of homogeneous parameters. Because of these considerations, Michaelis-Menten kinetics can even be inappropriate to apply at the population level. Our findings elucidate a novel origin of discrepancy between in vivo and in vitro kinetics, and offer potential utility for analysis of single-cell metabolomic data