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A peer-reviewed version of this preprint was published in PeerJ on 9February 2017.
View the peer-reviewed version (peerj.com/articles/2969), which is thepreferred citable publication unless you specifically need to cite this preprint.
Washburne AD, Silverman JD, Leff JW, Bennett DJ, Darcy JL, Mukherjee S,Fierer N, David LA. 2017. Phylogenetic factorization of compositional datayields lineage-level associations in microbiome datasets. PeerJ 5:e2969https://doi.org/10.7717/peerj.2969
Phylogenetic factorization of compositional data yields
lineage-level associations in microbiome datasets
Alex D Washburne Corresp., 1 , Justin D Silverman 2, 3, 4, 5 , Jonathan W Leff 6 , Dominic J Bennett 7, 8 , John L Darcy 9 ,
Sayan Mukherjee 2, 10 , Noah Fierer 6 , Lawrence A David 2, 4, 5
1 Nicholas School of the Environment, Duke University, Durham, North Carolina, United States
2 Program for Computational Biology and Bioinformatics, Duke University, Durham, North Carolina, United States
3 Medical Scientist Training Program, Duke University, Durham, North Carolina, United States
4 Center for Genomic and Computational Biology, Duke University, Durham, North Carolina, United States
5 Department of Molecular Genetics and Microbiology, Duke University, Durham, North Carolina, United States
6 Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado, United States
7 Department of Earth Science and Engineering, Imperial College London, London, United Kingdom
8 Institute of Zoology, Zoological Society of London, London, United Kingdom
9 Department of Ecology and Evolution, University of Colorado Boulder, Boulder, Colorado, United States
10 Department of Statistical Science, Mathematics, and Computer Science, Duke University, Durham, North Carolina, United States
Corresponding Author: Alex D Washburne
Email address: [email protected]
Marker gene sequencing of microbial communities has generated big datasets of microbial
relative abundances varying across environmental conditions, sample sites and
treatments. These data often come with putative phylogenies, providing unique
opportunities to investigate how shared evolutionary history affects microbial abundance
patterns. Here, we present a method to identify the phylogenetic factors driving patterns
in microbial community composition. We use the method, "phylofactorization", to re-
analyze datasets from the human body and soil microbial communities, demonstrating
how phylofactorization is a dimensionality-reducing tool, an ordination-visualization tool,
and an inferential tool for identifying edges in the phylogeny along which putative
functional ecological traits may have arisen.
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.2685v1 | CC BY 4.0 Open Access | rec: 3 Jan 2017, publ: 3 Jan 2017
P❤②❧♦❣❡♥❡t✐❝ ❢❛❝t♦r✐③❛t✐♦♥ ♦❢ ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛
②✐❡❧❞s ❧✐♥❡❛❣❡✲❧❡✈❡❧ ❛ss♦❝✐❛t✐♦♥s ✐♥ ♠✐❝r♦❜✐♦♠❡
❞❛t❛s❡ts
❉❡❝❡♠❜❡r ✷✼✱ ✷✵✶✻
❆✉t❤♦rs✿ ❆❧❡① ❉ ❲❛s❤❜✉r♥❡1,†✱ ❏✉st✐♥ ❉ ❙✐❧✈❡r♠❛♥2,3,4,5✱ ❏♦♥❛t❤❛♥ ❲ ▲❡✛6✱
❉♦♠✐♥✐❝ ❏ ❇❡♥♥❡tt7,8✱ ❏♦❤♥ ▲✳ ❉❛r❝②9✱ ❙❛②❛♥ ▼✉❦❤❡r❥❡❡2,10✱ ◆♦❛❤ ❋✐❡r❡r6✱ ❛♥❞
▲❛✇r❡♥❝❡ ❆ ❉❛✈✐❞2,4,5
1 ◆✐❝❤♦❧❛s ❙❝❤♦♦❧ ♦❢ t❤❡ ❊♥✈✐r♦♥♠❡♥t✱ ❉✉❦❡ ❯♥✐✈❡rs✐t②✱ ❉✉r❤❛♠✱ ◆♦rt❤ ❈❛r✲
♦❧✐♥❛✱ ❯♥✐t❡❞ ❙t❛t❡s
2 Pr♦❣r❛♠ ❢♦r ❈♦♠♣✉t❛t✐♦♥❛❧ ❇✐♦❧♦❣② ❛♥❞ ❇✐♦✐♥❢♦r♠❛t✐❝s✱ ❉✉❦❡ ❯♥✐✈❡rs✐t②✱
❉✉r❤❛♠✱ ◆♦rt❤ ❈❛r♦❧✐♥❛✱ ❯♥✐t❡❞ ❙t❛t❡s
3 ▼❡❞✐❝❛❧ ❙❝✐❡♥t✐st ❚r❛✐♥✐♥❣ Pr♦❣r❛♠✱ ❉✉❦❡ ❯♥✐✈❡rs✐t②✱ ❉✉r❤❛♠✱ ◆♦rt❤ ❈❛r✲
♦❧✐♥❛✱ ❯♥✐t❡❞ ❙t❛t❡s
4 ❈❡♥t❡r ❢♦r ●❡♥♦♠✐❝ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥❛❧ ❇✐♦❧♦❣②✱ ❉✉❦❡ ❯♥✐✈❡rs✐t②✱ ❉✉r❤❛♠✱
◆♦rt❤ ❈❛r♦❧✐♥❛✱ ❯♥✐t❡❞ ❙t❛t❡s
5 ❉❡♣❛rt♠❡♥t ♦❢ ▼♦❧❡❝✉❧❛r ●❡♥❡t✐❝s ❛♥❞ ▼✐❝r♦❜✐♦❧♦❣②✱ ❉✉❦❡ ❯♥✐✈❡rs✐t②✱ ❉✉r❤❛♠✱
◆♦rt❤ ❈❛r♦❧✐♥❛✱ ❯♥✐t❡❞ ❙t❛t❡s
6 ❈♦♦♣❡r❛t✐✈❡ ■♥st✐t✉t❡ ❢♦r ❘❡s❡❛r❝❤ ✐♥ ❊♥✈✐r♦♥♠❡♥t❛❧ ❙❝✐❡♥❝❡s ✭❈■❘❊❙✮✱ ❯♥✐✲
✈❡rs✐t② ♦❢ ❈♦❧♦r❛❞♦✱ ❇♦✉❧❞❡r✱ ❈♦❧♦r❛❞♦✱ ❯♥✐t❡❞ ❙t❛t❡s
7❉❡♣❛rt♠❡♥t ♦❢ ❊❛rt❤ ❙❝✐❡♥❝❡ ❛♥❞ ❊♥❣✐♥❡❡r✐♥❣✱ ■♠♣❡r✐❛❧ ❈♦❧❧❡❣❡ ▲♦♥❞♦♥✱ ▲♦♥✲
❞♦♥ ❯❑
8■♥st✐t✉t❡ ♦❢ ❩♦♦❧♦❣②✱ ❩♦♦❧♦❣✐❝❛❧ ❙♦❝✐❡t② ♦❢ ▲♦♥❞♦♥✱ ▲♦♥❞♦♥ ❯❑
9❉❡♣❛rt♠❡♥t ♦❢ ❊❝♦❧♦❣② ❛♥❞ ❊✈♦❧✉t✐♦♥❛r② ❇✐♦❧♦❣②✱ ❯♥✐✈❡rs✐t② ♦❢ ❈♦❧♦r❛❞♦✱
❇♦✉❧❞❡r✱ ❈❖ ✽✵✸✵✾
10❉❡♣❛rt♠❡♥ts ♦❢ ❙t❛t✐st✐❝❛❧ ❙❝✐❡♥❝❡✱ ▼❛t❤❡♠❛t✐❝s✱ ❛♥❞ ❈♦♠♣✉t❡r ❙❝✐❡♥❝❡✱ ❉✉❦❡
❯♥✐✈❡rs✐t②✱ ❉✉r❤❛♠✱ ◆❈ ✷✼✼✵✽
✶
†❈♦rr❡s♣♦♥❞✐♥❣ ❛✉t❤♦r❀ ❝♦♥t❛❝t ❛t ❛❧❡①✳❞✳✇❛s❤❜✉r♥❡❅❣♠❛✐❧✳❝♦♠
✷
❆❜str❛❝t✶
▼❛r❦❡r ❣❡♥❡ s❡q✉❡♥❝✐♥❣ ♦❢ ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t✐❡s ❤❛s ❣❡♥❡r❛t❡❞ ❜✐❣ ❞❛t❛s❡ts✷
♦❢ ♠✐❝r♦❜✐❛❧ r❡❧❛t✐✈❡ ❛❜✉♥❞❛♥❝❡s ✈❛r②✐♥❣ ❛❝r♦ss ❡♥✈✐r♦♥♠❡♥t❛❧ ❝♦♥❞✐t✐♦♥s✱ s❛♠✲✸
♣❧❡ s✐t❡s ❛♥❞ tr❡❛t♠❡♥ts✳ ❚❤❡s❡ ❞❛t❛ ♦❢t❡♥ ❝♦♠❡ ✇✐t❤ ♣✉t❛t✐✈❡ ♣❤②❧♦❣❡♥✐❡s✱✹
♣r♦✈✐❞✐♥❣ ✉♥✐q✉❡ ♦♣♣♦rt✉♥✐t✐❡s t♦ ✐♥✈❡st✐❣❛t❡ ❤♦✇ s❤❛r❡❞ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②✺
❛✛❡❝ts ♠✐❝r♦❜✐❛❧ ❛❜✉♥❞❛♥❝❡ ♣❛tt❡r♥s✳ ❍❡r❡✱ ✇❡ ♣r❡s❡♥t ❛ ♠❡t❤♦❞ t♦ ✐❞❡♥t✐❢②✻
t❤❡ ♣❤②❧♦❣❡♥❡t✐❝ ❢❛❝t♦rs ❞r✐✈✐♥❣ ♣❛tt❡r♥s ✐♥ ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t② ❝♦♠♣♦s✐t✐♦♥✳✼
❲❡ ✉s❡ t❤❡ ♠❡t❤♦❞✱ ✏♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✑✱ t♦ r❡✲❛♥❛❧②③❡ ❞❛t❛s❡ts ❢r♦♠ ❤✉♠❛♥✽
❜♦❞② ❛♥❞ s♦✐❧ ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t✐❡s✱ ❞❡♠♦♥str❛t✐♥❣ ❤♦✇ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✐s✾
❛ ❞✐♠❡♥s✐♦♥❛❧✐t②✲r❡❞✉❝✐♥❣ t♦♦❧✱ ❛♥ ♦r❞✐♥❛t✐♦♥✲✈✐s✉❛❧✐③❛t✐♦♥ t♦♦❧✱ ❛♥❞ ❛♥ ✐♥❢❡r❡♥✲✶✵
t✐❛❧ t♦♦❧ ❢♦r ✐❞❡♥t✐❢②✐♥❣ ❡❞❣❡s ✐♥ t❤❡ ♣❤②❧♦❣❡♥② ❛❧♦♥❣ ✇❤✐❝❤ ♣✉t❛t✐✈❡ ❢✉♥❝t✐♦♥❛❧✶✶
❡❝♦❧♦❣✐❝❛❧ tr❛✐ts ♠❛② ❤❛✈❡ ❛r✐s❡♥✳✶✷
■♥tr♦❞✉❝t✐♦♥✶✸
▼✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t✐❡s ♣❧❛② ✐♠♣♦rt❛♥t r♦❧❡s ✐♥ ❤✉♠❛♥ ❬✻❪✱ ❧✐✈❡st♦❝❦ ❬✶✽❪ ❛♥❞✶✹
♣❧❛♥t ❬✸❪ ❤❡❛❧t❤✱ ❜✐♦❣❡♦❝❤❡♠✐❝❛❧ ❝②❝❧❡s ❬✷✱ ✶✷❪✱ t❤❡ ♠❛✐♥t❡♥❛♥❝❡ ♦❢ ❡❝♦s②st❡♠✶✺
♣r♦❞✉❝t✐✈✐t② ❬✹✵❪✱ ❛♥❞ ❜✐♦r❡♠❡❞✐❛t✐♦♥ ❬✷✻❪✳ ●✐✈❡♥ t❤❡ ✐♠♣♦rt❛♥❝❡ ♦❢ ♠✐❝r♦❜✐❛❧✶✻
❝♦♠♠✉♥✐t✐❡s ❛♥❞ t❤❡ ✈❛st ♥✉♠❜❡r ♦❢ ✉♥❝✉❧t✉r❡❞ ❛♥❞ ✉♥❞❡s❝r✐❜❡❞ ♠✐❝r♦❜❡s ❛s✲✶✼
s♦❝✐❛t❡❞ ✇✐t❤ ❛♥✐♠❛❧ ❛♥❞ ♣❧❛♥t ❤♦sts ❛♥❞ ✐♥ ♥❛t✉r❛❧ ❛♥❞ ❡♥❣✐♥❡❡r❡❞ s②st❡♠s✱✶✽
✉♥❞❡rst❛♥❞✐♥❣ t❤❡ ❢❛❝t♦rs ❞❡t❡r♠✐♥✐♥❣ ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t② str✉❝t✉r❡ ❛♥❞ ❢✉♥❝✲✶✾
t✐♦♥ ✐s ♠❛❥♦r ❝❤❛❧❧❡♥❣❡ ❢♦r ♠♦❞❡r♥ ❜✐♦❧♦❣②✳✷✵
▼❛r❦❡r ❣❡♥❡ s❡q✉❡♥❝✐♥❣ ✭❡✳❣✳ ✶✻❙ r❘◆❆ ❣❡♥❡ s❡q✉❡♥❝✐♥❣ t♦ ❛ss❡ss ❜❛❝t❡r✐❛❧ ❛♥❞✷✶
❛r❝❤❛❡❛❧ ❞✐✈❡rs✐t② ❛♥❞ ✶✽❙ ♠❛r❦❡rs ❢♦r ❊✉❦❛r②♦t✐❝ ❞✐✈❡rs✐t②✮ ✐s ♥♦✇ ♦♥❡ ♦❢ t❤❡✷✷
♠♦st ❝♦♠♠♦♥❧② ✉s❡❞ ❛♣♣r♦❛❝❤❡s ❢♦r ❞❡s❝r✐❜✐♥❣ ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t✐❡s✱ q✉❛♥t✐✲✷✸
❢②✐♥❣ t❤❡ r❡❧❛t✐✈❡ ❛❜✉♥❞❛♥❝❡s ♦❢ ✐♥❞✐✈✐❞✉❛❧ ♠✐❝r♦❜✐❛❧ t❛①❛✱ ❛♥❞ ❝❤❛r❛❝t❡r✐③✐♥❣✷✹
❤♦✇ ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t✐❡s ❝❤❛♥❣❡ ❛❝r♦ss s♣❛❝❡✱ t✐♠❡✱ ♦r ✐♥ r❡s♣♦♥s❡ t♦ ❦♥♦✇♥✷✺
❜✐♦t✐❝ ♦r ❛❜✐♦t✐❝ ❣r❛❞✐❡♥ts✳✷✻
❆♥❛❧②③✐♥❣ t❤❡s❡ ❞❛t❛ ✐s ❝❤❛❧❧❡♥❣✐♥❣ ❞✉❡ t♦ t❤❡ ♣❡❝✉❧✐❛r ♥♦✐s❡ str✉❝t✉r❡ ♦❢ s❡q✉❡♥❝❡✲✷✼
❝♦✉♥t ❞❛t❛ ❬✸✽❪✱ t❤❡ ✐♥❤❡r❡♥t❧② ❝♦♠♣♦s✐t✐♦♥❛❧ ♥❛t✉r❡ ♦❢ t❤❡ ❞❛t❛ ❬✶✻❪✱ ❞❡❝✐❞✐♥❣✷✽
t❤❡ t❛①♦♥♦♠✐❝ s❝❛❧❡ ♦❢ ✐♥✈❡st✐❣❛t✐♦♥ ❬✼✱ ✽✱ ✸✾❪✱ ❛♥❞ t❤❡ ❤✐❣❤✲❞✐♠❡♥s✐♦♥❛❧✐t② ♦❢✷✾
s♣❡❝✐❡s✲r✐❝❤ ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t✐❡s ❬✶✹❪✳ ❚❤❡r❡ ✐s ❛ ❣r❡❛t ♥❡❡❞ ❛♥❞ ♦♣♣♦rt✉♥✐t②✸✵
t♦ ❞❡✈❡❧♦♣ t♦♦❧s t♦ ♠♦r❡ ❡✣❝✐❡♥t❧② ❛♥❛❧②③❡ t❤❡s❡ ❞❛t❛s❡ts ❛♥❞ ❧❡✈❡r❛❣❡ ✐♥❢♦r✲✸✶
♠❛t✐♦♥ ♦♥ t❤❡ ♣❤②❧♦❣❡♥❡t✐❝ r❡❧❛t✐♦♥s❤✐♣s ❛♠♦♥❣ t❛①❛ t♦ ❜❡tt❡r ✐❞❡♥t✐❢② ✇❤✐❝❤✸✷
✸
❝❧❛❞❡s ❛r❡ ❞r✐✈✐♥❣ ❞✐✛❡r❡♥❝❡s ✐♥ ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t② ❝♦♠♣♦s✐t✐♦♥ ❛❝r♦ss s❛♠♣❧❡✸✸
❝❛t❡❣♦r✐❡s ♦r ♠❡❛s✉r❡❞ ❜✐♦t✐❝ ♦r ❛❜✐♦t✐❝ ❣r❛❞✐❡♥ts ❬✸✵❪✳✸✹
▼❛♥② ♦❢ t❤❡s❡ ❝❤❛❧❧❡♥❣❡s ❝❛♥ ❜❡ r❡s♦❧✈❡❞ ❜② ♣❡r❢♦r♠✐♥❣ r❡❣r❡ss✐♦♥ ♦♥ ❝❧❛❞❡s✸✺
✐❞❡♥t✐✜❡❞ ✐♥ t❤❡ ♣❤②❧♦❣❡♥②✳ ■♥ t❤✐s ♣❛♣❡r✱ ✇❡ t❛❦❡ ♦♥ t❤❡s❡ ❝❤❛❧❧❡♥❣❡s ❜② ❞❡✲✸✻
✈❡❧♦♣✐♥❣ ❛ ♠❡❛♥s t♦ ♣❡r❢♦r♠ r❡❣r❡ss✐♦♥ ♦❢ ❜✐♦t✐❝✴❛❜✐♦t✐❝ ❣r❛❞✐❡♥ts ♦♥ ✈❛r✐❛❜❧❡s✸✼
❝♦rr❡s♣♦♥❞✐♥❣ t♦ ❜r❛♥❝❤❡s ✐♥ t❤❡ ♣❤②❧♦❣❡♥❡t✐❝ tr❡❡✱ t❤❡r❡❜② ❛❧❧♦✇✐♥❣ ❞✐♠❡♥s✐♦♥✲✸✽
❛❧✐t② r❡❞✉❝t✐♦♥ ✇✐t❤ ❛ ❝❧❡❛r ♣❤②❧♦❣❡♥❡t✐❝ ✐♥t❡r♣r❡t❛t✐♦♥ ❛♥❞ ❝♦♥s✐st❡♥t ✇✐t❤ t❤❡✸✾
❝♦♠♣♦s✐t✐♦♥❛❧ ♥❛t✉r❡ ♦❢ t❤❡ ❞❛t❛✳✹✵
❈♦♥s✐❞❡r ❛ st✉❞② ♦♥ t❤❡ ❡✛❡❝t ♦❢ ♦①❛③♦❧✐❞✐♥♦♥❡s✱ ✇❤✐❝❤ ❛✛❡❝t ❣r❛♠✲♣♦s✐t✐✈❡ ❜❛❝✲✹✶
t❡r✐❛✱ ♦♥ ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t② ❝♦♠♣♦s✐t✐♦♥✳ ❘❛t❤❡r t❤❛♥ r❡❣r❡ss✐♦♥ ♦❢ ❛♥t✐❜✐♦t✐❝✹✷
tr❡❛t♠❡♥t ♦♥ ❛❜✉♥❞❛♥❝❡ ❛t ♥✉♠❡r♦✉s t❛①♦♥♦♠✐❝ ❧❡✈❡❧s✱ st❛t✐st✐❝❛❧ ❛♥❛❧②s✐s ♦❢✹✸
❜❛❝t❡r✐❛❧ ❝♦♠♠✉♥✐t✐❡s tr❡❛t❡❞ ✇✐t❤ ❛♥ ♦①❛③♦❧✐❞✐♥♦♥❡ s❤♦✉❧❞ ✐♥st❛♥t❧② ✐❞❡♥t✐❢②✹✹
t❤❡ s♣❧✐t ❜❡t✇❡❡♥ ❣r❛♠✲♣♦s✐t✐✈❡ ❛♥❞ ❣r❛♠✲♥❡❣❛t✐✈❡ ❜❛❝t❡r✐❛ ❛s t❤❡ ♠♦st ✐♠♣♦r✲✹✺
t❛♥t ♣❤②❧♦❣❡♥❡t✐❝ ❢❛❝t♦r ❞❡t❡r♠✐♥✐♥❣ r❡s♣♦♥s❡ t♦ ♦①❛③♦❧✐❞✐♥♦♥❡s✳ ❙✉❜s❡q✉❡♥t✹✻
❢❛❝t♦rs s❤♦✉❧❞ t❤❡♥ ❜❡ ✐❞❡♥t✐✜❡❞ ❜② ❝♦♠♣❛r✐♥❣ ❜❛❝t❡r✐❛ ✇✐t❤✐♥ t❤❡ ♣r❡✈✐♦✉s❧②✲✹✼
✐❞❡♥t✐✜❡❞ ❣r♦✉♣s✿ ✐❞❡♥t✐❢② ❝❧❛❞❡s ✇✐t❤✐♥ ❣r❛♠✲♣♦s✐t✐✈❡s ✇❤✐❝❤ ♠❛② ❜❡ ♠♦r❡✹✽
r❡s✐st❛♥t ♦r s✉s❝❡♣t✐❜❧❡ t❤❛♥ t❤❡ r❡♠❛✐♥✐♥❣ ❣r❛♠✲♣♦s✐t✐✈❡s✳ ❙♣❧✐tt✐♥❣ t❤❡ ♣❤②✲✹✾
❧♦❣❡♥② ❛t ❡❛❝❤ ✐♥❢❡r❡♥❝❡ ❛♥❞ ♠❛❦✐♥❣ ❝♦♠♣❛r✐s♦♥s ✇✐t❤✐♥ t❤❡ s♣❧✐t ❣r♦✉♣s ❡♥s✉r❡s✺✵
t❤❛t s✉❜s❡q✉❡♥t ✐♥❢❡r❡♥❝❡s ❛r❡ ✐♥❞❡♣❡♥❞❡♥t ♦❢ t❤❡ ❣r❛♠ ♣♦s✐t✐✈❡ ✲ ❣r❛♠ ♥❡❣❛✲✺✶
t✐✈❡ s♣❧✐t ✇❤✐❝❤ ✇❡ ❤❛✈❡ ❛❧r❡❛❞② ♦❜t❛✐♥❡❞✳ ❆❧❧ ♦❢ t❤✐s ❛♥❛❧②s✐s ♠✉st ❜❡ ❞♦♥❡✺✷
❝♦♥s✐st❡♥t ✇✐t❤ t❤❡ ❝♦♠♣♦s✐t✐♦♥❛❧ ♥❛t✉r❡ ♦❢ s❡q✉❡♥❝❡ ❝♦✉♥t ❞❛t❛✳✺✸
❍❡r❡✱ ✇❡ ♣r♦✈✐❞❡ ❛ ♠❡t❤♦❞ t♦ ❛♥❛❧②③❡ ♣❤②❧♦❣❡♥❡t✐❝❛❧❧②✲str✉❝t✉r❡❞ ❝♦♠♣♦s✐t✐♦♥❛❧✺✹
❞❛t❛✳ ❚❤❡ ❛❧❣♦r✐t❤♠✱ r❡❢❡rr❡❞ t♦ ❛s ✏♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✑✱ ✐t❡r❛t✐✈❡❧② ✐❞❡♥t✐✜❡s✺✺
t❤❡ ♠♦st ✐♠♣♦rt❛♥t ❝❧❛❞❡s ❞r✐✈✐♥❣ ✈❛r✐❛t✐♦♥ ✐♥ t❤❡ ❞❛t❛ t❤r♦✉❣❤ t❤❡✐r ❛ss♦❝✐❛✲✺✻
t✐♦♥s ✇✐t❤ ✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡s✳ ❈❧❛❞❡s ❛r❡ ❝❤♦s❡♥ ❜❛s❡❞ ♦♥ s♦♠❡ ♠❡tr✐❝ ♦❢✺✼
t❤❡ str❡♥❣t❤ ♦r ✐♠♣♦rt❛♥❝❡ ♦❢ t❤❡✐r r❡❣r❡ss✐♦♥s ✇✐t❤ ♠❡t❛✲❞❛t❛✱ ❛♥❞ s✉❜s❡q✉❡♥t✺✽
❝❧❛❞❡s ❛r❡ ❝❤♦s❡♥ ❜② ❝♦♠♣❛r✐s♦♥ ♦❢ s✉❜✲❝❧❛❞❡s ✇✐t❤✐♥ t❤❡ ♣r❡✈✐♦✉s❧②✲✐❞❡♥t✐✜❡❞✺✾
❜✐♥s ♦❢ ♣❤②❧♦❣❡♥❡t✐❝ ❣r♦✉♣s✳ ❊❛❝❤ ✏❢❛❝t♦r✑ ✐❞❡♥t✐✜❡❞ ❝♦rr❡s♣♦♥❞s t♦ ❛♥ ❡❞❣❡ ✐♥✻✵
t❤❡ ♣❤②❧♦❣❡♥②✱ ❛♥❞ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❜✉✐❧❞s ♦♥ ❧✐t❡r❛t✉r❡ ❢r♦♠ ❝♦♠♣♦s✐t✐♦♥❛❧✻✶
❞❛t❛ ❛♥❛❧②s✐s t♦ ❝♦♥str✉❝t ❛ s❡t ♦❢ ♦rt❤♦❣♦♥❛❧ ❛①❡s ❝♦rr❡s♣♦♥❞✐♥❣ t♦ t❤♦s❡ ❡❞❣❡s❀✻✷
t❤❡ ♦✉t♣✉t ♦rt❤♦♥♦r♠❛❧ ❜❛s✐s ❛❧❧♦✇s t❤❡ ♣r♦❥❡❝t✐♦♥ ♦❢ s❡q✉❡♥❝❡✲❝♦✉♥t r❡❧❛t✐✈❡✻✸
❛❜✉♥❞❛♥❝❡s ♦♥t♦ t❤❡s❡ ♣❤②❧♦❣❡♥❡t✐❝ ❛①❡s ❢♦r ❞✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥✱ ✈✐s✉❛❧✲✻✹
✐③❛t✐♦♥✱ ❛♥❞ st❛♥❞❛r❞ ♠✉❧t✐✈❛r✐❛t❡ st❛t✐st✐❝❛❧ ❛♥❛❧②s❡s✳ ❚❤❡ ✈✐s✉❛❧✐③❛t✐♦♥s ❛♥❞✻✺
✐♥❢❡r❡♥❝❡s ❞r❛✇♥ ❢r♦♠ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❝❛♥ ❜❡ t✐❡❞ ❜❛❝❦ t♦ s♣❧✐ts ✐♥ ❛ ❣✐✈❡♥✻✻
♣❤②❧♦❣❡♥❡t✐❝ tr❡❡ ❛♥❞ t❤❡r❡❜② ❛❧❧♦✇ r❡s❡❛r❝❤❡rs t♦ ❛♥♥♦t❛t❡ t❤❡ ♠✐❝r♦❜✐❛❧ ♣❤②✲✻✼
❧♦❣❡♥② ❢r♦♠ t❤❡ r❡s✉❧ts ♦❢ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡ts✳✻✽
✹
❲❡ s❤♦✇ ✇✐t❤ s✐♠✉❧❛t✐♦♥s t❤❛t ♣❤②❧♦❢❛❝t♦r ✐s ❛❜❧❡ t♦ ❝♦rr❡❝t❧② ✐❞❡♥t✐❢② ❛✛❡❝t❡❞✻✾
❝❧❛❞❡s✳ ❲❡ t❤❡♥ ♣❤②❧♦❢❛❝t♦r ❛ ❞❛t❛s❡t ♦❢ ❤✉♠❛♥ ♦r❛❧ ❛♥❞ ❢❡❝❛❧ ♠✐❝r♦❜✐♦♠❡s t♦✼✵
❞❡t❡r♠✐♥❡ t❤❡ ♣❤②❧♦❣❡♥❡t✐❝ ❢❛❝t♦rs ❞r✐✈✐♥❣ ✈❛r✐❛t✐♦♥ ✐♥ ❤✉♠❛♥ ❜♦❞② s✐t❡ ❬✹❪✱ ❛♥❞✼✶
❛ ❞❛t❛s❡t ♦❢ s♦✐❧ ♠✐❝r♦❜❡s ✉s✐♥❣ ❛ ♠✉❧t✐♣❧❡ r❡❣r❡ss✐♦♥ ♦❢ ♣❍✱ ❝❛r❜♦♥ ❝♦♥❝❡♥tr❛✲✼✷
t✐♦♥ ❛♥❞ ♥✐tr♦❣❡♥ ❝♦♥❝❡♥tr❛t✐♦♥ ❬✸✻❪✳ ■♥ t❤❡ ❤✉♠❛♥ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡t✱ ✇❡ ✜♥❞✼✸
t❤r❡❡ s♣❧✐ts ✐♥ t❤❡ ♣❤②❧♦❣❡♥② t❤❛t t♦❣❡t❤❡r ❝❛♣t✉r❡ ✶✼✳✻✪ ♦❢ t❤❡ ✈❛r✐❛t✐♦♥ ❝♦♠✲✼✹
♠✉♥✐t② ❝♦♠♣♦s✐t✐♦♥ ❛❝r♦ss t✇♦ ❜♦❞② s✐t❡s✳ ❲❡ ✉s❡ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ t♦ ✜♥❞✼✺
t❤❛t t❤❡ ❞♦♠✐♥❛♥t ❢❡❛t✉r❡s ❞r✐✈✐♥❣ ❜♦❞②✲s✐t❡ ✈❛r✐❛t✐♦♥ ❛r❡ ✐♥✈✐s✐❜❧❡ t♦ t❛①♦♥♦♠②✲✼✻
❜❛s❡❞ ❛♥❛❧②s❡s✱ ✐♥❝❧✉❞✐♥❣ s♣❧✐ts ❜❡t✇❡❡♥ ✉♥❝❧❛ss✐✜❡❞ ❖❚❯s✱ ♠♦♥♦♣❤②❧❡t✐❝ ❝❧❛❞❡s✼✼
t❤❛t s♣❛♥ s❡✈❡r❛❧ t❛①♦♥♦♠✐❝ ❣r♦✉♣s✱ ❛♥❞ ❛ s♣❡❝tr✉♠ ♦❢ ♣❤②❧♦❣❡♥❡t✐❝ s❝❛❧❡s ❢♦r✼✽
❜✐♥♥✐♥❣ ❖❚❯s ❜❛s❡❞ ♦♥ ❤❛❜✐t❛t ♣r❡❢❡r❡♥❝❡s✳ ■♥ t❤❡ s♦✐❧ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡t✱ ✇❡✼✾
✉s❡ ♣❤②❧♦❢❛❝t♦r✲❜❛s❡❞ ❞✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥ t♦ ✈✐s✉❛❧✐③❡ ❛♥❞ q✉❛♥t✐t❛t✐✈❡❧②✽✵
