A Continuous Threshold Model of Cascade Dynamics

Zhong, Yaofeng Desmond; Leonard, Naomi Ehrich

doi:10.1109/cdc40024.2019.9029844

Cited by 14 publications

(9 citation statements)

References 10 publications

(21 reference statements)

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“…In these systems, modulation of gain parameters is central to regulating real-time information processing [52] and implementing optimal decision-making strategies [42], [53], [54]. Consensus cascades in a neural network opinion model using a similar state feedback mechanism were recently explored in [55] for two options.…”

Section: A Dynamic State Feedback Law For Attentionmentioning

confidence: 99%

Nonlinear Opinion Dynamics with Tunable Sensitivity

Bizyaeva¹,

Franci²,

Leonard³

2020

Preprint

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We introduce a general model of continuous-time opinion dynamics for an arbitrary number of agents that communicate over a network and form real-valued opinions about an arbitrary number of options. Drawing inspiration from models in biology, physics, and social psychology, we apply a sigmoidal saturating function to inter-agent and intra-agent exchanges of opinions. The saturating function is the only nonlinearity in the model, yet we prove how it yields rapid and reliable formation of consensus, dissensus, and opinion cascades as a function of just a few parameters. We further show how the network opinion dynamics exhibit both robustness to disturbance and ultrasensitivity to inputs. We design feedback dynamics for system parameters that enable active tuning of implicit thresholds in opinion formation for sensitivity to inputs, robustness to changes in input, opinion cascades, and flexible transitions between consensus and dissensus. The general model can be used for systematic control design in a range of engineering problems including network systems, multi-robot coordination, task allocation, and decision making for spatial navigation. It can also be used for systematic examination of questions in biology and social science ranging from cognitive control and networks in the brain to resilience in collective animal behavior to changing environmental conditions to information spreading and political polarization in social networks.

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Section: A Dynamic State Feedback Law For Attentionmentioning

confidence: 99%

Nonlinear Opinion Dynamics with Tunable Sensitivity

Bizyaeva¹,

Franci²,

Leonard³

2020

Preprint

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“…The first inequality follows since P G P ,OR j (x i = 1) > P G C j (x i = 1) > P G P ,AND j (x i = 1). The rest follows from (10) and (11).…”

Section: B Duplex Permutation Networkmentioning

confidence: 99%

“…Lim et al [4] introduced and analyzed the notion of cascade and contagion centralities in the model of [3]. The LTM on single-layer networks has also been studied in [5]- [9] and generalized to continuous-time, realvalued dynamics in [10].…”

Section: Introductionmentioning

confidence: 99%

Influence Spread in the Heterogeneous Multiplex Linear Threshold Model

Zhong

Srivastava

Leonard

2022

IEEE Trans. Control Netw. Syst.

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The linear threshold model (LTM) has been used to study spread on single-layer networks defined by one inter-agent sensing modality and agents homogeneous in protocol. We define and analyze the heterogeneous multiplex LTM to study spread on multi-layer networks with each layer representing a different sensing modality and agents heterogeneous in protocol. Protocols are designed to distinguish signals from different layers: an agent becomes active if a sufficient number of its neighbors in each of any a of the m layers is active. We focus on Protocol OR, when a = 1, and Protocol AND, when a = m, which model agents that are most and least readily activated, respectively. We develop theory and algorithms to compute the size of the spread at steady state for any set of initially active agents and to analyze the role of distinguished sensing modalities, network structure, and heterogeneity. We show how heterogeneity manages the tension in spreading dynamics between sensitivity to inputs and robustness to disturbances.

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“…In future work we will explore how the sensitivity of the group to distributed input can be tuned with this parameter. Other future directions include expanding the analysis presented here to multi-option cascades with the general opinion dynamics model in [6] and to connect it to other continuous time and state-space models of opinion cascades such as [15].…”

Section: Dynamic Attention: Cascades and Tunable Sensitivity To Inputmentioning

confidence: 99%

Control of Agreement and Disagreement Cascades with Distributed Inputs

Bizyaeva¹,

Sorochkin²,

Franci³

et al. 2021

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For a group of autonomous communicating agents, the ability to distinguish a meaningful input from disturbance, and come to collective agreement or disagreement in response to that input, is paramount for carrying out coordinated objectives. In this work we study how a cascade of opinion formation spreads through a group of networked decision-makers in response to a distributed input signal. Using a nonlinear opinion dynamics model with dynamic feedback modulation of an attention parameter, we show how the triggering of an opinion cascade and the collective decision itself depend on both the distributed input and the node agreement and disagreement centrality, determined by the spectral properties of the network graph. We further show how the attention dynamics introduce an implicit threshold that distinguishes between distributed inputs that trigger cascades and ones that are rejected as disturbance.

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A Continuous Threshold Model of Cascade Dynamics

Cited by 14 publications

References 10 publications

Nonlinear Opinion Dynamics with Tunable Sensitivity

Nonlinear Opinion Dynamics with Tunable Sensitivity

Influence Spread in the Heterogeneous Multiplex Linear Threshold Model

Control of Agreement and Disagreement Cascades with Distributed Inputs

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