Runaway Merging of Black Holes: Analytical Constraint on the Timescale

Following the discovery of a black hole (BH) with a mass of 10^3-10^6 M(sun) in a starburst galaxy M82, we study formation of such a BH via successive merging of stellar-mass BHs within a star cluster. The merging has a runaway characteristic. This is because massive BHs sink into the cluster core and have a high number density, and because the merging probability is higher for more massive BHs. We use the Smoluchowski equation to study analytically the evolution of the BH mass distribution. Under favorable conditions, which are expected for some star clusters in starburst galaxies, the timescale of the runaway merging is at most of order 10^7 yr. This is short enough to account for the presence of a BH heavier than 10^3 M(sun) in an ongoing starburst region.Comment: 10 pages, no figures, to appear in The Astrophysical Journal (Letters

Dynamic Resilient Network Games with Applications to Multi-Agent Consensus

A cyber security problem in a networked system formulated as a resilient graph problem based on a game-theoretic approach is considered. The connectivity of the underlying graph of the network system is reduced by an attacker who removes some of the edges whereas the defender attempts to recover them. Both players are subject to energy constraints so that their actions are restricted and cannot be performed continuously. For this two-stage game, which is played repeatedly over time, we characterize the optimal strategies for the attacker and the defender in terms of edge connectivity and the number of connected components of the graph. The resilient graph game is then applied to a multi-agent consensus problem. We study how the attacks and the recovery on the edges affect the consensus process. Finally, we also provide numerical simulation to illustrate the results.Comment: 12 pages, 13 figure

Two-Player Incomplete Games of Resilient Multiagent Systems

Evolution of agents' dynamics of multiagent systems under consensus protocol in the face of jamming attacks is discussed, where centralized parties are able to influence the control signals of the agents. In this paper we focus on a game-theoretical approach of multiagent systems where the players have incomplete information on their opponents' strength. We consider repeated games with both simultaneous and sequential player actions where players update their beliefs of each other over time. The effect of the players' optimal strategies according to Bayesian Nash Equilibrium and Perfect Bayesian Equilibrium on agents' consensus is examined. It is shown that an attacker with incomplete knowledge may fail to prevent consensus despite having sufficient resources to do so.Comment: 9 pages, 6 figures. Accepted in IFAC-WC 202