ANAPT: Additive noise analysis for persistence thresholding

Myers, Audun; Khasawneh, Firas A.; Fasy, Brittany Terese

doi:10.3934/fods.2022005

Cited by 3 publications

(1 citation statement)

References 41 publications

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“…Dynamic TDA methods have been previously applied to analysing aggregation models, fish swarms and temporal networks [31,38,39]. However, zigzag persistence of dynamic data for larger systems was computationally out of reach until recently [40].…”

Section: Introductionmentioning

confidence: 99%

Zigzag persistence for coral reef resilience using a stochastic spatial model

McDonald,

Neuhausler,

Robinson

et al. 2023

J. R. Soc. Interface.

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A complex interplay between species governs the evolution of spatial patterns in ecology. An open problem in the biological sciences is characterizing spatio-temporal data and understanding how changes at the local scale affect global dynamics/behaviour. Here, we extend a well-studied temporal mathematical model of coral reef dynamics to include stochastic and spatial interactions and generate data to study different ecological scenarios. We present descriptors to characterize patterns in heterogeneous spatio-temporal data surpassing spatially averaged measures. We apply these descriptors to simulated coral data and demonstrate the utility of two topological data analysis techniques—persistent homology and zigzag persistence—for characterizing mechanisms of reef resilience. We show that the introduction of local competition between species leads to the appearance of coral clusters in the reef. We use our analyses to distinguish temporal dynamics stemming from different initial configurations of coral, showing that the neighbourhood composition of coral sites determines their long-term survival. Using zigzag persistence, we determine which spatial configurations protect coral from extinction in different environments. Finally, we apply this toolkit of multi-scale methods to empirical coral reef data, which distinguish spatio-temporal reef dynamics in different locations, and demonstrate the applicability to a range of datasets.

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Section: Introductionmentioning

confidence: 99%

Zigzag persistence for coral reef resilience using a stochastic spatial model

McDonald,

Neuhausler,

Robinson

et al. 2023

J. R. Soc. Interface.

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Graph-based confidence verification for BPSK signal analysis under low SNRs

Chen

Zhao

et al. 2023

Signal Processing

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Lean blowout detection using topological data analysis

Bhattacharya,

Mondal,

et al. 2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Modern lean premixed combustors are operated in ultra-lean mode to conform to strict emission norms. However, this causes the combustors to become prone to lean blowout (LBO). Online monitoring of combustion dynamics may help to avoid LBO and help the combustor run more safely and reliably. Previous studies have suggested various techniques to early predict LBO in single-burner combustors. In contrast, early detection of LBO in multi-burner combustors has been little explored to date. Recent studies have discovered significantly different combustion dynamics between multi-burner combustors and single-burner combustors. In the present paper, we show that some well-established early LBO detection techniques suitable for single-burner combustor are less effective in early detecting LBO in multi-burner combustors. To resolve this, we propose a novel tool, topological data analysis (TDA), for real-time LBO prediction in a wide range of combustor configurations. We find that the TDA metrics are computationally cheap and follow monotonic trends during the transition to LBO. This indicates that the TDA metrics can be used to fine-tune the LBO safety margin, which is a desirable feature from practical implementation point of view. Furthermore, we show that the sublevel set TDA metrics show approximately monotonic changes during the transition to LBO even with low sampling-rate signals. Sublevel set TDA is computationally inexpensive and does not require phase-space embedding. Therefore, TDA can potentially be used for real-time monitoring of combustor dynamics with simple, low-cost, and low sampling-rate sensors.

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ANAPT: Additive noise analysis for persistence thresholding

Cited by 3 publications

References 41 publications

Zigzag persistence for coral reef resilience using a stochastic spatial model

Zigzag persistence for coral reef resilience using a stochastic spatial model

Graph-based confidence verification for BPSK signal analysis under low SNRs

Lean blowout detection using topological data analysis

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