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paper/paper.md

@@ -47,31 +47,31 @@ Various forms of information can be extracted from neural timeseries data. Of th
 
 # Statement of need
 
-Analysis of phase-amplitude coupling, time delays, and non-sinusoidal waveshape provide important mechanistic insights into interneuronal communication [@Canolty2010;@Silchenko2010;@Sherman2016]. Studies of these features in neural timeseries data have been used to investigate core nervous system functions such as movement and memory, including their perturbation in disease [@deHemptinne2013;@Cole2017;@Bazzigaluppi2018;@Binns2024]. However, traditional methods for analysing this information have critical limitations that hinder their utility. In contrast, the bispectrum - the Fourier transform of the third order moment [@Nikias1987] - can be used for the analysis of phase-amplitude coupling [@Zandvoort2021], non-sinusoidal waveshape [@Bartz2019], and time delays [@Nikias1988], overcoming many of the limitations associated with traditional methods.
+Analysis of phase-amplitude coupling, time delays, and non-sinusoidal waveshape provide important insights into interneuronal communication [@Canolty2010;@Silchenko2010;@Sherman2016]. Studies of these features in neural data have been used to investigate core nervous system functions such as movement and memory, including their perturbation in disease [@deHemptinne2013;@Cole2017;@Bazzigaluppi2018;@Binns2024]. However, traditional methods for analysing this information have critical limitations that hinder their utility. In contrast, the bispectrum - the Fourier transform of the third order moment [@Nikias1987] - can be used for the analysis of phase-amplitude coupling [@Zandvoort2021], non-sinusoidal waveshape [@Bartz2019], and time delays [@Nikias1988], overcoming many of the limitations associated with traditional methods.
 
-Despite these benefits, the bispectrum has seen relatively little use in the field of neuroscience, in part due to the lack of an accessible, easy-to-use toolbox tailored to the analysis of electrophysiology data. Code written in MATLAB exists for electrophysiological analyses (see e.g., [github.com/sccn/roiconnect](https://github.com/sccn/roiconnect), [github.com/ZuseDre1/AnalyzingWaveshapeWithBicoherence](https://github.com/ZuseDre1/AnalyzingWaveshapeWithBicoherence)), however it is spread across multiple repositories, and often not in the form of a toolbox. Furthermore, use of this code requires a paid MATLAB license, limiting its accessibility. Code for computing the bispectrum can also be found written in the free-to-use Python language - e.g., @Bachetti2024 - however these implementations are not tailored to the analysis of electrophysiology data, limiting their use for neuroscience research. The `PyBispectra` package aims to address these limitations by providing a single, comprehensive toolbox for bispectral analysis of electrophysiology data (\autoref{fig:overview}), including tutorials to facilitate an understanding of these analyses in the context of neuroscience research.
+Despite these benefits, the bispectrum has seen relatively little use in the field of neuroscience, in part due to the lack of an accessible, easy-to-use toolbox tailored to electrophysiology data. Code written in MATLAB exists for some analyses (see e.g., [github.com/sccn/roiconnect](https://github.com/sccn/roiconnect), [github.com/ZuseDre1/AnalyzingWaveshapeWithBicoherence](https://github.com/ZuseDre1/AnalyzingWaveshapeWithBicoherence)), however it is spread across multiple repositories, and often not in the form of a toolbox. Furthermore, use of this code requires a paid MATLAB license, limiting its accessibility. Code for computing the bispectrum does exist in the free-to-use Python language - e.g., @Bachetti2024 - however these implementations are not tailored to use with electrophysiology data. The `PyBispectra` package addressed these problems by providing a single, comprehensive toolbox for bispectral analysis of electrophysiology data (\autoref{fig:overview}), including tutorials to facilitate an understanding of these analyses in the context of neuroscience research.
 
 ![Overview of the `PyBispectra` toolbox.\label{fig:overview}](Overview.png)
 