❝♦♥✜r♠ t❤❛t ♣❍ ❞r✐✈❡s ♠♦st ♦❢ t❤❡ ✈❛r✐❛t✐♦♥ ✐♥ t❤❡ s♦✐❧ ❞❛t❛s❡t ❜✉t ✇❡ ❡♠♣❤❛✲✽✶
s✐③❡ t❤❛t t❤❡ ❛①❡s ❢r♦♠ ♣❤②❧♦❢❛❝t♦r ♦r❞✐♥❛t✐♦♥✲✈✐s✉❛❧✐③❛t✐♦♥ ♣❧♦ts ❝♦rr❡s♣♦♥❞ t♦✽✷
✐❞❡♥t✐✜❛❜❧❡ ❡❞❣❡s ♦♥ t❤❡ ♣❤②❧♦❣❡♥② t❤❛t ❤❛✈❡ ❝❧❡❛r ❜✐♦❧♦❣✐❝❛❧ ✐♥t❡r♣r❡t❛t✐♦♥s✽✸
❛♥❞ ❝❛♥ ❜❡ ✉s❡❞ ❛♥❞ t❡st❡❞ ❛❝r♦ss st✉❞✐❡s✳ ❯s❡r✲❢r✐❡♥❞❧② ❝♦❞❡ ❢♦r ✐♠♣❧❡♠❡♥t✐♥❣✱✽✹
s✉♠♠❛r✐③✐♥❣ ❛♥❞ ✈✐s✉❛❧✐③✐♥❣ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✐s ♣r♦✈✐❞❡❞ ✐♥ ❛♥ ❘ ♣❛❝❦❛❣❡ ✲✽✺
✬♣❤②❧♦❢❛❝t♦r✬ ❛♥❞ ❛ t✉t♦r✐❛❧ ✐s ❛✈❛✐❧❛❜❧❡ ♦♥❧✐♥❡✳✽✻
▼❛t❡r✐❛❧s ✫ ▼❡t❤♦❞s✽✼
P❤②❧♦❣❡♥❡t✐❝❛❧❧②✲str✉❝t✉r❡❞ ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛✽✽
▼✐❝r♦❜✐♦♠❡ ❞❛t❛s❡ts ❛r❡ ✏♣❤②❧♦❣❡♥❡t✐❝❛❧❧②✲str✉❝t✉r❡❞ ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛✑✱ ❝♦♠✲✽✾
♣♦s✐t✐♦♥s ♦❢ ♣❛rts ❧✐♥❦❡❞ t♦❣❡t❤❡r ❜② ❛ ♣❤②❧♦❣❡♥② ❢♦r ✇❤✐❝❤ ♦♥❧② ✐♥❢❡r❡♥❝❡s ♦♥✾✵
r❡❧❛t✐✈❡ ❛❜✉♥❞❛♥❝❡s ❝❛♥ ❜❡ ❞r❛✇♥✳ ❚❤❡ ♣❤②❧♦❣❡♥② ✐s t❤❡ s❝❛✛♦❧❞✐♥❣ ❢♦r t❤❡✾✶
❡✈♦❧✉t✐♦♥ ♦❢ ✈❡rt✐❝❛❧❧②✲tr❛♥s♠✐tt❡❞ tr❛✐ts✱ ❛♥❞ ✈❡rt✐❝❛❧❧②✲tr❛♥s♠✐tt❡❞ tr❛✐ts ♠❛②✾✷
✉♥❞❡r❧✐❡ ❛♥ ♦r❣❛♥✐s♠✬s ❢✉♥❝t✐♦♥❛❧ ❡❝♦❧♦❣② ❛♥❞ r❡s♣♦♥s❡ t♦ ♣❡rt✉r❜❛t✐♦♥s ♦r ❡♥✈✐✲✾✸
r♦♥♠❡♥t❛❧ ❣r❛❞✐❡♥ts✳ P❡r❢♦r♠✐♥❣ ✐♥❢❡r❡♥❝❡ ♦♥ t❤❡ ❡❞❣❡s ✐♥ ❛ ♣❤②❧♦❣❡♥② ❞r✐✈✐♥❣✾✹
✈❛r✐❛t✐♦♥ ✐♥ t❤❡ ❞❛t❛ ❝❛♥ ❜❡ ✉s❡❢✉❧ ❢♦r ✐❞❡♥t✐❢②✐♥❣ ❝❧❛❞❡s ✇✐t❤ ♣✉t❛t✐✈❡ tr❛✐ts✾✺
❝❛✉s✐♥❣ r❡❧❛t❡❞ t❛①❛ t♦ r❡s♣♦♥❞ s✐♠✐❧❛r❧② t♦ tr❡❛t♠❡♥ts✱ ❜✉t s✉❝❤ ✐♥❢❡r❡♥❝❡s✾✻
♠✉st ❛❝❝♦✉♥t ❢♦r t❤❡ ❝♦♠♣♦s✐t✐♦♥❛❧ ♥❛t✉r❡ ♦❢ t❤❡ s❡q✉❡♥❝❡✲❝♦✉♥t ❞❛t❛✳✾✼
❆ st❛♥❞❛r❞ ❛♥❛❧②s✐s ♦❢ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡ts ✉s❡s ♦♥❧② t❤❡ ❞✐st❛❧ ❡❞❣❡s ♦❢ t❤❡ tr❡❡✾✽
✲ t❤❡ ❖❚❯s ✲ ❛♥❞ ❛ ❢❡✇ ❡❞❣❡s ✇✐t❤✐♥ t❤❡ tr❡❡ s❡♣❛r❛t✐♥❣ ▲✐♥♥❛❡❛♥ t❛①♦♥♦♠✐❝✾✾
❣r♦✉♣s✳ ❍♦✇❡✈❡r✱ ❛ ♣❤②❧♦❣❡♥② ♦❢ D t❛①❛ ❛♥❞ ♥♦ ♣♦❧②t♦♠✐❡s ✐s ❝♦♠♣♦s❡❞ ♦❢✶✵✵
✺
2D − 3 ❡❞❣❡s✱ ❡❛❝❤ ❝♦♥♥❡❝t✐♥❣ t✇♦ ❞✐s❥♦✐♥t s❡ts ♦❢ t❛①❛ ✐♥ t❤❡ tr❡❡ ✇✐t❤ ♥♦✶✵✶
❣✉❛r❛♥t❡❡ t❤❛t s♣❧✐ts ✐♥ ▲✐♥♥❛❡❛♥ t❛①♦♥♦♠② ❝♦rr❡s♣♦♥❞s t♦ ♣❤②❧♦❣❡♥❡t✐❝ s♣❧✐ts✶✵✷
❞r✐✈✐♥❣ ✈❛r✐❛t✐♦♥ ✐♥ ♦✉r ❞❛t❛s❡t✳ ❚❤✉s✱ ✐♥st❡❛❞ ♦❢ ❛♥❛❧②③✐♥❣ ❥✉st t❤❡ t✐♣s ❛♥❞ ❛✶✵✸
s❡r✐❡s ♦❢ ▲✐♥♥❛❡❛♥ s♣❧✐ts ✐♥ t❤❡ tr❡❡✱ ❛ ♠♦r❡ r♦❜✉st ❛♥❛❧②s✐s ♦❢ ♣❤②❧♦❣❡♥❡t✐❝❛❧❧②✲✶✵✹
str✉❝t✉r❡❞ ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛ s❤♦✉❧❞ ❛♥❛❧②③❡ ❛❧❧ ♦❢ t❤❡ ❡❞❣❡s ✐♥ t❤❡ tr❡❡✳ ❚♦✶✵✺
❞♦ t❤❛t✱ ✇❡ ❞r❛✇ ♦♥ t❤❡ ✐s♦♠❡tr✐❝ ❧♦❣✲r❛t✐♦ tr❛♥s❢♦r♠ ❢r♦♠ ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛✶✵✻
❛♥❛❧②s✐s✱ ✇❤✐❝❤ ❤❛s ❜❡❡♥ ✉s❡❞ t♦ s❡❛r❝❤ ❢♦r ❛ t❛①♦♥♦♠✐❝ s✐❣♥❛t✉r❡ ♦❢ ♦❜❡s✐t②✶✵✼
✐♥ t❤❡ ❤✉♠❛♥ ❣✉t ✢♦r❛ ❬✶✺❪ ❛♥❞ ✐♥❝♦r♣♦r❛t❡❞ ✐♥t♦ ♣❛❝❦❛❣❡s ❢♦r ❞♦✇♥str❡❛♠✶✵✽
♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥ts ❛♥❛❧②s✐s ❬✷✹❪✳ ❍♦✇❡✈❡r✱ t♦ t❤❡ ❜❡st ♦❢ ♦✉r ❦♥♦✇❧❡❞❣❡✱✶✵✾
t❤❡ ♣r❡✈✐♦✉s ❧✐t❡r❛t✉r❡ ✉s✐♥❣ t❤❡ ✐s♦♠❡tr✐❝ ❧♦❣✲r❛t✐♦ tr❛♥s❢♦r♠ ✐♥ ♠✐❝r♦❜✐♦♠❡✶✶✵
❞❛t❛s❡ts ❤❛s ✉s❡❞ r❛♥❞♦♠ ♦r st❛♥❞❛r❞ s❡q✉❡♥t✐❛❧ ❜✐♥❛r② ♣❛rt✐t✐♦♥s✱ ❛♥❞ ♥♦t✶✶✶
❡①♣❧✐❝✐t❧② ✐♥❝♦r♣♦r❛t❡❞ t❤❡ ♣❤②❧♦❣❡♥② ❛s t❤❡✐r s❡q✉❡♥t✐❛❧ ❜✐♥❛r② ♣❛rt✐t✐♦♥✳✶✶✷
❚❤❡ ■s♦♠❡tr✐❝ ▲♦❣✲❘❛t✐♦ ❚r❛♥s❢♦r♠ ♦❢ ❛ r♦♦t❡❞ ♣❤②❧♦❣❡♥②✶✶✸
❚❤❡ ✐s♦♠❡tr✐❝ ❧♦❣✲r❛t✐♦ ✭■▲❘✮ tr❛♥s❢♦r♠ ✇❛s ❞❡✈❡❧♦♣❡❞ ❛s ❛ ✇❛② t♦ tr❛♥s❢♦r♠✶✶✹
❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛ ❢r♦♠ t❤❡ s✐♠♣❧❡① ✐♥t♦ r❡❛❧ s♣❛❝❡ ✇❤❡r❡ st❛♥❞❛r❞ st❛t✐st✐❝❛❧✶✶✺
t♦♦❧s ❝❛♥ ❜❡ ❛♣♣❧✐❡❞ ❬✶✶✱ ✶✵❪✳ ❆ s❡q✉❡♥t✐❛❧ ❜✐♥❛r② ♣❛rt✐t✐♦♥ ✐s ✉s❡❞ t♦ ❝♦♥str✉❝t ❛✶✶✻
♥❡✇ s❡t ♦❢ ❝♦♦r❞✐♥❛t❡s✱ ❛♥❞ t❤❡ ♣❤②❧♦❣❡♥② ✐s ❛ ♥❛t✉r❛❧ ❝❤♦✐❝❡ ❢♦r t❤❡ s❡q✉❡♥t✐❛❧✶✶✼
❜✐♥❛r② ♣❛rt✐t✐♦♥ ✐♥ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡ts✳ ■♥st❡❛❞ ♦❢ ❛♥❛❧②③✐♥❣ r❡❧❛t✐✈❡ ❛❜✉♥✲✶✶✽
❞❛♥❝❡s✱ yi✱ ♦❢ D ❞✐✛❡r❡♥t ❖❚❯s✱ t❤❡ ■▲❘ tr❛♥s❢♦r♠ ♣r♦❞✉❝❡s D−1 ❝♦♦r❞✐♥❛t❡s✱✶✶✾
x∗i ✭❝❛❧❧❡❞ ✏❜❛❧❛♥❝❡s✑✮✳ ❊❛❝❤ ❜❛❧❛♥❝❡ ❝♦rr❡s♣♦♥❞s t♦ ❛ s✐♥❣❧❡ ✐♥t❡r♥❛❧ ♥♦❞❡ ♦❢ t❤❡✶✷✵
tr❡❡ ❛♥❞ r❡♣r❡s❡♥ts t❤❡ ❛✈❡r❛❣❡❞ ❞✐✛❡r❡♥❝❡ ✐♥ r❡❧❛t✐✈❡ ❛❜✉♥❞❛♥❝❡ ❜❡t✇❡❡♥ t❤❡✶✷✶
t❛①❛ ✐♥ t❤❡ t✇♦ s✐st❡r ❝❧❛❞❡s ❞❡s❝❡♥❞✐♥❣ ❢r♦♠ t❤❛t ♥♦❞❡ ✭t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡✐♥❣✶✷✷
❛♣♣r♦♣r✐❛t❡❧② ♠❡❛s✉r❡❞ ❛s ❛ ❧♦❣✲r❛t✐♦ ❞✉❡ t♦ t❤❡ ❝♦♠♣♦s✐t✐♦♥❛❧ ♥❛t✉r❡ ♦❢ t❤❡✶✷✸
❞❛t❛❀ s❡❡ ❙■ ❢♦r ♠♦r❡ ❞❡t❛✐❧❡❞ ❞❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ■▲❘ tr❛♥s❢♦r♠✮✳ ❋♦r ❛♥ ❛r❜✐✲✶✷✹
tr❛r② ♥♦❞❡ ✐♥❞✐❝❛t✐♥❣ t❤❡ s♣❧✐t ♦❢ ❛ ❣r♦✉♣✱ R ✇✐t❤ r ❡❧❡♠❡♥ts ❢r♦♠ t❤❡ ❣r♦✉♣✱ S✶✷✺
✇✐t❤ s ❡❧❡♠❡♥ts✱ t❤❡ ■▲❘ ❜❛❧❛♥❝❡ ❝❛♥ ❜❡ ✇r✐tt❡♥ ❛s✶✷✻
x∗{R,S} =
√
rs
r + slog
(
g(yR)
g(yS)
)
✭✶✮
✇❤❡r❡ g(yR) ✐s t❤❡ ❣❡♦♠❡tr✐❝ ♠❡❛♥ ♦❢ ❛❧❧ yi ❢♦r i ∈ R✳✶✷✼
❲❡ r❡❢❡r t♦ t❤❡ ■▲❘ tr❛♥s❢♦r♠ ❝♦rr❡s♣♦♥❞✐♥❣ t♦ ❛ r♦♦t❡❞ ♣❤②❧♦❣❡♥② ❛s t❤❡✶✷✽
✏r♦♦t❡❞ ■▲❘✑✳ ❚❤❡ r♦♦t❡❞ ■▲❘ ❝r❡❛t❡s ❛ s❡t ♦❢ ■▲❘ ❝♦♦r❞✐♥❛t❡s✱ {x∗i }✱ ✇❤❡r❡✶✷✾
❡❛❝❤ ❝♦♦r❞✐♥❛t❡ ❝♦rr❡s♣♦♥❞s t♦ t❤❡ ✏❜❛❧❛♥❝❡✑ ❜❡t✇❡❡♥ s✐st❡r ❝❧❛❞❡s ❛t ❡❛❝❤ s♣❧✐t✶✸✵
✐♥ t❤❡ ♣❤②❧♦❣❡♥❡t✐❝ tr❡❡✳ ❚❤❡ ❜❛❧❛♥❝❡s ✐♥ ❛ r♦♦t❡❞ ■▲❘ tr❛♥s❢♦r♠ ✐♥ ❡q✉❛t✐♦♥ ✭✶✮✶✸✶
❝❛♥ ❜❡ ✐♥t✉✐t❡❞ ❛s t❤❡ ❛✈❡r❛❣❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❛①❛ ✐♥ t✇♦ ❣r♦✉♣s✱ ❛♥❞ s♣❧✐ts✶✸✷
✻
✐♥ t❤❡ tr❡❡ ✇❤✐❝❤ ♠❡❛♥✐♥❣❢✉❧❧② ❞✐✛❡r❡♥t✐❛t❡ t❛①❛ ✇✐❧❧ ❜❡ t❤♦s❡ s♣❧✐ts ✐♥ ✇❤✐❝❤✶✸✸
t❤❡ ❛✈❡r❛❣❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❛①❛ ✐♥ t✇♦ ❣r♦✉♣s ❝❤❛♥❣❡s ♣r❡❞✐❝t❛❜❧② ✇✐t❤ ❛♥✶✸✹
✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡✳ ■♥❢❡r❡♥❝❡s ♦♥ ■▲❘ ❝♦♦r❞✐♥❛t❡s✱ t❤❡♥✱ ♠❛♣ t♦ ✐♥❢❡r❡♥❝❡s✶✸✺
♦♥ ❧✐♥❡❛❣❡s ✐♥ t❤❡ ♣❤②❧♦❣❡♥❡t✐❝ tr❡❡✳✶✸✻
❚❤❡ r♦♦t❡❞ ■▲❘ ❝♦♦r❞✐♥❛t❡s ♣r♦✈✐❞❡ ❛ ♥❛t✉r❛❧ ✇❛② t♦ ❛♥❛❧②③❡ ♠✐❝r♦❜✐♦t❛ ❞❛t❛✶✸✼
❛s t❤❡② ♠❡❛s✉r❡ t❤❡ ❞✐✛❡r❡♥❝❡ ✐♥ t❤❡ r❡❧❛t✐✈❡ ❛❜✉♥❞❛♥❝❡s ♦❢ s✐st❡r ❝❧❛❞❡s ❛♥❞✶✸✽
♠❛② ❜❡ ✉s❡❢✉❧ ✐♥ ✐❞❡♥t✐❢②✐♥❣ ❡✛❡❝ts ❝♦♥t❛✐♥❡❞ ✇✐t❤✐♥ ❝❧❛❞❡s s✉❝❤ ❛s ③❡r♦✲s✉♠✶✸✾
❝♦♠♣❡t✐t✐♦♥ ♦❢ ❝❧♦s❡ r❡❧❛t✐✈❡s ♦r t❤❡ s✉❜st✐t✉t✐♦♥ ♦❢ ♦♥❡ r❡❧❛t✐✈❡ ❢♦r ❛♥♦t❤❡r✶✹✵
❛❝r♦ss ❡♥✈✐r♦♥♠❡♥ts✳ ❍♦✇❡✈❡r✱ ✐❢ ✇❡ ❞❡s✐r❡ t♦ ❧✐♥❦ t❤❡ ❡✛❡❝t ♦❢ ❛ ❞❡s✐❣♥ ✈❛r✐❛❜❧❡✶✹✶
♦r ❛♥ ❡①t❡r♥❛❧ ❝♦✈❛r✐❛t❡ ✭❡✳❣✳ ❛♥t✐❜✐♦t✐❝s ✈s✳ ♥♦ ❛♥t✐❜✐♦t✐❝ tr❡❛t♠❡♥t✮ t♦ ❝❧❛❞❡s✶✹✷
✇✐t❤✐♥ t❤❡ ♣❤②❧♦❣❡♥②✱ t❤❡ ❜❡st ❝♦♠♣❛r✐s♦♥ ♠❛② ♥♦t ❜❡ ❜❡t✇❡❡♥ s✐st❡r ❝❧❛❞❡s✱ ❜✉t✶✹✸
✐♥st❡❛❞ ❜❡t✇❡❡♥ ❛❧❧ ♦t❤❡r ❝❧❛❞❡s✱ ❝♦♥tr♦❧❧✐♥❣ ❢♦r ❛♥② ♦t❤❡r ♣❤②❧♦❣❡♥❡t✐❝ s♣❧✐ts ♦r✶✹✹
❢❛❝t♦rs ✇❡ ♠❛② ❦♥♦✇ ♦❢ ✭❡✳❣✳ ✇❡ ♠❛② ❝♦♠♣❛r❡ ❛ ❧✐♥❡❛❣❡ ✇✐t❤✐♥ ❣r❛♠✲♣♦s✐t✐✈❡s✶✹✺
✇✐t❤ ❛❧❧ ♦t❤❡r ❣r❛♠✲♣♦s✐t✐✈❡s✱ ♦♥❝❡ ✇❡✬✈❡ ✐❞❡♥t✐✜❡❞ t❤❡ ❣r❛♠✲♣♦s✐t✐✈❡ ✈s✳ ❣r❛♠✲✶✹✻
♥❡❣❛t✐✈❡ s♣❧✐t ❛s ❛♥ ✐♠♣♦rt❛♥t ❢❛❝t♦r ❢♦r ❛♥t✐❜✐♦t✐❝ s✉s❝❡♣t✐❜✐❧✐t②✮✳ ❲❡ r❡❢❡r t♦✶✹✼
t❤✐s ✉♥r♦♦t❡❞ ❛♣♣r♦❛❝❤ ❛s ✬♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✬✳✶✹✽
❋♦r t❤❡ t❛s❦ ♦❢ ❧✐♥❦✐♥❣ ❛♥ ❡①t❡r♥❛❧ ❝♦✈❛r✐❛t❡ t♦ ✐♥❞✐✈✐❞✉❛❧ ❝❧❛❞❡s ✐♥ t❤❡ ♣❤②✲✶✹✾
❧♦❣❡♥②✱ ✇❡ ❡①❛♠✐♥❡ t❤r❡❡ ❢❡❛t✉r❡s ♦❢ t❤❡ r♦♦t❡❞ ■▲❘ t❤❛t ❝❛♥ ❜❡ ✐♠♣r♦✈❡❞ ♦♥✶✺✵
❜② ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❜② ❝♦♥s✐❞❡r✐♥❣ ❛ tr❡❛t♠❡♥t t❤❛t ❞❡❝r❡❛s❡s t❤❡ ❛❜✉♥❞❛♥❝❡✶✺✶
♦❢ ♦♥❡ ❛♥❞ ♦♥❧② ♦♥❡ ❝❧❛❞❡✱ B✱ ✇❤♦s❡ ❝❧♦s❡st r❡❧❛t✐✈❡ ✐s ❝❧❛❞❡ A✳ ❘❡❣r❡ss✐♦♥ ♦♥✶✺✷
t❤❡ r♦♦t❡❞ ■▲❘ ❝♦♦r❞✐♥❛t❡s ♠❛② ✐❞❡♥t✐❢② t❤❡ ❜❛❧❛♥❝❡ x∗{A,B} ❝♦rr❡s♣♦♥❞✐♥❣ t♦✶✺✸
t❤❡ ♠♦st r❡❝❡♥t ❝♦♠♠♦♥ ❛♥❝❡st♦r ♦❢ ❝❧❛❞❡s A ❛♥❞ B ❛s ❤❛✈✐♥❣ t❤❛t str♦♥❣❡st✶✺✹
r❡s♣♦♥s❡ t♦ t❤❡ tr❡❛t♠❡♥t✱ ❜✉t r❡❣r❡ss✐♦♥ ♦♥ t❤✐s ❝♦♦r❞✐♥❛t❡ ✇✐❧❧ s✉❣❣❡st t❤❛t✶✺✺
❝❧❛❞❡ B ❞❡❝r❡❛s❡s r❡❧❛t✐✈❡ t♦ A✱ ❧❡❛❞✐♥❣ t♦ str✉❝t✉r❡❞ r❡s✐❞✉❛❧s ✐♥ t❤❡ ♦r✐❣✐♥❛❧✶✺✻
❞❛t❛s❡t ❞✉❡ t♦ ❛♥ ✐♥❛❜✐❧✐t② t♦ ❛❝❝♦✉♥t ❢♦r t❤❡ ✐♥❝r❡❛s❡ ✐♥ ❝❧❛❞❡ B r❡❧❛t✐✈❡ t♦ t❤❡✶✺✼
r❡st ♦❢ t❤❡ ❖❚❯s ✐♥ t❤❡ ❞❛t❛ ✭❋✐❣✳ ✶❛✮✳ ❙❡❝♦♥❞✱ ❛❧❧ ♣❛rt✐t✐♦♥s ❜❡t✇❡❡♥ ❛✛❡❝t❡❞✶✺✽
❝❧❛❞❡ ❛♥❞ t❤❡ r♦♦t ✇✐❧❧ ❜❡ ❛✛❡❝t❡❞✳ ■❢ ❡❛❝❤ ❜❛❧❛♥❝❡ ✐s t❡st❡❞ ✐♥❞❡♣❡♥❞❡♥t❧②✱✶✺✾
t❤❡ r♦♦t❡❞ ■▲❘ ♠❛② ✐❞❡♥t✐❢② ♠❛♥② ❝❧❛❞❡s t❤❛t ❛r❡ ❛✛❡❝t❡❞ ❜② ❛♥t✐❜✐♦t✐❝s❀ t❤❡✶✻✵
❝♦rr❡❧❛t✐♦♥s ❜❡t✇❡❡♥ ❝♦♦r❞✐♥❛t❡s ❝❛♥ ②✐❡❧❞ ❛ ❤✐❣❤ ❢❛❧s❡✲♣♦s✐t✐✈❡ r❛t❡ ✐❢ ❥✉st ♦♥❡✶✻✶
❝❧❛❞❡ ✐s ❛✛❡❝t❡❞ ✭❋✐❣✳ ✶❜✮✳ ❋✐♥❛❧❧②✱ t❤❡ ■▲❘ tr❛♥s❢♦r♠❛t✐♦♥ ❞♦❡s ♥♦t ✇♦r❦ ✇✐t❤✶✻✷
♣♦❧②t♦♠✐❡s ❝♦♠♠♦♥ ✐♥ r❡❛❧✱ ✉♥r❡s♦❧✈❡❞ ♣❤②❧♦❣❡♥✐❡s✳ ❆♥② ♣♦❧②t♦♠② ✇✐❧❧ ♣r♦❞✉❝❡✶✻✸
❛ s♣❧✐t ✐♥ t❤❡ ♣❤②❧♦❣❡♥② ❜❡t✇❡❡♥ t❤r❡❡ ♦r ♠♦r❡ t❛①❛✱ ❛♥❞ t❤❡r❡ ✐s ♥♦ ❣❡♥❡r❛❧✶✻✹
✇❛② t♦ ❞❡s❝r✐❜❡ t❤❡ ❜❛❧❛♥❝❡ ♦❢ r❡❧❛t✐✈❡ ❛❜✉♥❞❛♥❝❡s ♦❢ t❤r❡❡ ♦r ♠♦r❡ ♣❛rts ✉s✐♥❣✶✻✺
♦♥❧② ♦♥❡ ❝♦♦r❞✐♥❛t❡✳✶✻✻
◆♦♥❡t❤❡❧❡ss✱ t❤❡ s✐♠♣❧✐❝✐t② ❛♥❞ t❤❡♦r❡t✐❝❛❧ ❢♦✉♥❞❛t✐♦♥s ✉♥❞❡r❧②✐♥❣ t❤❡ ■▲❘✱ ❛♥❞✶✻✼
t❤❡ ✐♥st❛♥t ❛♣♣❡❛❧ ♦❢ ❛♣♣❧②✐♥❣ ✐t t♦ t❤❡ s❡q✉❡♥t✐❛❧✲❜✐♥❛r② ♣❛rt✐t✐♦♥ ♦❢ t❤❡ ♣❤②✲✶✻✽
✼
❧♦❣❡♥②✱ ♠♦t✐✈❛t❡ t❤❡ r♦♦t❡❞ ■▲❘ ❛s ❛ s✐♠♣❧❡ t♦♦❧ ❢♦r ❛♥❛❧②s✐s ♦❢ t❤❡ ♣❤②❧♦❣❡♥❡t✐❝✶✻✾
str✉❝t✉r❡ ✐♥ ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛✳ ❋♦r t❤❛t r❡❛s♦♥✱ ✇❡ ✉s❡ t❤❡ r♦♦t❡❞ ■▲❘ ❛s ❛✶✼✵
❜❛s❡❧✐♥❡ ❢♦r ❝♦♠♣❛r✐s♦♥ ♦❢ ♦✉r ♠♦r❡ ❝♦♠♣❧✐❝❛t❡❞ ♠❡t❤♦❞ ♦❢ ♣❤②❧♦❣❡♥❡t✐❝ ❢❛❝t♦r✲✶✼✶
✐③❛t✐♦♥✳✶✼✷
P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✶✼✸
❚❤❡ s❤♦rt❝♦♠✐♥❣s ♦❢ t❤❡ r♦♦t❡❞ ■▲❘ ❝❛♥ ❜❡ r❡♠❡❞✐❡❞ ❜② ♠♦❞✐❢②✐♥❣ t❤❡ ■▲❘✶✼✹
tr❛♥s❢♦r♠ t♦ ❛♣♣❧② ♥♦t t♦ t❤❡ ♥♦❞❡s ♦r s♣❧✐ts ✐♥ ❛ ♣❤②❧♦❣❡♥②✱ ❜✉t t♦ t❤❡ ❡❞❣❡s ✐♥✶✼✺
❛♥ ✉♥r♦♦t❡❞ ♣❤②❧♦❣❡♥②✳ ❲❤✐❧❡ ■▲❘ ❝♦♦r❞✐♥❛t❡s ♦❢ ♥♦❞❡s ❛❧❧♦✇ ❛ ❝♦♠♣❛r✐s♦♥ ♦❢✶✼✻
s✐st❡r ❝❧❛❞❡s✱ ■▲❘ ❝♦♦r❞✐♥❛t❡s ❛❧♦♥❣ ❡❞❣❡s ❛❧❧♦✇ ❝♦♠♣❛r✐s♦♥ ♦❢ t❛①❛ ✇✐t❤ ♣✉t❛t✐✈❡✶✼✼
tr❛✐ts t❤❛t ❛r♦s❡ ❛❧♦♥❣ t❤❡ ❡❞❣❡ ❛❣❛✐♥st ❛❧❧ t❛①❛ ✇✐t❤♦✉t t❤♦s❡ ♣✉t❛t✐✈❡ tr❛✐ts✳✶✼✽
❚r❛✐ts ❛r✐s❡ ❛❧♦♥❣ ❡❞❣❡s ♦❢ t❤❡ ♣❤②❧♦❣❡♥② ❛♥❞ s♦✱ ❢♦r ❛♥♥♦t❛t✐♦♥ ♦❢ ♣❤②❧♦❣❡♥✐❡s✱✶✼✾
❡✛❡❝ts ✐♥ ❛ ❝❧❛❞❡ ❛r❡ ❜❡st ♠❛♣♣❡❞ t♦ ❛ ❝❤❛✐♥ ♦❢ ❡❞❣❡s ✐♥ t❤❡ ♣❤②❧♦❣❡♥②✳✶✽✵
❍♦✇❡✈❡r✱ t❤❡ ■▲❘ tr❛♥s❢♦r♠ r❡q✉✐r❡s ❛ s❡q✉❡♥t✐❛❧ ❜✐♥❛r② ♣❛rt✐t✐♦♥✱ ❛♥❞ t❤❡ ❡❞❣❡s✶✽✶
❞♦♥✬t ✐♠♠❡❞✐❛t❡❧② ♣r♦✈✐❞❡ ❛ ❝❧❡❛r ❝❛♥❞✐❞❛t❡ ❢♦r ❛ s❡q✉❡♥t✐❛❧ ❜✐♥❛r② ♣❛rt✐t✐♦♥✳ ■♥✶✽✷
✇❤❛t ✇❡ r❡❢❡r t♦ ❛s ✏♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✑✱ ♦♥❡ ❝❛♥ ✐t❡r❛t✐✈❡❧② ❝♦♥str✉❝t ❛ s❡q✉❡♥✲✶✽✸
t✐❛❧ ❜✐♥❛r② ♣❛rt✐t✐♦♥ ❢r♦♠ t❤❡ ✉♥r♦♦t❡❞ ♣❤②❧♦❣❡♥② ❜② ✉s✐♥❣ ❛ ❣r❡❡❞② ❛❧❣♦r✐t❤♠✶✽✹
❜② s❡q✉❡♥t✐❛❧❧② ❝❤♦♦s✐♥❣ ❡❞❣❡s ✇❤✐❝❤ ♠❛①✐♠✐③❡ ❛ r❡s❡❛r❝❤❡r✬s ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥✳✶✽✺
P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❝♦♥s✐sts ♦❢ ✸ st❡♣s ✭❋✐❣✳ ✷✮✿ ✭✶✮ ❈♦♥s✐❞❡r t❤❡ s❡t ♦❢ ♣♦ss✐❜❧❡✶✽✻
♣r✐♠❛r② ■▲❘ ❜❛s✐s ❡❧❡♠❡♥ts ❝♦rr❡s♣♦♥❞✐♥❣ t♦ ❛ ♣❛rt✐t✐♦♥ ❛❧♦♥❣ ❛♥② ❡❞❣❡ ✐♥ t❤❡✶✽✼
tr❡❡ ✭✐♥❝❧✉❞✐♥❣ t❤❡ t✐♣s✮✳ ✭✷✮ ❈❤♦♦s❡ t❤❡ ❡❞❣❡ ✇❤♦s❡ ❝♦rr❡s♣♦♥❞✐♥❣ ■▲❘ ❜❛s✐s✶✽✽
❡❧❡♠❡♥t ♠❛①✐♠✐③❡s s♦♠❡ ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥ ✲ s✉❝❤ ❛s t❤❡ t❡st✲st❛t✐st✐❝ ❢r♦♠ r❡✲✶✽✾
❣r❡ss✐♦♥ ♦r t❤❡ ♣❡r❝❡♥t ♦❢ ✈❛r✐❛t✐♦♥ ❡①♣❧❛✐♥❡❞ ✐♥ t❤❡ ♦r✐❣✐♥❛❧ ❞❛t❛s❡t ✲ ❛♥❞ t❤❡✶✾✵
❣r♦✉♣s ♦❢ t❛①❛ s♣❧✐t ❜② t❤❛t ❡❞❣❡ ❢♦r♠ t❤❡ ✜rst ♣❛rt✐t✐♦♥✳ ✭✸✮ ❘❡♣❡❛t st❡♣s ✶ ❛♥❞✶✾✶
✷✱ ❝♦♥str✉❝t✐♥❣ s✉❜s❡q✉❡♥t ■▲❘ ❜❛s✐s ❡❧❡♠❡♥ts ❝♦rr❡s♣♦♥❞✐♥❣ t♦ r❡♠❛✐♥✐♥❣ ❡❞❣❡s✶✾✷
✐♥ t❤❡ ♣❤②❧♦❣❡♥② ❛♥❞ ♠❛❞❡ ♦rt❤♦❣♦♥❛❧ t♦ ❛❧❧ ♣r❡✈✐♦✉s ♣❛rt✐t✐♦♥s ❜② ❧✐♠✐t✐♥❣ t❤❡✶✾✸
❝♦♠♣❛r✐s♦♥s t♦ t❛①❛ ✇✐t❤✐♥ t❤❡ ❣r♦✉♣s ♦❢ t❛①❛ ✉♥✲s♣❧✐t ❜② ♣r❡✈✐♦✉s ♣❛rt✐t✐♦♥s✳✶✾✹
❊①♣❧✐❝✐t❧②✱ t❤❡ ✜rst ✐t❡r❛t✐♦♥ ♦❢ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❝♦♥s✐❞❡rs ❛ s❡t ♦❢ ❝❛♥❞✐✲✶✾✺
❞❛t❡ ■▲❘ ❝♦♦r❞✐♥❛t❡s✱ {x∗e} ❝♦rr❡s♣♦♥❞✐♥❣ t♦ t❤❡ t✇♦ ❣r♦✉♣s ♦❢ t❛①❛ s♣❧✐t ❜②✶✾✻
❡❛❝❤ ❡❞❣❡✱ e✳ ❚❤❡♥✱ r❡❣r❡ss✐♦♥ ✐s ♣❡r❢♦r♠❡❞ ♦♥ ❡❛❝❤ ♦❢ t❤❡ ■▲❘ ❝♦♦r❞✐♥❛t❡s✱✶✾✼
x∗e ∼ f(X) ❢♦r ❛♥ ❛♣♣r♦♣r✐❛t❡ ❢✉♥❝t✐♦♥✱ f ❛♥❞ ❛ s❡t ♦❢ ✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡s✱✶✾✽
X✳ ❚❤❡ ❡❞❣❡✱ e+1 ✱ ✇❤✐❝❤ ♠❛①✐♠✐③❡s t❤❡ ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥ ✐s ❝❤♦s❡♥ ❛s t❤❡ ✜rst✶✾✾
♣❤②❧♦❣❡♥❡t✐❝ ❢❛❝t♦r✳ ■♥ t❤✐s ♣❛♣❡r✱ ♦✉r ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥ ✐s t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡✲✷✵✵
t✇❡❡♥ t❤❡ ♥✉❧❧ ❞❡✈✐❛♥❝❡ ♦❢ t❤❡ ■▲❘ ❝♦♦r❞✐♥❛t❡ ❛♥❞ t❤❡ ❞❡✈✐❛♥❝❡ ♦❢ t❤❡ ❣❡♥❡r❛❧✐③❡❞✷✵✶
❧✐♥❡❛r ♠♦❞❡❧ ❡①♣❧❛✐♥✐♥❣ t❤❛t ■▲❘ ❝♦♦r❞✐♥❛t❡ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ✐♥❞❡♣❡♥❞❡♥t✷✵✷
✽
✈❛r✐❛❜❧❡s✳ ❲❡ ✉s❡ t❤✐s ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥ ❛s ❛ ♠❡❛s✉r❡ ♦❢ t❤❡ ❛♠♦✉♥t ♦❢ ✈❛r✐❛♥❝❡✷✵✸
❡①♣❧❛✐♥❡❞ ❜② r❡❣r❡ss✐♦♥ ♦♥ ❡❛❝❤ ❡❞❣❡ ❜❡❝❛✉s❡ t❤❡ t♦t❛❧ ✈❛r✐❛♥❝❡ ✐♥ ❛ ❝♦♠♣♦s✐✲✷✵✹
t✐♦♥❛❧ ❞❛t❛s❡t ✐s ❝♦♥st❛♥t ❛♥❞ ❡q✉❛❧ t♦ t❤❡ s✉♠ ♦❢ t❤❡ ✈❛r✐❛♥❝❡s ♦❢ ❛❧❧ ■▲❘✷✵✺
❝♦♦r❞✐♥❛t❡s ❝♦rr❡s♣♦♥❞✐♥❣ t♦ ❛♥② s❡q✉❡♥t✐❛❧ ❜✐♥❛r② ♣❛rt✐t✐♦♥✳ ❈♦♥s❡q✉❡♥t❧②✱ ❛t✷✵✻
❡❛❝❤ ✐t❡r❛t✐♦♥ t❤❡r❡ ✐s ❛ ✜①❡❞ ❛♠♦✉♥t ♦❢ t❤❡ t♦t❛❧ ✈❛r✐❛♥❝❡ r❡♠❛✐♥✐♥❣ ✐♥ t❤❡✷✵✼
❞❛t❛s❡t✱ ❛♥❞ s♦ ❛t t❤❡ ❝❛♥❞✐❞❛t❡ ■▲❘ ❝♦♦r❞✐♥❛t❡ ✇❤✐❝❤ ❝❛♣t✉r❡s t❤❡ ❣r❡❛t❡st✷✵✽
