Cycle-flow–based module detection in directed recurrence networks

Banisch, Ralf; Conrad, Nataša Djurdjevac

doi:10.1209/0295-5075/108/68008

Cited by 11 publications

(12 citation statements)

References 29 publications

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“…6.2. For ϵ = 0 we observe the slow exponential decay that we expect in the presence of 3 ; blue stars) and P 1 = P + L (u 1 3 ; red circles) versus the step number k.…”

Section: By This Equation It Holds Thatpmentioning

confidence: 70%

“…Following this and similar connections between metastable sets of reversible processes and the dominant spectrum of P , many different methods for finding dominant metastable sets have been developed [8,32,24,29], while comparable approaches for NESS processes are almost totally missing with just a very few limited exceptions like [39,1] and [34], Sec. 5.3.…”

mentioning

confidence: 99%

“…Cycle decomposition. In order to arrive at a cycle decompositions of the probability flow F we follow [14,13] and [2,1]:…”

mentioning

confidence: 99%

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Finding Dominant Structures of Nonreversible Markov Processes

Conrad¹,

Weber²,

Schuźtte³

2016

Multiscale Model. Simul.

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Finding metastable sets as dominant structures of Markov processes has been shown to be especially useful in modeling interesting slow dynamics of various real world complex processes. Furthermore, coarse graining of such processes based on their dominant structures leads to better understanding and dimension reduction of observed systems. However, in many cases, e.g. for nonreversible Markov processes, dominant structures are often not formed by metastable sets but by important cycles or mixture of both. This paper aims at understanding and identifying these different types of dominant structures for reversible as well as nonreversible ergodic Markov processes. Our algorithmic approach generalizes spectral based methods for reversible process by using Schur decomposition techniques which can tackle also nonreversible cases. We illustrate the mathematical construction of our new approach by numerical experiments.

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“…6.2. For ϵ = 0 we observe the slow exponential decay that we expect in the presence of 3 ; blue stars) and P 1 = P + L (u 1 3 ; red circles) versus the step number k.…”

Section: By This Equation It Holds Thatpmentioning

confidence: 70%

mentioning

confidence: 99%

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Finding Dominant Structures of Nonreversible Markov Processes

Conrad¹,

Weber²,

Schuźtte³

2016

Multiscale Model. Simul.

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“…The model parameters are b, c, f, g = 0.7, e = 0.02, τ = 0.99 agents in his block have a green opinion. 3 An agent is more likely to change its behaviour to non-green, when interacting with two neighbours of non-green behaviour and the more agents in his block show a non-green behaviour.…”

Section: Interaction Rulesmentioning

confidence: 99%

Statistical analysis of tipping pathways in agent-based models

Helfmann

Heitzig

Koltai

et al. 2021

Eur. Phys. J. Spec. Top.

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Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals on the microscopic scale can lead to emergent dynamics on the macroscopic scale, for instance a sudden shift of majority opinion or behavior. Here we are introducing a methodology for studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations. Due to a large number of interacting individuals, agent-based models are high-dimensional, though usually a lower-dimensional structure of the emerging collective behaviour exists. We therefore apply Diffusion Maps, a non-linear dimension reduction technique, to reveal the intrinsic low-dimensional structure. We characterize the tipping behaviour by means of Transition Path Theory, which helps gaining a statistical understanding of the tipping paths such as their distribution, flux and rate. By systematically studying two agent-based models that exhibit a multitude of tipping pathways and cascading effects, we illustrate the practicability of our approach.

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“…An undertaking such as this is a major software development project and parts are being addressed at present. Some important developments for seismic spatial patterns are in Banish and Conrad (2014).…”

Section: Future Directionsmentioning

confidence: 99%

Nonlinear dynamical analysis of GNSS data: quantification, precursors and synchronisation

Hobbs

Ord

2018

Prog Earth Planet Sci

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The goal of any nonlinear dynamical analysis of a data series is to extract features of the dynamics of the underlying physical and chemical processes that produce that spatial pattern or time series; a by-product is to characterise the signal in terms of quantitative measures. In this paper, we briefly review the methodology involved in nonlinear analysis and explore time series for GNSS crustal displacements with a view to constraining the dynamics of the underlying tectonic processes responsible for the kinematics. We use recurrence plots and their quantification to extract the invariant measures of the tectonic system including the embedding dimension, the maximum Lyapunov exponent and the entropy and characterise the system using recurrence quantification analysis (RQA). These measures are used to develop a data model for some GNSS data sets in New Zealand. The resulting dynamical model is tested using nonlinear prediction algorithms. The behaviours of some RQA measures are shown to act as precursors to major jumps in crustal displacement rate. We explore synchronisation using cross-and joint-recurrence analyses between stations and show that generalised synchronisation occurs between GNSS time series separated by up to 600 km. Synchronisation between stations begins up to 250 to 400 days before a large displacement event and decreases immediately before the event. The results are used to speculate on the coupled processes that may be responsible for the tectonics of the observed crustal deformations and that are compatible with the results of nonlinear analysis. The overall aim is to place constraints on the nature of the global attractor that describes plate motions on the Earth.

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Cycle-flow–based module detection in directed recurrence networks

Cited by 11 publications

References 29 publications

Finding Dominant Structures of Nonreversible Markov Processes

Finding Dominant Structures of Nonreversible Markov Processes

Statistical analysis of tipping pathways in agent-based models

Nonlinear dynamical analysis of GNSS data: quantification, precursors and synchronisation

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