---
references:
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      day: 20
  author:
    - family: Alaoui
      given: Ahmed El
    - family: Mahoney
      given: Michael W.
  citation-key: AlaouiFast2014
  container-title: arXiv:1411.0306 [cs, stat]
  issued:
    - year: 2014
      month: 11
      day: 2
  title: Fast Randomized Kernel Methods With Statistical Guarantees
  type: article-journal
  URL: http://arxiv.org/abs/1411.0306

- id: AltschulerMassively2019
  author:
    - family: Altschuler
      given: Jason
    - family: Bach
      given: Francis
    - family: Rudi
      given: Alessandro
    - family: Niles-Weed
      given: Jonathan
  citation-key: AltschulerMassively2019
  container-title: Advances in Neural Information Processing Systems 32
  event-title: Neurips
  issued:
    - year: 2019
  language: en
  page: '11'
  publisher: Curran Associates, Inc.
  title: Massively Scalable Sinkhorn Distances via the Nyström Method
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    https://papers.nips.cc/paper/8693-massively-scalable-sinkhorn-distances-via-the-nystrom-method.pdf

- id: BachEquivalence2015
  accessed:
    - year: 2023
      month: 12
      day: 5
  author:
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      given: Francis
  citation-key: BachEquivalence2015
  issued:
    - year: 2015
      month: 11
      day: 9
  language: en
  number: arXiv:1502.06800
  publisher: arXiv
  title: >-
    On the Equivalence between Kernel Quadrature Rules and Random Feature
    Expansions
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- id: BachKernel2002
  author:
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      given: Francis R
    - family: Jordan
      given: Michael I
  citation-key: BachKernel2002
  container-title: Journal of Machine Learning Research
  issued:
    - year: 2002
      month: 7
  language: en
  page: '48'
  title: Kernel Independent Component Analysis
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- id: BachSharp2013
  accessed:
    - year: 2016
      month: 6
      day: 20
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      given: Francis R.
  citation-key: BachSharp2013
  container-title: COLT
  issued:
    - year: 2013
  page: 185–209
  title: Sharp analysis of low-rank kernel matrix approximations.
  type: paper-conference
  URL: http://www.jmlr.org/proceedings/papers/v30/Bach13.pdf
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- id: BakirLearning2004
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      day: 24
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      given: Gökhan H.
    - family: Weston
      given: Jason
    - family: Schölkopf
      given: Bernhard
  citation-key: BakirLearning2004
  container-title: Advances in neural information processing systems
  issue: '7'
  issued:
    - year: 2004
  page: 449–456
  title: Learning to find pre-images
  type: article-journal
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- id: BeylkinApproximation2010
  accessed:
    - year: 2016
      month: 8
      day: 3
  author:
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      given: Gregory
    - family: Monzón
      given: Lucas
  citation-key: BeylkinApproximation2010
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  DOI: 10.1016/j.acha.2009.08.011
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  issued:
    - year: 2010
      month: 3
  language: en
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- id: BraultRandom2016
  accessed:
    - year: 2016
      month: 8
      day: 31
  author:
    - family: Brault
      given: Romain
    - family: Buc
      given: Florence
      non-dropping-particle: d’Alché-
    - family: Heinonen
      given: Markus
  citation-key: BraultRandom2016
  container-title: Proceedings of The 8th Asian Conference on Machine Learning
  issued:
    - year: 2016
      month: 5
      day: 9
  page: 110–125
  title: Random Fourier features for operator-valued kernels
  type: paper-conference
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- id: BraultScaling
  accessed:
    - year: 2016
      month: 8
      day: 31
  author:
    - family: Brault
      given: Romain
    - family: Lim
      given: Néhémy
    - family: Buc
      given: Florence
      non-dropping-particle: d’Alché-
  citation-key: BraultScaling
  title: >-
    Scaling up Vector Autoregressive Models With Operator-Valued Random Fourier
    Features.
  type: article-journal
  URL: https://aaltd16.irisa.fr/files/2016/08/AALTD16_paper_11.pdf