❢r❛❝t✐♦♥ ♦❢ t❤❡ t♦t❛❧ ✈❛r✐❛♥❝❡ ✐♥ t❤❡ ❞❛t❛s❡t ✐s t❤❡ ♦♥❡ ✇✐t❤ t❤❡ ❣r❡❛t❡st ❛♠♦✉♥t✷✵✾
♦❢ ✈❛r✐❛♥❝❡ ❡①♣❧❛✐♥❡❞ ❜② t❤❡ r❡❣r❡ss✐♦♥✳ ❆❢t❡r ✐❞❡♥t✐❢②✐♥❣ e+1 ✱ ✇❡ ❝✉t t❤❡ tr❡❡ ✐♥✷✶✵
t✇♦ s✉❜✲tr❡❡s ❛❧♦♥❣ t❤❡ ❡❞❣❡✱ e+1 ✳✷✶✶
❋♦r t❤❡ s❡❝♦♥❞ ✐t❡r❛t✐♦♥✱ ❛♥♦t❤❡r s❡t ♦❢ ❝❛♥❞✐❞❛t❡ ■▲❘ ❝♦♦r❞✐♥❛t❡s ✐s ❝♦♥str✉❝t❡❞✷✶✷
s✉❝❤ t❤❛t t❤❡✐r ✉♥❞❡r❧②✐♥❣ ❜❛❧❛♥❝✐♥❣ ❡❧❡♠❡♥ts ❛r❡ ♦rt❤♦❣♦♥❛❧ t♦ t❤❡ ✜rst ■▲❘✷✶✸
❝♦♦r❞✐♥❛t❡✳ ❖rt❤♦❣♦♥❛❧✐t② ✐s ❡♥s✉r❡❞ ❜② ❝♦♥str✉❝t✐♥❣ ■▲❘ ❝♦♦r❞✐♥❛t❡s ❝♦♥tr❛st✲✷✶✹
✐♥❣ t❤❡ ❛❜✉♥❞❛♥❝❡s ♦❢ t❛①❛ ❛❧♦♥❣ ❡❛❝❤ ❡❞❣❡✱ r❡str✐❝t✐♥❣ t❤❡ ❝♦♥tr❛st t♦ ❛❧❧ t❛①❛✷✶✺
✇✐t❤✐♥ t❤❡ s✉❜✲tr❡❡ ✐♥ ✇❤✐❝❤ t❤❡ ❡❞❣❡ ✐s ❢♦✉♥❞✳ ❆ ♥❡✇ ❡❞❣❡✱ e+2 ✱ ✇❤✐❝❤ ♠❛①✐♠✐③❡s✷✶✻
t❤❡ ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥ ✐s ❝❤♦s❡♥ ❛s t❤❡ s❡❝♦♥❞ ❢❛❝t♦r✱ t❤❡ s✉❜✲tr❡❡ ❝♦♥t❛✐♥✐♥❣ t❤✐s✷✶✼
❡❞❣❡ ✐s ❝✉t ❛❧♦♥❣ t❤✐s ❡❞❣❡ t♦ ♣r♦❞✉❝❡ t✇♦ s✉❜✲tr❡❡s✱ ❛♥❞ t❤❡ ♣r♦❝❡ss ✐s r❡♣❡❛t❡❞✷✶✽
✉♥t✐❧ ❛ ❞❡s✐r❡❞ ♥✉♠❜❡r ♦❢ ❢❛❝t♦rs ✐s r❡❛❝❤❡❞ ♦r ✉♥t✐❧ ❛ st♦♣♣✐♥❣ ❝r✐t❡r✐♦♥ ✐s ♠❡t✳✷✶✾
▼♦r❡ ❞❡t❛✐❧s ♦♥ t❤❡ ❛❧❣♦r✐t❤♠✱ ❛❧♦♥❣ ✇✐t❤ ❛ ❞✐s❝✉ss✐♦♥ ♦♥ ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥s✱✷✷✵
✐s ❝♦♥t❛✐♥❡❞ ✐♥ t❤❡ ❙■✳✷✷✶
❲❤✐❧❡ ♦♥❡ ❝♦✉❧❞ ✉s❡ ♦t❤❡r ♠❡t❤♦❞s ♦❢ ❛♠❛❧❣❛♠❛t✐♥❣ ❛❜✉♥❞❛♥❝❡s ❛❧♦♥❣ ❡❞❣❡s✱✷✷✷
t❤❡ ❝♦♥❝❡♣t✉❛❧ ✐♠♣♦rt❛♥❝❡ ♦❢ ✉s✐♥❣ t❤❡ ■▲❘ tr❛♥s❢♦r♠ ✐s t✇♦❢♦❧❞✿ t❤❡ ■▲❘ tr❛♥s✲✷✷✸
❢♦r♠ ❤❛s ♣r♦✈❡♥ ❛s②♠♣t♦t✐❝ ♥♦r♠❛❧✐t② ♣r♦♣❡rt✐❡s ❢♦r ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛ t♦ ❛❧❧♦✇✷✷✹
t❤❡ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ st❛♥❞❛r❞ ♠✉❧t✐✈❛r✐❛t❡ ♠❡t❤♦❞s ❬✶✶❪✱ ❛♥❞ t❤❡ ■▲❘ tr❛♥s❢♦r♠✷✷✺
s❡r✈❡s ❛s ❛ ♠❡❛s✉r❡ ♦❢ ❝♦♥tr❛st ❜❡t✇❡❡♥ t✇♦ ❣r♦✉♣s✳ ❚❤❡ ❧♦❣✲r❛t✐♦ ✉s❡❞ ✐♥ ♣❤②❧♦✲✷✷✻
❢❛❝t♦r ✐s ❛♥ ❛✈❡r❛❣❡❞ r❛t✐♦ ♦❢ ❛❜✉♥❞❛♥❝❡s ♦❢ t❛①❛ ♦♥ t✇♦ s✐❞❡s ♦❢ ❛♥ ❡❞❣❡ ✭s❡❡✷✷✼
s✉♣♣❧❡♠❡♥t ❢♦r ♠♦r❡ ❞❡t❛✐❧✮✱ t❤✉s ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ s❡❛r❝❤❡s t❤❡ tr❡❡ ❢♦r t❤❡✷✷✽
❡❞❣❡ ✇❤✐❝❤ ❤❛s t❤❡ ♠♦st ♣r❡❞✐❝t❛❜❧❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❛①❛ ♦♥ ❡❛❝❤ s✐❞❡ ♦❢ t❤❡✷✷✾
❡❞❣❡✱ ♦r✱ ♣✉t ❞✐✛❡r❡♥t❧②✱ t❤❡ ❡❞❣❡ ✇❤✐❝❤ ❜❡st ❞✐✛❡r❡♥t✐❛t❡s t❛①❛ ♦♥ ❡❛❝❤ s✐❞❡✳✷✸✵
❚❤✉s✱ ❡❛❝❤ ❡❞❣❡ t❤❛t ❞✐✛❡r❡♥t✐❛t❡s t❛①❛ ❛♥❞ t❤❡✐r r❡s♣♦♥s❡s t♦ ✐♥❞❡♣❡♥❞❡♥t✷✸✶
✈❛r✐❛❜❧❡s ✐s ❝♦♥s✐❞❡r❡❞ ❛ ♣❤②❧♦❣❡♥❡t✐❝ ✏❢❛❝t♦r✑ ❞r✐✈✐♥❣ ✈❛r✐❛t✐♦♥ ✐♥ t❤❡ ❞❛t❛✳✷✸✷
❚❤❡ ♦✉t♣✉t ♦❢ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✐s ❛ s❡t ♦❢ ♦rt❤♦❣♦♥❛❧✱ s❡q✉❡♥t✐❛❧❧② ✏❧❡ss ✐♠✲✷✸✸
♣♦rt❛♥t✑ ■▲❘ ❜❛s✐s ❡❧❡♠❡♥ts✱ t❤❡✐r ♣r❡❞✐❝t❡❞ ❜❛❧❛♥❝❡s✱ ❛♥❞ ❛❧❧ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥✷✸✹
♦❜t❛✐♥❡❞ ❢r♦♠ r❡❣r❡ss✐♦♥✳ ❆❢t❡r t❤❡ ✜rst ✐t❡r❛t✐♦♥ ♦❢ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✱ ✇❡ ❛r❡✷✸✺
❧❡❢t ✇✐t❤ ❛♥ ■▲❘ ❜❛s✐s ❡❧❡♠❡♥t ❝♦rr❡s♣♦♥❞✐♥❣ t♦ t❤❡ ❡❞❣❡ ✇❤✐❝❤ ♠❛①✐♠✐③❡❞ ♦✉r✷✸✻
♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥ ❛♥❞ s♣❧✐t t❤❡ ❞❛t❛s❡t ✐♥t♦ t✇♦ ❞✐s❥♦✐♥t s✉❜✲tr❡❡s✱ ♦r s❡ts ♦❢✷✸✼
❖❚❯s t❤❛t ✇❡ ❤❡♥❝❡❢♦rt❤ r❡❢❡r t♦ ❛s ✏❜✐♥s✑✱ ❛♥❞ ✇❡ ❤❛✈❡ ❛♥ ❡st✐♠❛t❡❞ ■▲❘✷✸✽
✾
❜❛❧❛♥❝✐♥❣ ❡❧❡♠❡♥t✱ x̂∗1(X)✱ ✇❤❡r❡ X ✐s ♦✉r s❡t ♦❢ ✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡s✳ ❙✉❜✲✷✸✾
s❡q✉❡♥t ❢❛❝t♦rs ✇✐❧❧ s♣❧✐t t❤❡ ❜✐♥s ❢r♦♠ ♣r❡✈✐♦✉s st❡♣s✱ ❛♥❞ ❛❢t❡r n ✐t❡r❛t✐♦♥s✷✹✵
♦♥❡ ❤❛s n ❢❛❝t♦rs t❤❛t ❝❛♥ ❜❡ ♠❛♣♣❡❞ t♦ t❤❡ ♣❤②❧♦❣❡♥②✱ n + 1 ❜✐♥s ❢♦r ❜✐♥✲✷✹✶
♥✐♥❣ t❛①❛ ❜❛s❡❞ ♦♥ t❤❡✐r ♣❤②❧♦❣❡♥❡t✐❝ ❢❛❝t♦rs✱ n ❡st✐♠❛t❡s ♦❢ ■▲❘ ❜❛❧❛♥❝✐♥❣✷✹✷
❡❧❡♠❡♥ts✱ ❛♥❞ ❛♥ ♦rt❤♦♥♦r♠❛❧ ■▲❘ ❜❛s✐s t❤❛t ❝❛♥ ❜❡ ✉s❡❞ t♦ ♣r♦❥❡❝t t❤❡ ❞❛t❛✷✹✸
♦♥t♦ ❛ ❧♦✇❡r ❞✐♠❡♥s✐♦♥❛❧ s♣❛❝❡✳ ❚❤❡ s❡q✉❡♥t✐❛❧ s♣❧✐tt✐♥❣ ♦❢ ❜✐♥s ✐♥ ♣❤②❧♦❢❛❝t♦r✲✷✹✹
✐③❛t✐♦♥ ❡♥s✉r❡s s❡q✉❡♥t✐❛❧❧② ✐♥❞❡♣❡♥❞❡♥t ✐♥❢❡r❡♥❝❡s ✲ ❤❛✈✐♥❣ ❛❧r❡❛❞② ✐❞❡♥t✐✜❡❞✷✹✺
❣r♦✉♣ B ❛s ❤②♣❡r✲❛❜✉♥❞❛♥t r❡❧❛t✐✈❡ t♦ ❣r♦✉♣ A ✐♥ t❤❡ ❡①❛♠♣❧❡ ✐❧❧✉str❛t❡❞ ✐♥✷✹✻
❋✐❣✳ ✷✱ ❞♦✇♥str❡❛♠ ❢❛❝t♦rs ♠✉st ❛♥❛❧②③❡ s✉❜✲❝♦♠♣♦s✐t✐♦♥s ❡♥t✐r❡❧② ✇✐t❤✐♥ B✷✹✼
❛♥❞ ✇✐t❤✐♥ A✳✷✹✽
❈♦♠♣✉t❛t✐♦♥❛❧ ❚♦♦❧s✷✹✾
P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✇❛s ❞♦♥❡ ✉s✐♥❣ t❤❡ ❘ ♣❛❝❦❛❣❡ ✏♣❤②❧♦❢❛❝t♦r✑ ❛✈❛✐❧❛❜❧❡ ❛t✷✺✵
❤tt♣s✿✴✴❣✐t❤✉❜✳❝♦♠✴r❡♣t❛❧❡①✴♣❤②❧♦❢❛❝t♦r✳ ❚❤❡ ❘ ♣❛❝❦❛❣❡ ❝♦♥t❛✐♥s ❞❡t❛✐❧❡❞ ❤❡❧♣✷✺✶
✜❧❡s t❤❛t ❞❡♠♦ t❤❡ ✉s❡ ♦❢ t❤❡ ♣❛❝❦❛❣❡✱ ❛♥❞ t❤❡ ❡①❛❝t ❝♦❞❡ ✉s❡❞ ✐♥ ❛♥❛❧②s❡s ❛♥❞✷✺✷
✈✐s✉❛❧✐③❛t✐♦♥ ✐♥ t❤✐s ♣❛♣❡r ❛r❡ ❛✈❛✐❧❛❜❧❡ ✐♥ t❤❡ s✉♣♣❧❡♠❡♥t❛r② ♠❛t❡r✐❛❧s✳ ❚❤❡✷✺✸
r♦♦t❡❞ ■▲❘ tr❛♥s❢♦r♠ ✇❛s ♣❡r❢♦r♠❡❞ ❛s ❞❡s❝r✐❜❡❞ ✐♥ ❬✶✵❪ ✇❤❡r❡ t❤❡ s❡q✉❡♥t✐❛❧✷✺✹
❜✐♥❛r② ♣❛rt✐t✐♦♥ ✇❛s t❤❡ r♦♦t❡❞ ♣❤②❧♦❣❡♥②✳✷✺✺
P♦✇❡r ❆♥❛❧②s✐s ♦❢ ❘♦♦t❡❞ ■▲❘ ❛♥❞ P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✷✺✻
❚♦ ❝♦♠♣❛r❡ t❤❡ ❛❜✐❧✐t② ♦❢ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❛♥❞ t❤❡ r♦♦t❡❞ ■▲❘ t♦ ✐❞❡♥t✐❢②✷✺✼
❝❧❛❞❡s ♦❢ ❖❚❯s ✇✐t❤ s❤❛r❡❞ ❛ss♦❝✐❛t✐♦♥s ✇✐t❤ ✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡s✱ ✇❡ s✐♠✉✲✷✺✽
❧❛t❡❞ r❛♥❞♦♠ ❝♦♠♠✉♥✐t✐❡s ♦❢ D = 50 ❖❚❯s ❛♥❞ p = 40 s❛♠♣❧❡s ❜② s✐♠✉❧❛t✐♥❣✷✺✾
r❛♥❞♦♠ ❛❜s♦❧✉t❡ ❛❜✉♥❞❛♥❝❡s✱ Ni,j ✱ s✉❝❤ t❤❛t logNi,j ✇❡r❡ ✐✳✐✳❞ ●❛✉ss✐❛♥ r❛♥✲✷✻✵
❞♦♠ ✈❛r✐❛❜❧❡s ✇✐t❤ ♠❡❛♥ µ = 8 ❛♥❞ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥ σ = 0.5✳ ❚❤❡ ❖❚❯s✷✻✶
✇❡r❡ ❝♦♥♥❡❝t❡❞ ❜② ❛ r❛♥❞♦♠ tr❡❡ ✭t❤❡ tr❡❡ r❡♠❛✐♥❡❞ ❝♦♥st❛♥t ❛❝r♦ss ❛❧❧ s✐♠✉❧❛✲✷✻✷
t✐♦♥s✮✱ ❛♥❞ t❤❡♥ ❡✐t❤❡r ✶ ♦r ✸ ❝❧❛❞❡s ✇❡r❡ r❛♥❞♦♠❧② ❝❤♦s❡♥ t♦ ❤❛✈❡ ❛ss♦❝✐❛t✐♦♥s✷✻✸
✇✐t❤ ❛ ❜✐♥❛r② ✏❡♥✈✐r♦♥♠❡♥t✑ ✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡ ✇✐t❤ p = 20 s❛♠♣❧❡s ❢♦r ❡❛❝❤✷✻✹
♦❢ ✐ts t✇♦ ✈❛❧✉❡s t♦ r❡♣r❡s❡♥t ❛♥ ❡q✉❛❧ s❛♠♣❧✐♥❣ ♦❢ ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t✐❡s ❛❝r♦ss✷✻✺
t✇♦ ❡♥✈✐r♦♥♠❡♥ts✳✷✻✻
❋♦r s✐♠✉❧❛t✐♦♥s ✇✐t❤ ♦♥❡ s✐❣♥✐✜❝❛♥t ❝❧❛❞❡✱ t❤❡ ❛❜✉♥❞❛♥❝❡s ♦❢ ❛❧❧ t❤❡ ❖❚❯s✷✻✼
✇✐t❤✐♥ t❤❛t ❝❧❛❞❡ ✐♥❝r❡❛s❡❞ ❜② ❛ ❢❛❝t♦r a ✐♥ t❤❡ s❡❝♦♥❞ ❡♥✈✐r♦♥♠❡♥t ✇❤❡r❡ a ∈✷✻✽
{1.5, 3, 6}✳ ❋♦r s✐♠✉❧❛t✐♦♥s ✇✐t❤ t❤r❡❡ s✐❣♥✐✜❝❛♥t ❝❧❛❞❡s✱ t❤❡ t❤r❡❡ ❝❧❛❞❡s ✇❡r❡✷✻✾
❞r❛✇♥ ❛t r❛♥❞♦♠ ❛♥❞ r❛♥❞♦♠❧② ❛ss✐❣♥❡❞ ❛ ❢♦❧❞✲❝❤❛♥❣❡ ❢r♦♠ t❤❡ s❡t {πb, 0.5b, exp(−b)}✷✼✵
✐♥ ❛ r❛♥❞♦♠❧② ❝❤♦s❡♥ ❡♥✈✐r♦♥♠❡♥t ✇❤❡r❡ b ∈ {1, 2, 5}✳ ❋♦r ❡❛❝❤ ❢♦❧❞✲❝❤❛♥❣❡✱✷✼✶
✶✵
✺✵✵ r❡♣❧✐❝❛t❡s ✇❡r❡ r✉♥ t♦ ❝♦♠♣❛r❡ t❤❡ ♣♦✇❡r ♦❢ t❤❡ r♦♦t❡❞ ■▲❘ ❛♥❞ ♣❤②❧♦❢❛❝✲✷✼✷
t♦r✐③❛t✐♦♥ ✐♥ ❝♦rr❡❝t❧② ✐❞❡♥t✐❢②✐♥❣ t❤❡ ❛✛❡❝t❡❞ ❝❧❛❞❡s✳✷✼✸
❘❡❣r❡ss✐♦♥ ♦❢ r♦♦t❡❞ ■▲❘ ❝♦♦r❞✐♥❛t❡s ✇❛s ♣❡r❢♦r♠❡❞ ❛♥❞ t❤❡ ❝♦♦r❞✐♥❛t❡s ✇❡r❡✷✼✹
r❛♥❦❡❞ ❜② t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡✐r ♥✉❧❧ ❞❡✈✐❛♥❝❡ ❛♥❞ t❤❡ ♠♦❞❡❧ ❞❡✈✐❛♥❝❡✳✷✼✺
❚❤❡ ❛❜✐❧✐t② ♦❢ ❛ r♦♦t❡❞ ■▲❘ ❝♦♦r❞✐♥❛t❡ t♦ ✐❞❡♥t✐❢② t❤❡ ❝♦rr❡❝t ✶ ❝❧❛❞❡ ♦r ✸ ❝❧❛❞❡s✷✼✻
✇❛s ♠❡❛s✉r❡❞ ❜② t❤❡ ♣❡r❝❡♥t ♦❢ ✐ts t♦♣ ✶ ♦r ✸ ■▲❘ ❝♦♦r❞✐♥❛t❡s✱ r❡s♣❡❝t✐✈❡❧②✱✷✼✼
✇❤✐❝❤ ❝♦rr❡s♣♦♥❞❡❞ t♦ t❤❡ ♥♦❞❡ ♦♥ t❤❡ tr❡❡ ❢r♦♠ ✇❤✐❝❤ t❤❡ ❛✛❡❝t❡❞ ❝❧❛❞❡✭s✮✷✼✽
♦r✐❣✐♥❛t❡❞✳ ❚❤❡ ❛❜✐❧✐t② ♦❢ ♣❤②❧♦❢❛❝t♦r t♦ ✐❞❡♥t✐❢② t❤❡ ❝♦rr❡❝t ✶ ❝❧❛❞❡ ♦r ✸ ❝❧❛❞❡s✷✼✾
✇❛s ♠❡❛s✉r❡❞ ❜② t❤❡ ♣❡r❝❡♥t ♦❢ t❤❡ ❢❛❝t♦rs t❤❛t ❝♦rr❡❝t❧② s♣❧✐t ❛♥ ❛✛❡❝t❡❞ ❝❧❛❞❡✷✽✵
❢r♦♠ t❤❡ r❡st ✭❡✳❣✳ t❤❡ ♣❡r❝❡♥t ♦❢ ❢❛❝t♦rs ❝♦rr❡s♣♦♥❞✐♥❣ t♦ ❡❞❣❡s ❛❧♦♥❣ ✇❤✐❝❤ ❛✷✽✶
tr❛✐t ❛r♦s❡✮✳✷✽✷
❋♦r t❤❡ ✸ ❝❧❛❞❡ s✐♠✉❧❛t✐♦♥s✱ ✇❡ ❛❧s♦ ❝♦♠♣❛r❡❞ t❤❡ ❛♠♦✉♥t ♦❢ ✈❛r✐❛♥❝❡ ❡①♣❧❛✐♥❡❞✷✽✸
❜② ✸ ❢❛❝t♦rs ✐♥ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✇✐t❤ t❤❡ ❛♠♦✉♥t ♦❢ ✈❛r✐❛♥❝❡ ❡①♣❧❛✐♥❡❞ ❜② t❤❡✷✽✹
t♦♣ ✸ ■▲❘ ❝♦♦r❞✐♥❛t❡s ✐♥ t❤❡ r♦♦t❡❞ ■▲❘✳ ❚❤❡ ❛♠♦✉♥t ♦❢ ✈❛r✐❛♥❝❡ ❡①♣❧❛✐♥❡❞✷✽✺
✇❛s ♠❡❛s✉r❡❞ ❛s t❤❡ ❞✐✛❡r❡♥❝❡ ✐♥ t❤❡ ♥✉❧❧ ❞❡✈✐❛♥❝❡ ❛♥❞ t❤❡ ♠♦❞❡❧ ❞❡✈✐❛♥❝❡✱✷✽✻
s✉♠♠❡❞ ❛❝r♦ss ❛❧❧ t❤r❡❡ ❢❛❝t♦rs ♦r t❤❡ t♦♣ ✸ ■▲❘ ❝♦♦r❞✐♥❛t❡s✳✷✽✼
❑❙✲❜❛s❡❞ ❙t♦♣♣✐♥❣ ❋✉♥❝t✐♦♥ ❢♦r P❤②❧♦❋❛❝t♦r✷✽✽
❲❤✐❧❡ ❛ r❡s❡❛r❝❤❡r ❝❛♥ ✐t❡r❛t❡ t❤r♦✉❣❤ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✉♥t✐❧ ❛ ❢✉❧❧ ❜❛s✐s ♦❢✷✽✾
D− 1 ■▲❘ ❝♦♦r❞✐♥❛t❡s ✐s ❝♦♥str✉❝t❡❞✱ t❤❡ r❡s❡❛r❝❤❡r ♠❛② ❜❡ ✐♥t❡r❡st❡❞ ✐♥ st♦♣✲✷✾✵
♣✐♥❣ t❤❡ ✐t❡r❛t✐♦♥ ❜❡❢♦r❡ t❤❡ ❢✉❧❧ ❜❛s✐s ✐s ❝♦♥str✉❝t❡❞ ❛♥❞ ❢♦❝✉s t❤❡✐r ❛♥❛❧②s✐s✷✾✶
❛♥❞ ✐♥t❡r♣r❡t❛t✐♦♥s ♦♥ ❛ ❝♦♥s❡r✈❛t✐✈❡ s✉❜s❡t ♦❢ t❤❡ tr✉❡ ♥✉♠❜❡r ♦❢ ♣❤②❧♦❣❡♥❡t✐❝✷✾✷
❢❛❝t♦rs✳ ❲❡ ✐♠♣❧❡♠❡♥t❡❞ ❛ st♦♣♣✐♥❣ ❢✉♥❝t✐♦♥ ❜❛s❡❞ ♦♥ ❛ ❑♦❧♠♦❣♦r♦✈✲❙♠✐r♥♦✈✷✾✸
✭❑❙✮ t❡st ♦❢ t❤❡ ❞✐str✐❜✉t✐♦♥ ♦❢ P✲✈❛❧✉❡s ❢r♦♠ ❛♥❛❧②s❡s ♦❢ ✈❛r✐❛♥❝❡ ♦❢ t❤❡ r❡✲✷✾✹
❣r❡ss✐♦♥s ♦♥ ❝❛♥❞✐❞❛t❡ ■▲❘ ❝♦♦r❞✐♥❛t❡s✳ ■❢ t❤❡r❡ ✐s ♥♦ ♣❤②❧♦❣❡♥❡t✐❝ s✐❣♥❛❧✱ ✇❡✷✾✺
❛♥t✐❝✐♣❛t❡ t❤❡ tr✉❡ ❞✐str✐❜✉t✐♦♥ ♦❢ P✲✈❛❧✉❡s t♦ ❜❡ ✉♥✐❢♦r♠ ✭❛❧❜❡✐t ✇✐t❤ s♦♠❡✷✾✻
❞❡♣❡♥❞❡♥❝❡ ❛♠♦♥❣ t❤❡ P✲✈❛❧✉❡s ❞✉❡ t♦ ♦✈❡r❧❛♣ ✐♥ t❤❡ ❖❚❯s ✉s❡❞ ✐♥ t❤❡ ■▲❘✷✾✼
❝♦♦r❞✐♥❛t❡s✮✳ ❚❤✉s✱ ✇❡ t❡st❡❞ t❤❡ ❛❜✐❧✐t② ♦❢ ♣❤②❧♦❢❛❝t♦r t♦ ❝♦rr❡❝t❧② ✐❞❡♥t✐❢② t❤❡✷✾✽
♥✉♠❜❡r ♦❢ ❝❧❛❞❡s ✐❢ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✐s st♦♣♣❡❞ ✇❤❡♥ ❛ ❑❙ t❡st ♦❢ t❤❡ P✲✈❛❧✉❡s✷✾✾
♣r♦❞✉❝❡s ✐ts ♦✇♥ P✲✈❛❧✉❡ PKS > 0.05✳✸✵✵
❲❡ s✐♠✉❧❛t❡❞ ✸✵✵ r❡♣❧✐❝❛t❡ ❝♦♠♠✉♥✐t✐❡s ✇✐t❤ M ❝❧❛❞❡s ❢♦r ❡❛❝❤ M ∈ {1, ..., 10}✳✸✵✶
❋♦r s✐♠✉❧❛t✐♦♥s ✇✐t❤ M ❝❧❛❞❡s✱ D = 50 ❛♥❞ p = 40 ❝♦♠♠✉♥✐t✐❡s ✇❡r❡ s✐♠✉❧❛t❡❞✸✵✷
❛s ❛❜♦✈❡ ❛♥❞ ❢♦❧❞ ❝❤❛♥❣❡s✱ c✱ ✇❡r❡ ❞r❛✇♥ ❛s ❧♦❣✲♥♦r♠❛❧ r❛♥❞♦♠ ✈❛r✐❛❜❧❡s ✇❤❡r❡✸✵✸
log(ck) ✇❡r❡ ✐✳✐✳❞ ●❛✉ss✐❛♥ r❛♥❞♦♠ ✈❛r✐❛❜❧❡s ✇✐t❤ µ = 0 ❛♥❞ σ = 3 ❢♦r k =✸✵✹
1, ...,M ✳ ❚❤❡ ♥✉♠❜❡r ♦❢ ❝❧❛❞❡s ✐❞❡♥t✐✜❡❞ ❜② ♣❤②❧♦❢❛❝t♦r ❢♦r ❛ ❣✐✈❡♥ tr✉❡ ♥✉♠❜❡r✸✵✺
✶✶
♦❢ ❝❧❛❞❡s✱ KM,r✱ ✇❛s t❛❧❧✐❡❞ ❢♦r r = 1, ..., 300✳ ❲❡ ❝❛❧❝✉❧❛t❡ t❤❡ ♠❡❛♥ K̄M ❛❝r♦ss✸✵✻
❛❧❧ r❡♣❧✐❝❛t❡s ❛♥❞✱ ❢♦r ✈✐s✉❛❧✐③❛t✐♦♥ ♣✉r♣♦s❡s✱ ✐♥t❡r♣♦❧❛t❡ t❤❡ α = 0.025 ❛♥❞✸✵✼
α = 0.975 q✉❛♥t✐❧❡s ❜② ✜♥❞✐♥❣ t❤❡ ❜❡st ✜t ♦❢ ❛ ❧♦❣✐st✐❝ ❢✉♥❝t✐♦♥ t♦ t❤❡ ❝✉♠✉❧❛t✐✈❡✸✵✽
❞✐str✐❜✉t✐♦♥ ♦❢ {KM,r}r=300r=1 ❢♦r ❡❛❝❤ M ✳✸✵✾
❆♥❛❧②s✐s ♦❢ ❋❡❝❛❧✴❖r❛❧ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛✸✶✵
✶✻❙ ❛♠♣❧✐❝♦♥ s❡q✉❡♥❝✐♥❣ ❞❛t❛ ❢r♦♠ ❈❛♣♦r❛s♦ ❡t ❛❧✳ ✭✷✵✶✶✮ ❬✹❪ ✇❡r❡ ❞♦✇♥❧♦❛❞❡❞✸✶✶
❢r♦♠ t❤❡ ▼●✲❘❆❙❚ ❞❛t❛❜❛s❡ ✭❤tt♣✿✴✴♠❡t❛❣❡♥♦♠✐❝s✳❛♥❧✳❣♦✈✴✮ ❛❧♦♥❣ ✇✐t❤ ❛s✲✸✶✷
s♦❝✐❛t❡❞ ♠❡t❛❞❛t❛✳ ◗■■▼❊ ❬✺❪ ✇❛s ✉s❡❞ t♦ tr✐♠ ♣r✐♠❡rs ❢r♦♠ t❤❡s❡ ❞❛t❛✱ ❛♥❞✸✶✸
t♦ ❝❧✉st❡r ❖❚❯s ✇✐t❤ t❤❡ ●r❡❡♥❣❡♥❡s r❡❢❡r❡♥❝❡ ❞❛t❛❜❛s❡ ✭▼❛② ✷✵✶✸ ✈❡rs✐♦♥❀✸✶✹
❤tt♣✿✴✴❣r❡❡♥❣❡♥❡s✳❧❜❧✳❣♦✈✮✳ ▲♦♥❣❡r s❡q✉❡♥❝❡ ❧❡♥❣t❤s ✐♥ t❤❡ ❣r❡❡♥❣❡♥❡s ❞❛t❛❜❛s❡✸✶✺
✭⑦✶✹✵✵ ❇P✮ ❝♦♠♣❛r❡❞ t♦ t❤❡ ♦r✐❣✐♥❛❧ ■❧❧✉♠✐♥❛ s❡q✉❡♥❝❡s ✭⑦✶✷✸ ❇P✮ ❛❧❧♦✇s ♠♦r❡✸✶✻
✐♥❢♦r♠❛t✐✈❡ ❜❛s❡ ♣❛✐rs ❢♦r ♣❤②❧♦❣❡♥❡t✐❝ tr❡❡ ❝♦♥str✉❝t✐♦♥✳ ❲❡ ✉s❡❞ t❤❡ ♣❤②❧♦✲✸✶✼
❣❡♥❡t✐❝ tr❡❡ t❤❛t ✐s ✐♥❝❧✉❞❡❞ ✇✐t❤ t❤❡ ❣r❡❡♥❣❡♥❡s ❞❛t❛❜❛s❡ ❢♦r ❛❧❧ ❛♥❛❧②s❡s✳ ❚❤❡✸✶✽
r❡s✉❧t✐♥❣ ❖❚❯ t❛❜❧❡ ✇❛s r❛r❡✜❡❞ t♦ ✻✵✵✵ s❡q✉❡♥❝❡s ♣❡r s❛♠♣❧❡✳✸✶✾
✶✵ t✐♠❡ ♣♦✐♥ts ✇❡r❡ r❛♥❞♦♠❧② ❞r❛✇♥ ❢r♦♠ ❡❛❝❤ ♦❢ t❤❡ ♠❛❧❡ t♦♥❣✉❡✱ ❢❡♠❛❧❡✸✷✵
t♦♥❣✉❡✱ ♠❛❧❡ ❢❡❝❡s ❛♥❞ ❢❡♠❛❧❡ ❢❡❝❡s ❞❛t❛s❡ts✱ ❣✐✈✐♥❣ ❛ t♦t❛❧ ♦❢ ♥❂✷✵ s❛♠♣❧❡s ❛t✸✷✶
❡❛❝❤ s✐t❡✳ ❚❛①❛ ♣r❡s❡♥t ✐♥ ❢❡✇❡r t❤❛♥ ✸✵ ♦❢ t❤❡ ✹✵ s❛♠♣❧❡s ✇❡r❡ ❞✐s❝❛r❞❡❞✱ ❛♥❞✸✷✷
♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✇❛s ❞♦♥❡ ❜② ❛❞❞✐♥❣ ♣s❡✉❞♦✲❝♦✉♥ts ♦❢ ✵✳✻✺ t♦ ❛❧❧ ✵ ❡♥tr✐❡s ✐♥✸✷✸
t❤❡ ❞❛t❛s❡t ❬✶❪✱ ❝♦♥✈❡rt✐♥❣ ❝♦✉♥ts ✐♥ ❡❛❝❤ s❛♠♣❧❡ t♦ r❡❧❛t✐✈❡ ❛❜✉♥❞❛♥❝❡s✱ ❛♥❞✸✷✹
t❤❡♥ r❡❣r❡ss✐♥❣ t❤❡ ■▲❘ ❝♦♦r❞✐♥❛t❡s ❛❣❛✐♥st ❜♦❞② s✐t❡✳ ❚❤❡ ❝♦♠♣❧❡t❡ ❘ s❝r✐♣t✸✷✺
✐s ❛✈❛✐❧❛❜❧❡ ✐♥ t❤❡ ✜❧❡ ✏❉❛t❛ ❆♥❛❧②s✐s ♣✐♣❡❧✐♥❡ ♦❢ t❤❡ ❋❚ ♠✐❝r♦❜✐♦♠❡✑✳✸✷✻
❈♦♠♣❧❡t❡ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ♦❢ t❤✐s ❞❛t❛s❡t ✇❛s ♣❡r❢♦r♠❡❞ ❜② st♦♣♣✐♥❣ t❤❡ ❛❧✲✸✷✼
❣♦r✐t❤♠ ✇❤❡♥ ❛ ❑❙✲t❡st ♦♥ t❤❡ ✉♥✐❢♦r♠✐t② ♦❢ P✲✈❛❧✉❡s ❢r♦♠ ❛♥❛❧②s❡s ♦❢ ✈❛r✐❛♥❝❡✸✷✽
♦❢ r❡❣r❡ss✐♦♥ ♦♥ ❝❛♥❞✐❞❛t❡ ■▲❘✲❝♦♦r❞✐♥❛t❡s ②✐❡❧❞❡❞ PKS > 0.05✳ ❚❤❡s❡ r❡s✉❧ts✸✷✾
✇❡r❡ ❝♦♠♣❛r❡❞ ✇✐t❤ ❛ st❛♥❞❛r❞✱ ♠✉❧t✐♣❧❡ ❤②♣♦t❤❡s✐s✲t❡st✐♥❣ ❛♥❛❧②s✐s ♦❢ ❈▲❘✲✸✸✵
tr❛♥s❢♦r♠❡❞ ❞❛t❛✳ ❚❤❡ s✉♠♠❛r② ♦❢ t❤❡ t❛①♦♥♦♠✐❝ ❞❡t❛✐❧ ❛t t❤❡ ✜rst t❤r❡❡ ❢❛❝t♦rs✸✸✶
✐s ♣r♦✈✐❞❡❞ ✐♥ t❤❡ r❡s✉❧ts s❡❝t✐♦♥✱ ❛♥❞ ❛ ❢✉❧❧ ❧✐st ♦❢ t❤❡ t❛①❛ ❢❛❝t♦r❡❞ ❛t ❡❛❝❤ st❡♣✸✸✷
✐s ❛✈❛✐❧❛❜❧❡ ✐♥ t❤❡ s✉♣♣❧❡♠❡♥t ❛♥❞ ❝❛♥ ❜❡ ❢✉rt❤❡r ❡①♣❧♦r❡❞ ✉s✐♥❣ t❤❡ ❘ ♣✐♣❡❧✐♥❡✸✸✸
♣r♦✈✐❞❡❞✳✸✸✹
❆♥❛❧②s✐s ♦❢ ❙♦✐❧ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛✸✸✺
❚❤❡ s♦✐❧ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡t ❢r♦♠ ❬✸✻❪ ✇❛s ✐♥❝❧✉❞❡❞ t♦ ✐❧❧✉str❛t❡ t❤❡ ❛❜✐❧✐t②✸✸✻
♦❢ ♣❤②❧♦❢❛❝t♦r t♦ ✇♦r❦ ♦♥ ❜✐❣❣❡r ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡ts ✇✐t❤ ❝♦♥t✐♥✉♦✉s ✐♥❞❡♣❡♥✲✸✸✼
❞❡♥t ✈❛r✐❛❜❧❡s ❛♥❞ ♠✉❧t✐♣❧❡ r❡❣r❡ss✐♦♥✳ ❉❡t❛✐❧s ♦♥ s❛♠♣❧❡ ❝♦❧❧❡❝t✐♦♥✱ s❡q✉❡♥❝✐♥❣✱✸✸✽
✶✷
♠❡t❛✲❞❛t❛ ♠❡❛s✉r❡♠❡♥ts ❛♥❞ ❖❚❯ ❝❧✉st❡r✐♥❣ ❛r❡ ❛✈❛✐❧❛❜❧❡ ✐♥ ❬✸✻❪✳ ❚❤❡ ♣❤②✲✸✸✾
❧♦❣❡♥② ✇❛s ❝♦♥str✉❝t❡❞ ❜② ❛❧✐❣♥✐♥❣ r❡♣r❡s❡♥t❛t✐✈❡ s❡q✉❡♥❝❡s ✉s✐♥❣ ❙■◆❆ ❬✸✹❪✱✸✹✵
tr✐♠♠✐♥❣ ❜❛s❡s t❤❛t r❡♣r❡s❡♥t❡❞ ❣❛♣s ✐♥ ≥✷✵✪ ♦❢ s❡q✉❡♥❝❡s✱ ❛♥❞ ✉s✐♥❣ ❢❛sttr❡❡✸✹✶
❬✸✸❪✳✸✹✷
