206 research outputs found
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
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