9,636 research outputs found
Riemann-Liouville Fractional Cosine Functions
In this paper, a new notion, named Riemann-Liouville fractional cosine
function is presented. It is proved that a Riemann-Liouville -order
fractional cosine function is equivalent to Riemann-Liouville -order
fractional resolvents introduced in [Z.D. Mei, J.G. Peng, Y. Zhang, Math.
Nachr. 288, No. 7, 784-797 (2015)]
Infection Spreading and Source Identification: A Hide and Seek Game
The goal of an infection source node (e.g., a rumor or computer virus source)
in a network is to spread its infection to as many nodes as possible, while
remaining hidden from the network administrator. On the other hand, the network
administrator aims to identify the source node based on knowledge of which
nodes have been infected. We model the infection spreading and source
identification problem as a strategic game, where the infection source and the
network administrator are the two players. As the Jordan center estimator is a
minimax source estimator that has been shown to be robust in recent works, we
assume that the network administrator utilizes a source estimation strategy
that can probe any nodes within a given radius of the Jordan center. Given any
estimation strategy, we design a best-response infection strategy for the
source. Given any infection strategy, we design a best-response estimation
strategy for the network administrator. We derive conditions under which a Nash
equilibrium of the strategic game exists. Simulations in both synthetic and
real-world networks demonstrate that our proposed infection strategy infects
more nodes while maintaining the same safety margin between the true source
node and the Jordan center source estimator
Identifying Infection Sources and Regions in Large Networks
Identifying the infection sources in a network, including the index cases
that introduce a contagious disease into a population network, the servers that
inject a computer virus into a computer network, or the individuals who started
a rumor in a social network, plays a critical role in limiting the damage
caused by the infection through timely quarantine of the sources. We consider
the problem of estimating the infection sources and the infection regions
(subsets of nodes infected by each source) in a network, based only on
knowledge of which nodes are infected and their connections, and when the
number of sources is unknown a priori. We derive estimators for the infection
sources and their infection regions based on approximations of the infection
sequences count. We prove that if there are at most two infection sources in a
geometric tree, our estimator identifies the true source or sources with
probability going to one as the number of infected nodes increases. When there
are more than two infection sources, and when the maximum possible number of
infection sources is known, we propose an algorithm with quadratic complexity
to estimate the actual number and identities of the infection sources.
Simulations on various kinds of networks, including tree networks, small-world
networks and real world power grid networks, and tests on two real data sets
are provided to verify the performance of our estimators
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