25,749 research outputs found
Theories for influencer identification in complex networks
In social and biological systems, the structural heterogeneity of interaction
networks gives rise to the emergence of a small set of influential nodes, or
influencers, in a series of dynamical processes. Although much smaller than the
entire network, these influencers were observed to be able to shape the
collective dynamics of large populations in different contexts. As such, the
successful identification of influencers should have profound implications in
various real-world spreading dynamics such as viral marketing, epidemic
outbreaks and cascading failure. In this chapter, we first summarize the
centrality-based approach in finding single influencers in complex networks,
and then discuss the more complicated problem of locating multiple influencers
from a collective point of view. Progress rooted in collective influence
theory, belief-propagation and computer science will be presented. Finally, we
present some applications of influencer identification in diverse real-world
systems, including online social platforms, scientific publication, brain
networks and socioeconomic systems.Comment: 24 pages, 6 figure
Robustness analysis of a Maximum Correntropy framework for linear regression
In this paper we formulate a solution of the robust linear regression problem
in a general framework of correntropy maximization. Our formulation yields a
unified class of estimators which includes the Gaussian and Laplacian
kernel-based correntropy estimators as special cases. An analysis of the
robustness properties is then provided. The analysis includes a quantitative
characterization of the informativity degree of the regression which is
appropriate for studying the stability of the estimator. Using this tool, a
sufficient condition is expressed under which the parametric estimation error
is shown to be bounded. Explicit expression of the bound is given and
discussion on its numerical computation is supplied. For illustration purpose,
two special cases are numerically studied.Comment: 10 pages, 5 figures, To appear in Automatic
Small gain theorems for large scale systems and construction of ISS Lyapunov functions
We consider interconnections of n nonlinear subsystems in the input-to-state
stability (ISS) framework. For each subsystem an ISS Lyapunov function is given
that treats the other subsystems as independent inputs. A gain matrix is used
to encode the mutual dependencies of the systems in the network. Under a small
gain assumption on the monotone operator induced by the gain matrix, a locally
Lipschitz continuous ISS Lyapunov function is obtained constructively for the
entire network by appropriately scaling the individual Lyapunov functions for
the subsystems. The results are obtained in a general formulation of ISS, the
cases of summation, maximization and separation with respect to external gains
are obtained as corollaries.Comment: provisionally accepted by SIAM Journal on Control and Optimizatio
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