Quadruple-star systems are not always nested triples: a machine learning approach to dynamical stability Article Swipe

PDF

Pavan Vynatheya , Rosemary A. Mardling , Adrian S. Hamers ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2301.09930

The dynamical stability of quadruple-star systems has traditionally been treated as a problem involving two `nested' triples which constitute a quadruple. In this novel study, we employed a machine learning algorithm, the multi-layer perceptron (MLP), to directly classify 2+2 and 3+1 quadruples based on their stability (or long-term boundedness). The training data sets for the classification, comprised of $5\times10^5$ quadruples each, were integrated using the highly accurate direct $N$-body code MSTAR. We also carried out a limited parameter space study of zero-inclination systems to directly compare quadruples to triples. We found that both our quadruple MLP models perform better than a `nested' triple MLP approach, which is especially significant for 3+1 quadruples. The classification accuracies for the 2+2 MLP and 3+1 MLP models are 94% and 93% respectively, while the scores for the `nested' triple approach are 88% and 66% respectively. This is a crucial implication for quadruple population synthesis studies. Our MLP models, which are very simple and almost instantaneous to implement, are available on GitHub, along with Python3 scripts to access them.

Related Topics

Artificial Intelligence

Mathematical Analysis

Concepts

Perceptron Stability (learning theory) Nested loop join Computer science Star (game theory) Population Code (set theory) Scripting language Algorithm Simple (philosophy) Parameter space Artificial intelligence Dynamical systems theory Pattern recognition (psychology) Mathematics Machine learning Artificial neural network Data mining Statistics Programming language Set (abstract data type) Physics Quantum mechanics Philosophy Epistemology Sociology Demography Mathematical analysis

Metadata

Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2301.09930
PDF: https://arxiv.org/pdf/2301.09930
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4318143626

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4318143626

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.2301.09930

Digital Object Identifier
Title: Quadruple-star systems are not always nested triples: a machine learning approach to dynamical stability

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2023

Year of publication
Publication date: 2023-01-24

Full publication date if available
Authors: Pavan Vynatheya, Rosemary A. Mardling, Adrian S. Hamers

List of authors in order
Landing page: https://arxiv.org/abs/2301.09930

Publisher landing page
PDF URL: https://arxiv.org/pdf/2301.09930

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://arxiv.org/pdf/2301.09930

Direct OA link when available
Concepts: Perceptron, Stability (learning theory), Nested loop join, Computer science, Star (game theory), Population, Code (set theory), Scripting language, Algorithm, Simple (philosophy), Parameter space, Artificial intelligence, Dynamical systems theory, Pattern recognition (psychology), Mathematics, Machine learning, Artificial neural network, Data mining, Statistics, Programming language, Set (abstract data type), Physics, Quantum mechanics, Philosophy, Epistemology, Sociology, Demography, Mathematical analysis