 # Features
 
 ## Phase-amplitude coupling
 
-Phase-amplitude coupling refers to the interaction between the phase of a lower frequency oscillation and the amplitude of a higher frequency oscillation, either within or across signals. It has been posited as a mechanism for the integration of neural information across spatiotemporal scales [@Canolty2010], with pathological alterations in coupling seen in neurological disorders [@deHemptinne2013;@Bazzigaluppi2018]. Common methods for quantifying phase-amplitude coupling include the Canolty approach [@Canolty2006] and modulation index [@Tort2010], which involve bandpass filtering signals in the frequency bands of interest and using the Hilbert transform to extract the phase and amplitude information. This approach has several limitations. First, the bandpass filters require precise properties that are not readily apparent, with incorrect filter properties smearing information across a broad spectral range, hindering the analysis of frequency-specific interactions [@Zandvoort2021]. Second, the Hilbert transform is a relatively demanding procedure, contributing to a high computational cost of the analysis. Finally, when analysing interactions between different signals, spurious coupling estimates can arise due to interactions within each signal which cannot be easily corrected for [@PellegriniPreprint]. In contrast, the bispectrum captures phase-amplitude coupling whilst overcoming these limitations. Specifically, coupling information is captured without requiring bandpass filtering, preserving the spectral resolution and reducing the risk of misinterpreting results [@Zandvoort2021]. Furthermore, bispectral analysis is computationally efficient, relying on the computationally cheap Fourier transform. Finally, spurious across-signal coupling estimates can be corrected for using bispectral antisymmetrisation [@Chella2014;@PellegriniPreprint]. `PyBispectra` provides the tools for performing bispectral phase-amplitude coupling analysis, with options for antisymmetrisation. Also supported is a univariate normalisation procedure [@Shahbazi2014], bounding coupling scores between 0 and 1 to enhance interpretability. Altogether, the bispectrum is a robust and computationally efficient approach for phase-amplitude coupling analysis, overcoming key limitations of traditional methods.
+Phase-amplitude coupling refers to the interaction between the phase of a lower frequency oscillation and the amplitude of a higher frequency oscillation. It has been posited as a mechanism for the integration of neural information across spatiotemporal scales [@Canolty2010], with perturbations seen in disease [@deHemptinne2013;@Bazzigaluppi2018]. Common methods for quantifying phase-amplitude coupling include the Canolty approach [@Canolty2006] and modulation index [@Tort2010], which involve bandpass filtering signals in the frequency bands of interest and using the Hilbert transform to extract the phase and amplitude information. This approach has several limitations. First, the bandpass filters require precise properties that are not readily apparent, with poorly designed filters smearing information across a broad spectral range, hindering the analysis of frequency-specific interactions [@Zandvoort2021]. Second, the Hilbert transform is a relatively demanding procedure, contributing to a high computational cost of the analysis. Finally, when analysing interactions between different signals, spurious coupling estimates can arise due to interactions within each signal which cannot be corrected for [@PellegriniPreprint]. In contrast, the bispectrum captures phase-amplitude coupling whilst overcoming these limitations. Specifically, analysing coupling does not require bandpass filtering, preserving the spectral resolution and reducing the risk of misinterpreting results [@Zandvoort2021]. Furthermore, bispectral analysis is computationally efficient, relying on the computationally cheap Fourier transform. Finally, spurious across-signal coupling estimates can be corrected for using bispectral antisymmetrisation [@Chella2014;@PellegriniPreprint]. `PyBispectra` provides the tools for performing bispectral phase-amplitude coupling analysis, with options for antisymmetrisation and a univariate normalisation procedure [@Shahbazi2014] that bounds coupling scores between 0 and 1 to enhance interpretability.
 
 ## Time delays
 
-Time delay analysis identifies latencies of information transfer between signals, complementing structural analyses using electrophysiology data [@Silchenko2010;@Binns2024] to provide additional insight into the physical connections between brain regions. A traditional approach for time delay analysis is cross-correlation, quantifying the similarity of signals at a set of time lags. However, this approach has key limitations, including its limited robustness to noise [@Nikias1988] and a vulnerability to spurious zero time lag interactions arising due to volume conduction and source mixing in the sensor space. On the other hand, the bispectrum is resilient to Gaussian noise sources in the data [@Nikias1988], and the process of antisymmetrisation can be used to correct for spurious zero time lag interactions [@Chella2014]. `PyBispectra` provides tools for time delay analysis using the bispectrum, with options for antisymmetrisation, offering a robust method for the analysis of time delays in electrophysiology data that overcomes key limitations of traditional methods.
+Time delay analysis identifies latencies of information transfer between signals, providing additional insight into the physical connections between brain regions using electrophysiology data [@Silchenko2010;@Binns2024]. A traditional time delay analysis method is cross-correlation, quantifying the similarity of signals at a set of time lags. However, this approach has a limited robustness to noise [@Nikias1988] and a vulnerability to spurious zero time lag interactions arising due to volume conduction and source mixing in the sensor space. On the other hand, the bispectrum is resilient to Gaussian noise sources in the data [@Nikias1988], and antisymmetrisation can be used to correct for spurious zero time lag interactions [@Chella2014]. `PyBispectra` provides tools for bispectral time delay analysis, with options for antisymmetrisation.
 
