PH.bib

@book{Topology_and_data,
	Author= {Herbert Edelsbrunner and John Harer},
	Journal = {American Mathematical Society},
	Title = {Computational Topology: An Introduction},
	year = { 2010}
}

@article{williamson1989box,
  title={The box plot: a simple visual method to interpret data},
  author={Williamson, David F and Parker, Robert A and Kendrick, Juliette S},
  journal={Annals of internal medicine},
  volume={110},
  number={11},
  pages={916--921},
  year={1989},
  publisher={American College of Physicians}
}


@article{10.1007/s00454-002-2885-2,
	author = {Edelsbrunner and Letscher and Zomorodian},
	title = {Topological Persistence and Simplification},
	year = {2002},
	issue_date = {November  2002},
	publisher = {Springer-Verlag},
	address = {Berlin, Heidelberg},
	volume = {28},
	number = {4},
	issn = {0179-5376},
	url = {https://doi.org/10.1007/s00454-002-2885-2},
	doi = {10.1007/s00454-002-2885-2},
	abstract = {We formalize a notion of topological simplification within the framework of a filtration, which is the history of a growing complex. We classify a topological change that happens during growth as either a feature or noise depending on its lifetime or persistence within the filtration. We give fast algorithms for computing persistence and experimental evidence for their speed and utility.
	},
	journal = {Discrete Comput. Geom.},
	month = nov,
	pages = {511–533},
	numpages = {23}
}

@INPROCEEDINGS{7493506,  
	author={E. {Wong} and S. {Palande} and B. {Wang} and B. {Zielinski} and J. {Anderson} and P. T. {Fletcher}},  
	booktitle={2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI)},   
	title={Kernel partial least squares regression for relating functional brain network topology to clinical measures of behavior},   
	year={2016},  
	volume={},  
	number={},  
	pages={1303-1306},
}

@article{Horak_2009,
	doi = {10.1088/1742-5468/2009/03/p03034},
	url = {https://doi.org/10.1088%2F1742-5468%2F2009%2F03%2Fp03034},
	year = 2009,
	month = {mar},
	publisher = {{IOP} Publishing},
	volume = {2009},
	number = {03},
	pages = {P03034},
	author = {Danijela Horak and Slobodan Maleti{\'{c}} and Milan Rajkovi{\'{c}}},
	title = {Persistent homology of complex networks},
	journal = {Journal of Statistical Mechanics: Theory and Experiment}
}

@ARTICLE{6307875,  
	author={H. {Lee} and H. {Kang} and M. K. {Chung} and B. {Kim} and D. S. {Lee}},  
	journal={IEEE Transactions on Medical Imaging},   
	title={Persistent Brain Network Homology From the Perspective of Dendrogram},   
	year={2012},  
	volume={31},  
	number={12},  
	pages={2267-2277},
}

@INPROCEEDINGS{7164127,  
	author={B. {Cassidy} and C. {Rae} and V. {Solo}},  
	booktitle={2015 IEEE 12th International Symposium on Biomedical Imaging (ISBI)},   
	title={Brain activity: Conditional dissimilarity and persistent homology},   
	year={2015},  
	pages={1356-1359},}


@INPROCEEDINGS{Donato,  
	author={I. {Donato} and G. {Petri} and M. {Scolamiero} and F. {Vaccarino}},
	booktitle={Proceedings of the European Conference on Complex Systems},   
	title={Decimation of Fast States and Weak Nodes: Topological Variation via Persistent Homology},   
	year={2012},  
	journal={Springer Proceedings in Complexity},}


@article{10.1371/journal.pcbi.1002581,
	author = {Dabaghian, Y. AND Mémoli, F. AND Frank, L. AND Carlsson, G.},
	journal = {PLOS Computational Biology},
	publisher = {Public Library of Science},
	title = {A Topological Paradigm for Hippocampal Spatial Map Formation Using Persistent Homology},
	year = {2012},
	month = {08},
	volume = {8},
	url = {https://doi.org/10.1371/journal.pcbi.1002581},
	pages = {1-14},
	number = {8},
	doi = {10.1371/journal.pcbi.1002581}
}

