Generalized Voter-Like Models on Heterogeneous Networks

Moretti, Paolo; Baronchelli, Andrea; Starnini, Michele; Pastor-Satorras, Romualdo

doi:10.1007/978-1-4614-6729-8_14

Cited by 6 publications

(12 citation statements)

References 31 publications

(73 reference statements)

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“…Additionally, it is worth considering the ability of agents to provide a motion bias to neighbours, thereby including in the study reinforced random walks (Perna and Latty, 2014;Schroeder et al, 2017). The characterisation of the interaction network resulting from the given mobility pattern can be done in terms of degree distribution and other properties relevant from a network theory point of view (Holme and Saramäki, 2012), while the macroscopic analysis of the effects of the interaction topology on the collective outcome needs to take into account heterogeneous mean field approximations (Moretti et al, 2013).…”

Section: Discussionmentioning

confidence: 99%

Balancing exploitation of renewable resources by a robot swarm

2018

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Renewable resources like fish stock or forests should be exploited at a rate that supports regeneration and sustainability-a complex problem that requires adaptive approaches to maintain a sufficiently high exploitation while avoiding depletion. In presence of oblivious agents that cannot keep track of all available resources-a frequent condition in swarm robotics-ensuring that the exploitation effort is correctly balanced is particularly challenging. Additionally, the possibility to exploit resources by multiple robots opens the way to focusing the effort either on a single or on multiple resources in parallel. This means that the swarm needs to collectively decide whether to remain cohesive or split among multiple resources, as a function of the ability of the available resources to replenish after exploitation. In this paper, we propose a decentralised strategy for a swarm of robots that adapts to the available resources and balances the effort among them, hence allowing to maximise the exploitation rate while avoiding to completely deplete the resources. A detailed analysis of the strategy parameters provides insights on the working principles and expected performance of the robot swarm.

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Section: Discussionmentioning

confidence: 99%

Balancing exploitation of renewable resources by a robot swarm

2018

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“…By a union bound combined with the bound in (21) and the definitions of L and R, we find that there exists a C 3 > 0 such that…”

Section: Proofs For the Simple Norros-reittu Networkmentioning

confidence: 99%

Voter models on subcritical scale‐free random graphs

Fernley

Ortgiese

2022

Random Struct Algorithms

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The voter model is a classical interacting particle system modelling how consensus is formed across a network. We analyse the time to consensus for the voter model when the underlying graph is a subcritical scale-free random graph. Moreover, we generalise the model to include a 'temperature' parameter. The interplay between the temperature and the structure of the random graph leads to a very rich phase diagram, where in the different phases different parts of the underlying geometry dominate the time to consensus. Finally, we also consider a discursive voter model, where voters discuss their opinions with their neighbours. Our proofs rely on the well-known duality to coalescing random walks and a detailed understanding of the structure of the random graphs.

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“…The original voter model has only two possible states: 0 or 1. The general voter model [3,4] generalizes this original model. One of the variants of the voter model is the Naming Game [5], in which each node has a set of states that evolves conditioned on its own state as well as its neighbors.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, there have been some studies to predict the state density in complex networks. Moretti et al [4] analyzed the general voter model by the mean-field approximation on networks that disregard the specific connection pattern. Sahneh et al [19] constructed a generalized epidemic spreading model for multistate and multilayer networks and provide a mean-field approximation for the overall density.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, surprisingly, we prove that just a single simulation of the Monte Carlo simulation can efficiently approximate the true expected state density with any finite number of states and network structures that have degree ω(log n). Previous mean-field approximation studies [4,[20][21][22] addressed only a limited set of GOSMs that cannot be approximated in other GOSMs, but our theorem is applicable to all stable GOSM.…”

Section: Introductionmentioning

confidence: 99%

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Efficient spread-size approximation of opinion spreading in general social networks

et al. 2019

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In contemporary society, understanding how information, such as trends and viruses, spreads in various social networks is an important topic in many areas. However, it is difficult to mathematically measure how widespread the information is, especially for a general network structure. There have been studies on opinion spreading, but many studies are limited to specific spreading models such as the susceptible-infected-recovered model and the independent cascade model, and it is difficult to apply these studies to various situations. In this paper, we first suggest a general opinion spreading model (GOSM) that generalizes a large class of popular spreading models. In this model, each node has one of several states, and the state changes through interaction with neighboring nodes at discrete time intervals. Next, we show that many GOSMs have a stable property that is a GOSM version of a uniform equicontinuity. Then, we provide an approximation method to approximate the expected spread size for stable GOSMs. For the approximation method, we propose a concentration theorem that guarantees that a generalized mean-field theorem calculates the expected spreading size within small error bounds for finite time steps for a slightly dense network structure. Furthermore, we prove that a "single simulation" of running the Monte Carlo simulation is sufficient to approximate the expected spreading size. We conduct experiments on both synthetic and real-world networks and show that our generalized approximation method well predicts the state density of the various models, especially in graphs with a large number of nodes. Experimental results show that the generalized mean-field approximation and a single Monte Carlo simulation converge as shown in the concentration theorem.

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Generalized Voter-Like Models on Heterogeneous Networks

Cited by 6 publications

References 31 publications

Balancing exploitation of renewable resources by a robot swarm

Balancing exploitation of renewable resources by a robot swarm

Voter models on subcritical scale‐free random graphs

Efficient spread-size approximation of opinion spreading in general social networks

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