 ## Non-sinusoidal waveshapes
 
-Non-sinusoidal signals can indicate particular properties of interneuronal communication [@Sherman2016], with pathological alterations seen in neurological disorders [@Cole2017]. Various non-sinusoidal properties can be identified, among them sawtooth signals and a dominance of peaks or troughs. Analysis of these characteristics can be performed on timeseries data using peak finding-based procedures - see e.g., @Cole2017 - however this is computationally demanding for high sampling rate data. Furthermore, this analysis is complicated by a desire in neuroscience to isolate frequency-specific neural activity, with bandpass filtering suppressing non-sinusoidal information [@Bartz2019]. More complicated procedures must therefore be used, which risk contamination from frequencies outside the band of interest - see e.g., @Cole2017. In contrast, the bispectrum captures frequency-resolved non-sinusoidal information directly [@Bartz2019], in a computationally efficient manner that minimises the impact of high sampling rate timeseries. `PyBispectra` provides tools for analysing non-sinusoidal waveshapes using the bispectrum, including the option of univariate normalisation [@Shahbazi2014] to bound values in a standardised range for improved interpretability. Altogether, the bispectrum is a robust and computationally efficient method for the analysis of non-sinusoidal features in electrophysiology data, overcoming key limitations of traditional methods.
+Non-sinusoidal signals indicates particular properties of interneuronal communication [@Sherman2016], with perturbations seen in disease [@Cole2017]. Various non-sinusoidal properties can be identified, among them sawtooth signals and a dominance of peaks or troughs. Analysis of these characteristics can be performed on timeseries data using peak finding-based procedures - see e.g., @Cole2017 - however this is computationally demanding for high sampling rate data. Furthermore, the analysis is complicated by a desire to isolate frequency-specific neural activity, with bandpass filtering suppressing non-sinusoidal information [@Bartz2019]. Attempts to address this remain limited by a risk of contamination from frequencies outside the band of interest - see e.g., @Cole2017. In contrast, the bispectrum captures frequency-resolved non-sinusoidal information directly [@Bartz2019], in a computationally efficient manner that minimises the impact of high sampling rate data. `PyBispectra` provides tools for analysing non-sinusoidal waveshapes using the bispectrum, including the option of univariate normalisation [@Shahbazi2014] to bound values in a standardised range for improved interpretability.
 
 ## Supplementary tools for bispectral analyses
 
-Two common issues faced in the analysis of electrophysiology data are dealing with a limited signal-to-noise ratio, and obtaining interpretable results from high-dimensional data [@Cohen2022]. Spatio-spectral decomposition is a multivariate technique that addresses these problems, using linear filters to capture the key aspects of frequency band-specific information in a high signal-to-noise ratio, low-dimensional space [@Nikulin2011]. This decomposition can be applied for the multivariate analysis of non-sinusoidal waveshapes, with extensions like harmonic power maximisation available to more specifically target non-sinusoidal information [@Bartz2019]. `PyBispectra` provides tools for using spatio-spectral filtering to enhance the signal-to-noise ratio and reduce the dimensionality of electrophysiology data.
+Two common issues faced in the analysis of electrophysiology data are dealing with a limited signal-to-noise ratio, and obtaining interpretable results from high-dimensional data [@Cohen2022]. Spatio-spectral decomposition is a multivariate technique that addresses these problems, capturing the key aspects of frequency band-specific information in a high signal-to-noise ratio, low-dimensional space [@Nikulin2011]. This decomposition can be applied for the multivariate analysis of non-sinusoidal waveshapes, with extensions like harmonic power maximisation available that more specifically target non-sinusoidal information [@Bartz2019]. `PyBispectra` provides tools for using spatio-spectral filtering to enhance the signal-to-noise ratio and reduce the dimensionality of electrophysiology data.
 
-Other practical features of `PyBispectra` include dedicated plotting tools for the visualisation of results from phase-amplitude coupling, time delay, and non-sinusoidal waveshape analyses to aid interpretability. Additionally, data formats follow conventions from popular electrophysiological signal processing packages like `MNE-Python` [@Gramfort2013], and helper functions are provided as wrappers around `MNE-Python` and `SciPy` [@Virtanen2020] tools to facilitate data processing prior to bispectral analyses. Furthermore, other cross-frequency tools for amplitude-amplitude coupling and phase-phase coupling are also provided, following literature recommendations for identifying genuine phase-amplitude coupling [@Giehl2021]. Finally, the various forms of analysis are accompanied by detailed tutorials, helping to facilitate an understanding of how these tools can be used to analyse electrophysiology data.
+Other practical features of `PyBispectra` include dedicated plotting tools for the visualisation of results to aid interpretability. Additionally, data formats follow conventions from popular signal processing packages like `MNE-Python` [@Gramfort2013], and helper functions are provided as wrappers around `MNE-Python` and `SciPy` [@Virtanen2020] tools to facilitate data processing prior to bispectral analyses. Furthermore, cross-frequency tools for amplitude-amplitude and phase-phase coupling are also provided, following literature recommendations for identifying genuine phase-amplitude coupling [@Giehl2021]. Finally, the various analyses are accompanied by detailed tutorials, facilitating an understanding of how the bispectrum can be used to analyse electrophysiology data.
 
 # Conclusion