❚❤❡ ❝♦♠♣❧❡t❡ ❞❛t❛s❡t ❝♦♥t❛✐♥❡❞ ✶✷✸✱✽✺✶ ❖❚❯s ❛♥❞ ✺✽✵ s❛♠♣❧❡s✳ ❉❛t❛ ✇❡r❡✸✹✸
✜❧t❡r❡❞ t♦ ✐♥❝❧✉❞❡ ❛❧❧ ❖❚❯s ✇✐t❤ ♦♥ ❛✈❡r❛❣❡ ✷ ♦r ♠♦r❡ s❡q✉❡♥❝❡s ❝♦✉♥t❡❞ ❛❝r♦ss✸✹✹
❛❧❧ s❛♠♣❧❡s✱ s❤r✐♥❦✐♥❣ t❤❡ ❞❛t❛s❡t t♦ ❉❂✸✱✸✼✾ ❖❚❯s✳ ❚❤❡ ❞❛t❛ ✇❡r❡ ❢✉rt❤❡r✸✹✺
tr✐♠♠❡❞ t♦ ✐♥❝❧✉❞❡ ♦♥❧② t❤♦s❡ s❛♠♣❧❡s ✇✐t❤ ❛✈❛✐❧❛❜❧❡ ♣❍✱ ❈ ❛♥❞ ◆ ♠❡t❛✲❞❛t❛✱✸✹✻
r❡❞✉❝✐♥❣ t❤❡ s❛♠♣❧❡ s✐③❡ t♦ ♥❂✺✺✶✳✸✹✼
P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✇❛s ❞♦♥❡ ❜② ❛❞❞✐♥❣ ♣s❡✉❞♦✲❝♦✉♥ts ♦❢ ✵✳✻✺ t♦ ❛❧❧ ✵ ❡♥tr✐❡s ✐♥✸✹✽
t❤❡ ❞❛t❛s❡t ❬✶❪✱ ❝♦♥✈❡rt✐♥❣ ❝♦✉♥ts ✐♥ ❡❛❝❤ s❛♠♣❧❡ t♦ r❡❧❛t✐✈❡ ❛❜✉♥❞❛♥❝❡s✱ ❛♥❞✸✹✾
♣❡r❢♦r♠✐♥❣ ♠✉❧t✐♣❧❡ r❡❣r❡ss✐♦♥ ♦❢ ♣❍✱ ❈ ❛♥❞ ◆ ♦♥ ■▲❘ ❝♦♦r❞✐♥❛t❡s✳ ❚❤❡ ✜rst✸✺✵
t❤r❡❡ ❢❛❝t♦rs ❛r❡ ✉s❡❞ ❢♦r ♦r❞✐♥❛t✐♦♥✲✈✐s✉❛❧✐③❛t✐♦♥✳ ❚♦ ❞❡t❡r♠✐♥❡ t❤❡ r❡❧❛t✐✈❡✸✺✶
✐♠♣♦rt❛♥❝❡ ♦❢ ❡❛❝❤ ❛❜✐♦t✐❝ ✈❛r✐❛❜❧❡ ✐♥ ❞r✐✈✐♥❣ ♣❤②❧♦❣❡♥❡t✐❝ ♣❛tt❡r♥s ♦❢ ♠✐❝r♦❜✐❛❧✸✺✷
❝♦♠♠✉♥✐t② ❝♦♠♣♦s✐t✐♦♥✱ ✇❡ ✉s❡❞ t❤❡ lmg ♠❡t❤♦❞ ❢r♦♠ t❤❡ ❘ ♣❛❝❦❛❣❡ ✬r❡❧❛✐♠♣♦✬✸✺✸
❬✶✾❪ ✇❤✐❝❤ ❛✈❡r❛❣❡s t❤❡ s❡q✉❡♥t✐❛❧ s✉♠s ♦❢ sq✉❛r❡s ♦✈❡r ❛❧❧ ♦r❞❡r✐♥❣s ♦❢ r❡❣r❡ss♦rs✸✺✹
t♦ ♦❜t❛✐♥ ❛ ♠❡❛s✉r❡ ♦❢ r❡❧❛t✐✈❡ ✐♠♣♦rt❛♥❝❡ ♦❢ ❡❛❝❤ r❡❣r❡ss♦r ✐♥ t❤❡ ♠✉❧t✐✈❛r✐❛t❡✸✺✺
♠♦❞❡❧✳✸✺✻
❘❡s✉❧ts✸✺✼
❲❡ ✜♥❞ t❤r❡❡ ♠❛✐♥ r❡s✉❧ts✳ ❋✐rst✱ ✇❡ ✜♥❞ t❤❛t ♦✉r ❛❧❣♦r✐t❤♠ ♦✉t✲♣❡r❢♦r♠s ❛✸✺✽
st❛♥❞❛r❞ t♦♦❧ ❢♦r ❛♥❛❧②③✐♥❣ ❝♦♠♣♦s✐t✐♦♥s ♦❢ ♣❛rts r❡❧❛t❡❞ ❜② ❛ tr❡❡ ✲ ✇❤❛t ✇❡✸✺✾
r❡❢❡r t♦ ❛s t❤❡ ✏r♦♦t❡❞ ■▲❘✑ tr❛♥s❢♦r♠ ✲ ❛♥❞ t❤❛t ✇❡ ❝❛♥ ♦❜t❛✐♥ ❛ ❝♦♥s❡r✈❛t✐✈❡✸✻✵
❡st✐♠❛t❡ ♦❢ t❤❡ ♥✉♠❜❡r ♦❢ ♣❤②❧♦❣❡♥❡t✐❝ ❢❛❝t♦rs ✐♥ s✐♠✉❧❛t❡❞ ❞❛t❛s❡ts ❛ ✇✐t❤ ❛✸✻✶
❦♥♦✇♥ ♥✉♠❜❡r ♦❢ ❛✛❡❝t❡❞ ❝❧❛❞❡s✳ ❙❡❝♦♥❞✱ ✇❡ ♣❤②❧♦❢❛❝t♦r ❛ ❞❛t❛s❡t ♦❢ t❤❡ ❤✉✲✸✻✷
♠❛♥ ♦r❛❧ ❛♥❞ ❢❡❝❛❧ ♠✐❝r♦❜✐♦♠❡s ❛♥❞ ✜♥❞ t❤❛t t❤❡ t❤r❡❡ ❞♦♠✐♥❛♥t ❡❞❣❡s ✐♥ t❤❡✸✻✸
♣❤②❧♦❣❡♥② ❛❝❝♦✉♥t ❢♦r ✶✼✳✻✪ ♦❢ t❤❡ ✈❛r✐❛t✐♦♥ ✐♥ ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t✐❡s ❛❝r♦ss✸✻✹
t❤❡s❡ s❛♠♣❧❡ s✐t❡s✱ ❡❞❣❡s ✇❤✐❝❤ ❛r❡ ♥♦t ❛ss✐❣♥❡❞ ❛ ✉♥✐q✉❡ t❛①♦♥♦♠✐❝ ❧❛❜❡❧ ❛♥❞✸✻✺
❛r❡ t❤✉s ❞✐✣❝✉❧t ♦r ✐♠♣♦ss✐❜❧❡ t♦ ♦❜t❛✐♥ ❢r♦♠ t❛①♦♥♦♠✐❝✲❜❛s❡❞ ❛♥❛❧②s❡s✳ ❚❤✐r❞✱✸✻✻
✇❡ s❤♦✇ t❤❛t ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❝❛♥ ❜❡ ❝♦♠❜✐♥❡❞ ✇✐t❤ ♠✉❧t✐♣❧❡ r❡❣r❡ss✐♦♥ t♦✸✻✼
r❡✈❡❛❧ t❤❛t ♣❍ ❞r✐✈❡s t❤❡ ♠❛✐♥ ♣❤②❧♦❣❡♥❡t✐❝ ♣❛tt❡r♥s ♦❢ ❝♦♠♠✉♥✐t② ❝♦♠♣♦s✐✲✸✻✽
t✐♦♥ ✐♥ s♦✐❧ ♠✐❝r♦❜✐♦♠❡s✱ ❛♥❞ s❤♦✇ t❤❛t ✐♥ ❢♦✉r ❢❛❝t♦rs ✇❡ s♣❧✐t t❤❡ ❆❝✐❞♦❜❛❝✲✸✻✾
t❡r✐❛ t❤r❡❡ t✐♠❡s ✲ ✐♥❝❧✉❞✐♥❣ ♦♥❡ s♣❧✐t t❤❛t ✐❞❡♥t✐✜❡s ❛ ♠♦♥♦♣❤②❧❡t✐❝ ❝❧❛❞❡ ♦❢✸✼✵
❆❝✐❞♦❜❛❝t❡r✐❛ t❤❛t ❝♦♥s✐sts ♦❢ ❛❧❦❛❧✐♣❤✐❧❡s✳ ❋✐♥❛❧❧②✱ ✉s✐♥❣ t❤❡ s♦✐❧ ❞❛t❛s❡t✱ ✇❡✸✼✶
✶✸
❞❡♠♦♥str❛t❡ ❤♦✇ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ②✐❡❧❞s t✇♦ ❝♦♠♣❧✐♠❡♥t❛r② ♠❡t❤♦❞s ❢♦r ❞✐✲✸✼✷
♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥ ❛♥❞ ♦r❞✐♥❛t✐♦♥✲✈✐s✉❛❧✐③❛t✐♦♥ t❤❛t t❡❧❧ ❛ s✐♠♣❧✐✜❡❞ st♦r②✸✼✸
♦❢ ❤♦✇ t❤❡ ♠❛❥♦r ♣❤②❧♦❣❡♥❡t✐❝ ❣r♦✉♣s ♦❢ ❖❚❯s ❝❤❛♥❣❡ ✇✐t❤ ♣❍✳ ❚❤r♦✉❣❤♦✉t ♦✉r✸✼✹
r❡s✉❧ts✱ ✇❡ ❡♠♣❤❛s✐③❡ t❤❛t t❤❡ ♣❤②❧♦❣❡♥❡t✐❝ ✐♥❢❡r❡♥❝❡s ♠❛❞❡ ❜② ♣❤②❧♦❢❛❝t♦r✐③❛✲✸✼✺
t✐♦♥ ❝♦✉❧❞ ❜❡ ✐♥✈✐s✐❜❧❡ t♦ t❛①♦♥♦♠✐❝✲❜❛s❡❞ ❛♥❛❧②s❡s✱ ❛♥❞ ✇❡ ❝♦♥❝❡♣t✉❛❧❧② ❝♦♠✲✸✼✻
♣❛r❡ t❤❡ ❞✐♠❡♥s✐♦♥❛❧✐t②✲r❡❞✉❝t✐♦♥s ♦❢ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ t♦ t❤❡ ❧❡ss✲✐♥t❡r♣r❡t❛❜❧❡✸✼✼
♦✉t♣✉t ❢r♦♠ st❛♥❞❛r❞ ♦r❞✐♥❛t✐♦♥✲✈✐s✉❛❧✐③❛t✐♦♥ t♦♦❧s✳✸✼✽
P♦✇❡r ❆♥❛❧②s✐s ❛♥❞ ❈♦♥s❡r✈❛t✐✈❡ ❙t♦♣♣✐♥❣ ♦❢ P❤②❧♦❢❛❝t♦r✲✸✼✾
✐③❛t✐♦♥✸✽✵
P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ r❡♠❡❞✐❡s t❤❡ str✉❝t✉r❡❞ r❡s✐❞✉❛❧s ❢r♦♠ t❤❡ r♦♦t❡❞ ■▲❘ r❡✲✸✽✶
❣r❡ss✐♦♥ ♦♥ ❞❛t❛ ✇✐t❤ ❢♦❧❞✲❝❤❛♥❣❡s ✐♥ ❛❜✉♥❞❛♥❝❡s ✇✐t❤✐♥ ❝❧❛❞❡s✳ P❤②❧♦❢❛❝t♦r✲✸✽✷
✐③❛t✐♦♥ ❛❧s♦ r❡♠❡❞✐❡s t❤❡ ♣r♦❜❧❡♠ ♦❢ ❤✐❣❤ ❢❛❧s❡✲♣♦s✐t✐✈❡ r❛t❡s ❛r✐s✐♥❣ ❢r♦♠ t❤❡✸✽✸
♥❡st❡❞✲❞❡♣❡♥❞❡♥❝❡ ❛♥❞ ❝♦rr❡❧❛t❡❞ ❝♦♦r❞✐♥❛t❡s ♦❢ t❤❡ r♦♦t❡❞ ■▲❘ tr❛♥s❢♦r♠✱ ❛s✸✽✹
s❡q✉❡♥t✐❛❧ ✐♥❢❡r❡♥❝❡s ✐♥ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❛r❡ ✐♥❞❡♣❡♥❞❡♥t✳ P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✸✽✺
♦✉t✲♣❡r❢♦r♠s t❤❡ r♦♦t❡❞ ■▲❘ ✐♥ ✐❞❡♥t✐❢②✐♥❣ t❤❡ ❝♦rr❡❝t ❝❧❛❞❡s ✇✐t❤ ❛ ❣✐✈❡♥ ❢♦❧❞✲✸✽✻
❝❤❛♥❣❡ ✐♥ ❛❜✉♥❞❛♥❝❡ ✭❋✐❣s✳ ✸❛ ❛♥❞ ✸❜✮✱ ❛♥❞ ❝❛♥ ❜❡ ♣❛✐r❡❞ ✇✐t❤ ♦t❤❡r ❛❧❣♦r✐t❤♠s✸✽✼
❛ss❡ss✐♥❣ r❡s✐❞✉❛❧ str✉❝t✉r❡ t♦ st♦♣ ❢❛❝t♦r✐③❛t✐♦♥ ✇❤❡♥ t❤❡r❡ ✐s ♥♦ r❡s✐❞✉❛❧ str✉❝✲✸✽✽
t✉r❡ ❛♥❞ t❤✉s ❛❝❝✉r❛t❡❧② ✐❞❡♥t✐❢② t❤❡ ♥✉♠❜❡r ♦❢ ❛✛❡❝t❡❞ ❝❧❛❞❡s ✭❋✐❣✳ ✸❝✮✳ ❋✐✲✸✽✾
♥❛❧❧②✱ ❜② ❢♦❝✉s✐♥❣ t❤❡ ✐♥❢❡r❡♥❝❡s ♦♥ ❡❞❣❡s ✐♥st❡❛❞ ♦❢ ♥♦❞❡s ✐♥ t❤❡ ♣❤②❧♦❣❡♥②✱ t❤✐s✸✾✵
❛❧❣♦r✐t❤♠ ✇♦r❦s ♦♥ tr❡❡s ✇✐t❤ ♣♦❧②t♦♠✐❡s ❛♥❞ ❞♦❡s♥✬t r❡q✉✐r❡ ❛ ❢♦r❝❡❞ r❡s♦❧✉t✐♦♥✸✾✶
♦❢ ♣♦❧②t♦♠✐❡s t♦ ❝♦♥str✉❝t ❛ s❡q✉❡♥t✐❛❧ ❜✐♥❛r② ♣❛rt✐t✐♦♥ ♦❢ t❤❡ ❖❚❯s✳✸✾✷
❖r❛❧✲❋❡❝❛❧ ▼✐❝r♦❜✐♦♠❡✸✾✸
P❡r❢♦r♠✐♥❣ r❡❣r❡ss✐♦♥ ♦❢ s❛♠♣❧❡ s✐t❡ ♦♥ ❝❡♥t❡r❡❞ ❧♦❣✲r❛t✐♦ ✭❈▲❘✮ tr❛♥s❢♦r♠❡❞✸✾✹
❖❚❯ t❛❜❧❡s✱ ✇✐t❤ ✷✾✵ ❖❚❯s ❛♥❞ ✹✵ s❛♠♣❧❡s✱ ②✐❡❧❞❡❞ ✷✸✻ s✐❣♥✐✜❝❛♥t ❖❚❯s✸✾✺
❛t ❛ ❢❛❧s❡✲❞✐s❝♦✈❡r② r❛t❡ ♦❢ ✶✪❀ t❤❡ ♣❤②❧♦❣❡♥❡t✐❝ s✐❣♥❛❧ ♦❢ t❤❡s❡ ❖❚❯s ❢r♦♠✸✾✻
❈▲❘✲❜❛s❡❞ ✐♥❢❡r❡♥❝❡s ♠❛② ❜❡ ❞✐✣❝✉❧t t♦ ♣❛rs❡ ♦✉t✳ P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ♦❢ t❤❡✸✾✼
♦r❛❧✲❢❡❝❛❧ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡t ②✐❡❧❞❡❞ ✶✹✷ ❢❛❝t♦rs✱ t❤❡ t♦♣ t❤r❡❡ ♦❢ ✇❤✐❝❤ ❡①♣❧❛✐♥✸✾✽
✶✼✳✻✪ ♦❢ t❤❡ ✈❛r✐❛t✐♦♥ ✐♥ t❤❡ ❞❛t❛s❡t✱ ❢❛❝t♦rs ✇❤✐❝❤ ❝♦rr❡s♣♦♥❞ t♦ ❝❧❡❛r❧② ✈✐s✐❜❧❡✸✾✾
❜❧♦❝❦s ✐♥ ♣❤②❧♦❣❡♥❡t✐❝ ❤❡❛t♠❛♣s ♦❢ t❤❡ ❖❚❯ t❛❜❧❡ ✭❋✐❣✳ ✹✮✳ ❚❤❡ ❢❛❝t♦rs s♣❛♥✹✵✵
❛ r❛♥❣❡ ♦❢ t❛①♦♥♦♠✐❝ s❝❛❧❡s ❛♥❞ ❛❧❧ ♦❢ t❤❡♠ ✇♦✉❧❞ ❜❡ ✐♥✈✐s✐❜❧❡ t♦ t❛①♦♥♦♠✐❝✲✹✵✶
❜❛s❡❞ ❛♥❛❧②s❡s✳ ❇❡❧♦✇✱ ✇❡ s✉♠♠❛r✐③❡ t❤❡ ❢❛❝t♦rs ✲ t❤❡ P✲✈❛❧✉❡s ❢r♦♠ r❡❣r❡ss✐♦♥✱✹✵✷
t❤❡ t❛①❛ s♣❧✐t ❛t ❡❛❝❤ ❢❛❝t♦r✱ t❤❡ ❜♦❞② s✐t❡ ❛ss♦❝✐❛t✐♦♥s ♣r❡❞✐❝t❡❞ ❜② ❣❡♥❡r❛❧✲✹✵✸
✐③❡❞ ❧✐♥❡❛r ♠♦❞❡❧✐♥❣ ♦❢ t❤❡ ■▲❘ ❝♦♦r❞✐♥❛t❡ ❛❣❛✐♥st ❜♦❞② s✐t❡✱ ❛♥❞ ✜♥❡r ❞❡t❛✐❧✹✵✹
✶✹
❛❜♦✉t t❤❡ t❛①♦♥♦♠✐❝ ✐❞❡♥t✐t✐❡s ❛♥❞ ❦♥♦✇♥ ❡❝♦❧♦❣② ♦❢ ♠♦♥♦♣❤②❧❡t✐❝ t❛①❛ ❜❡✐♥❣✹✵✺
s♣❧✐t✳ P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ♦❢ t❤❡s❡ ❞❛t❛ ✐♥❞✐❝❛t❡s t❤❛t ❛ ❢❡✇ ❝❧❛❞❡s ❡①♣❧❛✐♥ ❛ ❧❛r❣❡✹✵✻
❢r❛❝t✐♦♥ ♦❢ t❤❡ ✈❛r✐❛t✐♦♥ ✐♥ t❤❡ ❞❛t❛✱ ❛♥❞ ♠❛♥② ♠♦r❡ ❝❧❛❞❡s ❝❛♥ ❜❡ ✐❞❡♥t✐✜❡❞ ❛s✹✵✼
❝♦♥t❛✐♥✐♥❣ t❤❡ s❛♠❡ ✐♥tr✐❝❛t❡ ❞❡t❛✐❧ ❛s t❤❡ ♣❤②❧♦❣❡♥❡t✐❝ ❢❛❝t♦rs ♣r❡s❡♥t❡❞ ❜❡❧♦✇✳✹✵✽
❚❤❡ ❜✐♦❧♦❣② ♦❢ ♠✐❝r♦❜✐❛❧ ❤✉♠❛♥✲❜♦❞②✲s✐t❡ ❛ss♦❝✐❛t✐♦♥ ❝❛♥ ❢♦❝✉s ♦♥ t❤❡s❡ ❞♦♠✲✹✵✾
✐♥❛♥t ❢❛❝t♦rs ✲ ✇❤✐❝❤ tr❛✐ts ❛♥❞ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r② ❞r✐✈❡ t❤❡s❡ ♠♦♥♦♣❤②❧❡t✐❝✹✶✵
❣r♦✉♣s✬ str♦♥❣✱ ❝♦♠♠♦♥ ❛ss♦❝✐❛t✐♦♥ ✇✐t❤ ❜♦❞② s✐t❡s❄✹✶✶
❚❤❡ ✜rst ❢❛❝t♦r ✭P = 4.90 × 10−30✮ s♣❧✐t ❆❝t✐♥♦❜❛❝t❡r✐❛ ❛♥❞ ❆❧♣❤❛✲✱ ❇❡t❛✲✹✶✷
✱ ●❛♠♠❛✲✱ ❛♥❞ ❉❡❧t❛✲♣r♦t❡♦❜❛❝t❡r✐❛ ❢r♦♠ ❊♣s✐❧♦♥♣r♦t❡♦❜❛❝t❡r✐❛ ❛♥❞ t❤❡ r❡st✹✶✸
✭❋✐❣✳ ❙✹✮✳ ❚❤❡ ✉♥❞❡r❧②✐♥❣ ❣❡♥❡r❛❧✐③❡❞ ❧✐♥❡❛r ♠♦❞❡❧ ♣r❡❞✐❝ts t❤❡ ❆❝t✐♥♦❜❛❝t❡r✐❛✹✶✹
❛♥❞ ♥♦♥✲❊♣s✐❧♦♥✲♣r♦t❡♦❜❛❝t❡r✐❛ t♦ ❜❡ ✵✳✹① ❛s ❛❜✉♥❞❛♥t ❛s t❤❡ r❡st ✐♥ t❤❡ ❣✉t ❛♥❞✹✶✺
✸✳✻① ❛s ❛❜✉♥❞❛♥t ❛s t❤❡ r❡st ✐♥ t❤❡ t♦♥❣✉❡✳ ❚❤❡ ❆❝t✐♥♦❜❛❝t❡r✐❛ ✐❞❡♥t✐✜❡❞ ❛s ♠♦r❡✹✶✻
❛❜✉♥❞❛♥t ✐♥ t❤❡ t♦♥❣✉❡ ✐♥❝❧✉❞❡ ❢♦✉r ♠❡♠❜❡rs ♦❢ t❤❡ ♣❧❛q✉❡✲❛ss♦❝✐❛t❡❞ ❢❛♠✐❧②✹✶✼
❆❝t✐♥♦♠②❝❡t❛❝❡❛❡✱ ♦♥❡ ✉♥❝❧❛ss✐✜❡❞ s♣❡❝✐❡s ♦❢ ❈♦r♥②❜❛❝t❡r✐✉♠✱ t❤r❡❡ ♠❡♠❜❡rs✹✶✽
♦❢ t❤❡ ♠♦✉t❤✲❛ss♦❝✐❛t❡❞ ❣❡♥✉s ❘♦t❤✐❛ ❬✷✸❪✱ ❛♥❞ ♦♥❡ ✉♥❝❧❛ss✐✜❡❞ s♣❡❝✐❡s ♦❢ t❤❡✹✶✾
✈❛❣✐♥❛❧✲❛ss♦❝✐❛t❡❞ ❣❡♥✉s ❆t♦♣♦❜✐✉♠ ❬✾❪✳ ❲✐t❤ ❛ st❛♥❞❛r❞ ♠✉❧t✐✈❛r✐❛t❡ ❛♥❛❧②s✐s✹✷✵
♦❢ t❤❡ ❈▲❘✲tr❛♥s❢♦r♠❡❞ ❞❛t❛✱ ❛❧❧ ♥✐♥❡ ♦❢ t❤❡s❡ ❆❝t✐♥♦❜❛❝t❡r✐❛ ✇❡r❡ ✐❞❡♥t✐✜❡❞✹✷✶
❛s s✐❣♥✐✜❝❛♥t❧② ♠♦r❡ ❛❜✉♥❞❛♥t ✐♥ t❤❡ t♦♥❣✉❡ ❢r♦♠ r❡❣r❡ss✐♦♥ ♦❢ t❤❡ ✐♥❞✐✈✐❞✉❛❧✹✷✷
❖❚❯s ✇❤❡♥ ✉s✐♥❣ ❡✐t❤❡r ❛ ✶✪ ❢❛❧s❡✲❞✐s❝♦✈❡r② r❛t❡ ♦r ❛ ❇♦♥❢❡r♦♥♥✐ ❝♦rr❡❝t✐♦♥ ✲✹✷✸
t❤❡s❡ ♠♦♥♦♣❤②❧❡t✐❝ t❛①❛ ❛❧❧ ✐♥❞✐✈✐❞✉❛❧❧② s❤♦✇ ❛ str♦♥❣ ♣r❡❢❡r❡♥❝❡ ❢♦r t❤❡ s❛♠❡✹✷✹
❜♦❞② s✐t❡✱ ❛♥❞ t❤❡✐r ❜❛s❛❧ ❜r❛♥❝❤ ✇❛s ✐❞❡♥t✐✜❡❞ ❛s ♦✉r ✜rst ♣❤②❧♦❣❡♥❡t✐❝ ❢❛❝✲✹✷✺
t♦r✳ ❚❤❡ r❡♠❛✐♥✐♥❣ ❆❧♣❤❛✲✱ ❇❡t❛✲✱ ●❛♠♠❛✲ ❛♥❞ ❉❡❧t❛✲♣r♦t❡♦❜❛❝t❡r✐❛ ❣r♦✉♣❡❞✹✷✻
✇✐t❤ t❤❡ ❆❝t✐♥♦❜❛❝t❡r✐❛ ❝♦♥s✐st❡❞ ♦❢ ✸✶ ❖❚❯s✱ ❛♥❞ t❤❡ ❊♣s✐❧♦♥♣r♦t❡♦❜❛❝t❡✐r❛✹✷✼
s♣❧✐t ❢r♦♠ t❤❡ r❡st ✇❡r❡ t❤r❡❡ ✉♥❝❧❛ss✐✜❡❞ s♣❡❝✐❡s ♦❢ t❤❡ ❣❡♥✉s ❈❛♠♣②❧♦❜❛❝t❡r✳✹✷✽
❚❤❡ ❣r♦✉♣✐♥❣ ♦❢ ❆❝t✐♥♦❜❛❝t❡r✐❛ ✇✐t❤ t❤❡ ♥♦♥✲❊♣s✐❧♦♥ Pr♦t❡♦❜❛❝t❡r✐❛ ♠♦t✐✈❛t❡s✹✷✾
t❤❡ ♥❡❡❞ ❢♦r ❛❝❝✉r❛t❡ ♣❤②❧♦❣❡♥✐❡s ✐♥ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✱ ❜✉t ❛❧s♦ ✐❧❧✉str❛t❡s t❤❡✹✸✵
♣r♦♠✐s❡ ♦❢ ✐❞❡♥t✐❢②✐♥❣ ❝❧❛❞❡s ♦❢ ✐♥t❡r❡st ✇❤❡r❡ t❤❡ ♣❤②❧♦❣❡♥② ✐s ❝♦rr❡❝t ❛♥❞ t❤❡✹✸✶
t❛①♦♥♦♠② ✐s ♥♦t✳✹✸✷
❚❤❡ s❡❝♦♥❞ ❢❛❝t♦r ✭P = 1.15 × 10−31✮ s♣❧✐ts ✶✻ ❋✐r♠✐❝✉t❡s ♦❢ t❤❡ ❝❧❛ss ❇❛❝✐❧❧✐✹✸✸
❢r♦♠ t❤❡ ♦❜❧✐❣❛t❡❧② ❛♥❛❡r♦❜✐❝ ❋✐r♠✐❝✉t❡s ❝❧❛ss ❈❧♦str✐❞✐❛ ❛♥❞ t❤❡ r❡♠❛✐♥✐♥❣✹✸✹
♣❛r❛♣❤②❧❡t✐❝ ❣r♦✉♣ ❝♦♥t❛✐♥✐♥❣ ❊♣s✐❧♦♥♣r♦t❡♦❜❛❝t❡r✐❛ ❛♥❞ t❤❡ r❡st✳ ❚❤❡ ❇❛❝✐❧❧✐✹✸✺
❛r❡✱ ♦♥ ❛✈❡r❛❣❡✱ ✵✳✸① ❛s ❛❜✉♥❞❛♥t ✐♥ t❤❡ ❣✉t ❛s t❤❡ ♣❛r❛♣❤②❧❡t✐❝ r❡♠❛✐♥✐♥❣ ❖❚❯s✹✸✻
❛♥❞ ✸✳✾① ❛s ❛❜✉♥❞❛♥t ✐♥ t❤❡ t♦♥❣✉❡✳ ❚❤❡ ✶✻ ❇❛❝✐❧❧✐ ❖❚❯s ❢❛❝t♦r❡❞ ❤❡r❡ ❝♦♥t❛✐♥✹✸✼
✶✷ ✉♥❝❧❛ss✐✜❡❞ s♣❡❝✐❡s ♦❢ t❤❡ ❣❡♥✉s ❙tr❡♣t♦❝♦❝❝✉s✱ ✇❡❧❧ ❦♥♦✇♥ ❢♦r ✐ts ❛ss♦❝✐❛t✐♦♥✹✸✽
✇✐t❤ t❤❡ ♠♦✉t❤ ❬✷✵❪✱ ♦♥❡ ♠❡♠❜❡r ♦❢ t❤❡ ❣❡♥✉s ▲❛❝t♦❝♦❝❝✉s✱ ♦♥❡ ✉♥❝❧❛ss✐✜❡❞✹✸✾
s♣❡❝✐❡s ♦❢ t❤❡ ♠✉❝♦s❛❧✲❛ss♦❝✐❛t❡❞ ❣❡♥✉s ●❡♠❡❧❧❛✱ ❛♥❞ t✇♦ ♠❡♠❜❡rs t❤❡ ❢❛♠✐❧②✹✹✵
✶✺
❈❛r♥♦❜❛❝t❡r✐❛❝❡❛❡ ♦❢t❡♥ ❛ss♦❝✐❛t❡❞ ✇✐t❤ ✜s❤ ❛♥❞ ♠❡❛t ♣r♦❞✉❝ts ❬✷✺❪✳✹✹✶
❚❤❡ t❤✐r❞ ❢❛❝t♦r ✭P = 1.37× 10−28✮ s❡♣❛r❛t❡❞ ✶✺ ♠❡♠❜❡rs ♦❢ t❤❡ ❇❛❝t❡r♦✐❞❡t❡s✹✹✷
❢❛♠✐❧② Pr❡✈♦t❡❧❧❛❝❡❛❡ ❢r♦♠ ❛❧❧ ♦t❤❡r ❇❛❝t❡r♦✐❞❡t❡s ❛♥❞ t❤❡ r❡♠❛✐♥✐♥❣ ♣❛r❛✲✹✹✸
♣❤②❧❡t✐❝ ❣r♦✉♣ ♦❢ ❖❚❯s ♥♦t s♣❧✐t ❜② ♣r❡✈✐♦✉s ❢❛❝t♦rs✳ ❚❤❡ Pr❡✈♦t❡❧❧❛❝❡❛❡ s♣❧✐t ✐♥✹✹✹
t❤❡ t❤✐r❞ ❢❛❝t♦r ✇❡r❡ ❛❧❧ ♦❢ t❤❡ ❣❡♥✉s Pr❡✈♦t❡❧❧❛✱ ✐♥❝❧✉❞✐♥❣ t❤❡ s♣❡❝✐❡s Pr❡✈♦t❡❧❧❛✹✹✺
♠❡❧❛♥✐♥♦❣❡♥✐❝❛ ❛♥❞ Pr❡✈♦t❡❧❧❛ ♥❛♥❝❡✐❡♥s✐s ❢♦✉♥❞ t♦ ❤❛✈❡ ❛❜✉♥❞❛♥❝❡s ✵✳✸① ❛s✹✹✻
❛❜✉♥❞❛♥t ✐♥ t❤❡ ❣✉t ❛♥❞ ✹✳✵① ❛s ❛❜✉♥❞❛♥t ✐♥ t❤❡ t♦♥❣✉❡ r❡❧❛t✐✈❡ t♦ t❤❡ ♦t❤❡r✹✹✼
t❛①❛ ❢r♦♠ ✇❤✐❝❤ t❤❡② ✇❡r❡ s♣❧✐t✳✹✹✽
❚❤❡s❡ ✜rst t❤r❡❡ ❢❛❝t♦rs ❝❛♣t✉r❡ ♠❛❥♦r ❜❧♦❝❦s ✈✐s✐❜❧❡ ✐♥ t❤❡ ❞❛t❛s❡t ❝❛♥ ❜❡ ✉s❡❞✹✹✾
❛s ❞✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥ t♦♦❧ ✇✐t❤ ❛ ♣❤②❧♦❣❡♥❡t✐❝ ✐♥t❡r♣r❡t❛t✐♦♥ ✭❋✐❣✳ ✹✮✳✹✺✵
❲❤✐❧❡ tr❛❞✐t✐♦♥❛❧ ♦r❞✐♥❛t✐♦♥✲✈✐s✉❛❧✐③❛t✐♦♥ t♦♦❧s ♠❛② ❝❛♣t✉r❡ ❧❛r❣❡r ❢r❛❝t✐♦♥s ♦❢✹✺✶
✈❛r✐❛t✐♦♥ ♦❢ t❤❡ ❞❛t❛✱ ♣❤②❧♦❣❡♥❡t✐❝ ❢❛❝t♦r✐③❛t✐♦♥ ②✐❡❧❞s ❛ ❢❡✇ ✈❛r✐❛❜❧❡s ✲ r❛t✐♦s ♦❢✹✺✷
❝❧❛❞❡s ✲ ✇❤✐❝❤ ❝❛♣t✉r❡ ❧❛r❣❡ ❜❧♦❝❦s ♦❢ ✈❛r✐❛t✐♦♥ ✐♥ t❤❡ ❞❛t❛ ❛♥❞ ❝❛♥ ❜❡ tr❛❝❡❞ t♦✹✺✸
s✐♥❣❧❡ ❡❞❣❡s ✐♥ t❤❡ ♣❤②❧♦❣❡♥② ❝♦rr❡s♣♦♥❞✐♥❣ t♦ ♠❡❛♥✐♥❣❢✉❧ s♣❧✐ts ❜❡t✇❡❡♥ t❛①❛✱✹✺✹
❡❞❣❡s ✇❤❡r❡ tr❛✐ts ❧✐❦❡❧② ❛r♦s❡ ✇❤✐❝❤ ❣♦✈❡r♥ t❤❡ ❞✐✛❡r❡♥t✐❛❧ ❛❜✉♥❞❛♥❝❡s ❛❝r♦ss✹✺✺
s❛♠♣❧❡ s✐t❡s ❛♥❞ ❡♥✈✐r♦♥♠❡♥t❛❧ ❣r❛❞✐❡♥ts ♦r r❡s♣♦♥s❡s t♦ tr❡❛t♠❡♥ts ✭❋✐❣✳ ✹❜✱✹✺✻
s✉♣♣❧❡♠❡♥t❛❧ ❋✐❣s✳ ❙✹✲❙✽✮✳✹✺✼
❯s✐♥❣ t❤❡ ❑❙✲t❡st st♦♣♣✐♥❣ ❝r✐t❡r✐♦♥✱ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✇❛s t❡r♠✐♥❛t❡❞ ❛t ✶✹✷✹✺✽
❢❛❝t♦rs✱ ❡❛❝❤ ❝♦rr❡s♣♦♥❞✐♥❣ t♦ ❛ ❜r❛♥❝❤ ✐♥ t❤❡ ♣❤②❧♦❣❡♥❡t✐❝ tr❡❡ s❡♣❛r❛t✐♥❣ t✇♦✹✺✾
❣r♦✉♣s ♦❢ ❖❚❯s ❜❛s❡❞ ♦♥ t❤❡✐r ❞✐✛❡r❡♥t✐❛❧ ❛❜✉♥❞❛♥❝❡s ✐♥ t❤❡ t♦♥❣✉❡ ❛♥❞ ❢❡✲✹✻✵
❝❡s✳ ❚❤❡s❡ ✶✹✷ ❢❛❝t♦rs ❞❡✜♥❡ ✶✹✸ ❣r♦✉♣s✱ ♦r ✇❤❛t ✇❡ ❝❛❧❧ ✬❜✐♥s✬✱ ♦❢ t❛①❛ ✇❤✐❝❤✹✻✶
r❡♠❛✐♥ ✉♥s♣❧✐t ❜② t❤❡ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✳ ❚❤❡ ❜✐♥s ✈❛r② ✐♥ s✐③❡❀ ✶✶✷ ❜✐♥s ❝♦♥✲✹✻✷
t❛✐♥❡❞ ♦♥❧② s✐♥❣❧❡ ❖❚❯s✱ ✇❤❡r❡❛s ✽ ✇❡r❡ ♠♦♥♦♣❤②❧❡t✐❝ ❝❧❛❞❡s ❛♥❞ t❤❡ r❡st ❛r❡✹✻✸
♣❛r❛♣❤②❧❡t✐❝ ❣r♦✉♣s ♦❢ ❖❚❯s✱ t❤❡ r❡s✉❧t ♦❢ t❛①❛ ✇✐t❤✐♥ ❛ ♠♦♥♦♣❤②❧❡t✐❝ ❣r♦✉♣✹✻✹
❜❡✐♥❣ ❢❛❝t♦r❡❞✱ ②✐❡❧❞✐♥❣ ♦♥❡ ♠♦♥♦♣❤②❧❡t✐❝ ❣r♦✉♣ ❛♥❞ ♦♥❡ ♣❛r❛♣❤②❧❡t✐❝ ❣r♦✉♣✳ ❖❢✹✻✺
t❤❡ ✶✶✷ s✐♥❣❧❡✲❖❚❯ ❜✐♥s ❡①tr❛❝t❡❞ ❢r♦♠ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✱ ✼✽ ✇❡r❡ ❛❧s♦ ✐❞❡♥✲✹✻✻
t✐✜❡❞ ❛s s✐❣♥✐✜❝❛♥t ❛t ❛ ❢❛❧s❡✲❞✐s❝♦✈❡r② r❛t❡ ♦❢ ✶✪✳ ❙♦♠❡ ♠♦♥♦♣❤②❧❡t✐❝ ❜✐♥s✹✻✼
✐♥❝❧✉❞❡❞ ❣r♦✉♣s ♦❢ ✉♥❝❧❛ss✐✜❡❞ ❣❡♥❡r❛ t❤❛t ✇♦✉❧❞ ♥♦t ❜❡ ❣r♦✉♣❡❞ ❛t t❤❡ ❣❡♥✉s✹✻✽
❧❡✈❡❧ ✉♥❞❡r st❛♥❞❛r❞ t❛①♦♥♦♠②✲❜❛s❡❞ ❛♥❛❧②s❡s✳ ❋♦r ✐♥st❛♥❝❡✱ t✇♦ ♠♦♥♦♣❤②❧❡t✐❝✹✻✾
❝❧❛❞❡s ♦❢ t❤❡ ❋✐r♠✐❝✉t❡s ❢❛♠✐❧② ▲❛❝❤♥♦s♣✐r❛❝❡❛❡ ✇❡r❡ ✐❞❡♥t✐✜❡❞ ❛s ❤❛✈✐♥❣ ❞✐❢✲✹✼✵
❢❡r❡♥t ♣r❡❢❡rr❡❞ ❜♦❞② s✐t❡s✱ ②❡t ❜♦t❤ ❝❧❛❞❡s ✇❡r❡ ✉♥❝❧❛ss✐✜❡❞ ❛t t❤❡ ❣❡♥✉s ❧❡✈❡❧✳✹✼✶
❚❛①♦♥♦♠✐❝✲❜❛s❡❞ ❛♥❛❧②s❡s ✇♦✉❧❞ ❡✐t❤❡r ♦♠✐t t❤❡s❡ ✉♥❝❧❛ss✐✜❡❞ ❣❡♥❡r❛✱ ♦r ❣r♦✉♣✹✼✷
t❤❡♠ t♦❣❡t❤❡r ❛♥❞ ♠❛❦❡ ✐t ❞✐✣❝✉❧t t♦ ♦❜s❡r✈❡ ❛ s✐❣♥❛❧ ❞✉❡ t♦ t❤❡ t✇♦ s✉❜✲❣r♦✉♣s✹✼✸
❤❛✈✐♥❣ ❞✐✛❡r❡♥t r❡s♣♦♥s❡s t♦ ❜♦❞② s✐t❡✳✹✼✹
✶✻
❙♦✐❧ ▼✐❝r♦❜✐♦♠❡✹✼✺
❚❤❡ s♦✐❧ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡t ✇❛s ♠✉❝❤ ❧❛r❣❡r ✲ ✸✱✸✼✾ ❖❚❯s ❛♥❞ ✺✽✵ s❛♠♣❧❡s✹✼✻
✲ ❛♥❞ ❛ ♠✉❝❤ s♠❛❧❧❡r ❢r❛❝t✐♦♥ ♦❢ t❤❡ ✈❛r✐❛t✐♦♥ ❝♦✉❧❞ ❜❡ ❡①♣❧❛✐♥❡❞ ❜② t❤❡ ❞♦♠✲✹✼✼
✐♥❛♥t ❢❛❝t♦rs r❡s✉❧t✐♥❣ ❢r♦♠ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✳ P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❝♦♥✜r♠❡❞✹✼✽