- id: CheneyCourse2009
  author:
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      given: Elliott Ward
    - family: Light
      given: William Allan
  citation-key: CheneyCourse2009
  ISBN: 978-0-8218-4798-5
  issued:
    - year: 2009
      month: 1
      day: 13
  language: en
  number-of-pages: '379'
  publisher: American Mathematical Soc.
  title: A Course in Approximation Theory
  type: book
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- id: ChengSpectrum2013
  accessed:
    - year: 2021
      month: 3
      day: 29
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      given: Xiuyuan
    - family: Singer
      given: Amit
  citation-key: ChengSpectrum2013
  container-title: 'Random Matrices: Theory and Applications'
  container-title-short: 'Random Matrices: Theory Appl.'
  DOI: 10.1142/S201032631350010X
  ISSN: 2010-3263, 2010-3271
  issue: '04'
  issued:
    - year: 2013
      month: 10
  language: en
  page: '1350010'
  title: The Spectrum of Random Inner-Product Kernel Matrices
  type: article-journal
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- id: ChoromanskiRecycling2016
  accessed:
    - year: 2016
      month: 6
      day: 8
  author:
    - family: Choromanski
      given: Krzysztof
    - family: Sindhwani
      given: Vikas
  citation-key: ChoromanskiRecycling2016
  container-title: arXiv:1605.09049 [cs, stat]
  issued:
    - year: 2016
      month: 5
      day: 29
  title: Recycling Randomness with Structure for Sublinear time Kernel Expansions
  type: article-journal
  URL: http://arxiv.org/abs/1605.09049

- id: ChoromanskiUnreasonable2017
  author:
    - family: Choromanski
      given: Krzysztof
    - family: Rowland
      given: Mark
    - family: Weller
      given: Adrian
  citation-key: ChoromanskiUnreasonable2017
  container-title: arXiv:1703.00864 [stat]
  issued:
    - year: 2017
      month: 3
      day: 2
  title: The Unreasonable Effectiveness of Random Orthogonal Embeddings
  type: article-journal
  URL: http://arxiv.org/abs/1703.00864

- id: CurtoF2F2017
  author:
    - family: Curto
      given: Joachim
    - family: Zarza
      given: Irene
    - family: Yang
      given: Feng
    - family: Smola
      given: Alexander J.
    - family: Van Gool
      given: Luc
  citation-key: CurtoF2F2017
  container-title: arXiv:1702.08159 [cs]
  issued:
    - year: 2017
      month: 2
      day: 27
  title: 'F2F: A Library For Fast Kernel Expansions'
  type: article-journal
  URL: http://arxiv.org/abs/1702.08159

- id: CutajarRandom2017
  author:
    - family: Cutajar
      given: Kurt
    - family: Bonilla
      given: Edwin V.
    - family: Michiardi
      given: Pietro
    - family: Filippone
      given: Maurizio
  citation-key: CutajarRandom2017
  container-title: PMLR
  event-title: International Conference on Machine Learning
  issued:
    - year: 2017
      month: 7
      day: 17
  title: Random Feature Expansions for Deep Gaussian Processes
  type: paper-conference
  URL: http://proceedings.mlr.press/v70/cutajar17a.html

- id: DrineasNystrom2005
  accessed:
    - year: 2014
      month: 10
      day: 10
  author:
    - family: Drineas
      given: Petros
    - family: Mahoney
      given: Michael W.
  citation-key: DrineasNystrom2005
  container-title: Journal of Machine Learning Research
  ISSN: 1532-4435
  issued:
    - year: 2005
      month: 12
  page: 2153–2175
  title: >-
    On the Nyström method for approximating a Gram matrix for improved
    kernel-based learning
  type: article-journal
  URL: http://jmlr.org/papers/volume6/drineas05a/drineas05a.pdf
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- id: ElKarouiSpectrum2010
  accessed:
    - year: 2021
      month: 3
      day: 29
  author:
    - family: El Karoui
      given: Noureddine
  citation-key: ElKarouiSpectrum2010
  container-title: The Annals of Statistics
  container-title-short: Ann. Statist.
  DOI: 10.1214/08-AOS648
  ISSN: 0090-5364
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    - year: 2010
      month: 2
      day: 1
  title: The spectrum of kernel random matrices
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  volume: '38'

- id: GlobersonLearning2016
  accessed:
    - year: 2016
      month: 6
      day: 29
  author:
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      given: Amir
    - family: Livni
      given: Roi
  citation-key: GlobersonLearning2016
  container-title: arXiv:1606.05316 [cs]
  issued:
    - year: 2016
      month: 6
      day: 16
  title: 'Learning Infinite-Layer Networks: Beyond the Kernel Trick'
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- id: GuhaniyogiBayesian2013
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    - year: 2022
      month: 9
      day: 22
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      given: Rajarshi
    - family: Dunson
      given: David B.
  citation-key: GuhaniyogiBayesian2013
  DOI: 10.48550/arXiv.1303.0642
  issued:
    - year: 2013
      month: 3
      day: 22
  number: arXiv:1303.0642
  publisher: arXiv
  title: Bayesian Compressed Regression
  type: article
  URL: http://arxiv.org/abs/1303.0642