@Article{Carstens2013,
	author={Carstens, C. J.
	and Horadam, K. J.},
	title={Persistent Homology of Collaboration Networks},
	journal={Mathematical Problems in Engineering},
	year={2013},
	month={Jun},
	day={04},
	publisher={Hindawi Publishing Corporation},
	volume={2013},
	pages={815035},
	abstract={Over the past few decades, network science has introduced several statistical measures to determine the topological structure of large networks. Initially, the focus was on binary networks, where edges are either present or not. Thus, many of the earlier measures can only be applied to binary networks and not to weighted networks. More recently, it has been shown that weighted networks have a rich structure, and several generalized measures have been introduced. We use persistent homology, a recent technique from computational topology, to analyse four weighted collaboration networks. We include the first and second Betti numbers for the first time for this type of analysis. We show that persistent homology corresponds to tangible features of the networks. Furthermore, we use it to distinguish the collaboration networks from similar random networks.},
	issn={1024-123X},
	doi={10.1155/2013/815035},
	url={https://doi.org/10.1155/2013/815035}
}

@INPROCEEDINGS{5872535,

	author={H. {Lee} and M. K. {Chung} and H. {Kang} and B. {Kim} and D. S. {Lee}},

	booktitle={2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro}, 

	title={Discriminative persistent homology of brain networks}, 

	year={2011},

	volume={},

	number={},

	pages={841-844},

	doi={10.1109/ISBI.2011.5872535}}

@Article{Saggar2018,
	author={Saggar, Manish
	and Sporns, Olaf
	and Gonzalez-Castillo, Javier
	and Bandettini, Peter A.
	and Carlsson, Gunnar
	and Glover, Gary
	and Reiss, Allan L.},
	title={Towards a new approach to reveal dynamical organization of the brain using topological data analysis},
	journal={Nature Communications},
	year={2018},
	month={Apr},
	day={11},
	volume={9},
	number={1},
	pages={1399},
	abstract={Little is known about how our brains dynamically adapt for efficient functioning. Most previous work has focused on analyzing changes in co-fluctuations between a set of brain regions over several temporal segments of the data. We argue that by collapsing data in space or time, we stand to lose useful information about the brain's dynamical organization. Here we use Topological Data Analysis to reveal the overall organization of whole-brain activity maps at a single-participant level---as an interactive representation---without arbitrarily collapsing data in space or time. Using existing multitask fMRI datasets, with the known ground truth about the timing of transitions from one task-block to next, our approach tracks both within- and between-task transitions at a much faster time scale ({\textasciitilde}4--9{\thinspace}s) than before. The individual differences in the revealed dynamical organization predict task performance. In summary, our approach distills complex brain dynamics into interactive and behaviorally relevant representations.},
	issn={2041-1723},
	doi={10.1038/s41467-018-03664-4},
	url={https://doi.org/10.1038/s41467-018-03664-4}
}

@ARTICLE{10.3389/fncom.2014.00051,

	AUTHOR={Ginestet, Cedric E. and Fournel, Arnaud P. and Simmons, Andrew},   

	TITLE={Statistical network analysis for functional MRI: summary networks and group comparisons},      

	JOURNAL={Frontiers in Computational Neuroscience},      

	VOLUME={8},      

	PAGES={51},     

	YEAR={2014},      

	URL={https://www.frontiersin.org/article/10.3389/fncom.2014.00051},       

	DOI={10.3389/fncom.2014.00051},      

	ISSN={1662-5188}
}

@article{bauer2021ripser,
  title={Ripser: efficient computation of Vietoris--Rips persistence barcodes},
  author={Bauer, Ulrich},
  journal={Journal of Applied and Computational Topology},
  volume={5},
  number={3},
  pages={391--423},
  year={2021},
  publisher={Springer}
}