t❤❛t t❤❡ ♣❍ ♦❢ t❤❡ ❡♥✈✐r♦♥♠❡♥t ♣❧❛②s ❛ ❞♦♠✐♥❛♥t r♦❧❡ ✐♥ t❤❡ ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉✲✹✼✾
♥✐t② ❝♦♠♣♦s✐t✐♦♥✱ ❝♦♥s✐st❡♥t ✇✐t❤ ♣r❡✈✐♦✉s ❛♥❛❧②s❡s ❜❛s❡❞ ♦♥ ▼❛♥t❡❧ t❡sts ❬✸✻❪✳✹✽✵
❉♦♠✐♥❛♥❝❡ ❛♥❛❧②s✐s ♦❢ t❤❡ ❣❡♥❡r❛❧✐③❡❞ ❧✐♥❡❛r ♠♦❞❡❧s ❛ss♦❝✐❛t❡❞ ✇✐t❤ ❡❛❝❤ ❢❛❝t♦r✹✽✶
❞❡t❡r♠✐♥❡❞ ♣❍ t♦ ❛❝❝♦✉♥t ❢♦r ❛♣♣r♦①✐♠❛t❡❧② ✾✷✳✽✼✪✱ ✽✾✳✼✽✪✱ ❛♥❞ ✾✷✳✾✹✪ ♦❢ t❤❡✹✽✷
❡①♣❧❛✐♥❡❞ ✈❛r✐❛♥❝❡ ✐♥ t❤❡ ✜rst✱ s❡❝♦♥❞✱ ❛♥❞ t❤✐r❞ ❢❛❝t♦r✱ r❡s♣❡❝t✐✈❡❧②✳ ❈ ❛♥❞ ◆✹✽✸
✇❡r❡ r❡❧❛t✐✈❡❧② ✉♥✐♠♣♦rt❛♥t✱ ❛♥❞ t❤❡ ❞♦♠✐♥❛♥❝❡ ♦❢ ♣❍ ✐♥ t❤❡ ✜rst t❤r❡❡ ❢❛❝t♦rs✹✽✹
❝❛♥ ❜❡ ✈✐s✉❛❧✐③❡❞ ❜② ♦r❞✐♥❛t✐♦♥✲✈✐s✉❛❧✐③❛t✐♦♥ ♣❧♦ts ♦❢ t❤❡ ■▲❘ ❝♦♦r❞✐♥❛t❡s ♦❢ t❤❡✹✽✺
✜rst t❤r❡❡ ❢❛❝t♦rs ✭❋✐❣✳ ✺❛✮✳✹✽✻
❚❤❡ ✜rst ❢❛❝t♦r s♣❧✐ts ❛ ❣r♦✉♣ ♦❢ ✷✵✻ ❖❚❯s ✐♥ t✇♦ ❝❧❛ss❡s ♦❢ ❆❝✐❞♦❜❛❝t❡r✐❛ ❢r♦♠✹✽✼
❛❧❧ ♦t❤❡r ❜❛❝t❡r✐❛✿ ❝❧❛ss ❆❝✐❞♦❜❛❝t❡r✐✐❛ ❛♥❞ ❝❧❛ss ❉❆✵✺✷ ❛r❡ s❤♦✇♥ t♦ ❞❡❝r❡❛s❡ ✐♥✹✽✽
r❡❧❛t✐✈❡ ❛❜✉♥❞❛♥❝❡ ✇✐t❤ ✐♥❝r❡❛s✐♥❣ ♣❍✳ ❚❤❡ s❡❝♦♥❞ ❢❛❝t♦r s♣❧✐t ✸✶ ❖❚❯s ✐♥ t❤❡✹✽✾
♦r❞❡r ❆❝t✐♥♦♠②❝❡t❛❧❡s ✭s♦♠❡ ❢r♦♠ t❤❡ ❢❛♠✐❧② ❚❤❡r♠♦♠♦♥♦s♣♦r❛❝❡❛❡ ❛♥❞ t❤❡✹✾✵
r❡st ✉♥❝❧❛ss✐✜❡❞ ❛t t❤❡ ❢❛♠✐❧② ❧❡✈❡❧✮ ❢r♦♠ t❤❡ r❡♠❛✐♥❞❡r ♦❢ ❛❧❧ ♦t❤❡r ❜❛❝t❡r✐❛✱✹✾✶
❛♥❞ t❤❡s❡ ♠♦♥♦♣❤②❧❡t✐❝ ❆❝t✐♥♦♠②❝❡t❛❧❡s ❛❧s♦ ❞❡❝r❡❛s❡ ✐♥ r❡❧❛t✐✈❡ ❛❜✉♥❞❛♥❝❡✹✾✷
✇✐t❤ ✐♥❝r❡❛s✐♥❣ ♣❍✳ ❚❤❡ t❤✐r❞ ❢❛❝t♦r ✐❞❡♥t✐✜❡❞ ❛♥♦t❤❡r ❝❧❛❞❡ ✇✐t❤✐♥ t❤❡ ♣❤②❧✉♠✹✾✸
❆❝✐❞♦❜❛❝t❡r✐❛ t♦ ❞❡❝r❡❛s❡ ✇✐t❤ ♣❍✿ ✶✶✺ ❜❛❝t❡r✐❛ ❢r♦♠ t❤❡ ❝❧❛ss❡s ❙♦❧✐❜❛❝t❡r❡s✹✾✹
❛♥❞ ❚▼✶✳✹✾✺
❚❤❡ ❢♦✉rt❤ ❢❛❝t♦r ✐❞❡♥t✐✜❡s ❛ ♠♦♥♦♣❤②❧❡t✐❝ ❝❧❛❞❡ ♦❢ ✶✾✸ ❖❚❯s ✐♥ t❤❡ r❡♠❛✐♥❞❡r✹✾✻
♦❢ ♣❤②❧✉♠ ❆❝✐❞♦❜❛❝t❡r✐❛ ✭✐✳❡✳ t❤♦s❡ ❆❝✐❞♦❜❛❝t❡r✐❛ ♥♦t ♠❡♥t✐♦♥❡❞ ❛❜♦✈❡ ✐♥ ❢❛❝✲✹✾✼
t♦rs ✶ ❛♥❞ ✸✮ ❛s ❤❛✈✐♥❣ r❡❧❛t✐✈❡ ❛❜✉♥❞❛♥❝❡s t❤❛t ✐♥❝r❡❛s❡ ✇✐t❤ ♣❍ ✭❞♦♠✐♥❛♥❝❡✹✾✽
❛♥❛❧②s✐s✿ ✾✹✳✼✾✪ ♦❢ ❡①♣❧❛✐♥❡❞ ✈❛r✐❛♥❝❡ ❛ttr✐❜✉t❛❜❧❡ t♦ ♣❍✮✳ ❯♥❧✐❦❡ t❤❡ ♣r❡✈✐♦✉s✹✾✾
t❤r❡❡ ❢❛❝t♦rs ❛❜♦✈❡ ✇❤✐❝❤ ✇❡r❡ ❛❝✐❞♦♣❤✐❧❡s✱ t❤✐s ♠♦♥♦♣❤②❧❡t✐❝ ❣r♦✉♣ ♦❢ ❆❝✐✲✺✵✵
❞♦❜❛❝t❡r✐❛ ❝♦♥s✐sts ♦❢ ❛❧❦❛❧✐♣❤✐❧❡s✱ ✇❤✐❝❤ ✐♥❝❧✉❞❡s t❤❡ ❝❧❛ss❡s ❆❝✐❞♦❜❛❝t❡r✐❛✲✻✱✺✵✶
❈❤❧♦r❛❝✐❞♦❜❛❝t❡r✐❛✱ ❙✵✺✸ ❛♥❞ t❤r❡❡ ❖❚❯s ✉♥❝❧❛ss✐✜❡❞ ❛t t❤❡ ❝❧❛ss ❧❡✈❡❧✳✺✵✷
❚❤❡ ✜rst ❢♦✉r ❢❛❝t♦rs ❞❡✜♥❡ ✺ ❜✐♥s ♦❢ ❖❚❯s t❤❛t ✇❡ r❡❢❡r t♦ ❛s ✏❜✐♥♥❡❞ ♣❤②❧♦✲✺✵✸
❣❡♥❡t✐❝ ✉♥✐ts✑ ♦r ❇P❯s✿ ❛ ♠♦♥♦♣❤②❧❡t✐❝ ❣r♦✉♣ ♦❢ ❆❝✐❞♦❜❛❝t❡r✐❛ ✭❝❧❛ss❡s ❈❤❧♦✲✺✵✹
r❛❝✐❞♦❜❛❝t❡r✐❛✱ ❆❝✐❞♦❜❛❝t❡r✐❛✲✻✱ ❛♥❞ ❙✵✸✺✮✱ ❛♥♦t❤❡r ♠♦♥♦♣❤②❧❡t✐❝ ❣r♦✉♣ ♦❢ ❆❝✐✲✺✵✺
❞♦❜❛❝t❡r✐❛ ✭❝❧❛ss❡s ❙♦❧✐❜❛❝t❡r❡s ❛♥❞ ❚▼✶✮✱ ❛ ♠♦♥♦♣❤②❧❡t✐❝ ❣r♦✉♣ ♦❢ s❡✈❡r❛❧✺✵✻
❢❛♠✐❧✐❡s ♦❢ t❤❡ ♦r❞❡r ❆❝t✐♥♦♠②❝❡t❛❧❡s✱ ❛ ♠♦♥♦♣❤②❧❡t✐❝ ❣r♦✉♣ ♦❢ ❆❝✐❞♦❜❛❝t❡r✐❛✺✵✼
✭❝❧❛ss❡s ❆❝✐❞♦❜❛❝t❡r✐✐❛ ❛♥❞ ❉❆✵✺✷✷✮✱ ❛♥❞ ❛ ♣❛r❛♣❤②❧❡t✐❝ ❛♠❛❧❣❛♠❛t✐♦♥ ♦❢ t❤❡✺✵✽
r❡♠❛✐♥✐♥❣ t❛①❛✳ ❇✐♥♥✐♥❣ t❤❡ ❖❚❯s ❜❛s❡❞ ♦♥ t❤❡s❡ ❇P❯s t❡❧❧s ❛ s✐♠♣❧✐✜❡❞ st♦r②✺✵✾
♦❢ ❤♦✇ ♣❍ ❞r✐✈❡s ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t② ❝♦♠♣♦s✐t✐♦♥ ✭❋✐❣✳ ✺❜✮✳✺✶✵
✶✼
❉✐s❝✉ss✐♦♥✺✶✶
❖✈❡r✈✐❡✇✺✶✷
❲❡ ❤❛✈❡ ✐♥tr♦❞✉❝❡❞ ❛ s✐♠♣❧❡ ❛♥❞ ❣❡♥❡r❛❧✐③❛❜❧❡ ❡①♣❧♦r❛t♦r② ❞❛t❛ ❛♥❛❧②s✐s ❛❧✲✺✶✸
❣♦r✐t❤♠✱ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✱ t♦ ✐❞❡♥t✐❢② ❝❧❛❞❡s ❞r✐✈✐♥❣ ✈❛r✐❛t✐♦♥ ✐♥ ♠✐❝r♦❜✐♦♠❡✺✶✹
❞❛t❛s❡ts✳ P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✐♥t❡❣r❛t❡s ❜♦t❤ t❤❡ ❝♦♠♣♦s✐t✐♦♥❛❧ ❛♥❞ ♣❤②❧♦❣❡♥❡t✐❝✺✶✺
str✉❝t✉r❡ ♦❢ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡ts ❛♥❞ ♣r♦❞✉❝❡s ♦✉t♣✉ts t❤❛t ❝♦♥t❛✐♥ ❜✐♦❧♦❣✐❝❛❧✺✶✻
✐♥❢♦r♠❛t✐♦♥✿ ❡✛❡❝ts ♦❢ ✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡s ♦♥ ❡❞❣❡s ✐♥ t❤❡ ♣❤②❧♦❣❡♥②✱ ✐♥❝❧✉❞✲✺✶✼
✐♥❣ t❤❡ t✐♣s ♦❢ t❤❡ tr❡❡ tr❛❞✐t✐♦♥❛❧❧② ❛♥❛❧②③❡❞✳ ❚❤❡ ♦✉t♣✉t ♦❢ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✺✶✽
❝♦♥t❛✐♥s ❛ s❡q✉❡♥❝❡ ♦❢ ✏❢❛❝t♦rs✑✱ ♦r s♣❧✐ts ✐♥ t❤❡ tr❡❡ ✐❞❡♥t✐❢②✐♥❣ s✉❜✲❣r♦✉♣s ♦❢✺✶✾
t❛①❛ ✇❤✐❝❤ r❡s♣♦♥❞ ❞✐✛❡r❡♥t❧② t♦ tr❡❛t♠❡♥t r❡❧❛t✐✈❡ t♦ ♦♥❡✲❛♥♦t❤❡r✳ ❚❤❡ s♣❧✐ts✺✷✵
✐❞❡♥t✐✜❡❞ ✐♥ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ♥❡❡❞ ♥♦t ❜❡ s♣❧✐ts ✐♥ t❤❡ ▲✐♥♥❛❡❛♥ t❛①♦♥♦♠②✺✷✶
❜✉t ❝❛♥ ✐❞❡♥t✐❢② str♦♥❣ r❡s♣♦♥s❡s ✐♥ ❝❧❛❞❡s ♦❢ ✉♥❝❧❛ss✐✜❡❞ t❛①❛✳ ❚❤❡ r❡s❡❛r❝❤❡r✺✷✷
❞♦❡s ♥♦t ♥❡❡❞ t♦ ❝❤♦♦s❡ ❛ t❛①♦♥♦♠✐❝ ❧❡✈❡❧ ❛t ✇❤✐❝❤ t♦ ♣❡r❢♦r♠ ❛♥❛❧②s✐s ✲ t❤♦s❡✺✷✸
t❛①♦♥♦♠✐❝ ❧❡✈❡❧s ❛r❡ ♦✉t♣✉t ❜❛s❡❞ ♦♥ ✇❤✐❝❤❡✈❡r ❝❧❛❞❡s ♠❛①✐♠✐③❡ t❤❡ ♦❜❥❡❝t✐✈❡✺✷✹
❢✉♥❝t✐♦♥✱ ❛♥❞ s♦ r❡s❡❛r❝❤❡rs ✇✐❧❧ ❜❡ ❛❜❧❡ t♦ ✐❞❡♥t✐❢② ♠✉❧t✐♣❧❡ t❛①♦♥♦♠✐❝ s❝❛❧❡s✺✷✺
♦❢ ✐♠♣♦rt❛♥❝❡✳✺✷✻
P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ♦✉t♣✉ts ❛♥ ✐s♦♠❡tr✐❝ ❧♦❣✲r❛t✐♦ tr❛♥s❢♦r♠ ♦❢ t❤❡ ❞❛t❛ ✇✐t❤✺✷✼
❦♥♦✇♥ ❛s②♠♣t♦t✐❝ ♥♦r♠❛❧✐t② ♣r♦♣❡rt✐❡s✱ ❝♦♦r❞✐♥❛t❡s t❤❛t ❝❛♥ ❜❡ ❛♥❛❧②③❡❞ ✇✐t❤✺✷✽
st❛♥❞❛r❞ ♠✉❧t✐✈❛r✐❛t❡ ♠❡t❤♦❞s ❬✸✷❪✳ ❚❤❡ r❡s✉❧t✐♥❣ ❝♦♦r❞✐♥❛t❡s ❝♦rr❡s♣♦♥❞ t♦✺✷✾
♣❛rt✐❝✉❧❛r ❡❞❣❡s ❜❡t✇❡❡♥ ❝❧❡❛r❧② ✐❞❡♥t✐✜❛❜❧❡ ♥♦❞❡s ✐♥ t❤❡ tr❡❡ ♦❢ ❧✐❢❡✱ ❛❧❧♦✇✲✺✸✵
✐♥❣ r❡s❡❛r❝❤❡rs t♦ ❛♥♥♦t❛t❡ ❛ ❣✐✈❡♥ ♣❤②❧♦❣❡♥❡t✐❝ tr❡❡ ✇✐t❤ ❝♦rr❡❧❛t✐♦♥s ❜❡t✇❡❡♥✺✸✶
❝❧❛❞❡s ❛♥❞ ✈❛r✐♦✉s ❡♥✈✐r♦♥♠❡♥t❛❧ ♠❡t❛✲❞❛t❛✱ s❛♠♣❧❡ ❝❛t❡❣♦r✐❡s✱ ♦r ❡①♣❡r✐♠❡♥t❛❧✺✸✷
tr❡❛t♠❡♥ts✳✺✸✸
❚❤❡ ♣❤②❧♦❣❡♥❡t✐❝ ✐♥❢❡r❡♥❝❡s ♦❜t❛✐♥❡❞ ❜② ♣❤②❧♦❢❛❝t♦r ✇♦✉❧❞ ❜❡ ❞✐✣❝✉❧t t♦ ♦❜t❛✐♥✺✸✹
✇✐t❤ ♦t❤❡r ♣r❡✲❡①✐st✐♥❣ ♠❡t❤♦❞s✳ ❚❤r❡❡ ✐t❡r❛t✐♦♥s ♦❢ ♣❤②❧♦❢❛❝t♦r✐③❛✐t♦♥ ♦♥ t❤❡✺✸✺
♦r❛❧✴❢❡❝❛❧ ❞❛t❛s❡t ②✐❡❧❞❡❞ t❤❡ t❤r❡❡ ♠❛❥♦r s♣❧✐ts ✐♥ t❤❡ ♣❤②❧♦❣❡♥②✱ ❛❧❧ ♦❢ ✇❤✐❝❤✺✸✻
❛r❡ ❝♦♥s✐st❡♥t ✇✐t❤ ❦♥♦✇♥ ❞✐str✐❜✉t✐♦♥s ♦❢ t❛①❛✱ ♥♦♥❡ ♦❢ ✇❤✐❝❤ ✇♦✉❧❞ ❜❡ r❡✈❡❛❧❡❞✺✸✼
❞✐r❡❝t❧② ❢r♦♠ ❛ t❛①♦♥♦♠✐❝✲❜❛s❡❞ ❛♥❛❧②s✐s✳ ❆❧❣♦r✐t❤♠s s✉❝❤ ❛s ♣❤②❧♦s✐❣♥❛❧ ❬✷✷❪✱✺✸✽
✇❤✐❝❤ tr❛❝❦ P✲✈❛❧✉❡s ✉♣ t❤❡ tr❡❡✱ ②✐❡❧❞ ✐♥❢❡r❡♥❝❡s ✇✐t❤ ♥❡st❡❞ ❞❡♣❡♥❞❡♥❝❡ ❛♥❞✺✸✾
✐❞❡♥t✐❢② ❝❧❛❞❡s ✇✐t❤ ❝♦♠♠♦♥ s✐❣♥✐✜❝❛♥❝❡✱ ②❡t ♥♦t ♥❡❝❡ss❛r✐❧② ❝❧❛❞❡s ✇✐t❤ ❝♦♠✲✺✹✵
♠♦♥ s✐❣♥❛❧ ♦r ❞✐r❡❝t✐♦♥ ♦❢ tr❡♥❞ ✲ ✐t ✐s ❛ ❝♦♠♠♦♥ s✐❣♥❛❧ s✉❝❤ ❛s ❛ s❤❛r❡❞ ❤❛❜✐t❛t✺✹✶
❛ss♦❝✐❛t✐♦♥✱ ♥♦t ❛ ❝♦♠♠♦♥ s✐❣♥✐✜❝❛♥❝❡ s✉❝❤ ❛s t❤❡ ❡①✐st❡♥❝❡ ♦❢ ❛ ❤❛❜✐t❛t ❛s✲✺✹✷
s♦❝✐❛t✐♦♥✱ ✇❤✐❝❤ ❜❡tt❡r ✐♥❞✐❝❛t❡s ❛ ♣✉t❛t✐✈❡ tr❛✐t ❞r✐✈✐♥❣ s❤❛r❡❞ r❡s♣♦♥s❡s ✐♥✺✹✸
♠✐❝r♦❜❡s✳ ■♥ t❤❡ ✶✹✷ ❢❛❝t♦rs ❛❜♦✈❡✱ ♣❤②❧♦❢❛❝t♦r ✐❞❡♥t✐✜❡❞ ♥✉♠❡r♦✉s ❝❧❛❞❡s ✇✐t❤✺✹✹
✶✽
❝♦♠♠♦♥ s✐❣♥✐✜❝❛♥❝❡ ②❡t ❞✐✛❡r❡♥t s✐❣♥❛❧s✳ P❤②❧♦❣❡♥❡t✐❝ ❦❡r♥❡❧✲❜❛s❡❞ ♠❡t❤♦❞s✺✹✺
❬✷✼✱ ✸✺✱ ✸✶❪ ✉s❡ t❤❡ ♣❤②❧♦❣❡♥② t♦ ♠♦❞✐❢② ❞✐st❛♥❝❡s✴❞✐ss✐♠✐❧❛r✐t✐❡s ❜❡t✇❡❡♥ s❛♠✲✺✹✻
♣❧❡s ❛♥❞ ❝❛♥ ❡❛s✐❧② ❞✐✛❡r❡♥t✐❛t❡ ❜❡t✇❡❡♥ ♦r❛❧ ❛♥❞ ❢❡❝❛❧ ❜♦❞② s✐t❡s✱ ❜✉t s✉❝❤✺✹✼
♥♦♠✐♥❛❧❧② s✐♠✐❧❛r ♠❡t❤♦❞s ❝❧❛ss✐❢② ❛♥❞ ❞✐✛❡r❡♥t✐❛t❡ s✐t❡s✱ ✇❤✐❝❤ ✐s ❛ ❝♦♥❝❡♣t✉✲✺✹✽
❛❧❧② ❞✐✛❡r❡♥t ❢r♦♠ ❝❧❛ss✐❢②✐♥❣ ❛♥❞ ♣r❡❞✐❝t✐♥❣ ❖❚❯ ❛❜✉♥❞❛♥❝❡s ❣✐✈❡♥ t❤❡✐r ♣❧❛❝❡✺✹✾
✐♥ t❤❡ ♣❤②❧♦❣❡♥②✳ ❙✐♠✐❧❛r❧②✱ ♣❤②❧♦❣❡♥❡t✐❝ ❝♦♠♣❛r❛t✐✈❡ ♠❡t❤♦❞s ✭P❈▼s✮ ❬✶✸✱ ✷✶❪✺✺✵
s✉❝❤ ❛s ♣❤②❧♦❣❡♥❡t✐❝ ❣❡♥❡r❛❧✐③❡❞ ❧❡❛st sq✉❛r❡s ❬✶✼✱ ✷✾❪ ❛r❡ ♥♦♠✐♥❛❧❧② s✐♠✐❧❛r ❜✉t✺✺✶
❝♦♥❝❡♣t✉❛❧❧② ❞✐st✐♥❝t ❢r♦♠ ♣❤②❧♦❢❛❝t♦r❀ ✇❤✐❧❡ P❈▼s ❛✐♠ ❝♦rr❡❝t ❢♦r t❤❡ ❞❡♣❡♥✲✺✺✷
❞❡♥❝❡ ♦❢ ♦❜s❡r✈❛t✐♦♥s ♦❢ ❡✈♦❧✉t✐♦♥❛r✐❧② r❡❧❛t❡❞ t❛①❛✱ ♦✉r ❣♦❛❧ ✐s ♥♦t t♦ ❝♦rr❡❝t✺✺✸
❢♦r s✉❝❤ ❞❡♣❡♥❞❡♥❝❡ ❜✉t t♦ ✐♥❢❡r ♣r❡❝✐s❡❧② ✇❤❡r❡ ♦♥ t❤❡ tr❡❡ s✉❝❤ ❞❡♣❡♥❞❡♥❝❡✺✺✹
❛♣♣❡❛rs t♦ ❛r✐s❡✳ ❲❤✐❧❡ ♠❛♥② t♦♦❧s ❡①✐st ❢♦r t❤❡ ♥♦♠✐♥❛❧❧② s✐♠✐❧❛r t❛s❦ ♦❢ ✏✉s✲✺✺✺
✐♥❣ t❤❡ ♣❤②❧♦❣❡♥② t♦ ❛♥❛❧②③❡ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛✑✱ t❤❡ ✉t✐❧✐t② ♦❢ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✺✺✻
❧✐❡s ✐♥ ✐ts ❛❜✐❧✐t② t♦ ❝♦♥str✉❝t ✈❛r✐❛❜❧❡s ❝♦rr❡s♣♦♥❞✐♥❣ t♦ ❡❞❣❡s ✐♥ t❤❡ ♣❤②❧♦❣❡♥②✺✺✼
❛❧♦♥❣ ✇❤✐❝❤ ♣✉t❛t✐✈❡ ❢✉♥❝t✐♦♥❛❧ ❡❝♦❧♦❣✐❝❛❧ tr❛✐ts ♠❛② ❤❛✈❡ ❛r✐s❡♥✱ ❝♦♥str✉❝t❡❞✺✺✽
s♦ ❛s t♦ ❛✈♦✐❞ ♥❡st❡❞ ❞❡♣❡♥❞❡♥❝❡ ❛♥❞ ♦✈❡r❧❛♣♣✐♥❣ ❝♦♠♣❛r✐s♦♥s t❤❛t ❢r❡q✉❡♥t t❤❡✺✺✾
❛♥❛❧②s✐s ♦❢ ❤✐❡r❛r❝❤✐❝❛❧❧② str✉❝t✉r❡❞✱ ❛♥❞ ❝♦♥str✉❝t❡❞ ✐♥ ❛ ♠❛♥♥❡r ❛♣♣r♦♣r✐❛t❡✺✻✵
❢♦r ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛✳✺✻✶
❋✉t✉r❡ ❲♦r❦✺✻✷
❚❤❡ ❣❡♥❡r❛❧✐t② ♦❢ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ♦♣❡♥s t❤❡ ❞♦♦r t♦ ❢✉t✉r❡ ✇♦r❦ ❡♠♣❧♦②✐♥❣✺✻✸
♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✇✐t❤ ♦t❤❡r ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥s✳ ❆s ✇❡ s❤♦✇❡❞ ✇✐t❤ t❤❡ ❤✉✲✺✻✹
♠❛♥ ♦r❛❧✴❢❡❝❛❧ ♠✐❝r♦❜✐♦♠❡s✱ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✐s ♥♦t r❡str✐❝t❡❞ t♦ ❜❛s❛❧ ❝❧❛❞❡s✱✺✻✺
❜✉t ✐♥❝❧✉❞❡s t❤❡ t✐♣s ❛s ♣♦ss✐❜❧❡ ❝❧❛❞❡s ♦❢ ✐♥t❡r❡st✱ ❜✉t t❤❡ ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥✺✻✻
✇❡ ✉s❡❞ ♠✐♥✐♠✐③❡❞ r❡s✐❞✉❛❧ ✈❛r✐❛♥❝❡ ✐♥ t❤❡ ✇❤♦❧❡ ❝♦♠♠✉♥✐t② ❛♥❞ t❤❡r❡❜② ♠❛②✺✻✼
♣r✐♦r✐t✐③❡ ❞❡❡♣❧② r♦♦t❡❞ ❡❞❣❡s ♦r ❛❜✉♥❞❛♥t t❛①❛ ✇✐t❤ ✇❡❛❦❡r ❡✛❡❝ts ♦✈❡r ✐♥❞✐✈✐❞✲✺✻✽
✉❛❧ ❖❚❯s ✇✐t❤ str♦♥❣❡r ❡✛❡❝ts✳ ❖t❤❡r ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥s ❝♦✉❧❞ ❜❡ ❝♦♥str✉❝t❡❞✺✻✾
t♦ ♠❡❡t t❤❡ ♥❡❡❞s ♦❢ t❤❡ r❡s❡❛r❝❤❡r✳ ■❢ r❡s❡❛r❝❤❡rs ❛r❡ ✐♥t❡r❡st❡❞ ✐♥ ✐❞❡♥t✐❢②✐♥❣✺✼✵
❜❛s❛❧ ❧✐♥❡❛❣❡s✱ t❤❡✐r ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥ ❝❛♥ ✇❡✐❣❤t ❡❞❣❡s ❜❛s❡❞ ♦♥ ❞✐st❛♥❝❡ ❢r♦♠✺✼✶
t❤❡ t✐♣s✳ ❆ r❡s❡❛r❝❤❡r ✐♥t❡r❡st❡❞ ✐♥ ✜♥❡✲t✉♥✐♥❣ t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❛ss✉♠♣t✐♦♥s✺✼✷
✐♥ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❝❛♥ ❞❡✜♥❡ ❛♥ ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥ t❤❛t ✐♥❝r❡❛s❡s ❡①♣❧✐❝✐t❧②✺✼✸
✇✐t❤ t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ❡❞❣❡ ❜❡✐♥❣ ❝♦♥s✐❞❡r❡❞ t♦ r❡✢❡❝t ❛♥ ❛ss✉♠♣t✐♦♥ t❤❛t t❤❡✺✼✹
♣r♦❜❛❜✐❧✐t② ♦❢ ❛ tr❛✐t ❛r✐s✐♥❣ ✐♥❝r❡❛s❡s ✇✐t❤ t❤❡ ❛♠♦✉♥t ♦❢ t✐♠❡ ❡❧❛♣s❡❞✳✺✼✺
❊❛❝❤ ❡❞❣❡ ✐❞❡♥t✐✜❡❞ ✐♥ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❝♦rr❡s♣♦♥❞s t♦ t✇♦ ❜✐♥s ♦❢ t❛①❛ ♦♥✺✼✻
❡❛❝❤ s✐❞❡ ♦❢ t❤❡ ❡❞❣❡✱ ❛♥❞ ❝♦♥s❡q✉❡♥t❧② ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❜r✐♥❣s ✐♥ t✇♦ ❝♦♠✲✺✼✼
♣❧❡♠❡♥t❛r② ♣❡rs♣❡❝t✐✈❡s ❢♦r ❛♥❛❧②③✐♥❣ t❤❡ ❞❛t❛✿ ❢❛❝t♦r✲❜❛s❡❞ ❛♥❛❧②s✐s ❛♥❞ ❜✐♥✲✺✼✽
❜❛s❡❞ ❛♥❛❧②s✐s✳ ❋❛❝t♦r✲❜❛s❡❞ ❛♥❛❧②s✐s ❧♦♦❦s ❛t t❤❡ ❡❛❝❤ ❢❛❝t♦r ❛s ❛♥ ✐♥❢❡r❡♥❝❡✺✼✾
✶✾
♦♥ ❛♥ ❡❞❣❡ ✐♥ t❤❡ ♣❤②❧♦❣❡♥②✱ ❝♦♥❞✐t✐♦♥❡❞ ♦♥ t❤❡ ♣r❡✈✐♦✉s ✐♥❢❡r❡♥❝❡s ❛❧r❡❛❞②✺✽✵
♠❛❞❡✱ ❛♥❞ ✐♥❞✐❝❛t✐♥❣ t❤❛t t❛①❛ ♦♥ ♦♥❡ s✐❞❡ ♦❢ ❛♥ ❡❞❣❡ r❡s♣♦♥❞ ❞✐✛❡r❡♥t❧② t♦✺✽✶
t❤❡ ✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡ ❝♦♠♣❛r❡❞ t♦ t❛①❛ ♦♥ t❤❡ ♦t❤❡r s✐❞❡ ♦❢ t❤❡ ❡❞❣❡✳ ❇✐♥✲✺✽✷
❜❛s❡❞ ❛♥❛❧②s✐s✱ ♦♥ t❤❡ ♦t❤❡r ❤❛♥❞✱ ❧♦♦❦s ❛t t❤❡ s❡t ♦❢ ❝❧❛❞❡s r❡s✉❧t✐♥❣ ❢r♦♠ ❛✺✽✸
❝❡rt❛✐♥ ♥✉♠❜❡r ♦❢ ❢❛❝t♦rs ✲ ✇❤❛t ✇❡ ❝❛❧❧ ❛ ✏❜✐♥♥❡❞ ♣❤②❧♦❣❡♥❡t✐❝ ✉♥✐t✑ ✭❇P❯✮✳✺✽✹
❚❤❡s❡ ❜✐♥s ✇✐❧❧ ❝r❡❛t❡ ❛ ❧♦✇❡r✲❞✐♠❡♥s✐♦♥❛❧✱ ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛s❡t ❛♥❞ ❝❛♥ ❜❡✺✽✺
❢r❡❡❞ ❢r♦♠ t❤❡ ✉♥❞❡r❧②✐♥❣ ■▲❘ ❝♦♦r❞✐♥❛t❡s ❢♦r ❞✐✛❡r❡♥t ❛♥❛❧②s❡s ♦♥ t❤❡s❡ ❛♠❛❧✲✺✽✻
❣❛♠❛t❡❞ ❝❧❛❞❡s✳✳ ❇P❯✲❜❛s❡❞ ❛♥❛❧②s✐s ❝❛♥ ✐♥❢♦r♠ s❡q✉❡♥❝❡ ❜✐♥♥✐♥❣ ✐♥ ❢✉t✉r❡✺✽✼
r❡s❡❛r❝❤ ❛✐♠❡❞ ❛t ❝♦♥tr♦❧❧✐♥❣ ❢♦r ♣r❡✈✐♦✉s❧②✲✐❞❡♥t✐✜❡❞ ♣❤②❧♦❣❡♥❡t✐❝ ❝❛✉s❡s ♦❢✺✽✽
✈❛r✐❛t✐♦♥✱ ❛♥❞ ❝♦♠❜✐♥❡ t❤❡ ❡✛❡❝ts ♦❢ ♠✉❧t✐♣❧❡ ✉♣✲str❡❛♠ ❢❛❝t♦rs ❢♦r ♣r❡❞✐❝t✐♦♥s✺✽✾
♦❢ ❖❚❯ ❛❜✉♥❞❛♥❝❡✳ ❙❡❡ t❤❡ s✉♣♣❧❡♠❡♥t❛r② t❡①t ❢♦r ❛ ♠♦r❡ ❞❡t❛✐❧❡❞ ❞✐s❝✉ss✐♦♥✺✾✵
♦❢ ❢❛❝t♦r✲❜❛s❡❞ ❛♥❞ ❜✐♥✲❜❛s❡❞ ❛♥❛❧②s❡s✳✺✾✶
❖♥❡ ❝♦♥❝❡♣t✉❛❧ ❝❤❛❧❧❡♥❣❡ ✇✐t❤ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❝r♦ss✲✈❛❧✐❞❛t✐♦♥ ❛♥❞ ❇P❯✲✺✾✷
❜❛s❡❞ ❛♥❛❧②s✐s ✐s t❤❡ tr❡❛t♠❡♥t ♦❢ ♣❛r❛♣❤②❧❡t✐❝ ✏r❡♠❛✐♥❞❡r✑ ❝❧❛❞❡s ✇❤✐❝❤ ♦❝❝✉r✺✾✸
❛❢t❡r ❢❛❝t♦r✐③❛t✐♦♥ ♦❢ ❡❞❣❡s ✇✐t❤✐♥ ❣r♦✉♣s t❤❛t s♣❧✐t ❛ ♠♦♥♦♣❤②❧❡t✐❝ ❝❧❛❞❡ ❢r♦♠✺✾✹
❛ ✏r❡♠❛✐♥❞❡r✑✱ ♣❛r❛♣❤②❧❡t✐❝ ❝❧❛❞❡ ♦r ❇P❯✳ ❚❤❡s❡ ♣❛r❛♣❤②❧❡t✐❝ ❇P❯s ❛r❡ ✐♥✲✺✾✺
❢♦r♠❛t✐✈❡ ❛s t❤❡② ❛r❡ t❤❡ ♥❡❝❡ss❛r② ❝♦♥tr❛sts ✇✐t❤ t❤❡ ♠♦♥♦♣❤②❧❡t✐❝ ❣r♦✉♣✱✺✾✻
❝♦♥❞✐t✐♦♥❡❞ ♦♥ ♣r❡✈✐♦✉s❧② ✐❞❡♥t✐✜❡❞ ♣❤②❧♦❣❡♥❡t✐❝ ❢❛❝t♦rs✱ ❛♥❞ t❤✉s s❡r✈❡ ❛s ❛✺✾✼
♠❡❛♥s ♦❢ ✐❞❡♥t✐❢②✐♥❣ t❤❡ ♣r❡s❡♥❝❡ ♦r ❛❜s❡♥❝❡ ♦❢ ❛ tr❛✐t ✐♥ t❤❡ ♠♦♥♦♣❤②❧❡t✐❝✺✾✽
❣r♦✉♣✳ ❋♦r ✐♥st❛♥❝❡✱ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ♦❢ ✈❡rt❡❜r❛t❡s ❜❛s❡❞ ♦♥ t❤❡✐r r❡❧❛t✐✈❡✺✾✾
❛❜✉♥❞❛♥❝❡ ✐♥ t❤❡ ❛✐r s❤♦✉❧❞ ✐❞❡♥t✐❢② t✇♦ ♠♦♥♦♣❤②❧❡t✐❝ ❣r♦✉♣s✿ ❜✐r❞s ❛♥❞ ❜❛ts✳✻✵✵
❚❤❡ ♠♦♥♦♣❤②❧❡t✐❝ ❣r♦✉♣s ❛r❡ ❞❡✜♥❡❞ ❜② t❤❡ ♣r❡s❡♥❝❡ ♦❢ ❛ s♣❡❝✐❛❧✐③❡❞ ❛❞❛♣t❛t✐♦♥✻✵✶
✲ ✇✐♥❣s ✲ ❛♥❞ t❤❡ ♣❛r❛♣❤②❧❡t✐❝ r❡♠❛✐♥❞❡r ✐s ❞❡✜♥❡❞ ❜② t❤❡ ❛❜s❡♥❝❡ ♦❢ ✇✐♥❣s❀ ❛♥②✻✵✷
❢✉t✉r❡ tr❡❛t♠❡♥t t❤❛t ❞✐✛❡r❡♥t✐❛❧❧② ❛✛❡❝ts ✇✐♥❣❡❞ ✈s✳ ♥♦♥✲✇✐♥❣❡❞ ♦r❣❛♥✐s♠s✻✵✸
✇✐❧❧ ❞✐✛❡r❡♥t✐❛❧❧② ❛✛❡❝t t❤❡ ❛❜✉♥❞❛♥❝❡s ♦❢ t❤❡s❡ ♠♦♥♦♣❤②❧❡t✐❝ ❣r♦✉♣s r❡❧❛t✐✈❡✻✵✹
t♦ t❤❡ ♣❛r❛♣❤②❧❡t✐❝ r❡♠❛✐♥❞❡r✳ ❈♦♥✈❡rs❡❧②✱ ✏❧❡❣s✑ ✐♥ t❤❡ ♦r❞❡r ❙q✉❛♠❛t❛ ❞✐s❛♣✲✻✵✺
♣❡❛r❡❞ ❛❧♦♥❣ ❡❞❣❡s ❝♦rr❡s♣♦♥❞✐♥❣ t♦ ❧❡❣❧❡ss ❧✐③❛r❞s ❛♥❞ s♥❛❦❡s❀ ✐♥ t❤✐s ❝❛s❡✱ t❤❡✻✵✻
♠♦♥♦♣❤②❧❡t✐❝ ❝❧❛❞❡s ❛r❡ ❞❡✜♥❡❞ ❜② t❤❡ ❛❜s❡♥❝❡ ♦❢ ❛ s♣❡❝✐❛❧✐③❡❞ ❛❞❛♣t❛t✐♦♥✱ ❧❡❣s✱✻✵✼
❛♥❞ t❤❡ ♣❛r❛♣❤②❧❡t✐❝ r❡♠❛✐♥❞❡r ✐s ❞❡✜♥❡❞ ❜② t❤❡ ♣r❡s❡♥❝❡ ♦❢ ❧❡❣s✳ ❲❤❡t❤❡r ❛✻✵✽