- id: KarRandom2012
  accessed:
    - year: 2021
      month: 3
      day: 4
  author:
    - family: Kar
      given: Purushottam
    - family: Karnick
      given: Harish
  citation-key: KarRandom2012
  container-title: Artificial Intelligence and Statistics
  event-title: Artificial Intelligence and Statistics
  ISSN: 1938-7228
  issued:
    - year: 2012
      month: 3
      day: 21
  language: en
  page: 583-591
  publisher: PMLR
  title: Random Feature Maps for Dot Product Kernels
  type: paper-conference
  URL: http://proceedings.mlr.press/v22/kar12.html

- id: KoltchinskiiRandom2000
  accessed:
    - year: 2021
      month: 3
      day: 29
  author:
    - family: Koltchinskii
      given: Vladimir
    - family: Giné
      given: Evarist
  citation-key: KoltchinskiiRandom2000
  container-title: Bernoulli
  DOI: 10.2307/3318636
  ISSN: 1350-7265
  issue: '1'
  issued:
    - year: 2000
  page: 113-167
  publisher: >-
    International Statistical Institute (ISI) and Bernoulli Society for
    Mathematical Statistics and Probability
  title: Random Matrix Approximation of Spectra of Integral Operators
  type: article-journal
  volume: '6'

- id: KwokPreImage2004
  accessed:
    - year: 2016
      month: 12
      day: 22
  author:
    - family: Kwok
      given: J.T.-Y.
    - family: Tsang
      given: I.W.-H.
  citation-key: KwokPreImage2004
  container-title: IEEE Transactions on Neural Networks
  DOI: 10.1109/TNN.2004.837781
  ISSN: 1045-9227
  issue: '6'
  issued:
    - year: 2004
      month: 11
  language: en
  page: 1517-1525
  title: The Pre-Image Problem in Kernel Methods
  type: article-journal
  URL: https://www.aaai.org/Papers/ICML/2003/ICML03-055.pdf
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- id: LeFastfoodapproximating2013
  accessed:
    - year: 2016
      month: 9
      day: 21
  author:
    - family: Le
      given: Quoc
    - family: Sarlós
      given: Tamás
    - family: Smola
      given: Alex
  citation-key: LeFastfoodapproximating2013
  container-title: Proceedings of the international conference on machine learning
  issued:
    - year: 2013
  title: Fastfood-approximating kernel expansions in loglinear time
  type: paper-conference
  URL: http://www.jmlr.org/proceedings/papers/v28/le13-supp.pdf

- id: MinhMercer2006
  accessed:
    - year: 2016
      month: 12
      day: 22
  author:
    - family: Minh
      given: Ha Quang
    - family: Niyogi
      given: Partha
    - family: Yao
      given: Yuan
  citation-key: MinhMercer2006
  collection-title: Lecture Notes in Computer Science
  container-title: International Conference on Computational Learning Theory
  DOI: 10.1007/11776420_14
  event-title: International Conference on Computational Learning Theory
  ISBN: 978-3-540-35294-5 978-3-540-35296-9
  issued:
    - year: 2006
  page: 154–168
  publisher: Springer
  title: Mercer’s theorem, feature maps, and smoothing
  type: paper-conference
  URL: http://www.math.pku.edu.cn/teachers/yaoy/publications/MinNiyYao06.pdf

- id: Pourkamali-AnarakiRandomized2016
  accessed:
    - year: 2016
      month: 9
      day: 6
  author:
    - family: Pourkamali-Anaraki
      given: Farhad
    - family: Becker
      given: Stephen
  citation-key: Pourkamali-AnarakiRandomized2016
  container-title: arXiv:1608.07597 [stat]
  issued:
    - year: 2016
      month: 8
      day: 26
  title: A Randomized Approach to Efficient Kernel Clustering
  type: article-journal
  URL: http://arxiv.org/abs/1608.07597

- id: PourkamaliAnarakiRandomized2016
  author:
    - family: Pourkamali-Anaraki
      given: Farhad
    - family: Becker
      given: Stephen
  citation-key: PourkamaliAnarakiRandomized2016
  container-title: arXiv:1612.06470 [cs, stat]
  issued:
    - year: 2016
      month: 12
      day: 19
  title: Randomized Clustered Nystrom for Large-Scale Kernel Machines
  type: article-journal
  URL: http://arxiv.org/abs/1612.06470