Top concepts (fields/topics) attached by OpenAlex
Cited by: 0

Total citation count in OpenAlex
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4318143626
doi	https://doi.org/10.48550/arxiv.2301.09930
ids.doi	https://doi.org/10.48550/arxiv.2301.09930
ids.openalex	https://openalex.org/W4318143626
fwci
type	preprint
title	Quadruple-star systems are not always nested triples: a machine learning approach to dynamical stability
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T11948
topics[0].field.id	https://openalex.org/fields/25
topics[0].field.display_name	Materials Science
topics[0].score	0.9987999796867371
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/2505
topics[0].subfield.display_name	Materials Chemistry
topics[0].display_name	Machine Learning in Materials Science
topics[1].id	https://openalex.org/T10913
topics[1].field.id	https://openalex.org/fields/22
topics[1].field.display_name	Engineering
topics[1].score	0.9965999722480774
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2208
topics[1].subfield.display_name	Electrical and Electronic Engineering
topics[1].display_name	Molecular Junctions and Nanostructures
topics[2].id	https://openalex.org/T10002
topics[2].field.id	https://openalex.org/fields/31
topics[2].field.display_name	Physics and Astronomy
topics[2].score	0.9955000281333923
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/3107
topics[2].subfield.display_name	Atomic and Molecular Physics, and Optics
topics[2].display_name	Advanced Chemical Physics Studies
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C60908668
concepts[0].level	3
concepts[0].score	0.7652019262313843
concepts[0].wikidata	https://www.wikidata.org/wiki/Q690207
concepts[0].display_name	Perceptron
concepts[1].id	https://openalex.org/C112972136
concepts[1].level	2
concepts[1].score	0.6214372515678406
concepts[1].wikidata	https://www.wikidata.org/wiki/Q7595718
concepts[1].display_name	Stability (learning theory)
concepts[2].id	https://openalex.org/C1306188
concepts[2].level	2
concepts[2].score	0.5958127379417419
concepts[2].wikidata	https://www.wikidata.org/wiki/Q4060687
concepts[2].display_name	Nested loop join
concepts[3].id	https://openalex.org/C41008148
concepts[3].level	0
concepts[3].score	0.540723979473114
concepts[3].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[3].display_name	Computer science
concepts[4].id	https://openalex.org/C2780897414
concepts[4].level	2
concepts[4].score	0.49506106972694397
concepts[4].wikidata	https://www.wikidata.org/wiki/Q7600592
concepts[4].display_name	Star (game theory)
concepts[5].id	https://openalex.org/C2908647359
concepts[5].level	2
concepts[5].score	0.49143755435943604
concepts[5].wikidata	https://www.wikidata.org/wiki/Q2625603
concepts[5].display_name	Population
concepts[6].id	https://openalex.org/C2776760102
concepts[6].level	3
concepts[6].score	0.4760708212852478
concepts[6].wikidata	https://www.wikidata.org/wiki/Q5139990
concepts[6].display_name	Code (set theory)
concepts[7].id	https://openalex.org/C61423126
concepts[7].level	2
concepts[7].score	0.46294131875038147
concepts[7].wikidata	https://www.wikidata.org/wiki/Q187432
concepts[7].display_name	Scripting language
concepts[8].id	https://openalex.org/C11413529
concepts[8].level	1
concepts[8].score	0.44827035069465637
concepts[8].wikidata	https://www.wikidata.org/wiki/Q8366
concepts[8].display_name	Algorithm
concepts[9].id	https://openalex.org/C2780586882
concepts[9].level	2
concepts[9].score	0.43497854471206665
concepts[9].wikidata	https://www.wikidata.org/wiki/Q7520643
concepts[9].display_name	Simple (philosophy)
concepts[10].id	https://openalex.org/C73586568
concepts[10].level	2
concepts[10].score	0.4290279746055603
concepts[10].wikidata	https://www.wikidata.org/wiki/Q2600211
concepts[10].display_name	Parameter space
concepts[11].id	https://openalex.org/C154945302
concepts[11].level	1
concepts[11].score	0.41935649514198303
concepts[11].wikidata	https://www.wikidata.org/wiki/Q11660
concepts[11].display_name	Artificial intelligence
concepts[12].id	https://openalex.org/C79379906
concepts[12].level	2
concepts[12].score	0.4165138602256775