@article{TERMENON2016172,
	title = "Reliability of graph analysis of resting state fMRI using test-retest dataset from the Human Connectome Project",
	journal = "NeuroImage",
	volume = "142",
	pages = "172 - 187",
	year = "2016",
	issn = "1053-8119",
	doi = "https://doi.org/10.1016/j.neuroimage.2016.05.062",
	author = "M. Termenon and A. Jaillard and C. Delon-Martin and S. Achard"
}

@Article{Aurich2015,
	author={Aurich, Nathassia K.
	and Alves Filho, Jos{\'e} O.
	and Marques da Silva, Ana M.
	and Franco, Alexandre R.},
	title={Evaluating the reliability of different preprocessing steps to estimate graph theoretical measures in resting state fMRI data},
	journal={Frontiers in neuroscience},
	year={2015},
	month={Feb},
	day={19},
	publisher={Frontiers Media S.A.},
	volume={9},
	pages={48-48},
	keywords={functional MRI; graph theory; pre-processing; reliability; resting state},
	abstract={With resting-state functional MRI (rs-fMRI) there are a variety of post-processing methods that can be used to quantify the human brain connectome. However, there is also a choice of which preprocessing steps will be used prior to calculating the functional connectivity of the brain. In this manuscript, we have tested seven different preprocessing schemes and assessed the reliability between and reproducibility within the various strategies by means of graph theoretical measures. Different preprocessing schemes were tested on a publicly available dataset, which includes rs-fMRI data of healthy controls. The brain was parcellated into 190 nodes and four graph theoretical (GT) measures were calculated; global efficiency (GEFF), characteristic path length (CPL), average clustering coefficient (ACC), and average local efficiency (ALE). Our findings indicate that results can significantly differ based on which preprocessing steps are selected. We also found dependence between motion and GT measurements in most preprocessing strategies. We conclude that by using censoring based on outliers within the functional time-series as a processing, results indicate an increase in reliability of GT measurements with a reduction of the dependency of head motion.},
	note={25745384[pmid]},
	note={PMC4333797[pmcid]},
	issn={1662-4548},
	doi={10.3389/fnins.2015.00048},
	url={https://pubmed.ncbi.nlm.nih.gov/25745384},
	url={https://doi.org/10.3389/fnins.2015.00048},
	language={eng}
}

@article{ANDELLINI2015183,
	title = "Test-retest reliability of graph metrics of resting state MRI functional brain networks: A review",
	journal = "Journal of Neuroscience Methods",
	volume = "253",
	pages = "183 - 192",
	year = "2015",
	issn = "0165-0270",
	doi = "https://doi.org/10.1016/j.jneumeth.2015.05.020",
	author = "Martina Andellini and Vittorio Cannatà and Simone Gazzellini and Bruno Bernardi and Antonio Napolitano",
	keywords = "Functional brain networks, Graph theory, Test-retest reliability, Resting state fMRI, Connectivity, Meta-summary reliability analysis, Review",
	abstract = "The employment of graph theory to analyze spontaneous fluctuations in resting state BOLD fMRI data has become a dominant theme in brain imaging studies and neuroscience. Analysis of resting state functional brain networks based on graph theory has proven to be a powerful tool to quantitatively characterize functional architecture of the brain and it has provided a new platform to explore the overall structure of local and global functional connectivity in the brain. Due to its increased use and possible expansion to clinical use, it is essential that the reliability of such a technique is very strongly assessed. In this review, we explore the outcome of recent studies in network reliability which apply graph theory to analyze connectome resting state networks. Therefore, we investigate which preprocessing steps may affect reproducibility the most. In order to investigate network reliability, we compared the test-retest (TRT) reliability of functional data of published neuroimaging studies with different preprocessing steps. In particular we tested influence of global signal regression, correlation metric choice, binary versus weighted link definition, frequency band selection and length of time-series. Statistical analysis shows that only frequency band selection and length of time-series seem to affect TRT reliability. Our results highlight the importance of the choice of the preprocessing steps to achieve more reproducible measurements."
}