- id: RahimiRandom2007
  accessed:
    - year: 2014
      month: 8
      day: 20
  author:
    - family: Rahimi
      given: Ali
    - family: Recht
      given: Benjamin
  citation-key: RahimiRandom2007
  container-title: Advances in neural information processing systems
  issued:
    - year: 2007
  page: 1177–1184
  publisher: Curran Associates, Inc.
  title: Random features for large-scale kernel machines
  type: paper-conference
  URL: >-
    http://papers.nips.cc/paper/3182-random-features-for-large-scale-kernel-machines

- id: RahimiUniform2008
  author:
    - family: Rahimi
      given: Ali
    - family: Recht
      given: Benjamin
  citation-key: RahimiUniform2008
  container-title: >-
    2008 46th Annual Allerton Conference on Communication, Control, and
    Computing
  DOI: 10.1109/ALLERTON.2008.4797607
  event-title: >-
    2008 46th Annual Allerton Conference on Communication, Control, and
    Computing
  issued:
    - year: 2008
      month: 9
  page: 555-561
  title: Uniform approximation of functions with random bases
  type: paper-conference

- id: RahimiWeighted2009
  accessed:
    - year: 2015
      month: 5
      day: 19
  author:
    - family: Rahimi
      given: Ali
    - family: Recht
      given: Benjamin
  citation-key: RahimiWeighted2009
  container-title: Advances in neural information processing systems
  issued:
    - year: 2009
  page: 1313–1320
  publisher: Curran Associates, Inc.
  title: >-
    Weighted Sums of Random Kitchen Sinks: Replacing minimization with
    randomization in learning
  type: paper-conference
  URL: >-
    http://papers.nips.cc/paper/3495-weighted-sums-of-random-kitchen-sinks-replacing-minimization-with-randomization-in-learning

- id: ScardapaneRandomness2017
  author:
    - family: Scardapane
      given: Simone
    - family: Wang
      given: Dianhui
  citation-key: ScardapaneRandomness2017
  container-title: 'Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery'
  DOI: 10.1002/widm.1200
  ISSN: 1942-4795
  issue: '2'
  issued:
    - year: 2017
      month: 3
      day: 1
  language: en
  title: 'Randomness in neural networks: an overview'
  type: article-journal
  URL: >-
    https://www.researchgate.net/publication/312057617_Randomness_in_Neural_Networks_An_Overview
  volume: '7'

- id: ScholkopfFast1998
  accessed:
    - year: 2016
      month: 7
      day: 25
  author:
    - family: Schölkopf
      given: Bernhard
    - family: Knirsch
      given: Phil
    - family: Smola
      given: Alex
    - family: Burges
      given: Chris
  citation-key: ScholkopfFast1998
  collection-title: Informatik aktuell
  container-title: Mustererkennung 1998
  DOI: 10.1007/978-3-642-72282-0_12
  editor:
    - family: Levi
      given: Paul
    - family: Schanz
      given: Michael
    - family: Ahlers
      given: Rolf-Jürgen
    - family: May
      given: Franz
  ISBN: 978-3-540-64935-9 978-3-642-72282-0
  issued:
    - year: 1998
  language: en
  page: 125-132
  publisher: Springer Berlin Heidelberg
  title: >-
    Fast Approximation of Support Vector Kernel Expansions, and an
    Interpretation of Clustering as Approximation in Feature Spaces
  type: chapter
  URL: http://alex.smola.org/papers/1998/SchKniSmoBur98.pdf

- id: ScholkopfKernel1997
  accessed:
    - year: 2014
      month: 10
      day: 9
  author:
    - family: Schölkopf
      given: Bernhard
    - family: Smola
      given: Alexander
    - family: Müller
      given: Klaus-Robert
  citation-key: ScholkopfKernel1997
  collection-title: Lecture Notes in Computer Science
  container-title: Artificial Neural Networks — ICANN'97
  DOI: 10.1007/BFb0020217
  editor:
    - family: Gerstner
      given: Wulfram
    - family: Germond
      given: Alain
    - family: Hasler
      given: Martin
    - family: Nicoud
      given: Jean-Daniel
  ISBN: 978-3-540-63631-1 978-3-540-69620-9
  issued:
    - year: 1997
      month: 1
      day: 1
  language: en
  page: 583-588
  publisher: Springer Berlin Heidelberg
  title: Kernel principal component analysis
  type: paper-conference

- id: ScholkopfLearning2002
  author:
    - family: Schölkopf
      given: Bernhard
    - family: Smola
      given: Alexander J.
  citation-key: ScholkopfLearning2002
  ISBN: 978-0-262-19475-4
  issued:
    - year: 2002
      month: 1
  language: en
  number-of-pages: '658'
  publisher: MIT Press
  title: >-
    Learning with Kernels: Support Vector Machines, Regularization,
    Optimization, and Beyond
  type: book