concepts[12].wikidata	https://www.wikidata.org/wiki/Q3174497
concepts[12].display_name	Dynamical systems theory
concepts[13].id	https://openalex.org/C153180895
concepts[13].level	2
concepts[13].score	0.3829291760921478
concepts[13].wikidata	https://www.wikidata.org/wiki/Q7148389
concepts[13].display_name	Pattern recognition (psychology)
concepts[14].id	https://openalex.org/C33923547
concepts[14].level	0
concepts[14].score	0.3367381989955902
concepts[14].wikidata	https://www.wikidata.org/wiki/Q395
concepts[14].display_name	Mathematics
concepts[15].id	https://openalex.org/C119857082
concepts[15].level	1
concepts[15].score	0.28695398569107056
concepts[15].wikidata	https://www.wikidata.org/wiki/Q2539
concepts[15].display_name	Machine learning
concepts[16].id	https://openalex.org/C50644808
concepts[16].level	2
concepts[16].score	0.23585215210914612
concepts[16].wikidata	https://www.wikidata.org/wiki/Q192776
concepts[16].display_name	Artificial neural network
concepts[17].id	https://openalex.org/C124101348
concepts[17].level	1
concepts[17].score	0.1445816159248352
concepts[17].wikidata	https://www.wikidata.org/wiki/Q172491
concepts[17].display_name	Data mining
concepts[18].id	https://openalex.org/C105795698
concepts[18].level	1
concepts[18].score	0.1349000632762909
concepts[18].wikidata	https://www.wikidata.org/wiki/Q12483
concepts[18].display_name	Statistics
concepts[19].id	https://openalex.org/C199360897
concepts[19].level	1
concepts[19].score	0.12291386723518372
concepts[19].wikidata	https://www.wikidata.org/wiki/Q9143
concepts[19].display_name	Programming language
concepts[20].id	https://openalex.org/C177264268
concepts[20].level	2
concepts[20].score	0.08911207318305969
concepts[20].wikidata	https://www.wikidata.org/wiki/Q1514741
concepts[20].display_name	Set (abstract data type)
concepts[21].id	https://openalex.org/C121332964
concepts[21].level	0
concepts[21].score	0.08028578758239746
concepts[21].wikidata	https://www.wikidata.org/wiki/Q413
concepts[21].display_name	Physics
concepts[22].id	https://openalex.org/C62520636
concepts[22].level	1
concepts[22].score	0.0
concepts[22].wikidata	https://www.wikidata.org/wiki/Q944
concepts[22].display_name	Quantum mechanics
concepts[23].id	https://openalex.org/C138885662
concepts[23].level	0
concepts[23].score	0.0
concepts[23].wikidata	https://www.wikidata.org/wiki/Q5891
concepts[23].display_name	Philosophy
concepts[24].id	https://openalex.org/C111472728
concepts[24].level	1
concepts[24].score	0.0
concepts[24].wikidata	https://www.wikidata.org/wiki/Q9471
concepts[24].display_name	Epistemology
concepts[25].id	https://openalex.org/C144024400
concepts[25].level	0
concepts[25].score	0.0
concepts[25].wikidata	https://www.wikidata.org/wiki/Q21201
concepts[25].display_name	Sociology
concepts[26].id	https://openalex.org/C149923435
concepts[26].level	1
concepts[26].score	0.0
concepts[26].wikidata	https://www.wikidata.org/wiki/Q37732
concepts[26].display_name	Demography
concepts[27].id	https://openalex.org/C134306372
concepts[27].level	1
concepts[27].score	0.0
concepts[27].wikidata	https://www.wikidata.org/wiki/Q7754
concepts[27].display_name	Mathematical analysis
keywords[0].id	https://openalex.org/keywords/perceptron
keywords[0].score	0.7652019262313843
keywords[0].display_name	Perceptron
keywords[1].id	https://openalex.org/keywords/stability
keywords[1].score	0.6214372515678406
keywords[1].display_name	Stability (learning theory)
keywords[2].id	https://openalex.org/keywords/nested-loop-join
keywords[2].score	0.5958127379417419
keywords[2].display_name	Nested loop join
keywords[3].id	https://openalex.org/keywords/computer-science
keywords[3].score	0.540723979473114
keywords[3].display_name	Computer science
keywords[4].id	https://openalex.org/keywords/star
keywords[4].score	0.49506106972694397
keywords[4].display_name	Star (game theory)
keywords[5].id	https://openalex.org/keywords/population
keywords[5].score	0.49143755435943604
keywords[5].display_name	Population
keywords[6].id	https://openalex.org/keywords/code
keywords[6].score	0.4760708212852478
keywords[6].display_name	Code (set theory)
