1,721,021 research outputs found
Effect of social influence on a two-party election: A Markovian multiagent model
Full text linkIn digital social networks, the filtering algorithms employed by the platform management to sieve the contents shared among the users can alter the social influence intensity. In this paper, a Markov multi-agent model of opinion dynamics is used to analyze possible opinion manipulation under apparently neutral interventions on the influence intensity. We consider a two-party election whose voters, modeled as heterogeneous agents, are connected in a social network with arbitrary topology. The equations describing the variance of the vote share, both in transient and steady state, are derived. The key is the solution of the second-order marginalization problem under the form of a numerically tractable characterization of pairwise joint probabilities of the voters' opinions. In particular, these probabilities are computed by means of a Lyapunov-like matrix differential equation driven by first-order moments. This result is used to answer some important questions, like the possible nonmonotonic effect of the influence intensity on the vote volatility and the interplay of topology and individuals' stubborness to determine the electoral balance between two parties
Stability, L 1 performance and state feedback design for linear systems in ice-cream cones
Full text linkThis paper considers linear systems which are positively invariant in a second-order cone (ice-cream cone). Three problems are addressed: (i) stability; (ii) L 1 performance; (iii) state feedback design for stabilisation and optimal L 1 performance while preserving cone invariance. We derive necessary and sufficient conditions via Linear Matrix Inequalities (LMI) for the solution of problems (i) and (ii). As for problem (iii), a full parametrization of feasible state feedback gains is provided, along with some LMI relaxations useful to compute a feasible gain. Finally, a numerical example is briefly discussed
Stochastic stability of Positive Markov Jump Linear Systems
No full textThis paper investigates on the stability properties of Positive Markov Jump Linear Systems (PMJLS's), i.e. Markov Jump Linear Systems with nonnegative state variables. Specific features of these systems are highlighted. In particular, a new notion of stability (Exponential Mean stability) is introduced and is shown to be equivalent to the standard notion of 1-moment stability. Moreover, various sufficient conditions for Exponential Almost-Sure stability are worked out, with different levels of conservatism. The implications among the different stability notions are discussed. It is remarkable that, thanks to the positivity assumption, some conditions can be checked by solving Linear Programming feasibility problems
Almost Sure Stability of Markov Jump Linear Systems With Deterministic Switching
No full textThe technical note studies a class of linear systems whose piecewise-constant dynamic matrix is subject to both stochastic jumps, governed by a Markov chain, and deterministic switches. These systems will be dubbed switching dynamics Markov jump linear systems (SD-MJLS). Sufficient conditions for exponential almost sure stability (EAS-stability) are established under either hard or average constraints on the dwell-time between switching instants. The proof relies on easy-to-check norm contractivity conditions and the ergodic law of large numbers
Design of stabilizing strategies for discrete-time dual switching linear systems
No full textDiscrete-time dual switching linear systems are piecewise linear systems subject to both stochastic and deterministic commutations. Stochastic jumps, well-suited to account for unpredictable events like faults or abrupt changes in the parameters, are modeled by means of a Markov chain. The deterministic switches are dictated by a scheduling signal, used as a control variable in order to achieve stochastic stability and guaranteed input/output performance. We derive sufficient conditions for the existence of a state-feedback switching law attaining these goals. Further, the more challenging co-design problem is addressed, namely the joint synthesis of a linear state-feedback controller and a stabilizing switching strategy ensuring a prescribed performance. The results are illustrated by means of a numerical example concerning a networked control system under occasional communication failures. © 2016 Elsevier Ltd. All rights reserved
Manipulating Opinions in Social Networks With Community Structure
No full textOnline social media have been one of the greatest drivers of societal change of the past two decades, but are now being recognized as one of the major causes of opinion radicalization and one of the most effective tools for opinion manipulation. Starting from a class of stochastic models of opinion dynamics, and considering different structures of social networks with increasingly realistic features (including a snapshot of the Facebook friendship network), we develop a mathematical model of different forms of opinion manipulation. We then explore how network properties, and in particular degree distribution and community structure, interact with the attack to amplify or reduce its effect on the population, both globally and on specific subsets. We find, in particular, that degree heterogeneity is key to making online social media susceptible to very effective attacks, even with relatively little effort. Communities instead play a more complex role, acting both as barriers to the spread of manipulated opinions through the whole population and as amplifiers of manipulated opinions when the target of the attack is a community of the online social medium. The results of our study can help design effective strategies to prevent the manipulation of opinions through online social media
H∞ co-design for discrete-time dual switching linear systems
No full textThis paper deals with dual switching linear systems in discrete-time. Such systems have piecewise linear dynamics, with switches dictated by two different sources. One is a stochastic switching signal modeled by a Markov chain. The other is a control discrete variable to be used for stabilization and disturbance attenuation. A first main result concerns the design of switching laws guaranteeing stability and H∞ performance. We then proceed to tackle the more challenging co-design problem, namely the joint synthesis of a linear state-feedback controller and a stabilizing switching strategy. © 2015 EUCA
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