@Article{Hilgetag2016,
	author={Hilgetag, Claus C.
	and Goulas, Alexandros},
	title={Is the brain really a small-world network?},
	journal={Brain Structure and Function},
	year={2016},
	month={May},
	day={01},
	volume={221},
	number={4},
	pages={2361-2366},
	issn={1863-2661},
	doi={10.1007/s00429-015-1035-6},
	url={https://doi.org/10.1007/s00429-015-1035-6}
}

@ARTICLE{10.3389/fnhum.2016.00096,

	AUTHOR={Papo, David and Zanin, Massimiliano and Martínez, Johann H. and Buldú, Javier M.},   

	TITLE={Beware of the Small-World Neuroscientist!},      

	JOURNAL={Frontiers in Human Neuroscience},      

	VOLUME={10},      

	PAGES={96},     

	YEAR={2016},      

	URL={https://www.frontiersin.org/article/10.3389/fnhum.2016.00096},       

	DOI={10.3389/fnhum.2016.00096},      

	ISSN={1662-5161}   
	
}

@article{GARRISON2015651,
	title = "The (in)stability of functional brain network measures across thresholds",
	journal = "NeuroImage",
	volume = "118",
	pages = "651 - 661",
	year = "2015",
	issn = "1053-8119",
	doi = "https://doi.org/10.1016/j.neuroimage.2015.05.046",
	url = "http://www.sciencedirect.com/science/article/pii/S1053811915004280",
	author = "Kathleen A. Garrison and Dustin Scheinost and Emily S. Finn and Xilin Shen and R. Todd Constable",
	keywords = "Network analysis, Graph theory, Functional connectivity, Resting state, Threshold",
	abstract = "The large-scale organization of the brain has features of complex networks that can be quantified using network measures from graph theory. However, many network measures were designed to be calculated on binary graphs, whereas functional brain organization is typically inferred from a continuous measure of correlations in temporal signal between brain regions. Thresholding is a necessary step to use binary graphs derived from functional connectivity data. However, there is no current consensus on what threshold to use, and network measures and group contrasts may be unstable across thresholds. Nevertheless, whole-brain network analyses are being applied widely with findings typically reported at an arbitrary threshold or range of thresholds. This study sought to evaluate the stability of network measures across thresholds in a large resting state functional connectivity dataset. Network measures were evaluated across absolute (correlation-based) and proportional (sparsity-based) thresholds, and compared between sex and age groups. Overall, network measures were found to be unstable across absolute thresholds. For example, the direction of group differences in a given network measure may change depending on the threshold. Network measures were found to be more stable across proportional thresholds. These results demonstrate that caution should be used when applying thresholds to functional connectivity data and when interpreting results from binary graph models."
}

@article{RUBINOV20101059,
	title = "Complex network measures of brain connectivity: Uses and interpretations",
	journal = "NeuroImage",
	volume = "52",
	number = "3",
	pages = "1059 - 1069",
	year = "2010",
	note = "Computational Models of the Brain",
	issn = "1053-8119",
	doi = "https://doi.org/10.1016/j.neuroimage.2009.10.003",
	url = "http://www.sciencedirect.com/science/article/pii/S105381190901074X",
	author = "Mikail Rubinov and Olaf Sporns",
	abstract = "Brain connectivity datasets comprise networks of brain regions connected by anatomical tracts or by functional associations. Complex network analysis—a new multidisciplinary approach to the study of complex systems—aims to characterize these brain networks with a small number of neurobiologically meaningful and easily computable measures. In this article, we discuss construction of brain networks from connectivity data and describe the most commonly used network measures of structural and functional connectivity. We describe measures that variously detect functional integration and segregation, quantify centrality of individual brain regions or pathways, characterize patterns of local anatomical circuitry, and test resilience of networks to insult. We discuss the issues surrounding comparison of structural and functional network connectivity, as well as comparison of networks across subjects. Finally, we describe a Matlab toolbox (http://www.brain-connectivity-toolbox.net) accompanying this article and containing a collection of complex network measures and large-scale neuroanatomical connectivity datasets."
}