keywords[7].id	https://openalex.org/keywords/scripting-language
keywords[7].score	0.46294131875038147
keywords[7].display_name	Scripting language
keywords[8].id	https://openalex.org/keywords/algorithm
keywords[8].score	0.44827035069465637
keywords[8].display_name	Algorithm
keywords[9].id	https://openalex.org/keywords/simple
keywords[9].score	0.43497854471206665
keywords[9].display_name	Simple (philosophy)
keywords[10].id	https://openalex.org/keywords/parameter-space
keywords[10].score	0.4290279746055603
keywords[10].display_name	Parameter space
keywords[11].id	https://openalex.org/keywords/artificial-intelligence
keywords[11].score	0.41935649514198303
keywords[11].display_name	Artificial intelligence
keywords[12].id	https://openalex.org/keywords/dynamical-systems-theory
keywords[12].score	0.4165138602256775
keywords[12].display_name	Dynamical systems theory
keywords[13].id	https://openalex.org/keywords/pattern-recognition
keywords[13].score	0.3829291760921478
keywords[13].display_name	Pattern recognition (psychology)
keywords[14].id	https://openalex.org/keywords/mathematics
keywords[14].score	0.3367381989955902
keywords[14].display_name	Mathematics
keywords[15].id	https://openalex.org/keywords/machine-learning
keywords[15].score	0.28695398569107056
keywords[15].display_name	Machine learning
keywords[16].id	https://openalex.org/keywords/artificial-neural-network
keywords[16].score	0.23585215210914612
keywords[16].display_name	Artificial neural network
keywords[17].id	https://openalex.org/keywords/data-mining
keywords[17].score	0.1445816159248352
keywords[17].display_name	Data mining
keywords[18].id	https://openalex.org/keywords/statistics
keywords[18].score	0.1349000632762909
keywords[18].display_name	Statistics
keywords[19].id	https://openalex.org/keywords/programming-language
keywords[19].score	0.12291386723518372
keywords[19].display_name	Programming language
keywords[20].id	https://openalex.org/keywords/set
keywords[20].score	0.08911207318305969
keywords[20].display_name	Set (abstract data type)
keywords[21].id	https://openalex.org/keywords/physics
keywords[21].score	0.08028578758239746
keywords[21].display_name	Physics
language	en
locations[0].id	pmh:oai:arXiv.org:2301.09930
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4306400194
locations[0].source.issn
locations[0].source.type	repository
locations[0].source.is_oa	True
locations[0].source.issn_l
locations[0].source.is_core	False
locations[0].source.is_in_doaj	False
locations[0].source.display_name	arXiv (Cornell University)
locations[0].source.host_organization	https://openalex.org/I205783295
locations[0].source.host_organization_name	Cornell University
locations[0].source.host_organization_lineage	https://openalex.org/I205783295
locations[0].license
locations[0].pdf_url	https://arxiv.org/pdf/2301.09930
locations[0].version	submittedVersion
locations[0].raw_type
locations[0].license_id
locations[0].is_accepted	False
locations[0].is_published	False
locations[0].raw_source_name
locations[0].landing_page_url	http://arxiv.org/abs/2301.09930
locations[1].id	doi:10.48550/arxiv.2301.09930
locations[1].is_oa	True
locations[1].source.id	https://openalex.org/S4306400194
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	True
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	arXiv (Cornell University)
locations[1].source.host_organization	https://openalex.org/I205783295
locations[1].source.host_organization_name	Cornell University
locations[1].source.host_organization_lineage	https://openalex.org/I205783295
locations[1].license
locations[1].pdf_url
locations[1].version
locations[1].raw_type	article
locations[1].license_id
locations[1].is_accepted	False
locations[1].is_published
locations[1].raw_source_name
locations[1].landing_page_url	https://doi.org/10.48550/arxiv.2301.09930
indexed_in	arxiv, datacite
authorships[0].author.id	https://openalex.org/A5063621152
authorships[0].author.orcid	https://orcid.org/0000-0003-3736-2059
authorships[0].author.display_name	Pavan Vynatheya
authorships[0].author_position	first
authorships[0].raw_author_name	Vynatheya, Pavan