- id: SolinHilbert2020
  accessed:
    - year: 2020
      month: 9
      day: 23
  author:
    - family: Solin
      given: Arno
    - family: Särkkä
      given: Simo
  citation-key: SolinHilbert2020
  container-title: Statistics and Computing
  container-title-short: Stat Comput
  DOI: 10.1007/s11222-019-09886-w
  ISSN: 0960-3174, 1573-1375
  issue: '2'
  issued:
    - year: 2020
      month: 3
  page: 419-446
  title: Hilbert Space Methods for Reduced-Rank Gaussian Process Regression
  type: article-journal
  URL: http://arxiv.org/abs/1401.5508
  volume: '30'

- id: StergeStatistical2021
  accessed:
    - year: 2021
      month: 5
      day: 31
  author:
    - family: Sterge
      given: Nicholas
    - family: Sriperumbudur
      given: Bharath
  citation-key: StergeStatistical2021
  container-title: arXiv:2105.08875 [cs, math, stat]
  issued:
    - year: 2021
      month: 5
      day: 18
  title: Statistical Optimality and Computational Efficiency of Nyström Kernel PCA
  type: article-journal
  URL: http://arxiv.org/abs/2105.08875

- id: StroblApproximate2017
  author:
    - family: Strobl
      given: Eric V.
    - family: Zhang
      given: Kun
    - family: Visweswaran
      given: Shyam
  citation-key: StroblApproximate2017
  container-title: arXiv:1702.03877 [stat]
  issued:
    - year: 2017
      month: 2
      day: 13
  title: >-
    Approximate Kernel-based Conditional Independence Tests for Fast
    Non-Parametric Causal Discovery
  type: article-journal
  URL: http://arxiv.org/abs/1702.03877

- id: SutherlandError2015
  accessed:
    - year: 2022
      month: 2
      day: 24
  author:
    - family: Sutherland
      given: Danica J.
    - family: Schneider
      given: Jeff
  citation-key: SutherlandError2015
  collection-title: UAI'15
  container-title: >-
    Proceedings of the Thirty-First Conference on Uncertainty in Artificial
    Intelligence
  event-place: Arlington, Virginia, USA
  ISBN: 978-0-9966431-0-8
  issued:
    - year: 2015
      month: 7
      day: 12
  page: 862–871
  publisher: AUAI Press
  publisher-place: Arlington, Virginia, USA
  title: On the error of random fourier features
  type: paper-conference
  URL: http://arxiv.org/abs/1506.02785

- id: TompkinsFourier2018
  accessed:
    - year: 2021
      month: 1
      day: 25
  author:
    - family: Tompkins
      given: Anthony
    - family: Ramos
      given: Fabio
  citation-key: TompkinsFourier2018
  container-title: Proceedings of the AAAI Conference on Artificial Intelligence
  container-title-short: AAAI
  ISSN: 2374-3468
  issue: '1'
  issued:
    - year: 2018
      month: 4
      day: 29
  language: en
  number: '1'
  title: Fourier Feature Approximations for Periodic Kernels in Time-Series Modelling
  type: article-journal
  URL: https://ojs.aaai.org/index.php/AAAI/article/view/11696
  volume: '32'

- id: VedaldiEfficient2012
  author:
    - family: Vedaldi
      given: A.
    - family: Zisserman
      given: A.
  citation-key: VedaldiEfficient2012
  container-title: IEEE Transactions on Pattern Analysis and Machine Intelligence
  DOI: 10.1109/TPAMI.2011.153
  ISSN: 0162-8828
  issue: '3'
  issued:
    - year: 2012
      month: 3
  number: '3'
  page: 480-492
  title: Efficient Additive Kernels via Explicit Feature Maps
  type: article-journal
  URL: http://eprints.pascal-network.org/archive/00006964/01/vedaldi10.pdf
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- id: VempatiGeneralized2010
  accessed:
    - year: 2020
      month: 2
      day: 25
  author:
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      given: Sreekanth
    - family: Vedaldi
      given: Andrea
    - family: Zisserman
      given: Andrew
    - family: Jawahar
      given: C. V.
  citation-key: VempatiGeneralized2010
  container-title: Procedings of the British Machine Vision Conference 2010
  DOI: 10.5244/C.24.2
  event-place: Aberystwyth
  event-title: British Machine Vision Conference 2010
  ISBN: 978-1-901725-40-7
  issued:
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...