tr❛✐t ❝❛♥ ❜❡ ✢❡①✐❜❧② ❞❡✜♥❡❞ ❛s ❡✐t❤❡r t❤❡ ♣r❡s❡♥❝❡ ♦❢ ❛❜s❡♥❝❡ ♦❢ ❛ s♣❡❝✐❛❧✐③❡❞✻✵✾
❛❞❛♣t❛t✐♦♥ ✐s ❛♥ ✐♠♣♦rt❛♥t t❤❡♦r❡t✐❝❛❧ ❝♦♥s✐❞❡r❛t✐♦♥✱ ❜✉t ❝♦♥s✐❞❡r✐♥❣ ♠♦♥♦✲✻✶✵
♣❤②❧❡t✐❝ ❇P❯s ❛♥❞ t❤❡✐r ❝♦♠♣❧❡♠❡♥t❛r② ♣❛r❛♣❤②❧❡t✐❝ ❇P❯s ❛s ❡q✉❛❧❧② ❧✐❦❡❧②✻✶✶
t♦ ❤❛✈❡ t❤❡ ♣r❡s❡♥❝❡ ♦r ❛❜s❡♥❝❡ ♦❢ ❛ tr❛✐t ❛♥❞ ❛s t❤❡ ♥❡❝❡ss❛r② ❝♦♠♣❛r✐s♦♥ ❢♦r✻✶✷
❝r♦ss✲✈❛❧✐❞❛t✐♦♥ ✐s ❛♥ ✐♠♣♦rt❛♥t ❡♠♣✐r✐❝❛❧ ❝♦♥s✐❞❡r❛t✐♦♥✳ P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ♣✐♥✲✻✶✸
♣♦✐♥ts t❤❡ ❝♦♥tr❛sts t♦ ❜❡ ♠❛❞❡ ❢♦r ♠✐❝r♦❜✐❛❧ ❣❡♥♦♠✐❝ ❛♥❞ ♣❤②s✐♦❧♦❣✐❝❛❧ st✉❞✐❡s✻✶✹
❛✐♠✐♥❣ t♦ ✐❞❡♥t✐❢② t❤❡ ❝❛✉s❡s ♦❢ ❞✐✛❡r❡♥t✐❛❧ ❛❜✉♥❞❛♥❝❡s ♦r r❡s♣♦♥s❡s t♦ tr❡❛t✲✻✶✺
✷✵
♠❡♥ts ❛❝r♦ss ❖❚❯s✳ ●❡♥♦♠✐❝✴♣❤②s✐♦❧♦❣✐❝❛❧ ✐♥✈❡st✐❣❛t✐♦♥s ❛♥❞ ❝r♦ss✲✈❛❧✐❞❛t✐♦♥✻✶✻
♦❢ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ♠✉st ✉♥❞❡rst❛♥❞ ❛♥❞ ❣r❛♣♣❧❡ ✇✐t❤ t❤❡ ❝❤♦✐❝❡ ♦❢ ❛♣♣r♦♣r✐✲✻✶✼
❛t❡ ❝♦♠♣❛r✐s♦♥s ♦❢ t❛①❛✱ ❛♥❞ t❤❛t ♠❛② r❡q✉✐r❡ ❛ ❢❛✐r ❝♦♥tr❛st ♦❢ ❛ ♠♦♥♦♣❤②❧❡t✐❝✻✶✽
❝❧❛❞❡ t♦ ❛ ♣❛r❛♣❤②❧❡t✐❝ ♦♥❡✳✻✶✾
P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✇✐❧❧ ❜❡♥❡✜t ❢r♦♠ ❝♦♠♠✉♥✐t② ❞✐s❝✉ss✐♦♥ ❛♥❞ ❢✉rt❤❡r r❡s❡❛r❝❤✻✷✵
♦✈❡r❝♦♠✐♥❣ ❣❡♥❡r❛❧ st❛t✐st✐❝❛❧ ❝❤❛❧❧❡♥❣❡s ❝♦♠♠♦♥ t♦ ❣r❡❡❞② ❛❧❣♦r✐t❤♠s ❛♥❞ ❛♥❛❧✲✻✷✶
②s✐s ♦❢ ♣❤②❧♦❣❡♥❡t✐❝❛❧❧②✲str✉❝t✉r❡❞ ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛✳ ❋♦r ✐♥st❛♥❝❡✱ t❤❡ ❧♦❣✲✻✷✷
r❛t✐♦ tr❛♥s❢♦r♠ ❛t t❤❡ ❤❡❛rt ♦❢ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ r❡q✉✐r❡s r❡s❡❛r❝❤❡rs ❞❡❛❧ ✇✐t❤✻✷✸
③❡r♦s ✐♥ ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛s❡ts✳ ❲❤✐❧❡ t❤❡r❡ ❛r❡ ♠❛♥② ♠❡t❤♦❞s ❢♦r ❞❡❛❧✐♥❣ ✇✐t❤✻✷✹
③❡r♦s ❬✶✱ ✷✽✱ ✸✷❪✱ ✐t✬s ✉♥❝❧❡❛r ✇❤✐❝❤ ♠❡t❤♦❞ ✐s ♠♦st r♦❜✉st ❢♦r ❞♦✇♥str❡❛♠ ♣❤②❧♦✲✻✷✺
❢❛❝t♦r✐③❛t✐♦♥ ♦❢ s♣❛rs❡ ❖❚❯ t❛❜❧❡s✳ ❙❡❝♦♥❞✱ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❛s ♣r❡s❡♥t❡❞ ❤❡r❡✻✷✻
♦♥❧② s❡q✉❡♥t✐❛❧❧② ✐♥❢❡rs ■▲❘ ❡❧❡♠❡♥ts ❛♥❞ ❞♦❡s ♥♦t ❛❧❧♦✇ ❢♦r s✐♠✉❧t❛♥❡♦✉s ✐♥✲✻✷✼
❢❡r❡♥❝❡ ♦❢ ■▲❘ ❜❛s✐s ❡❧❡♠❡♥ts ✲ t❤❡ s❡t ♦❢ ❢❛❝t♦rs ✐❞❡♥t✐✜❡❞ ❛❢t❡r n ✐t❡r❛t✐♦♥s✻✷✽
♠❛② ❡①♣❧❛✐♥ ❧❡ss ✈❛r✐❛t✐♦♥ ❝♦♠❜✐♥❡❞ t❤❛♥ ❛♥ ❛❧t❡r♥❛t✐✈❡ s❡t ♦❢ ❢❛❝t♦rs t❤❛t ❞✐❞✻✷✾
♥♦t ♠❛①✐♠✐③❡ t❤❡ ❡①♣❧❛✐♥❡❞ ✈❛r✐❛♥❝❡ ❛t ❡❛❝❤ ✐t❡r❛t✐♦♥✳ ❚❤✐s ❧✐♠✐t❛t✐♦♥ ♠❛②✻✸✵
❜❡ ♦✈❡r❝♦♠❡ ❜② r✉♥♥✐♥❣ ♠❛♥② r❡♣❧✐❝❛t❡s ♦❢ ❛ st♦❝❤❛st✐❝ ❣r❡❡❞② ❛❧❣♦r✐t❤♠ ❛♥❞✻✸✶
❝❤♦♦s✐♥❣ t❤❛t ✇❤✐❝❤ ♠❛①✐♠✐③❡s t❤❡ ❡①♣❧❛✐♥❡❞ ✈❛r✐❛♥❝❡ ❛❢t❡r n ❢❛❝t♦rs✳ ❚❤✐r❞✱✻✸✷
t❤❡ r❡s❡❛r❝❤❡r ♠✉st ❝❤♦♦s❡ ❛♥ ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥ ✇❤✐❝❤ ♠❛t❝❤❡s ❤❡r q✉❡st✐♦♥✱✻✸✸
❛♥❞ ❢✉t✉r❡ r❡s❡❛r❝❤ ❝❛♥ ♠❛♣ ♦✉t ✇❤✐❝❤ ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥s ❛r❡ ❛♣♣r♦♣r✐❛t❡ ❢♦r✻✸✹
✇❤✐❝❤ q✉❡st✐♦♥s ✐♥ ♠✐❝r♦❜✐❛❧ ❡❝♦❧♦❣②✳ ❋♦✉rt❤✱ ❧✐❦❡ ❛♥② ♠❡t❤♦❞ ♣❡r❢♦r♠✐♥❣ ✐♥❢❡r✲✻✸✺
❡♥❝❡ ❜❛s❡❞ ♦♥ ♣❤②❧♦❣❡♥❡t✐❝ str✉❝t✉r❡✱ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❛ss✉♠❡s ❛♥ ❛❝❝✉r❛t❡✻✸✻
♣❤②❧♦❣❡♥②✳ ❆❝❝✉r❛t❡ st❛t✐st✐❝❛❧ st❛t❡♠❡♥ts ❛❜♦✉t ❛ r❡s❡❛r❝❤❡r✬s ❝♦♥✜❞❡♥❝❡ ✐♥✻✸✼
♣❤②❧♦❢❛❝t♦rs ♠✉st ✐♥❝♦r♣♦r❛t❡ t❤❡ ✉♥❝❡rt❛✐♥t② ✐♥ ♦✉r ❝♦♥str✉❝t❡❞ ♣❤②❧♦❣❡♥②✳✻✸✽
❋✐❢t❤✱ ♣❤②❧♦❣❡♥❡t✐❝✲❜❛s❡❞ ♠❡t❤♦❞s ♠❛② ❜❡ s❡♥s✐t✐✈❡ t♦ t❤❡ ❜✐♥♥✐♥❣ ❛♥❞ ✜❧t❡r✐♥❣✻✸✾
♠❡t❤♦❞s ❢♦r s❡q✉❡♥❝❡✲❝♦✉♥t ❞❛t❛✳ ❖✉r ✜❧t❡r✐♥❣ ♠❡t❤♦❞s ❤❡r❡ ✇❡r❡ ❝❤♦s❡♥ t♦✻✹✵
❛❧❧♦✇ s♦♠❡✇❤❛t st❛♥❞❛r❞ ❛♥❞ s✐♠♣❧✐✜❡❞ ❛♥❛❧②s✐s ♦❢ ❝♦♠♠♦♥ ❖❚❯s ♣r❡s❡♥t ✐♥✻✹✶
♠❛♥② ♦❢ t❤❡ s❛♠♣❧❡s✱ ❜✉t t❤❡s❡ ✜❧t❡r✐♥❣ ♣r♦t♦❝♦❧s ♠✐❣❤t ♥♦t ❜❡ ♦♣t✐♠❛❧ ❢♦r r❡✲✻✹✷
s❡❛r❝❤❡rs ✇✐t❤ ♦t❤❡r r❡s❡❛r❝❤ q✉❡st✐♦♥s ❛♥❞ ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥s✳ ❋✉t✉r❡ ✇♦r❦ ❝❛♥✻✹✸
✐♥✈❡st✐❣❛t❡ t❤❡ s❡♥s✐t✐✈✐t② ♦❢ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ t♦ ♠②r✐❛❞ ❜✐♥♥✐♥❣ ❛♥❞ ✜❧t❡r✐♥❣✻✹✹
♠❡t❤♦❞s ❣✐✈❡♥ t❤❡ ♦❜❥❡❝t✐✈❡s ❛♥❞ ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ r❡s❡❛r❝❤❡r✳ ❋✐♥❛❧❧②✱✻✹✺
❢✉t✉r❡ r❡s❡❛r❝❤ ❝❛♥ ✐♥✈❡st✐❣❛t❡ t❤❡ ✉♥✐q✉❡ ❦✐♥❞s ♦❢ ❡rr♦rs ✐♥ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✿✻✹✻
✐♥ ❛❞❞✐t✐♦♥ t♦ t❤❡ ♠✉❧t✐♣❧❡✲❤②♣♦t❤❡s✐s t❡st✐♥❣ ♦❢ ❡❞❣❡s✱ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ♠❛②✻✹✼
♣r♦♣❛❣❛t❡ ❡rr♦rs ✐♥ t❤❡ ❣r❡❡❞② ❛❧❣♦r✐t❤♠✱ ❛♥❞✱ ❡✈❡♥ ✇❤❡♥ t❛①❛ ❛r❡ ❝♦rr❡❝t❧②✻✹✽
❢❛❝t♦r❡❞ ✐♥t♦ t❤❡ ❛♣♣r♦♣r✐❛t❡ ❢✉♥❝t✐♦♥❛❧ ❜✐♥s✱ t❤❡ ♣r❡s❡♥❝❡ ♦❢ ♠✉❧t✐♣❧❡ ❢❛❝t♦rs✻✹✾
✐♥ t❤❡ s❛♠❡ r❡❣✐♦♥ ♦❢ t❤❡ tr❡❡ ❝❛♥ ❧❡❛❞ t♦ ✉♥❝❡rt❛✐♥t② ❛❜♦✉t t❤❡ ❡①❛❝t ❡❞❣❡✻✺✵
❛❧♦♥❣ ✇❤✐❝❤ ❛ ♣✉t❛t✐✈❡ tr❛✐t ❛r♦s❡ ✭s❡❡ s✉♣♣❧❡♠❡♥t ❢♦r ♠♦r❡ ❞✐s❝✉ss✐♦♥ ♦♥ t❤❡✻✺✶
✷✶
✉♥❝❡rt❛✐♥t② ♦❢ ✇❤✐❝❤ ❡❞❣❡ t♦ ❛♥♥♦t❛t❡✮✳✻✺✷
■♥❝♦r♣♦r❛t✐♥❣ t❤❛t ♣❤②❧♦❣❡♥❡t✐❝ str✉❝t✉r❡ ✐♥t♦ t❤❡ ❛♥❛❧②s✐s ♦❢ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡ts✻✺✸
❤❛s ❜❡❡♥ ❛ ♠❛❥♦r ❝❤❛❧❧❡♥❣❡ ❬✸✵❪✱ ❛♥❞ ♥♦✇ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ♣r♦✈✐❞❡s ❛ ❣❡♥❡r❛❧✻✺✹
❢r❛♠❡✇♦r❦ ❢♦r r✐❣♦r♦✉s ❡①♣❧♦r❛t✐♦♥ ♦❢ ♣❤②❧♦❣❡♥❡t✐❝❛❧❧②✲str✉❝t✉r❡❞ ❝♦♠♣♦s✐t✐♦♥❛❧✻✺✺
❞❛t❛s❡ts✳ ❚❤❡ s♦✐❧ ❞❛t❛s❡t ❛♥❛❧②③❡❞ ❛❜♦✈❡✱ ❢♦r ✐♥st❛♥❝❡✱ ❝♦♥t❛✐♥s ✸✱✸✼✾ ❖❚❯s✻✺✻
❛♥❞ ✺✽✵ s❛♠♣❧❡s✱ ❛♥❞ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ♦❢ t❤❡ ❝❧❛❞❡s ❛✛❡❝t❡❞ ❜② ♣❍ ✐♥ t❤❡✻✺✼
s♦✐❧ ❞❛t❛s❡t ②✐❡❧❞❡❞ ♥♦t ❥✉st t❤❡ t❤r❡❡ ❞♦♠✐♥❛♥t ❢❛❝t♦rs ✉s❡❞ ❢♦r ♦r❞✐♥❛t✐♦♥✲✻✺✽
✈✐s✉❛❧✐③❛t✐♦♥✱ ❜✉t ✷✱✹✸✵ ❢❛❝t♦rs ✐♥ ❛❧❧✱ ❡❛❝❤ ✇✐t❤ ❛♥ ✐♥tr✐❝❛t❡ ♣❤②❧♦❣❡♥❡t✐❝ st♦r②✳✻✺✾
▼❛♥② ❆❝✐❞♦❜❛❝t❡r✐❛ ❛r❡ ❛❝✐❞♦♣❤✐❧❡s✱ ❜✉t s♦♠❡ ✲ ❈❤❧♦r❛❝✐❞♦❜❛❝t❡r✐❛✱ ❆❝✐❞♦❜❛❝t❡r✐❛✲✻✻✵
✻✱ ❙✵✸✺✱ ❛♥❞ s♦♠❡ ✉♥❞❡s❝r✐❜❡❞ ❝❧❛ss❡s ♦❢ ❜❛❝t❡r✐❛ ❢❛❝t♦r❡❞ ❤❡r❡ ✲ ❛♣♣❡❛r t♦ ❜❡ ❛❧✲✻✻✶
❦❛❧✐♣❤✐❧❡s✳ ❇② ✐♥❝♦r♣♦r❛t✐♥❣ t❤❡ ♣❤②❧♦❣❡♥❡t✐❝ str✉❝t✉r❡ ♦❢ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡ts✱✻✻✷
t❤❡ ❜✐❣ ❞❛t❛ ♦❢ t❤❡ ♠♦❞❡r♥ s❡q✉❡♥❝❡✲❝♦✉♥t ❜♦♦♠ ❥✉st ❣♦t ❜✐❣❣❡r✱ ❛♥❞ ❢✉t✉r❡✻✻✸
r❡s❡❛r❝❤ ✇✐❧❧ ♥❡❡❞ t♦ ❝♦♥s✐❞❡r ❤♦✇ t♦ ♦r❣❛♥✐③❡✱ ❛♥❛❧②③❡ ❛♥❞ ✈✐s✉❛❧✐③❡ t❤❡ ❧❛r❣❡✻✻✹
❛♠♦✉♥ts ♦❢ ♣❤②❧♦❣❡♥❡t✐❝ ❞❡t❛✐❧ t❤❛t ❝❛♥ ♥♦✇ ❜❡ ♦❜t❛✐♥❡❞ ❢r♦♠ t❤❡ ❛♥❛❧②s✐s ♦❢✻✻✺
♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡ts✳✻✻✻
❈♦♥❝❧✉s✐♦♥s✻✻✼
P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✐s ❛ r♦❜✉st t♦♦❧ ❢♦r ❛♥❛❧②③✐♥❣ ♠❛r❦❡r ❣❡♥❡ s❡q✉❡♥❝❡✲❝♦✉♥t✻✻✽
❞❛t❛s❡ts ❢♦r ♣❤②❧♦❣❡♥❡t✐❝ ♣❛tt❡r♥s ✉♥❞❡r❧②✐♥❣ ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t② r❡s♣♦♥s❡s✻✻✾
t♦ ✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡s✳ P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❛❝❝♦✉♥ts ❢♦r t❤❡ ❝♦♠♣♦s✐t✐♦♥❛❧ ♥❛✲✻✼✵
t✉r❡ ♦❢ t❤❡ ❞❛t❛ ❛♥❞ t❤❡ ✉♥❞❡r❧②✐♥❣ ♣❤②❧♦❣❡♥② ❛♥❞ ♣r♦❞✉❝❡s ✐♥❢❡r❡♥❝❡s t❤❛t ❛r❡✻✼✶
✐♥❞❡♣❡♥❞❡♥t ❛♥❞ ♠♦r❡ ♣♦✇❡r❢✉❧ t❤❛♥ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ t❤❡ ■▲❘ tr❛♥s❢♦r♠ t♦ t❤❡✻✼✷
r♦♦t❡❞ ♣❤②❧♦❣❡♥②✳ ❚❤❡ ❘ ♣❛❝❦❛❣❡ ✬♣❤②❧♦❢❛❝t♦r✬ ❤❛s ❜✉✐❧t✲✐♥ ♣❛r❛❧❧❡❧✐③❛t✐♦♥ t❤❛t✻✼✸
❝❛♥ ❜❡ ✉s❡❞ t♦ ❛♥❛❧②③❡ ❧❛r❣❡ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡ts✱ ❛♥❞ ❛❧❧♦✇s ❣❡♥❡r❛❧✐③❡❞ ❧✐♥❡❛r✻✼✹
♠♦❞❡❧✐♥❣ t♦ ✐❞❡♥t✐❢② ❝❧❛❞❡s ✇❤✐❝❤ r❡s♣♦♥❞ t♦ tr❡❛t♠❡♥ts ♦r ♠✉❧t✐♣❧❡ ❡♥✈✐r♦♥✲✻✼✺
♠❡♥t❛❧ ❣r❛❞✐❡♥ts✳✻✼✻
P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❝❛♥ ❝♦♥♥❡❝t t❤❡ ♣✐♣❡❧✐♥❡ ♦❢ ♠✐❝r♦❜✐♦♠❡ st✉❞✐❡s t♦ ❢♦❝✉s❡❞✻✼✼
st✉❞✐❡s ♦❢ ♠✐❝r♦❜✐❛❧ ♣❤②s✐♦❧♦❣②✳ ❆s r❡s❡❛r❝❤❡rs ✐❞❡♥t✐❢② ❧✐♥❡❛❣❡s ✇✐t❤ ♣✉t❛t✐✈❡✻✼✽
❢✉♥❝t✐♦♥❛❧ ❡❝♦❧♦❣✐❝❛❧ r❡s♣♦♥s❡s✱ t❛①❛ ✇✐t❤✐♥ t❤♦s❡ ❧✐♥❡❛❣❡s ✲ ❡✈❡♥ ✐❢ t❤❡② ❛r❡ ♥♦t✻✼✾
t❤❡ s❛♠❡ ❖❚❯s ✲ ❝❛♥ ❜❡ ❝✉❧t✐✈❛t❡❞ ❛♥❞ t❤❡✐r ❣❡♥♦♠❡s s❝r❡❡♥❡❞ t♦ ✉♥❝♦✈❡r t❤❡✻✽✵
♣❤②s✐♦❧♦❣✐❝❛❧ ♠❡❝❤❛♥✐s♠s ✉♥❞❡r❧②✐♥❣ t❤❡ ❧✐♥❡❛❣❡s✬ s❤❛r❡❞ r❡s♣♦♥s❡✳✻✽✶
P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✐♠♣r♦✈❡s t❤❡ ♣✐♣❡❧✐♥❡ ❢♦r ❛♥❛❧②③✐♥❣ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡ts ❜②✻✽✷
❛❧❧♦✇✐♥❣ r❡s❡❛r❝❤❡rs t♦ ♦❜❥❡❝t✐✈❡❧② ❞❡t❡r♠✐♥❡ t❤❡ ❛♣♣r♦♣r✐❛t❡ ♣❤②❧♦❣❡♥❡t✐❝ s❝❛❧❡s✻✽✸
❢♦r ❛♥❛❧②③✐♥❣ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡ts ✲ ❛ ❢❛♠✐❧② ❤❡r❡✱ ❛♥ ✉♥❝❧❛ss✐✜❡❞ s♣❧✐t t❤❡r❡ ✲✻✽✹
✷✷
✐♥st❡❛❞ ♦❢ ♣❡r❢♦r♠✐♥❣ ♠✉❧t✐♣❧❡ ❝♦♠♣❛r✐s♦♥s ❛t ❡❛❝❤ t❛①♦♥♦♠✐❝ ❧❡✈❡❧✳ ■♥st❡❛❞ ♦❢✻✽✺
♣r✐♥❝✐♣❧❡ ❝♦♠♣♦♥❡♥ts ❛♥❛❧②s✐s ♦r ♣r✐♥❝✐♣❧❡ ❝♦♦r❞✐♥❛t❡s ❛♥❛❧②s✐s✱ ♣❤②❧♦❢❛❝t♦r✐③❛✲✻✽✻
t✐♦♥ ❝❛♥ ❜❡ ✉s❡❞ ❛s ❢♦r ❡①♣❧♦r❛t♦r② ❞❛t❛ ❛♥❛❧②s✐s ❛♥❞ ❞✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥✻✽✼
t♦♦❧ ✐♥ ✇❤✐❝❤ t❤❡ ✏❝♦♠♣♦♥❡♥ts✑ ❛r❡ ✐❞❡♥t✐✜❛❜❧❡ ❝❧❛❞❡s ✐♥ t❤❡ tr❡❡ ♦❢ ❧✐❢❡✱ ❛ ❢❛r✻✽✽
♠♦r❡ ✐♥t✉✐t✐✈❡ ❛♥❞ ✐♥❢♦r♠❛t✐✈❡ ❝♦♠♣♦♥❡♥t ❢♦r ❜✐♦❧♦❣✐❝❛❧ ✈❛r✐❛t✐♦♥ t❤❛♥ ♠✉❧t✐✲✻✽✾
s♣❡❝✐❡s ❧♦❛❞✐♥❣s✳✻✾✵
P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❝❛♥ ❛❧❧♦✇ r❡s❡❛r❝❤❡rs t♦ ❛♥♥♦t❛t❡ ♦♥❧✐♥❡ ❞❛t❛❜❛s❡s ♦❢ t❤❡✻✾✶
♠✐❝r♦❜✐❛❧ tr❡❡ ♦❢ ❧✐❢❡✱ ♣❡r♠✐tt✐♥❣ ♣r❡❞✐❝t✐♦♥s ❛❜♦✉t t❤❡ ♣❤②s✐♦❧♦❣② ♦❢ ✉♥❝❧❛ss✐✲✻✾✷
✜❡❞ ❛♥❞ ✉♥❝❤❛r❛❝t❡r✐③❡❞ ❧✐❢❡ ❢♦r♠s ❜❛s❡❞ ♦♥ ♣r❡✈✐♦✉s ♣❤②❧♦❣❡♥❡t✐❝ ✐♥❢❡r❡♥❝❡s ✐♥✻✾✸
s❡q✉❡♥❝❡✲❝♦✉♥t ❞❛t❛✳ ❇② ❛❧❧♦✇✐♥❣ r❡s❡❛r❝❤❡rs t♦ ♠❛❦❡ ✐♥❢❡r❡♥❝❡s ♦♥ t❤❡ s❛♠❡✻✾✹
tr❡❡ ❛♥❞ ♣♦t❡♥t✐❛❧❧② ❛♥♥♦t❛t❡ ❛♥ ♦♥❧✐♥❡ tr❡❡ ♦❢ ❧✐❢❡✱ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ♠❛② ❜r✐♥❣✻✾✺
♦♥ ❛ ♥❡✇ ❡r❛ ♦❢ ❝❤❛r❛❝t❡r✐③✐♥❣ ❤✐❣❤✲t❤r♦✉❣❤♣✉t ♣❤②❧♦❣❡♥❡t✐❝ ❛♥♥♦t❛t✐♦♥s✱ ✜❧❧✐♥❣✻✾✻
✐♥ t❤❡ ❣❛♣s t❤❡ ♠✐❝r♦❜✐❛❧ tr❡❡ ♦❢ ❧✐❢❡✳✻✾✼
❆♥ ❘ ♣❛❝❦❛❣❡ ❢♦r ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✇✐t❤ ✉s❡r✲❢r✐❡♥❞❧② ♣❛r❛❧❧❡❧✐③❛t✐♦♥ ✐s ♥♦✇✻✾✽
❛✈❛✐❧❛❜❧❡ ♦♥❧✐♥❡ ❛t ❤tt♣s✿✴✴❣✐t❤✉❜✳❝♦♠✴r❡♣t❛❧❡①✴♣❤②❧♦❢❛❝t♦r✳✻✾✾
❆❝❦♥♦✇❧❡❞❣♠❡♥ts✼✵✵
❆❉❲ ✇♦✉❧❞ ❧✐❦❡ t♦ ❛❝❦♥♦✇❧❡❞❣❡ ▲✳ ▼❛ ❢♦r ❤✐s ❢❡❡❞❜❛❝❦ ❛♥❞ ❤❡❧♣ ✐♥❝♦r♣♦r❛t✐♥❣✼✵✶
t❤✐s ♠❡t❤♦❞ ✐♥t♦ t❤❡ st❛t✐st✐❝❛❧ ❧✐t❡r❛t✉r❡✳ ❚❤✐s ♣❛♣❡r ✐s ♣✉❜❧✐s❤❡❞ ❜② s✉♣♣♦rt✼✵✷
❢r♦♠ ❛♥❞ ✐♥ ❧♦✈✐♥❣ ♠❡♠♦r② ♦❢ ❉✳ ◆❡♠❡r❣✉t✳✼✵✸
❘❡❢❡r❡♥❝❡s✼✵✹
❬✶❪ ❏♦❤♥ ❆✐t❝❤✐s♦♥✳ ❚❤❡ st❛t✐st✐❝❛❧ ❛♥❛❧②s✐s ♦❢ ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛✳ ✶✾✽✻✳✼✵✺
❬✷❪ ❘✐❝❤❛r❞ ❉ ❇❛r❞❣❡tt✱ ❈❤r✐s ❋r❡❡♠❛♥✱ ❛♥❞ ◆✐❝❤♦❧❛s ❏ ❖st❧❡✳ ▼✐❝r♦❜✐❛❧ ❝♦♥✲✼✵✻
tr✐❜✉t✐♦♥s t♦ ❝❧✐♠❛t❡ ❝❤❛♥❣❡ t❤r♦✉❣❤ ❝❛r❜♦♥ ❝②❝❧❡ ❢❡❡❞❜❛❝❦s✳ ❚❤❡ ■❙▼❊✼✵✼
❏♦✉r♥❛❧✱ ✷✭✽✮✿✽✵✺✕✽✶✹✱ ✷✵✵✽✳✼✵✽
❬✸❪ ❘♦❡❧❛♥❞ ▲ ❇❡r❡♥❞s❡♥✱ ❈♦r♥❡ ▼❏ P✐❡t❡rs❡✱ ❛♥❞ P❡t❡r ❆❍▼ ❇❛❦❦❡r✳ ❚❤❡ r❤✐✲✼✵✾
③♦s♣❤❡r❡ ♠✐❝r♦❜✐♦♠❡ ❛♥❞ ♣❧❛♥t ❤❡❛❧t❤✳ ❚r❡♥❞s ✐♥ ♣❧❛♥t s❝✐❡♥❝❡✱ ✶✼✭✽✮✿✹✼✽✕✼✶✵
✹✽✻✱ ✷✵✶✷✳✼✶✶
❬✹❪ ❏ ●r❡❣♦r② ❈❛♣♦r❛s♦✱ ❈❤r✐st✐❛♥ ▲ ▲❛✉❜❡r✱ ❊❧✐③❛❜❡t❤ ❑ ❈♦st❡❧❧♦✱ ❉♦♥♥❛✼✶✷
❇❡r❣✲▲②♦♥s✱ ❆♥t♦♥✐♦ ●♦♥③❛❧❡③✱ ❏❡ss❡ ❙t♦♠❜❛✉❣❤✱ ❉❛♥ ❑♥✐❣❤ts✱ P❛✇❡❧✼✶✸
✷✸
●❛❥❡r✱ ❏❛❝q✉❡s ❘❛✈❡❧✱ ◆♦❛❤ ❋✐❡r❡r✱ ❡t ❛❧✳ ▼♦✈✐♥❣ ♣✐❝t✉r❡s ♦❢ t❤❡ ❤✉♠❛♥✼✶✹
♠✐❝r♦❜✐♦♠❡✳ ●❡♥♦♠❡ ❇✐♦❧✱ ✶✷✭✺✮✿❘✺✵✱ ✷✵✶✶✳✼✶✺
❬✺❪ ❏ ●r❡❣♦r② ❈❛♣♦r❛s♦✱ ❈❤r✐st✐❛♥ ▲ ▲❛✉❜❡r✱ ❲✐❧❧✐❛♠ ❆ ❲❛❧t❡rs✱ ❉♦♥♥❛ ❇❡r❣✲✼✶✻
▲②♦♥s✱ ❏❛♠❡s ❍✉♥t❧❡②✱ ◆♦❛❤ ❋✐❡r❡r✱ ❙❛r❛❤ ▼ ❖✇❡♥s✱ ❏❛s♦♥ ❇❡t❧❡②✱ ▲♦✉✐s❡✼✶✼
❋r❛s❡r✱ ▼❛r❦✉s ❇❛✉❡r✱ ❡t ❛❧✳ ❯❧tr❛✲❤✐❣❤✲t❤r♦✉❣❤♣✉t ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t②✼✶✽
❛♥❛❧②s✐s ♦♥ t❤❡ ✐❧❧✉♠✐♥❛ ❤✐s❡q ❛♥❞ ♠✐s❡q ♣❧❛t❢♦r♠s✳ ❚❤❡ ■❙▼❊ ❥♦✉r♥❛❧✱✼✶✾
✻✭✽✮✿✶✻✷✶✕✶✻✷✹✱ ✷✵✶✷✳✼✷✵
❬✻❪ ❍✉♠❛♥ ▼✐❝r♦❜✐♦♠❡ Pr♦❥❡❝t ❈♦♥s♦rt✐✉♠ ❡t ❛❧✳ ❙tr✉❝t✉r❡✱ ❢✉♥❝t✐♦♥ ❛♥❞✼✷✶
❞✐✈❡rs✐t② ♦❢ t❤❡ ❤❡❛❧t❤② ❤✉♠❛♥ ♠✐❝r♦❜✐♦♠❡✳ ◆❛t✉r❡✱ ✹✽✻✭✼✹✵✷✮✿✷✵✼✕✷✶✹✱✼✷✷
✷✵✶✷✳✼✷✸
❬✼❪ ❏♦❡❧ ❈r❛❝r❛❢t✳ ❙♣❡❝✐❡s ❝♦♥❝❡♣ts ❛♥❞ s♣❡❝✐❛t✐♦♥ ❛♥❛❧②s✐s✳ ■♥ ❈✉rr❡♥t ♦r✲✼✷✹
♥✐t❤♦❧♦❣②✱ ♣❛❣❡s ✶✺✾✕✶✽✼✳ ❙♣r✐♥❣❡r✱ ✶✾✽✸✳✼✷✺
❬✽❪ ❏♦❡❧ ❈r❛❝r❛❢t✳ ❙♣❡❝✐❡s ❝♦♥❝❡♣ts ✐♥ t❤❡♦r❡t✐❝❛❧ ❛♥❞ ❛♣♣❧✐❡❞ ❜✐♦❧♦❣②✿ ❛ s②st❡♠✲✼✷✻
❛t✐❝ ❞❡❜❛t❡ ✇✐t❤ ❝♦♥s❡q✉❡♥❝❡s✳ ❙♣❡❝✐❡s ❝♦♥❝❡♣ts ❛♥❞ ♣❤②❧♦❣❡♥❡t✐❝ t❤❡♦r②✿✼✷✼
❆ ❞❡❜❛t❡✱ ♣❛❣❡s ✸✵✕✹✸✱ ✷✵✵✵✳✼✷✽
❬✾❪ ❚❛♦ ❉✐♥❣ ❛♥❞ P❛tr✐❝❦ ❉ ❙❝❤❧♦ss✳ ❉②♥❛♠✐❝s ❛♥❞ ❛ss♦❝✐❛t✐♦♥s ♦❢ ♠✐❝r♦❜✐❛❧✼✷✾
❝♦♠♠✉♥✐t② t②♣❡s ❛❝r♦ss t❤❡ ❤✉♠❛♥ ❜♦❞②✳ ◆❛t✉r❡✱ ✺✵✾✭✼✺✵✵✮✿✸✺✼✱ ✷✵✶✹✳✼✸✵
❬✶✵❪ ❏✉❛♥ ❏♦sé ❊❣♦③❝✉❡ ❛♥❞ ❱❡r❛ P❛✇❧♦✇s❦②✲●❧❛❤♥✳ ●r♦✉♣s ♦❢ ♣❛rts ❛♥❞ t❤❡✐r✼✸✶
❜❛❧❛♥❝❡s ✐♥ ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛ ❛♥❛❧②s✐s✳ ▼❛t❤❡♠❛t✐❝❛❧ ●❡♦❧♦❣②✱ ✸✼✭✼✮✿✼✾✺✕✼✸✷
✽✷✽✱ ✷✵✵✺✳✼✸✸
❬✶✶❪ ❏✉❛♥ ❏♦sé ❊❣♦③❝✉❡✱ ❱❡r❛ P❛✇❧♦✇s❦②✲●❧❛❤♥✱ ●❧òr✐❛ ▼❛t❡✉✲❋✐❣✉❡r❛s✱ ❛♥❞✼✸✹
❈❛r❧❡s ❇❛r❝❡❧♦✲❱✐❞❛❧✳ ■s♦♠❡tr✐❝ ❧♦❣r❛t✐♦ tr❛♥s❢♦r♠❛t✐♦♥s ❢♦r ❝♦♠♣♦s✐t✐♦♥❛❧✼✸✺
❞❛t❛ ❛♥❛❧②s✐s✳ ▼❛t❤❡♠❛t✐❝❛❧ ●❡♦❧♦❣②✱ ✸✺✭✸✮✿✷✼✾✕✸✵✵✱ ✷✵✵✸✳✼✸✻
❬✶✷❪ P❛✉❧ ● ❋❛❧❦♦✇s❦✐✱ ❚♦♠ ❋❡♥❝❤❡❧✱ ❛♥❞ ❊❞✇❛r❞ ❋ ❉❡❧♦♥❣✳ ❚❤❡ ♠✐❝r♦❜✐❛❧✼✸✼
❡♥❣✐♥❡s t❤❛t ❞r✐✈❡ ❡❛rt❤✬s ❜✐♦❣❡♦❝❤❡♠✐❝❛❧ ❝②❝❧❡s✳ s❝✐❡♥❝❡✱ ✸✷✵✭✺✽✼✾✮✿✶✵✸✹✕✼✸✽
✶✵✸✾✱ ✷✵✵✽✳✼✸✾
❬✶✸❪ ❏♦s❡♣❤ ❋❡❧s❡♥st❡✐♥✳ P❤②❧♦❣❡♥✐❡s ❛♥❞ t❤❡ ❝♦♠♣❛r❛t✐✈❡ ♠❡t❤♦❞✳ ❆♠❡r✐❝❛♥✼✹✵
◆❛t✉r❛❧✐st✱ ♣❛❣❡s ✶✕✶✺✱ ✶✾✽✺✳✼✹✶
❬✶✹❪ ◆♦❛❤ ❋✐❡r❡r ❛♥❞ ❘♦❜❡rt ❇ ❏❛❝❦s♦♥✳ ❚❤❡ ❞✐✈❡rs✐t② ❛♥❞ ❜✐♦❣❡♦❣r❛♣❤② ♦❢ s♦✐❧✼✹✷
❜❛❝t❡r✐❛❧ ❝♦♠♠✉♥✐t✐❡s✳ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ◆❛t✐♦♥❛❧ ❆❝❛❞❡♠② ♦❢ ❙❝✐❡♥❝❡s ♦❢✼✹✸
t❤❡ ❯♥✐t❡❞ ❙t❛t❡s ♦❢ ❆♠❡r✐❝❛✱ ✶✵✸✭✸✮✿✻✷✻✕✻✸✶✱ ✷✵✵✻✳✼✹✹