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5061120015
authorships[1].author.orcid	https://orcid.org/0000-0001-7362-3311
authorships[1].author.display_name	Rosemary A. Mardling
authorships[1].author_position	middle
authorships[1].raw_author_name	Mardling, Rosemary A.
authorships[1].is_corresponding	False
authorships[2].author.id	https://openalex.org/A5023106503
authorships[2].author.orcid	https://orcid.org/0000-0003-1004-5635
authorships[2].author.display_name	Adrian S. Hamers
authorships[2].author_position	last
authorships[2].raw_author_name	Hamers, Adrian S.
authorships[2].is_corresponding	False
has_content.pdf	True
has_content.grobid_xml	True
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://arxiv.org/pdf/2301.09930
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Quadruple-star systems are not always nested triples: a machine learning approach to dynamical stability
has_fulltext	False
is_retracted	False
updated_date	2025-11-06T06:51:31.235846
primary_topic.id	https://openalex.org/T11948
primary_topic.field.id	https://openalex.org/fields/25
primary_topic.field.display_name	Materials Science
primary_topic.score	0.9987999796867371
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/2505
primary_topic.subfield.display_name	Materials Chemistry
primary_topic.display_name	Machine Learning in Materials Science
related_works	https://openalex.org/W2046765700, https://openalex.org/W4384345686, https://openalex.org/W2357937784, https://openalex.org/W2547618384, https://openalex.org/W4394391052, https://openalex.org/W2145834781, https://openalex.org/W2577782152, https://openalex.org/W262455470, https://openalex.org/W4242899858, https://openalex.org/W2356327704
cited_by_count	0
locations_count	2
best_oa_location.id	pmh:oai:arXiv.org:2301.09930
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4306400194
best_oa_location.source.issn
best_oa_location.source.type	repository
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l
best_oa_location.source.is_core	False
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	arXiv (Cornell University)
best_oa_location.source.host_organization	https://openalex.org/I205783295
best_oa_location.source.host_organization_name	Cornell University
best_oa_location.source.host_organization_lineage	https://openalex.org/I205783295
best_oa_location.license
best_oa_location.pdf_url	https://arxiv.org/pdf/2301.09930
best_oa_location.version	submittedVersion
best_oa_location.raw_type
best_oa_location.license_id
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name
best_oa_location.landing_page_url	http://arxiv.org/abs/2301.09930
primary_location.id	pmh:oai:arXiv.org:2301.09930
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4306400194
primary_location.source.issn
primary_location.source.type	repository
primary_location.source.is_oa	True
primary_location.source.issn_l
primary_location.source.is_core	False
primary_location.source.is_in_doaj	False
primary_location.source.display_name	arXiv (Cornell University)
primary_location.source.host_organization	https://openalex.org/I205783295
primary_location.source.host_organization_name	Cornell University
primary_location.source.host_organization_lineage	https://openalex.org/I205783295
primary_location.license
primary_location.pdf_url	https://arxiv.org/pdf/2301.09930
primary_location.version	submittedVersion
primary_location.raw_type
primary_location.license_id
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name
primary_location.landing_page_url	http://arxiv.org/abs/2301.09930
publication_date	2023-01-24
publication_year	2023
referenced_works_count	0
abstract_inverted_index.a	11, 19, 27, 75, 100, 143
abstract_inverted_index.In	21
abstract_inverted_index.We	71, 89
abstract_inverted_index.as	10
abstract_inverted_index.is	106, 142
abstract_inverted_index.of	3, 57, 80
abstract_inverted_index.on	43, 165
abstract_inverted_index.to	35, 83, 87, 161, 171
abstract_inverted_index.we	25
abstract_inverted_index.(or	46
abstract_inverted_index.2+2	38, 117
abstract_inverted_index.3+1	40, 110, 120
abstract_inverted_index.66%	139
abstract_inverted_index.88%	137
