19,950 research outputs found
Bounded Confidence under Preferential Flip: A Coupled Dynamics of Structural Balance and Opinions
In this work we study the coupled dynamics of social balance and opinion
formation. We propose a model where agents form opinions under bounded
confidence, but only considering the opinions of their friends. The signs of
social ties -friendships and enmities- evolve seeking for social balance,
taking into account how similar agents' opinions are. We consider both the case
where opinions have one and two dimensions. We find that our dynamics produces
the segregation of agents into two cliques, with the opinions of agents in one
clique differing from those in the other. Depending on the level of bounded
confidence, the dynamics can produce either consensus of opinions within each
clique or the coexistence of several opinion clusters in a clique. For the
uni-dimensional case, the opinions in one clique are all below the opinions in
the other clique, hence defining a "left clique" and a "right clique". In the
two-dimensional case, our numerical results suggest that the two cliques are
separated by a hyperplane in the opinion space. We also show that the
phenomenon of unidimensional opinions identified by DeMarzo, Vayanos and
Zwiebel (Q J Econ 2003) extends partially to our dynamics. Finally, in the
context of politics, we comment about the possible relation of our results to
the fragmentation of an ideology and the emergence of new political parties.Comment: 8 figures, PLoS ONE 11(10): e0164323, 201
Partial containment control over signed graphs
In this paper, we deal with the containment control problem in presence of
antagonistic interactions. In particular, we focus on the cases in which it is
not possible to contain the entire network due to a constrained number of
control signals. In this scenario, we study the problem of selecting the nodes
where control signals have to be injected to maximize the number of contained
nodes. Leveraging graph condensations, we find a suboptimal and computationally
efficient solution to this problem, which can be implemented by solving an
integer linear problem. The effectiveness of the selection strategy is
illustrated through representative simulations.Comment: 6 pages, 3 figures, accepted for presentation at the 2019 European
Control Conference (ECC19), Naples, Ital
Differential Inequalities in Multi-Agent Coordination and Opinion Dynamics Modeling
Distributed algorithms of multi-agent coordination have attracted substantial
attention from the research community; the simplest and most thoroughly studied
of them are consensus protocols in the form of differential or difference
equations over general time-varying weighted graphs. These graphs are usually
characterized algebraically by their associated Laplacian matrices. Network
algorithms with similar algebraic graph theoretic structures, called being of
Laplacian-type in this paper, also arise in other related multi-agent control
problems, such as aggregation and containment control, target surrounding,
distributed optimization and modeling of opinion evolution in social groups. In
spite of their similarities, each of such algorithms has often been studied
using separate mathematical techniques. In this paper, a novel approach is
offered, allowing a unified and elegant way to examine many Laplacian-type
algorithms for multi-agent coordination. This approach is based on the analysis
of some differential or difference inequalities that have to be satisfied by
the some "outputs" of the agents (e.g. the distances to the desired set in
aggregation problems). Although such inequalities may have many unbounded
solutions, under natural graphic connectivity conditions all their bounded
solutions converge (and even reach consensus), entailing the convergence of the
corresponding distributed algorithms. In the theory of differential equations
the absence of bounded non-convergent solutions is referred to as the
equation's dichotomy. In this paper, we establish the dichotomy criteria of
Laplacian-type differential and difference inequalities and show that these
criteria enable one to extend a number of recent results, concerned with
Laplacian-type algorithms for multi-agent coordination and modeling opinion
formation in social groups.Comment: accepted to Automatic
Visualizing Structural Balance in Signed Networks
Network visualization has established as a key complement to network analysis
since the large variety of existing network layouts are able to graphically
highlight different properties of networks. However, signed networks, i.e.,
networks whose edges are labeled as friendly (positive) or antagonistic
(negative), are target of few of such layouts and none, to our knowledge, is
able to show structural balance, i.e., the tendency of cycles towards including
an even number of negative edges, which is a well-known theory for studying
friction and polarization.
In this work we present Structural-balance-viz: a novel visualization method
showing whether a connected signed network is balanced or not and, in the
latter case, how close the network is to be balanced. Structural-balance-viz
exploits spectral computations of the signed Laplacian matrix to place
network's nodes in a Cartesian coordinate system resembling a balance (a
scale). Moreover, it uses edge coloring and bundling to distinguish positive
and negative interactions. The proposed visualization method has
characteristics desirable in a variety of network analysis tasks:
Structural-balance-viz is able to provide indications of balance/polarization
of the whole network and of each node, to identify two factions of nodes on the
basis of their polarization, and to show their cumulative characteristics.
Moreover, the layout is reproducible and easy to compare.
Structural-balance-viz is validated over synthetic-generated networks and
applied to a real-world dataset about political debates confirming that it is
able to provide meaningful interpretations
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