✷✹
❬✶✺❪ ▼❛r✐❡❧ ▼ ❋✐♥✉❝❛♥❡✱ ❚❤♦♠❛s ❏ ❙❤❛r♣t♦♥✱ ❚✐♠♦t❤② ❏ ▲❛✉r❡♥t✱ ❛♥❞ ❑❛t❤❡r✲✼✹✺
✐♥❡ ❙ P♦❧❧❛r❞✳ ❆ t❛①♦♥♦♠✐❝ s✐❣♥❛t✉r❡ ♦❢ ♦❜❡s✐t② ✐♥ t❤❡ ♠✐❝r♦❜✐♦♠❡❄ ❣❡tt✐♥❣✼✹✻
t♦ t❤❡ ❣✉ts ♦❢ t❤❡ ♠❛tt❡r✳ P❧♦❙ ♦♥❡✱ ✾✭✶✮✿❡✽✹✻✽✾✱ ✷✵✶✹✳✼✹✼
❬✶✻❪ ❏♦♥❛t❤❛♥ ❋r✐❡❞♠❛♥ ❛♥❞ ❊r✐❝ ❏ ❆❧♠✳ ■♥❢❡rr✐♥❣ ❝♦rr❡❧❛t✐♦♥ ♥❡t✇♦r❦s ❢r♦♠✼✹✽
❣❡♥♦♠✐❝ s✉r✈❡② ❞❛t❛✳ P▲♦❙ ❈♦♠♣✉t ❇✐♦❧✱ ✽✭✾✮✿❡✶✵✵✷✻✽✼✱ ✷✵✶✷✳✼✹✾
❬✶✼❪ ❆❧❛♥ ●r❛❢❡♥✳ ❚❤❡ ♣❤②❧♦❣❡♥❡t✐❝ r❡❣r❡ss✐♦♥✳ P❤✐❧♦s♦♣❤✐❝❛❧ ❚r❛♥s❛❝t✐♦♥s ♦❢✼✺✵
t❤❡ ❘♦②❛❧ ❙♦❝✐❡t② ♦❢ ▲♦♥❞♦♥✳ ❙❡r✐❡s ❇✱ ❇✐♦❧♦❣✐❝❛❧ ❙❝✐❡♥❝❡s✱ ✸✷✻✭✶✷✸✸✮✿✶✶✾✕✼✺✶
✶✺✼✱ ✶✾✽✾✳✼✺✷
❬✶✽❪ ❑❡✐t❤ ●r❡❣❣✳ ❊♥❣✐♥❡❡r✐♥❣ ❣✉t ✢♦r❛ ♦❢ r✉♠✐♥❛♥t ❧✐✈❡st♦❝❦ t♦ r❡❞✉❝❡ ❢♦r❛❣❡✼✺✸
t♦①✐❝✐t②✿ ♣r♦❣r❡ss ❛♥❞ ♣r♦❜❧❡♠s✳ ❚r❡♥❞s ✐♥ ❜✐♦t❡❝❤♥♦❧♦❣②✱ ✶✸✭✶✵✮✿✹✶✽✕✹✷✶✱✼✺✹
✶✾✾✺✳✼✺✺
❬✶✾❪ ❯❧r✐❦❡ ●rö♠♣✐♥❣✳ ❘❡❧❛t✐✈❡ ✐♠♣♦rt❛♥❝❡ ❢♦r ❧✐♥❡❛r r❡❣r❡ss✐♦♥ ✐♥ r✿ t❤❡ ♣❛❝❦✲✼✺✻
❛❣❡ r❡❧❛✐♠♣♦✳ ❏♦✉r♥❛❧ ♦❢ st❛t✐st✐❝❛❧ s♦❢t✇❛r❡✱ ✶✼✭✶✮✿✶✕✷✼✱ ✷✵✵✻✳✼✺✼
❬✷✵❪ ❇ ●✉❣❣❡♥❤❡✐♠✳ ❙tr❡♣t♦❝♦❝❝✐ ♦❢ ❞❡♥t❛❧ ♣❧❛q✉❡s✳ ❈❛r✐❡s r❡s❡❛r❝❤✱ ✷✭✷✮✿✶✹✼✕✼✺✽
✶✻✸✱ ✶✾✻✽✳✼✺✾
❬✷✶❪ P❛✉❧ ❍ ❍❛r✈❡② ❛♥❞ ▼❛r❦ ❉ P❛❣❡❧✳ ❚❤❡ ❝♦♠♣❛r❛t✐✈❡ ♠❡t❤♦❞ ✐♥ ❡✈♦❧✉t✐♦♥❛r②✼✻✵
❜✐♦❧♦❣②✱ ✈♦❧✉♠❡ ✷✸✾✳ ❖①❢♦r❞ ✉♥✐✈❡rs✐t② ♣r❡ss ❖①❢♦r❞✱ ✶✾✾✶✳✼✻✶
❬✷✷❪ ❋r❛♥ç♦✐s ❑❡❝❦✱ ❋ré❞ér✐❝ ❘✐♠❡t✱ ❆❣♥❡s ❇♦✉❝❤❡③✱ ❛♥❞ ❆❧❛✐♥ ❋r❛♥❝✳ ♣❤②❧♦s✐❣✲✼✻✷
♥❛❧✿ ❛♥ r ♣❛❝❦❛❣❡ t♦ ♠❡❛s✉r❡✱ t❡st✱ ❛♥❞ ❡①♣❧♦r❡ t❤❡ ♣❤②❧♦❣❡♥❡t✐❝ s✐❣♥❛❧✳✼✻✸
❊❝♦❧♦❣② ❛♥❞ ❡✈♦❧✉t✐♦♥✱ ✻✭✾✮✿✷✼✼✹✕✷✼✽✵✱ ✷✵✶✻✳✼✻✹
❬✷✸❪ ❖♠r② ❑♦r❡♥✱ ❆②♠é ❙♣♦r✱ ❏❡♥♥② ❋❡❧✐♥✱ ❋r✐❞❛ ❋å❦✱ ❏❡ss❡ ❙t♦♠❜❛✉❣❤✱✼✻✺
❱❛❧❡♥t✐♥❛ ❚r❡♠❛r♦❧✐✱ ❈❛r❧ ❏♦❤❛♥ ❇❡❤r❡✱ ❘♦❜ ❑♥✐❣❤t✱ ❇❥ör♥ ❋❛❣❡r❜❡r❣✱✼✻✻
❘✉t❤ ❊ ▲❡②✱ ❡t ❛❧✳ ❍✉♠❛♥ ♦r❛❧✱ ❣✉t✱ ❛♥❞ ♣❧❛q✉❡ ♠✐❝r♦❜✐♦t❛ ✐♥ ♣❛t✐❡♥ts✼✻✼
✇✐t❤ ❛t❤❡r♦s❝❧❡r♦s✐s✳ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ◆❛t✐♦♥❛❧ ❆❝❛❞❡♠② ♦❢ ❙❝✐❡♥❝❡s✱✼✻✽
✶✵✽✭❙✉♣♣❧❡♠❡♥t ✶✮✿✹✺✾✷✕✹✺✾✽✱ ✷✵✶✶✳✼✻✾
❬✷✹❪ ❑✐♠✲❆♥❤ ▲❡ ❈❛♦✱ ▼❛r②✲❊❧❧❡♥ ❈♦st❡❧❧♦✱ ❱❛♥❡ss❛ ❆♥♥❡ ▲❛❦✐s✱ ❋r❛♥❝♦✐s ❇❛r✲✼✼✵
t♦❧♦✱ ❳✐♥✲❨✐ ❈❤✉❛✱ ❘❡♠✐ ❇r❛③❡✐❧❧❡s✱ ❛♥❞ P❛s❝❛❧❡ ❘♦♥❞❡❛✉✳ ♠✐①♠❝✿ ❛ ♠✉❧✲✼✼✶
t✐✈❛r✐❛t❡ st❛t✐st✐❝❛❧ ❢r❛♠❡✇♦r❦ t♦ ❣❛✐♥ ✐♥s✐❣❤t ✐♥t♦ ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t✐❡s✳✼✼✷
❜✐♦❘①✐✈✱ ♣❛❣❡ ✵✹✹✷✵✻✱ ✷✵✶✻✳✼✼✸
❬✷✺❪ ❏ør❣❡♥ ❏ ▲❡✐s♥❡r✱ ❇✐r❣✐t ●r♦t❤ ▲❛✉rs❡♥✱ ❍❡r✈é Pré✈♦st✱ ❉❥❛♠❡❧ ❉r✐❞❡r✱ ❛♥❞✼✼✹
P❛✇ ❉❛❧❣❛❛r❞✳ ❈❛r♥♦❜❛❝t❡r✐✉♠✿ ♣♦s✐t✐✈❡ ❛♥❞ ♥❡❣❛t✐✈❡ ❡✛❡❝ts ✐♥ t❤❡ ❡♥✈✐✲✼✼✺
r♦♥♠❡♥t ❛♥❞ ✐♥ ❢♦♦❞s✳ ❋❊▼❙ ♠✐❝r♦❜✐♦❧♦❣② r❡✈✐❡✇s✱ ✸✶✭✺✮✿✺✾✷✕✻✶✸✱ ✷✵✵✼✳✼✼✻
✷✺
❬✷✻❪ ● ▲✐✱ ❲ ❍✉❛♥❣✱ ❉◆ ▲❡r♥❡r✱ ❛♥❞ ❳ ❩❤❛♥❣✳ ❊♥r✐❝❤♠❡♥t ♦❢ ❞❡❣r❛❞✐♥❣ ♠✐✲✼✼✼
❝r♦❜❡s ❛♥❞ ❜✐♦r❡♠❡❞✐❛t✐♦♥ ♦❢ ♣❡tr♦❝❤❡♠✐❝❛❧ ❝♦♥t❛♠✐♥❛♥ts ✐♥ ♣♦❧❧✉t❡❞ s♦✐❧✳✼✼✽
❲❛t❡r ❘❡s❡❛r❝❤✱ ✸✹✭✶✺✮✿✸✽✹✺✕✸✽✺✸✱ ✷✵✵✵✳✼✼✾
❬✷✼❪ ❈❛t❤❡r✐♥❡ ▲♦③✉♣♦♥❡ ❛♥❞ ❘♦❜ ❑♥✐❣❤t✳ ❯♥✐❢r❛❝✿ ❛ ♥❡✇ ♣❤②❧♦❣❡♥❡t✐❝ ♠❡t❤♦❞✼✽✵
❢♦r ❝♦♠♣❛r✐♥❣ ♠✐❝r♦❜✐❛❧ ❝♦♠♠✉♥✐t✐❡s✳ ❆♣♣❧✐❡❞ ❛♥❞ ❡♥✈✐r♦♥♠❡♥t❛❧ ♠✐❝r♦❜✐✲✼✽✶
♦❧♦❣②✱ ✼✶✭✶✷✮✿✽✷✷✽✕✽✷✸✺✱ ✷✵✵✺✳✼✽✷
❬✷✽❪ ❏♦s❡♣ ❆ ▼❛rtí♥✲❋❡r♥á♥❞❡③✱ ❈❛r❧❡s ❇❛r❝❡❧ó✲❱✐❞❛❧✱ ❛♥❞ ❱❡r❛ P❛✇❧♦✇s❦②✲✼✽✸
●❧❛❤♥✳ ❉❡❛❧✐♥❣ ✇✐t❤ ③❡r♦s ❛♥❞ ♠✐ss✐♥❣ ✈❛❧✉❡s ✐♥ ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛ s❡ts✼✽✹
✉s✐♥❣ ♥♦♥♣❛r❛♠❡tr✐❝ ✐♠♣✉t❛t✐♦♥✳ ▼❛t❤❡♠❛t✐❝❛❧ ●❡♦❧♦❣②✱ ✸✺✭✸✮✿✷✺✸✕✷✼✽✱✼✽✺
✷✵✵✸✳✼✽✻
❬✷✾❪ ❊♠✐❧✐❛ P ▼❛rt✐♥s ❛♥❞ ❚❤♦♠❛s ❋ ❍❛♥s❡♥✳ P❤②❧♦❣❡♥✐❡s ❛♥❞ t❤❡ ❝♦♠♣❛r❛t✐✈❡✼✽✼
♠❡t❤♦❞✿ ❛ ❣❡♥❡r❛❧ ❛♣♣r♦❛❝❤ t♦ ✐♥❝♦r♣♦r❛t✐♥❣ ♣❤②❧♦❣❡♥❡t✐❝ ✐♥❢♦r♠❛t✐♦♥ ✐♥t♦✼✽✽
t❤❡ ❛♥❛❧②s✐s ♦❢ ✐♥t❡rs♣❡❝✐✜❝ ❞❛t❛✳ ❆♠❡r✐❝❛♥ ◆❛t✉r❛❧✐st✱ ♣❛❣❡s ✻✹✻✕✻✻✼✱ ✶✾✾✼✳✼✽✾
❬✸✵❪ ❏❡♥♥✐❢❡r ❇❍ ▼❛rt✐♥②✱ ❙t✉❛rt ❊ ❏♦♥❡s✱ ❏❛② ❚ ▲❡♥♥♦♥✱ ❛♥❞ ❆❞❛♠ ❈ ▼❛r✲✼✾✵
t✐♥②✳ ▼✐❝r♦❜✐♦♠❡s ✐♥ ❧✐❣❤t ♦❢ tr❛✐ts✿ ❆ ♣❤②❧♦❣❡♥❡t✐❝ ♣❡rs♣❡❝t✐✈❡✳ ❙❝✐❡♥❝❡✱✼✾✶
✸✺✵✭✻✷✻✶✮✿❛❛❝✾✸✷✸✱ ✷✵✶✺✳✼✾✷
❬✸✶❪ ❏✐❡ ◆✐♥❣ ❛♥❞ ❘♦❜❡rt ● ❇❡✐❦♦✳ P❤②❧♦❣❡♥❡t✐❝ ❛♣♣r♦❛❝❤❡s t♦ ♠✐❝r♦❜✐❛❧ ❝♦♠✲✼✾✸
♠✉♥✐t② ❝❧❛ss✐✜❝❛t✐♦♥✳ ▼✐❝r♦❜✐♦♠❡✱ ✸✭✶✮✿✶✱ ✷✵✶✺✳✼✾✹
❬✸✷❪ ❱❡r❛ P❛✇❧♦✇s❦②✲●❧❛❤♥ ❛♥❞ ❆♥t♦♥❡❧❧❛ ❇✉❝❝✐❛♥t✐✳ ❈♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛ ❛♥❛❧✲✼✾✺
②s✐s✿ ❚❤❡♦r② ❛♥❞ ❛♣♣❧✐❝❛t✐♦♥s✳ ❏♦❤♥ ❲✐❧❡② ✫ ❙♦♥s✱ ✷✵✶✶✳✼✾✻
❬✸✸❪ ▼♦r❣❛♥ ◆ Pr✐❝❡✱ P❛r❛♠✈✐r ❙ ❉❡❤❛❧✱ ❛♥❞ ❆❞❛♠ P ❆r❦✐♥✳ ❋❛sttr❡❡ ✷✕✼✾✼
❛♣♣r♦①✐♠❛t❡❧② ♠❛①✐♠✉♠✲❧✐❦❡❧✐❤♦♦❞ tr❡❡s ❢♦r ❧❛r❣❡ ❛❧✐❣♥♠❡♥ts✳ P❧♦❙ ♦♥❡✱✼✾✽
✺✭✸✮✿❡✾✹✾✵✱ ✷✵✶✵✳✼✾✾
❬✸✹❪ ❊❧♠❛r Pr✉❡ss❡✱ ❏ör❣ P❡♣❧✐❡s✱ ❛♥❞ ❋r❛♥❦ ❖❧✐✈❡r ●❧ö❝❦♥❡r✳ ❙✐♥❛✿ ❛❝❝✉✲✽✵✵
r❛t❡ ❤✐❣❤✲t❤r♦✉❣❤♣✉t ♠✉❧t✐♣❧❡ s❡q✉❡♥❝❡ ❛❧✐❣♥♠❡♥t ♦❢ r✐❜♦s♦♠❛❧ r♥❛ ❣❡♥❡s✳✽✵✶
❇✐♦✐♥❢♦r♠❛t✐❝s✱ ✷✽✭✶✹✮✿✶✽✷✸✕✶✽✷✾✱ ✷✵✶✷✳✽✵✷
❬✸✺❪ ❊❧✐③❛❜❡t❤ P✉r❞♦♠✳ ❆♥❛❧②s✐s ♦❢ ❛ ❞❛t❛ ♠❛tr✐① ❛♥❞ ❛ ❣r❛♣❤✿ ▼❡t❛❣❡♥♦♠✐❝✽✵✸
❞❛t❛ ❛♥❞ t❤❡ ♣❤②❧♦❣❡♥❡t✐❝ tr❡❡✳ ❚❤❡ ❆♥♥❛❧s ♦❢ ❆♣♣❧✐❡❞ ❙t❛t✐st✐❝s✱ ♣❛❣❡s✽✵✹
✷✸✷✻✕✷✸✺✽✱ ✷✵✶✶✳✽✵✺
❬✸✻❪ ❑❡❧❧② ❙ ❘❛♠✐r❡③✱ ❏♦♥❛t❤❛♥ ❲ ▲❡✛✱ ❆❧❜❡rt ❇❛r❜❡rá♥✱ ❙❝♦tt ❚❤♦♠❛s ❇❛t❡s✱✽✵✻
❏❛s♦♥ ❇❡t❧❡②✱ ❚❤♦♠❛s ❲ ❈r♦✇t❤❡r✱ ❊✉❣❡♥❡ ❋ ❑❡❧❧②✱ ❊♠✐❧② ❊ ❖❧❞✜❡❧❞✱✽✵✼
❊ ❆s❤❧❡② ❙❤❛✇✱ ❈❤r✐st♦♣❤❡r ❙t❡❡♥❜♦❝❦✱ ❡t ❛❧✳ ❇✐♦❣❡♦❣r❛♣❤✐❝ ♣❛tt❡r♥s ✐♥✽✵✽
✷✻
❋✐❣✉r❡ ✶✿ ❙❤♦rt❝♦♠✐♥❣s ♦❢ ❘♦♦t❡❞ ■▲❘ ✭❛✮ ❚❤❡ ✐s♦♠❡tr✐❝ ❧♦❣✲r❛t✐♦ tr❛♥s❢♦r♠ ❝♦rr❡s♣♦♥❞✐♥❣ t♦
❛ ♣❤②❧♦❣❡♥② r♦♦t❡❞ ❛t t❤❡ ❝♦♠♠♦♥ ❛♥❝❡st♦r ✐s ✐♥❛❝❝✉r❛t❡ ❢♦r ❣❡♦♠❡tr✐❝ ❝❤❛♥❣❡s ✇✐t❤✐♥ ❝❧❛❞❡s✳ ❍❡r❡✱
❛❜s♦❧✉t❡ ❛❜✉♥❞❛♥❝❡s ♦❢ ✺✵ t❛①❛ ✐♥ ✸✵ s❛♠♣❧❡s ♣❡r s✐t❡ ✇❡r❡ s✐♠✉❧❛t❡❞ ❛❝r♦ss t✇♦ s✐t❡s✳ ❆♥ ❛✛❡❝t❡❞
❝❧❛❞❡✱ B✱ ✐s ✉♣✲r❡♣r❡s❡♥t❡❞ ✐♥ t❤❡ s❡❝♦♥❞ s✐t❡✳ ❘❡❣r❡ss✐♦♥ ♦♥ t❤❡ r♦♦t❡❞ ■▲❘ ❝♦♦r❞✐♥❛t❡s✱ x∗i ✱ ❛❣❛✐♥st
t❤❡ s❛♠♣❧❡ s✐t❡ ✐♥❞✐❝❛t❡❞ t❤❛t t❤❡ ♣❛rt✐t✐♦♥ s❡♣❛r❛t✐♥❣ ❝❧❛❞❡ A,B✱ r❡❢❡rr❡❞ t♦ ❛s x∗{A,B}✱ ❤❛❞ t❤❡
❤✐❣❤❡st t❡st✲st❛t✐st✐❝✱ ❜✉t t❤❡ r♦♦t❡❞ ■▲❘ ♣r❡❞✐❝ts ❢♦❧❞✲❝❤❛♥❣❡s ✐♥ B r❡❧❛t✐✈❡ t♦ A✱ ♥♦t ❢♦❧❞ ❝❤❛♥❣❡s
✐♥ B r❡❧❛t✐✈❡ t♦ t❤❡ r❡st ♦❢ t❤❡ t❛①❛✳ ✭❜✮ ❈♦♥s❡q✉❡♥t❧②✱ ✇❤❡♥ ♦♥❡ ❝❧❛❞❡ ✐♥❝r❡❛s❡ ✐♥ ❛❜✉♥❞❛♥❝❡
✇❤✐❧❡ t❤❡ r❡st r❡♠❛✐♥ ✉♥❛✛❡❝t❡❞✱ ♣❛rt✐t✐♦♥s ❜❡t✇❡❡♥ t❤❡ ❛✛❡❝t❡❞ ❝❧❛❞❡ ❛♥❞ t❤❡ r♦♦t ✇✐❧❧ ❛❧s♦ ❤❛✈❡ ❛
s✐❣♥❛❧ ❧❡❛❞✐♥❣ t♦ ❛ ❝♦rr❡❧❛t✐♦♥ ✐♥ t❤❡ ❝♦♦r❞✐♥❛t❡s ❛❧♦♥❣ t❤❡ ♣❛t❤ ❢r♦♠ B t♦ t❤❡ r♦♦t✳ ❚❤❡ ❝♦rr❡❧❛t✐♦♥
♣❧♦tt❡❞ ❤❡r❡ ✐s t❤❡ ❛❜s♦❧✉t❡ ✈❛❧✉❡ ♦❢ t❤❡ ❝♦rr❡❧❛t✐♦♥ ❝♦❡✣❝✐❡♥t✱ ❛♥❞ t❤❡ ❜❛s❡❧✐♥❡ ❝♦rr❡❧❛t✐♦♥ ✇❛s
❡st✐♠❛t❡❞ ❛s t❤❡ ❛✈❡r❛❣❡ ❛❜s♦❧✉t❡ ✈❛❧✉❡ ♦❢ t❤❡ ❝♦rr❡❧❛t✐♦♥ ❝♦❡✣❝✐❡♥t ❜❡t✇❡❡♥ ■▲❘ ❝♦♦r❞✐♥❛t❡s ♥♦t
❛❧♦♥❣ t❤❡ r♦♦t✲♣❛t❤ ♦❢ t❤❡ ❛✛❡❝t❡❞ ❝❧❛❞❡✳
❜❡❧♦✇✲❣r♦✉♥❞ ❞✐✈❡rs✐t② ✐♥ ♥❡✇ ②♦r❦ ❝✐t②✬s ❝❡♥tr❛❧ ♣❛r❦ ❛r❡ s✐♠✐❧❛r t♦ t❤♦s❡✽✵✾
♦❜s❡r✈❡❞ ❣❧♦❜❛❧❧②✳ ■♥ Pr♦❝✳ ❘✳ ❙♦❝✳ ❇✱ ✈♦❧✉♠❡ ✷✽✶✱ ♣❛❣❡ ✷✵✶✹✶✾✽✽✳ ❚❤❡✽✶✵
❘♦②❛❧ ❙♦❝✐❡t②✱ ✷✵✶✹✳✽✶✶
❬✸✼❪ ▲✐❛♠ ❏ ❘❡✈❡❧❧✳ ♣❤②t♦♦❧s✿ ❛♥ r ♣❛❝❦❛❣❡ ❢♦r ♣❤②❧♦❣❡♥❡t✐❝ ❝♦♠♣❛r❛t✐✈❡ ❜✐♦❧♦❣②✽✶✷
✭❛♥❞ ♦t❤❡r t❤✐♥❣s✮✳ ▼❡t❤♦❞s ✐♥ ❊❝♦❧♦❣② ❛♥❞ ❊✈♦❧✉t✐♦♥✱ ✸✭✷✮✿✷✶✼✕✷✷✸✱ ✷✵✶✷✳✽✶✸
❬✸✽❪ ▼❛r❦ ❉ ❘♦❜✐♥s♦♥✱ ❉❛✈✐s ❏ ▼❝❈❛rt❤②✱ ❛♥❞ ●♦r❞♦♥ ❑ ❙♠②t❤✳ ❡❞❣❡r✿ ❛✽✶✹
❜✐♦❝♦♥❞✉❝t♦r ♣❛❝❦❛❣❡ ❢♦r ❞✐✛❡r❡♥t✐❛❧ ❡①♣r❡ss✐♦♥ ❛♥❛❧②s✐s ♦❢ ❞✐❣✐t❛❧ ❣❡♥❡ ❡①✲✽✶✺
♣r❡ss✐♦♥ ❞❛t❛✳ ❇✐♦✐♥❢♦r♠❛t✐❝s✱ ✷✻✭✶✮✿✶✸✾✕✶✹✵✱ ✷✵✶✵✳✽✶✻
❬✸✾❪ ▼✐❦❤❛✐❧ ❚✐❦❤♦♥♦✈✱ ❘♦❜❡rt ❲ ▲❡❛❝❤✱ ❛♥❞ ◆❡❞ ❙ ❲✐♥❣r❡❡♥✳ ■♥t❡r♣r❡t✐♥❣ ✶✻s✽✶✼
♠❡t❛❣❡♥♦♠✐❝ ❞❛t❛ ✇✐t❤♦✉t ❝❧✉st❡r✐♥❣ t♦ ❛❝❤✐❡✈❡ s✉❜✲♦t✉ r❡s♦❧✉t✐♦♥✳ ❚❤❡✽✶✽
■❙▼❊ ❥♦✉r♥❛❧✱ ✾✭✶✮✿✻✽✕✽✵✱ ✷✵✶✺✳✽✶✾
❬✹✵❪ ▼❛r❝❡❧ ●❆ ❱❛♥ ❉❡r ❍❡✐❥❞❡♥✱ ❘✐❝❤❛r❞ ❉ ❇❛r❞❣❡tt✱ ❛♥❞ ◆✐❝♦ ▼✽✷✵
❱❛♥ ❙tr❛❛❧❡♥✳ ❚❤❡ ✉♥s❡❡♥ ♠❛❥♦r✐t②✿ s♦✐❧ ♠✐❝r♦❜❡s ❛s ❞r✐✈❡rs ♦❢ ♣❧❛♥t ❞✐✈❡r✲✽✷✶
s✐t② ❛♥❞ ♣r♦❞✉❝t✐✈✐t② ✐♥ t❡rr❡str✐❛❧ ❡❝♦s②st❡♠s✳ ❊❝♦❧♦❣② ❧❡tt❡rs✱ ✶✶✭✸✮✿✷✾✻✕✽✷✷
✸✶✵✱ ✷✵✵✽✳✽✷✸
❋✐❣✉r❡s✽✷✹
✽✷✺
✷✼
❋✐❣✉r❡ ✷✿ P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✿ ✭❛✮ P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❝❤❛♥❣❡s ✈❛r✐❛❜❧❡s ❢r♦♠ t✐♣s ♦❢ t❤❡ ♣❤②✲
❧♦❣❡♥② ✭❖❚❯s ✉s❡❞ ✐♥ ❛♥❛❧②s✐s ♦❢ ♠✐❝r♦❜✐♦♠❡ ❞❛t❛s❡ts✮ t♦ ❡❞❣❡s ♦❢ t❤❡ ♣❤②❧♦❣❡♥② ✇✐t❤ t❤❡ ❧❛r❣❡st
♣r❡❞✐❝t❛❜❧❡ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ t❛①❛ ♦♥ ❡❛❝❤ s✐❞❡ ♦❢ t❤❡ ❡❞❣❡✳ ❚♦ ✐❧❧✉str❛t❡ t❤✐s ♠❡t❤♦❞✱ ✇❡ ❝♦♥s✐❞❡r
t❤❡ tr❡❛t♠❡♥t ♦❢ ❛ ❜❛❝t❡r✐❛❧ ❝♦♠♠✉♥✐t② ✇✐t❤ ❛♥ ♦①❛③♦❧✐❞✐♥♦♥❡✳ ❖①❛③♦❧✐❞✐♥♦♥❡s t❛r❣❡t ❣r❛♠✲♣♦s✐t✐✈❡
❜❛❝t❡r✐❛ ❛♥❞ ✇✐❧❧ ❧✐❦❡❧② ❧❡❛❞ t♦ ❛ ❞❡❝r❡❛s❡ ✐♥ t❤❡ r❡❧❛t✐✈❡ ❛❜✉♥❞❛♥❝❡s ♦❢ ❣r❛♠✲♣♦s✐t✐✈❡ ❜❛❝t❡r✐❛
✭❛♥t✐❜✐♦t✐❝ s✉s❝❡♣t✐❜❧❡ ❝❧❛❞❡✱ ❆✱ ❤❛✈✐♥❣ t❤❡ ❛♥t✐❜✐♦t✐❝ t❛r❣❡t✮✳ ❆♠♦♥❣ t❤❡ ❛♥t✐❜✐♦t✐❝ s✉s❝❡♣t✐❜❧❡
❜❛❝t❡r✐❛✱ ♣❤②❧♦❢❛❝t♦r ❝❛♥ ✐❞❡♥t✐❢② ♠♦♥♦♣❤②❧❡t✐❝ ❝❧❛❞❡s t❤❛t ❛r❡ r❡s✐st❛♥t r❡❧❛t✐✈❡ t♦ ♦t❤❡r ❛♥t✐❜✐♦t✐❝✲
s✉s❝❡♣t✐❜❧❡ ❜❛❝t❡r✐❛ ❞✉❡ t♦ ❛ ✈❡rt✐❝❛❧❧②✲tr❛♥s♠✐tt❡❞ tr❛✐t ✭❇✮ s✉❝❤ ❛s t❤❡ ❧♦ss ♦❢ t❤❡ ❛♥t✐❜✐♦t✐❝ t❛r❣❡t
♦r ❡♥③②♠❡s t❤❛t ❜r❡❛❦ ❞♦✇♥ t❤❡ ❛♥t✐❜✐♦t✐❝✳ ✭❜✮ ❚❤❡ t✇♦ ♣❤②❧♦❣❡♥❡t✐❝ ❢❛❝t♦rs ♣r♦❞✉❝❡ t❤r❡❡ ♠❡❛♥✲
✐♥❣❢✉❧ ❜✐♥s ♦❢ t❛①❛ ✲ t❤♦s❡ s✉s❝❡♣t✐❜❧❡ t♦ ❛♥t✐❜✐♦t✐❝s ✭❆✮✱ t❤♦s❡ ✇✐t❤✐♥ t❤❡ s✉s❝❡♣t✐❜❧❡ ❝❧❛❞❡ t❤❛t ❛r❡
r❡s✐st❛♥t t♦ ❛♥t✐❜✐♦t✐❝s ✭❆✰❇✮✱ ❛♥❞ ❛ ♣♦t❡♥t✐❛❧❧② ♣❛r❛♣❤②❧❡t✐❝ r❡♠❛✐♥❞❡r✳ ✭❝✮ P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥
✐s ❛ ❣r❡❡❞② ❛❧❣♦r✐t❤♠ t♦ ❡①tr❛❝t t❤❡ ❡❞❣❡s ✇❤✐❝❤ ❝❛♣t✉r❡ t❤❡ ♠♦st ♣r❡❞✐❝t❛❜❧❡ ❞✐✛❡r❡♥❝❡s ✐♥ t❤❡
r❡s♣♦♥s❡ ♦❢ r❡❧❛t✐✈❡ ❛❜✉♥❞❛♥❝❡s ❛♠♦♥❣ t❛①❛ ♦♥ t❤❡ t✇♦ s✐❞❡s ♦❢ ❡❛❝❤ ❡❞❣❡✳ ✭❝✱ t♦♣ r♦✇✮ ❋♦r t❤❡
✜rst ✐t❡r❛t✐♦♥✱ ❛❧❧ ❡❞❣❡s ❛r❡ ❝♦♥s✐❞❡r❡❞ ✲ ❛♥ ■▲❘ ❝♦♦r❞✐♥❛t❡ ✐s ❝r❡❛t❡❞ ❢♦r ❡❛❝❤ ❡❞❣❡ ✉s✐♥❣ ❡q✉❛t✐♦♥
✭✶✮ ❛♥❞ t❤❡ ■▲❘ ❝♦♦r❞✐♥❛t❡ ✐s r❡❣r❡ss❡❞ ❛❣❛✐♥st t❤❡ ✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡✳ ❚❤❡ ❡❞❣❡ ✇❤✐❝❤ ♠❛①✲
✐♠✐③❡s t❤❡ ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥ ✐s ❝❤♦s❡♥✳ ❉❡♣✐❝t❡❞ ❛❜♦✈❡✱ t❤❡ ✜rst ❢❛❝t♦r ❝♦rr❡s♣♦♥❞s t♦ t❤❡ ❡❞❣❡
s❡♣❛r❛t✐♥❣ ❛♥t✐❜✐♦t✐❝ s✉s❝❡♣t✐❜❧❡ ❜❛❝t❡r✐❛ ❢r♦♠ t❤❡ r❡st✳ ❚❤❡♥✱ t❤❡ tr❡❡ ✐s s♣❧✐t ✲ ❛❧❧ s✉❜s❡q✉❡♥t
❝♦♠♣❛r✐s♦♥s ❛❧♦♥❣ ❡❞❣❡s ✇✐❧❧ ❜❡ ❝♦♥t❛✐♥❡❞ ✇✐t❤✐♥ t❤❡ s✉❜✲tr❡❡s✳ ❚❤❡ ❝♦♥❝❡♣t✉❛❧ ❥✉st✐✜❝❛t✐♦♥ ❢♦r
❧✐♠✐t✐♥❣ ❝♦♠♣❛r✐s♦♥s ✇✐t❤✐♥ s✉❜✲tr❡❡s ✐s t♦ ♣r❡✈❡♥t ♦✈❡r✲❧❛♣♣✐♥❣ ❝♦♠♣❛r✐s♦♥s✿ ♦♥❝❡ ✇❡ ✐❞❡♥t✐❢② t❤❡
❛♥t✐❜✐♦t✐❝ s✉s❝❡♣t✐❜❧❡ ❝❧❛❞❡✱ ✇❡ ✇❛♥t t♦ ❧♦♦❦ ❛t ✇❤✐❝❤ t❛①❛ ✇✐t❤✐♥ t❤❛t ❝❧❛❞❡ ❜❡❤❛✈❡ ❞✐✛❡r❡♥t❧② ❢r♦♠
♦t❤❡r t❛①❛ ✇✐t❤✐♥ t❤❛t ❝❧❛❞❡✳ ✭❝✱ ❜♦tt♦♠ r♦✇✮ ❋♦r t❤❡ s❡❝♦♥❞ ✐t❡r❛t✐♦♥✱ t❤❡ r❡♠❛✐♥✐♥❣ ❡❞❣❡s ❛r❡
❝♦♥s✐❞❡r❡❞✱ ■▲❘ ❝♦♦r❞✐♥❛t❡s ✇✐t❤✐♥ s✉❜✲tr❡❡s ❛r❡ ❝♦♥str✉❝t❡❞✳ ❚❤❡ ❡❞❣❡ ♠❛①✐♠✐③✐♥❣ t❤❡ ♦❜❥❡❝t✐✈❡
❢✉♥❝t✐♦♥ ✐s s❡❧❡❝t❡❞ ❛♥❞ t❤❡ tr❡❡ ✐s s♣❧✐t ❛t t❤❛t ❡❞❣❡✳ ❋♦r ♠♦r❡ ❞❡t❛✐❧s✱ s❡❡ t❤❡ s❡❝t✐♦♥ ✏P❤②❧♦❋❛❝t♦r✑
✐♥ t❤❡ s✉♣♣❧❡♠❡♥t❛❧ ✐♥❢♦✳
❋✐❣✉r❡ ✸✿ ✭❛✮ P♦✇❡r ❆♥❛❧②s✐s ✲ ✶ ❈❧❛❞❡✳ ❚❤❡ r♦♦t❡❞ ■▲❘ tr❛♥s❢♦r♠ t❤❛t ♠✐♥✐♠✐③❡s r❡s✐❞✉❛❧
✈❛r✐❛♥❝❡ ✇❤❡♥ r❡❣r❡ss❡❞ ❛❣❛✐♥st s❛♠♣❧❡ s✐t❡ ✐s ❧❡ss ❛❜❧❡ t♦ ✐❞❡♥t✐❢② t❤❡ ❝♦rr❡❝t ❝❧❛❞❡ ❝♦♠♣❛r❡❞
t♦ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❢♦r ❛ ✈❛r✐❡t② ♦❢ ❡✛❡❝t s✐③❡s✱ a✱ ❛♥❞ s❛♠♣❧❡ s✐③❡s✳ ✭❜✮ ❚❤r❡❡ ❙✐❣♥✐✜❝❛♥t
❈❧❛❞❡s✿ ❲❤❡♥ t❤r❡❡ s✐❣♥✐✜❝❛♥t ❝❧❛❞❡s ❛r❡ ❝❤♦s❡♥ ❛♥❞ ❣✐✈❡♥ ❛ s❡t ♦❢ ❡✛❡❝ts ✐♥❝r❡❛s✐♥❣ ✐♥ ✐♥t❡♥s✐t②
✇✐t❤ t❤❡ ♣❛r❛♠❡t❡r b✱ ❝❤♦♦s✐♥❣ t❤❡ t♦♣ r♦♦t❡❞ ■▲❘ ❝♦♦r❞✐♥❛t❡s ✉♥❞❡r ♣❡r❢♦r♠s ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥
✐♥ ❝♦rr❡❝t❧② ✐❞❡♥t✐❢②✐♥❣ t❤❡ ❛✛❡❝t❡❞ ❝❧❛❞❡s✳ P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❛❧s♦ ❡①♣❧❛✐♥s ♠♦r❡ ✈❛r✐❛t✐♦♥ ✐♥ t❤❡
❞❛t❛✿ ❛❝r♦ss ❡✛❡❝t s✐③❡s✱ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ❡①♣❧❛✐♥s ✷ ♦r❞❡rs ♦❢ ♠❛❣♥✐t✉❞❡ ♠♦r❡ ♦❢ t❤❡ ✈❛r✐❛♥❝❡
✐♥ t❤❡ ❞❛t❛s❡t t❤❛♥ t❤❡ s❡q✉❡♥t✐❛❧ r♦♦t❡❞ ■▲❘✳ ✭❝✮ ❙t♦♣♣✐♥❣ P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥✿ P❧♦ts ♦❢ t❤❡
tr✉❡ ♥✉♠❜❡r ♦❢ ❛✛❡❝t❡❞ ❝❧❛❞❡s ✐♥ s✐♠✉❧❛t❡❞ ❞❛t❛s❡ts ❛❣❛✐♥st t❤❡ ♥✉♠❜❡r ♦❢ ❝❧❛❞❡s ✐❞❡♥t✐✜❡❞ ❜② t❤❡
❘ ♣❛❝❦❛❣❡ ✬♣❤②❧♦❢❛❝t♦r✬✳ ❖♥❡ ❝❛♥ t❡r♠✐♥❛t❡ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✇❤❡♥ t❤❡ tr✉❡ ♥✉♠❜❡r ♦❢ ❛✛❡❝t❡❞
❝❧❛❞❡ ✐s ✉♥❦♥♦✇♥ ❜② ❝❤♦♦s✐♥❣ ❛ st♦♣♣✐♥❣ ❢✉♥❝t✐♦♥ ❛✐♠❡❞ ❛t st♦♣♣✐♥❣ ✇❤❡♥ t❤❡r❡ ✐s ♥♦ ❡✈✐❞❡♥❝❡ ♦❢
❛ r❡♠❛✐♥✐♥❣ s✐❣♥❛❧✳ ❇② st♦♣♣✐♥❣ t❤❡ ✐t❡r❛t✐♦♥ ✇❤❡♥ t❤❡ ❞✐str✐❜✉t✐♦♥ ♦❢ P✲✈❛❧✉❡s ❢r♦♠ ❛♥❛❧②s❡s ♦❢
✈❛r✐❛♥❝❡ ♦❢ r❡❣r❡ss✐♦♥ ♦♥ ❝❛♥❞✐❞❛t❡ ■▲❘ ❜❛s✐s ❡❧❡♠❡♥ts ✐s ✉♥✐❢♦r♠ ✭s♣❡❝✐✜❝❛❧❧②✱ st♦♣♣✐♥❣ ✇❤❡♥ ❛
❑❙ t❡st ❛❣❛✐♥st ❛ ✉♥✐❢♦r♠ ❞✐str✐❜✉t✐♦♥ ②✐❡❧❞s P > 0.05✮✱ ✇❡ ♦❜t❛✐♥ ❛ ❝♦♥s❡r✈❛t✐✈❡ ❡st✐♠❛t❡ ♦❢ t❤❡
♥✉♠❜❡r ♦❢ ♣❤②❧♦❣❡♥❡t✐❝ ❢❛❝t♦rs ✐♥ t❤❡ ❞❛t❛✳
✷✽
❋✐❣✉r❡ ✹✿ P❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ♦❢ ❤✉♠❛♥ ❢❡❝❡s✴t♦♥❣✉❡ ❞❛t❛s❡t ✐❞❡♥t✐✜❡s ❝❧❛❞❡s ✇✐t❤ ❞✐❢✲
❢❡r❡♥t ❤❛❜✐t❛t ♣r❡❢❡r❡♥❝❡s✳ ✭❛✮ P❤②❧♦❣❡♥❡t✐❝ str✉❝t✉r❡ ✐s ✈✐s✐❜❧❡ ❛s ❜❧♦❝❦s ✉s✐♥❣ ❛ ♣❤②❧♦❣❡♥❡t✐❝
❤❡❛t♠❛♣ ❢r♦♠ t❤❡ ❘ ♣❛❝❦❛❣❡ ✬♣❤②t♦♦❧s✬ ❬✸✼❪✳ ❚❤❡ ✜rst ❢❛❝t♦r s❡♣❛r❛t❡s ❆❝t✐♥♦❜❛❝t❡r✐❛ ❛♥❞ s♦♠❡
Pr♦t❡♦❜❛❝t❡r✐❛ ❢r♦♠ t❤❡ r❡st✱ t❤❡ s❡❝♦♥❞ ❢❛❝t♦r s❡♣❛r❛t❡s t❤❡ ❝❧❛ss ❇❛❝✐❧❧✐ ❢r♦♠ t❤❡ r❡♠❛✐♥✐♥❣ ♥♦♥✲
Pr♦t❡♦❜❛❝t❡r✐❛ ❛♥❞ ♥♦♥✲❆❝t✐♥♦❜❛❝t❡r✐❛✱ t❤❡ t❤✐r❞ ❢❛❝t♦r ♣✉❧❧s ♦✉t t❤❡ ❣❡♥✉s Pr❡✈♦t❡❧❧❛ ❢r♦♠ ❇❛❝✲