@article{DRAKESMITH2015313,
	title = "Overcoming the effects of false positives and threshold bias in graph theoretical analyses of neuroimaging data",
	journal = "NeuroImage",
	volume = "118",
	pages = "313 - 333",
	year = "2015",
	issn = "1053-8119",
	doi = "https://doi.org/10.1016/j.neuroimage.2015.05.011",
	url = "http://www.sciencedirect.com/science/article/pii/S1053811915003912",
	author = "M. Drakesmith and K. Caeyenberghs and A. Dutt and G. Lewis and A.S. David and D.K. Jones",
	abstract = "Graph theory (GT) is a powerful framework for quantifying topological features of neuroimaging-derived functional and structural networks. However, false positive (FP) connections arise frequently and influence the inferred topology of networks. Thresholding is often used to overcome this problem, but an appropriate threshold often relies on a priori assumptions, which will alter inferred network topologies. Four common network metrics (global efficiency, mean clustering coefficient, mean betweenness and smallworldness) were tested using a model tractography dataset. It was found that all four network metrics were significantly affected even by just one FP. Results also show that thresholding effectively dampens the impact of FPs, but at the expense of adding significant bias to network metrics. In a larger number (n=248) of tractography datasets, statistics were computed across random group permutations for a range of thresholds, revealing that statistics for network metrics varied significantly more than for non-network metrics (i.e., number of streamlines and number of edges). Varying degrees of network atrophy were introduced artificially to half the datasets, to test sensitivity to genuine group differences. For some network metrics, this atrophy was detected as significant (p<0.05, determined using permutation testing) only across a limited range of thresholds. We propose a multi-threshold permutation correction (MTPC) method, based on the cluster-enhanced permutation correction approach, to identify sustained significant effects across clusters of thresholds. This approach minimises requirements to determine a single threshold a priori. We demonstrate improved sensitivity of MTPC-corrected metrics to genuine group effects compared to an existing approach and demonstrate the use of MTPC on a previously published network analysis of tractography data derived from a clinical population. In conclusion, we show that there are large biases and instability induced by thresholding, making statistical comparisons of network metrics difficult. However, by testing for effects across multiple thresholds using MTPC, true group differences can be robustly identified."
}

@INPROCEEDINGS{7270846,

	author={M. {Narayan} and G. I. {Allen}},

	booktitle={2015 International Workshop on Pattern Recognition in NeuroImaging}, 

	title={Population Inference for Node Level Differences in Multi-subject Functional Connectivity}, 

	year={2015},

	volume={},

	number={},

	pages={53-56},

	doi={10.1109/PRNI.2015.34}}

@Article{Simpson2013,
	author={Simpson, Sean L.
	and Bowman, F. DuBois
	and Laurienti, Paul J.},
	title={Analyzing complex functional brain networks: Fusing statistics and network science to understand the brain(*{\textdagger})},
	journal={Statistics surveys},
	year={2013},
	volume={7},
	pages={1-36},
	keywords={Graph theory; connectivity; fMRI; network model; neuroimaging; small-world},
	abstract={Complex functional brain network analyses have exploded over the last decade, gaining traction due to their profound clinical implications. The application of network science (an interdisciplinary offshoot of graph theory) has facilitated these analyses and enabled examining the brain as an integrated system that produces complex behaviors. While the field of statistics has been integral in advancing activation analyses and some connectivity analyses in functional neuroimaging research, it has yet to play a commensurate role in complex network analyses. Fusing novel statistical methods with network-based functional neuroimage analysis will engender powerful analytical tools that will aid in our understanding of normal brain function as well as alterations due to various brain disorders. Here we survey widely used statistical and network science tools for analyzing fMRI network data and discuss the challenges faced in filling some of the remaining methodological gaps. When applied and interpreted correctly, the fusion of network scientific and statistical methods has a chance to revolutionize the understanding of brain function.},
	note={25309643[pmid]},
	note={PMC4189131[pmcid]},
	issn={1935-7516},
	doi={10.1214/13-SS103},
	url={https://pubmed.ncbi.nlm.nih.gov/25309643},
	url={https://doi.org/10.1214/13-SS103},
	language={eng}
}