abstract_inverted_index.93%	126
abstract_inverted_index.94%	124
abstract_inverted_index.MLP	95, 103, 118, 121, 152
abstract_inverted_index.Our	151
abstract_inverted_index.The	0, 49, 112
abstract_inverted_index.and	39, 119, 125, 138, 158
abstract_inverted_index.are	123, 136, 155, 163
abstract_inverted_index.for	53, 109, 115, 131, 146
abstract_inverted_index.has	6
abstract_inverted_index.our	93
abstract_inverted_index.out	74
abstract_inverted_index.the	31, 54, 64, 116, 129, 132
abstract_inverted_index.two	14
abstract_inverted_index.This	141
abstract_inverted_index.also	72
abstract_inverted_index.been	8
abstract_inverted_index.both	92
abstract_inverted_index.code	69
abstract_inverted_index.data	51
abstract_inverted_index.sets	52
abstract_inverted_index.than	99
abstract_inverted_index.that	91
abstract_inverted_index.this	22
abstract_inverted_index.very	156
abstract_inverted_index.were	61
abstract_inverted_index.with	168
abstract_inverted_index.along	167
abstract_inverted_index.based	42
abstract_inverted_index.each,	60
abstract_inverted_index.found	90
abstract_inverted_index.novel	23
abstract_inverted_index.space	78
abstract_inverted_index.study	79
abstract_inverted_index.their	44
abstract_inverted_index.them.	173
abstract_inverted_index.using	63
abstract_inverted_index.which	17, 105, 154
abstract_inverted_index.while	128
abstract_inverted_index.(MLP),	34
abstract_inverted_index.MSTAR.	70
abstract_inverted_index.access	172
abstract_inverted_index.almost	159
abstract_inverted_index.better	98
abstract_inverted_index.direct	67
abstract_inverted_index.highly	65
abstract_inverted_index.models	96, 122
abstract_inverted_index.scores	130
abstract_inverted_index.simple	157
abstract_inverted_index.study,	24
abstract_inverted_index.triple	102, 134
abstract_inverted_index.GitHub,	166
abstract_inverted_index.Python3	169
abstract_inverted_index.carried	73
abstract_inverted_index.compare	85
abstract_inverted_index.crucial	144
abstract_inverted_index.limited	76
abstract_inverted_index.machine	28
abstract_inverted_index.models,	153
abstract_inverted_index.perform	97
abstract_inverted_index.problem	12
abstract_inverted_index.scripts	170
abstract_inverted_index.systems	5, 82
abstract_inverted_index.treated	9
abstract_inverted_index.triples	16
abstract_inverted_index.$N$-body	68
abstract_inverted_index.`nested'	15, 101, 133
abstract_inverted_index.accurate	66
abstract_inverted_index.approach	135
abstract_inverted_index.classify	37
abstract_inverted_index.directly	36, 84
abstract_inverted_index.employed	26
abstract_inverted_index.learning	29
abstract_inverted_index.studies.	150
abstract_inverted_index.training	50
abstract_inverted_index.triples.	88
abstract_inverted_index.approach,	104
abstract_inverted_index.available	164
abstract_inverted_index.comprised	56
abstract_inverted_index.dynamical	1
abstract_inverted_index.involving	13
abstract_inverted_index.long-term	47
abstract_inverted_index.parameter	77
abstract_inverted_index.quadruple	94, 147
abstract_inverted_index.stability	2, 45
abstract_inverted_index.synthesis	149
abstract_inverted_index.accuracies	114
abstract_inverted_index.algorithm,	30
abstract_inverted_index.constitute	18
abstract_inverted_index.especially	107
abstract_inverted_index.implement,	162
abstract_inverted_index.integrated	62
abstract_inverted_index.perceptron	33
abstract_inverted_index.population	148
abstract_inverted_index.quadruple.	20
abstract_inverted_index.quadruples	41, 59, 86
abstract_inverted_index.implication	145
abstract_inverted_index.multi-layer	32
abstract_inverted_index.quadruples.	111
abstract_inverted_index.significant	108
abstract_inverted_index.$5\times10^5$	58
abstract_inverted_index.boundedness).	48
abstract_inverted_index.instantaneous	160
abstract_inverted_index.respectively,	127
abstract_inverted_index.respectively.	140
abstract_inverted_index.traditionally	7
abstract_inverted_index.classification	113
abstract_inverted_index.quadruple-star	4
abstract_inverted_index.classification,	55
abstract_inverted_index.zero-inclination	81
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	3
citation_normalized_percentile