t❡r♦✐❞❡t❡s ❛♥❞ ✐♥❞✐❝❛t❡s t❤❛t ✐t✱ ✉♥❧✐❦❡ ♠❛♥② ♦t❤❡r t❛①❛ ✐♥ ❇❛❝t❡r♦✐❞❡t❡s✱ ✐s ✉♥r❡♣r❡s❡♥t❡❞ ✐♥ t❤❡
t♦♥❣✉❡✳ ❊❛❝❤ ❢❛❝t♦r ❝❛♣t✉r❡s ❛ ♠❛❥♦r ❜❧♦❝❦ ♦❢ ✈❛r✐❛t✐♦♥ ✐♥ t❤❡ ❞❛t❛✱ ❛♥❞ t❤❡ ♦rt❤♦❣♦♥❛❧✐t② ♦❢ t❤❡
■▲❘ ❝♦♦r❞✐♥❛t❡s ❢r♦♠ ❡❛❝❤ ❢❛❝t♦r ❛❧❧♦✇ ♠✉❧t✐♣❧❡ ❢❛❝t♦rs t♦ ❜❡ ❝♦♠❜✐♥❡❞ ❡❛s✐❧② ❢♦r ❡st✐♠❛t❡s ♦❢ ❝♦♠✲
♠✉♥✐t② ❝♦♠♣♦s✐t✐♦♥✳ ✭❜✮ ❚❤❡s❡ t❤r❡❡ ❢❛❝t♦rs s♣❧✐ts t❤❡ ♣❤②❧♦❣❡♥② ✐♥t♦ ❢♦✉r ❜✐♥s✳ ❚❤r❡❡ ♦❢ t❤♦s❡
❜✐♥s ❛r❡ ♠♦♥♦♣❤②❧❡t✐❝ ❛♥❞ t❤❡ ✜♥❛❧ ❜✐♥ ✐s ❛ ✏r❡♠❛✐♥❞❡r✑ ❜✐♥✱ ❝♦♥t❛✐♥✐♥❣ t❛①❛ s♣❧✐t ♦✛ ❜② t❤❡ ♣r❡✈✐✲
♦✉s ♠♦♥♦♣❤②❧❡t✐❝ ❜✐♥s✳ ❚❤❡ t❤r❡❡ ❢❛❝t♦rs ❛r❡ ✐❞❡♥t✐✜❛❜❧❡ ❡❞❣❡s ❜❡t✇❡❡♥ ♥♦❞❡s t❤❛t ❝❛♥ ❜❡ ♠❛♣♣❡❞
t♦ ❛♥ ♦♥❧✐♥❡ ❞❛t❛❜❛s❡ ❝♦♥t❛✐♥✐♥❣ t❤♦s❡ ♥♦❞❡s✳ ❚❤❡ t❛①♦♥♦♠✐❝ ❛ss✐❣♥♠❡♥t ✉s❡❞ ❤❡r❡ ✐s t❤❡ ❞❡❢❛✉❧t
❢♦r t❤❡ ❘ ♣❛❝❦❛❣❡ ✬♣❤②❧♦❢❛❝t♦r✬✱ ♥❛♠❡❧② t❤❡ s❡t ♦❢ ❛❧❧ s❤♦rt❡st✲✉♥✐q✉❡ ♣r❡✜①❡s t❤❛t s❡♣❛r❛t❡ ❡❛❝❤
♠♦♥♦♣❤②❧❡t✐❝ ❜✐♥ ❢r♦♠ ✐ts ❝♦♠♣❧❡♠❡♥t✳
❋✐❣✉r❡ ✺✿ ❉✐♠❡♥s✐♦♥❛❧✐t② ❘❡❞✉❝t✐♦♥ ❛♥❞ ❖r❞✐♥❛t✐♦♥✲❱✐s✉❛❧✐③❛t✐♦♥ ♦❢ s♦✐❧ ♠✐❝r♦❜✐♦♠❡
❞❛t❛s❡t✳ P❤②❧♦❢❛❝t♦r ♣r❡s❡♥ts t✇♦ ❝♦♠♣❧❡♠❡♥t❛r② ♠❡t❤♦❞s ❢♦r ♣r♦❥❡❝t✐♥❣ ❛♥❞ ✈✐s✉❛❧✐③✐♥❣ t❤❡ ❤✐❣❤✲
❞✐♠❡♥s✐♦♥❛❧ ♣❤②❧♦❣❡♥❡t✐❝❛❧❧②✲str✉❝t✉r❡❞ ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛✳ ✭❛✮ ❚❤❡ ■▲❘ ❝♦♦r❞✐♥❛t❡s ❤❛✈❡ ❛s②♠♣✲
t♦t✐❝ ♥♦r♠❛❧✐t② ♣r♦♣❡rt✐❡s ❛♥❞ ♣r♦✈✐❞❡ ❜✐♦❧♦❣✐❝❛❧❧② ✐♥❢♦r♠❛t✐✈❡ ♦r❞✐♥❛t✐♦♥✲✈✐s✉❛❧✐③❛t✐♦♥ ♣❧♦ts✳ ❍❡r❡✱
✇❡ ✇❡ ✈✐s✉❛❧✐③❡ t❤❛t ♣❍ ✐s ❛ ♠✉❝❤ ❜❡tt❡r ♣r❡❞✐❝t♦r t❤❛♥ ◆ ♦❢ t❤❡ ♠❛❥♦r ♣❤②❧♦❣❡♥❡t✐❝ ❢❛❝t♦rs ✐♥ ❈❡♥✲
tr❛❧ P❛r❦ s♦✐❧s✳ ❉♦♠✐♥❛♥❝❡ ❛♥❛❧②s✐s ✐♥❞✐❝❛t❡❞ t❤❛t ♣❍ ❛❝❝♦✉♥ts ❢♦r ❛♣♣r♦①✐♠❛t❡❧② ✾✷✳✽✼✪✱ ✽✾✳✼✽✪✱
❛♥❞ ✾✷✳✾✹✪ ♦❢ t❤❡ ❡①♣❧❛✐♥❡❞ ✈❛r✐❛♥❝❡ ✐♥ t❤❡ ✜rst✱ s❡❝♦♥❞✱ ❛♥❞ t❤✐r❞ ❢❛❝t♦r✱ r❡s♣❡❝t✐✈❡❧②✱ ❝♦♥s✐st❡♥t
✇✐t❤ ♣r❡✈✐♦✉s r❡s✉❧ts ❜❛s❡❞ ♦♥ ❇r❛②✲❈✉rt✐s ❞✐st❛♥❝❡s ❛♥❞ ▼❛♥t❡❧ t❡sts s❤♦✇✐♥❣ t❤❡ ❞♦♠✐♥❛♥❝❡ ♦❢
♣❍ ✐♥ str✉❝t✉r✐♥❣ s♦✐❧ ♠✐❝r♦❜✐♦♠❡s ❬✸✻❪✳ ✭❜✮ ❊✈❡r② ❡❞❣❡ s❡♣❛r❛t❡s ♦♥❡ ❣r♦✉♣ ♦❢ t❛①❛ ✐♥t♦ t✇♦✱ ❛♥❞
t❤❡ ❞✐s❥♦✐♥t ❣r♦✉♣s ♦❢ t❛①❛ ❞❡✜♥❡❞ ❜② ❛ ❝♦♠♠♦♥ ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ✲ ✇❤❛t ✇❡ r❡❢❡r t♦ ❛s ❜✐♥s ✲ ❝❛♥
❜❡ ✉s❡❞ t♦ ❛♠❛❧❣❛♠❛t❡ ❖❚❯s ❛♥❞ ❝♦♥str✉❝t ❛ ❧♦✇❡r✲❞✐♠❡♥s✐♦♥❛❧✱ ❝♦♠♣♦s✐t✐♦♥❛❧ ❞❛t❛s❡t ♦❢ ✏❜✐♥♥❡❞
♣❤②❧♦❣❡♥❡t✐❝ ✉♥✐ts✑ ✭❇P❯s✮✳ P❧♦tt✐♥❣ t❤❡ ♦❜s❡r✈❡❞ r❡❧❛t✐✈❡ ❛❜✉♥❞❛♥❝❡s ♦❢ ❇P❯s ❛♥❞ t❤❡ r❡❧❛t✐✈❡
❛❜✉♥❞❛♥❝❡s ♦❢ ❇P❯s ♣r❡❞✐❝t❡❞ ❜② ♣❤②❧♦❢❛❝t♦r✐③❛t✐♦♥ ②✐❡❧❞s ❛ s✐♠♣❧❡✱ ♣❤②❧♦❣❡♥❡t✐❝ st♦r② ♦❢ ♠✐❝r♦❜✐❛❧
❛ss♦❝✐❛t✐♦♥s ✇✐t❤ ♣❍✳✳ ❲❤✐❧❡ ♠❛♥② ❆❝✐❞♦❜❛❝t❡r✐❛ t❤r✐✈❡ ❛t ❧♦✇ ♣❍✱ t❤❡r❡ ✐s ❛ ♠♦♥♦♣❤②❧❡t✐❝ ❣r♦✉♣ ♦❢
✬❛❝✐❞♦♣❤♦❜✐❝✬ ❆❝✐❞♦❜❛❝t❡r✐❛ ✇❤✐❝❤ t❤r✐✈❡s ❛t ❤✐❣❤❡r ♣❍ ❛♥❞ ✐s ❝♦♠♣r✐s❡❞ ♦❢ ❝❧❛ss❡s ❈❤❧♦r❛❝✐❞♦❜❛❝t❡✲
r✐❛✱ ❆❝✐❞♦❜❛❝t❡r✐❛✲✻✱ ❙✵✸✺ ❛♥❞ t✇♦ ❖❚❯s ✉♥❝❧❛ss✐✜❡❞ ❛t t❤❡ ❝❧❛ss ❧❡✈❡❧✳ ❆❧s♦✱ ❛ ♠♦♥♦♣❤②❧❡t✐❝ ❝❧❛❞❡
♦❢ ❆❝t✐♥♦♠②❝❡t❛❧❡s ✐s ❤✐❣❤❧② ❛❝✐❞♦♣❤✐❧✐❝ ❛♥❞ ❝♦♥s✐sts ♦❢ ✸✶ ❖❚❯s✱ ✷✽ ♦❢ ✇❤✐❝❤ ❛r❡ ✉♥❝❧❛ss✐✜❡❞ ❛t
t❤❡ ❢❛♠✐❧② ❧❡✈❡❧❀ t❤❡ r❡♠❛✐♥✐♥❣ ❆❝t✐♥♦♠②❝❡t❛❧❡s ❛r❡ ✐♥ t❤❡ r❡♠❛✐♥❞❡r ❜✐♥ s❤♦✇ ❛ ✈❡r② ✇❡❛❦ ❛✣♥✐t②
❢♦r ❧♦✇ ♣❍ s♦✐❧s✳ ◆♦♥❡ ♦❢ t❤❡s❡ ❜✐♥s ♦❢ ❖❚❯s ❝♦rr❡s♣♦♥❞ t♦ ❛ s✐♥❣❧❡ t❛①♦♥♦♠✐❝ ❣r♦✉♣✐♥❣✱ ❜✉t ❛❧❧ ♦❢
t❤❡♠ ❛r❡ ❝❤❛r❛❝t❡r✐③❡❞ ❛♥❞ ❝❧❛ss✐✜❡❞ ❜② t❤❡✐r ❧♦❝❛t✐♦♥s ♦♥ ♦♥❡ s✐❞❡ ♦r t❤❡ ♦t❤❡r ♦❢ ❢♦✉r ❡❞❣❡s ✇✐t❤✐♥
t❤❡ ♣❤②❧♦❣❡♥②✳
✷✾
Figure 1
Shortcomings of Rooted ILR
(a) The isometric log-ratio transform corresponding to a phylogeny rooted at the common
ancestor is inaccurate for geometric changes within clades. Here, absolute abundances of 50
taxa in 30 samples per site were simulated across two sites. An affected clade, B, is up-
represented in the second site. Regression on the rooted ILR coordinates, x_{i}^{*}, against
the sample site indicated that the partition separating clade {A,B} , referred to as
x_{\{A,B\}}^{*}, had the highest test-statistic, but the rooted ILR predicts fold-changes in B
relative to A, not fold changes in B relative to the rest of the taxa. (b) Consequently, when
one clade increase in abundance while the rest remain unaffected, partitions between the
affected clade and the root will also have a signal leading to a correlation in the coordinates
along the path from B to the root. The correlation plotted here is the absolute value of the
correlation coefficient, and the baseline correlation was estimated as the average absolute
value of the correlation coefficient between ILR coordinates not along the root-path of the
affected clade.
Figure 2
Phylofactorization
(a) Phylofactorization changes variables from tips of the phylogeny (OTUs used in analysis of
microbiome datasets) to edges of the phylogeny with the largest predictable differences
between taxa on each side of the edge. To illustrate this method, we consider the treatment
of a bacterial community with an oxazolidinone. Oxazolidinones target gram-positive bacteria
and will likely lead to a decrease in the relative abundances of gram-positive bacteria
(antibiotic susceptible clade, A, having the antibiotic target). Among the antibiotic
susceptible bacteria, phylofactor can identify monophyletic clades that are resistant relative
to other antibiotic-susceptible bacteria due to a vertically-transmitted trait (B) such as the
loss of the antibiotic target or enzymes that break down the antibiotic. (b) The two
phylogenetic factors produce three meaningful bins of taxa - those susceptible to antibiotics
(A), those within the susceptible clade that are resistant to antibiotics (A+B), and a
potentially paraphyletic remainder. (c) Phylofactorization is a greedy algorithm to extract the
edges which capture the most predictable differences in the response of relative abundances
among taxa on the two sides of each edge. (c, top row) For the first iteration, all edges are
considered - an ILR coordinate is created for each edge using equation (1) and the ILR
coordinate is regressed against the independent variable. The edge which maximizes the
objective function is chosen. Depicted above, the first factor corresponds to the edge
separating antibiotic susceptible bacteria from the rest. Then, the tree is split - all
subsequent comparisons along edges will be contained within the sub-trees. The conceptual
justification for limiting comparisons within sub-trees is to prevent over-lapping comparisons:
once we identify the antibiotic susceptible clade, we want to look at which taxa within that
clade behave differently from other taxa within that clade. (c, bottom row) For the second
iteration, the remaining edges are considered, ILR coordinates within sub-trees are
constructed. The edge maximizing the objective function is selected and the tree is split at
that edge. For more details, see the section “PhyloFactor” in the supplemental info.
Figure 3
Phylofactorization can correctly identify affected clades and be stopped at a
conservative number of phylogenetic factors.
(a) Power Analysis - 1 Clade. The rooted ILR transform that minimizes residual variance when
regressed against sample site is less able to identify the correct clade compared to
phylofactorization for a variety of effect sizes, a, and sample sizes. (b) Three Significant
Clades: When three significant clades are chosen and given a set of effects increasing in
intensity with the parameter b, choosing the top rooted ILR coordinates under performs
phylofactorization in correctly identifying the affected clades. Phylofactorization also explains
more variation in the data: across effect sizes, phylofactorization explains 2 orders of
magnitude more of the variance in the dataset than the sequential rooted ILR. (c) Stopping
Phylofactorization: Plots of the true number of affected clades in simulated datasets against
the number of clades identified by the R package 'phylofactor'. One can terminate
phylofactorization when the true number of affected clade is unknown by choosing a
stopping function aimed at stopping when there is no evidence of a remaining signal. By
stopping the iteration when the distribution of P-values from analyses of variance of
regression on candidate ILR basis elements is uniform (specifically, stopping when a KS test
against a uniform distribution yields P>0.05), we obtain a conservative estimate of the
number of phylogenetic factors in the data.
Figure 4
Phylofactorization of human feces/tongue dataset identifies clades differentiating body
sites
(a) Phylogenetic structure is visible as blocks using a phylogenetic heatmap from the R
package 'phytools' (Revell, 2012). The first factor separates Actinobacteria and some
Proteobacteria from the rest, the second factor separates the class Bacilli from the remaining
non-Proteobacteria and non-Actinobacteria, the third factor pulls out the genus Prevotella
from Bacteroidetes and indicates that it, unlike many other taxa in Bacteroidetes, is
unrepresented in the tongue. Each factor captures a major block of variation in the data, and
the orthogonality of the ILR coordinates from each factor allow multiple factors to be
combined easily for estimates of community composition. (b) These three factors splits the
phylogeny into four bins. Three of those bins are monophyletic and the final bin is a
“remainder” bin, containing taxa split off by the previous monophyletic bins. The three
factors are identifiable edges between nodes that can be mapped to an online database
containing those nodes. The taxonomic assignment used here is the set of all shortest-
unique-prefixes that separate the taxa in each bin.
Figure 5
Dimensionality Reduction and Ordination-Visualization of soil microbiome dataset
Phylofactor presents two complementary methods for projecting and visualizing the high-
dimensional phylogenetically-structured compositional data. (a) The ILR coordinates have
asymptotic normality properties and provide biologically informative ordination-visualization
plots. Here, we we see that pH is a much better predictor than N of the major phylogenetic
factors in Central Park soils. Dominance analysis indicated that pH accounts for
approximately 92.87%, 89.78%, and 92.94% of the explained variance in the first, second,
and third factor, respectively, consistent with previous results based on Bray-Curtis distances
and Mantel tests showing the dominance of pH in structuring soil microbiomes (Ramirez,
2014). (b) Every edge separates one group of taxa into two, and the disjoint groups of taxa
defined by a common phylofactorization - what we refer to as bins - can be used to
amalgamate OTUs and construct a lower-dimensional, compositional dataset of “binned
phylogenetic units” (BPUs). Plotting the observed relative abundances of BPUs and the
relative abundances of BPUs predicted by phylofactorization yields a simple, phylogenetic
story of microbial associations with pH.. While low pH is dominated by Amany Acidobacteria
thrive at low pH, there is a monophyletic group of 'acidophobic' Acidobacteria which thrives
at higher pH and isthat includes comprised of classes Chloracidobacteria, Acidobacteria-6, ,
and S035 and two OTUs unclassified at the class level. The acidophobic Acidobacteria
increase in relative abundance with pH. Also, a monophyletic clade of Actinomycetales is
highly acidophilic and consists of 31 OTUs, 28 of which are unclassified at the family level;
the remaining Actinomycetales are in the remainder bin show a very weak affinity for low pH
soils. None of these bins of OTUs correspond to a single taxonomic grouping, but all of them
are characterized and classified by their locations on one side or the other of four edges
within the phylogeny.