@book{ghrist2014elementary,
	title={Elementary applied topology},
	author={Ghrist, Robert W},
	volume={1},
	year={2014},
	publisher={Createspace Seattle}
}


@book{oudot2015persistence,
	title={Persistence theory: from quiver representations to data analysis},
	author={Oudot, Steve Y},
	volume={209},
	year={2015},
	publisher={American Mathematical Society Providence}
}

@book{zomorodian2005topology,
	title={Topology for computing},
	author={Zomorodian, Afra J},
	volume={16},
	year={2005},
	publisher={Cambridge university press}
}


@article{weinberger2011persistent,
	title={What is... persistent homology},
	author={Weinberger, Shmuel},
	journal={Notices of the AMS},
	volume={58},
	number={1},
	pages={36--39},
	year={2011}
}

@article{ghrist2008barcodes,
	title={Barcodes: the persistent topology of data},
	author={Ghrist, Robert},
	journal={Bulletin of the American Mathematical Society},
	volume={45},
	number={1},
	pages={61--75},
	year={2008}
}

@article{edelsbrunner2008surveys,
	title={Surveys on Discrete and Computational Geometry},
	author={Edelsbrunner, H and Harer, J},
	journal={Contemporary Mathematics (American Mathematical Society, Providence, RI)},
	volume={453},
	pages={257--282},
	year={2008}
}

@article{edelsbrunner2014proceedings,
	title={Proceedings of the European Congress of Mathematics},
	author={Edelsbrunner, H and Morozov, D},
	year={2014},
	publisher={European Mathematical Society}
}

@article{patania2017topological,
	title={Topological analysis of data},
	author={Patania, Alice and Vaccarino, Francesco and Petri, Giovanni},
	journal={EPJ Data Science},
	volume={6},
	pages={1--6},
	year={2017},
	publisher={Springer}
}

@article{fornito2010can,
	title={What can spontaneous fluctuations of the blood oxygenation-level-dependent signal tell us about psychiatric disorders?},
	author={Fornito, Alex and Bullmore, Edward T},
	journal={Current opinion in psychiatry},
	volume={23},
	number={3},
	pages={239--249},
	year={2010},
	publisher={LWW}
}

@article{miller2016multimodal,
	title={Multimodal population brain imaging in the UK Biobank prospective epidemiological study},
	author={Miller, Karla L and Alfaro-Almagro, Fidel and Bangerter, Neal K and Thomas, David L and Yacoub, Essa and Xu, Junqian and Bartsch, Andreas J and Jbabdi, Saad and Sotiropoulos, Stamatios N and Andersson, Jesper LR and others},
	journal={Nature neuroscience},
	volume={19},
	number={11},
	pages={1523--1536},
	year={2016},
	publisher={Nature Publishing Group}
}

@article{di2014autism,
	title={The autism brain imaging data exchange: towards a large-scale evaluation of the intrinsic brain architecture in autism},
	author={Di Martino, Adriana and Yan, Chao-Gan and Li, Qingyang and Denio, Erin and Castellanos, Francisco X and Alaerts, Kaat and Anderson, Jeffrey S and Assaf, Michal and Bookheimer, Susan Y and Dapretto, Mirella and others},
	journal={Molecular psychiatry},
	volume={19},
	number={6},
	pages={659--667},
	year={2014},
	publisher={Nature Publishing Group}
}

@article{bellec2017neuro,
	title={The neuro bureau ADHD-200 preprocessed repository},
	author={Bellec, Pierre and Chu, Carlton and Chouinard-Decorte, Francois and Benhajali, Yassine and Margulies, Daniel S and Craddock, R Cameron},
	journal={Neuroimage},
	volume={144},
	pages={275--286},
	year={2017},
	publisher={Elsevier}
}

@article{rubinov2010complex,
	title={Complex network measures of brain connectivity: uses and interpretations},
	author={Rubinov, Mikail and Sporns, Olaf},
	journal={Neuroimage},
	volume={52},
	number={3},
	pages={1059--1069},
	year={2010},
	publisher={Elsevier}
}

@article{nooner2012nki,
	title={The NKI-Rockland sample: a model for accelerating the pace of discovery science in psychiatry},
	author={Nooner, Kate Brody and Colcombe, Stanley and Tobe, Russell and Mennes, Maarten and Benedict, Melissa and Moreno, Alexis and Panek, Laura and Brown, Shaquanna and Zavitz, Stephen and Li, Qingyang and others},
	journal={Frontiers in neuroscience},
	volume={6},
	pages={152},
	year={2012},
	publisher={Frontiers}
}

@article{feinberg2010multiplexed,
	title={Multiplexed echo planar imaging for sub-second whole brain FMRI and fast diffusion imaging},
	author={Feinberg, David A and Moeller, Steen and Smith, Stephen M and Auerbach, Edward and Ramanna, Sudhir and Glasser, Matt F and Miller, Karla L and Ugurbil, Kamil and Yacoub, Essa},
	journal={PloS one},
	volume={5},
	number={12},
	pages={e15710},
	year={2010},
	publisher={Public Library of Science San Francisco, USA}
}

@article{thomas2011organization,
	title={The organization of the human cerebral cortex estimated by intrinsic functional connectivity},
	author={Thomas Yeo, BT and Krienen, Fenna M and Sepulcre, Jorge and Sabuncu, Mert R and Lashkari, Danial and Hollinshead, Marisa and Roffman, Joshua L and Smoller, Jordan W and Z{\"o}llei, Lilla and Polimeni, Jonathan R and others},
	journal={Journal of neurophysiology},
	volume={106},
	number={3},
	pages={1125--1165},
	year={2011},
	publisher={American Physiological Society Bethesda, MD}
}

@article{smith2011network,
	title={Network modelling methods for FMRI},
	author={Smith, Stephen M and Miller, Karla L and Salimi-Khorshidi, Gholamreza and Webster, Matthew and Beckmann, Christian F and Nichols, Thomas E and Ramsey, Joseph D and Woolrich, Mark W},
	journal={Neuroimage},
	volume={54},
	number={2},
	pages={875--891},
	year={2011},
	publisher={Elsevier}
}

@article{vallender1974calculation,
	title={Calculation of the Wasserstein distance between probability distributions on the line},
	author={Vallender, SS},
	journal={Theory of Probability \& Its Applications},
	volume={18},
	number={4},
	pages={784--786},
	year={1974},
	publisher={SIAM}
}

@article{edelsbrunner2013persistent,
	title={Persistent homology: theory and practice},
	author={Edelsbrunner, Herbert},
	year={2013}
}

@article{skalski2018statistical,
	title={A statistical test and sample size recommendations for comparing community composition following PCA},
	author={Skalski, John R and Richins, Shelby M and Townsend, Richard L},
	journal={PloS one},
	volume={13},
	number={10},
	pages={e0206033},
	year={2018},
	publisher={Public Library of Science San Francisco, CA USA}
}

@article{jea_hera,
  title={Geometry helps to compare persistence diagrams},
  author={Kerber, Michael and Morozov, Dmitriy and Nigmetov, Arnur},
  journal={Journal of Experimental Algorithmics (JEA)},
  volume={22},
  pages={1--20},
  year={2017},
  publisher={ACM New York, NY, USA}
}

@article{carroll1998multidimensional,
  title={Multidimensional scaling},
  author={Carroll, J Douglas and Arabie, Phipps},
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