# Hyperbolic Benchmarking Unveils Network Topology-Feature Relationship in GNN Performance

Roya Aliakbarisani, Robert Jankowski, M. Ćngeles Serrano, and MariĆ”n BoguĆ±Ć”

arXiv:2406.02772
(2024)

⇕ abstract

# Renormalization of networks with weak geometric coupling

Jasper van der Kolk, MariĆ”n BoguĆ±Ć”, and M. Ćngeles Serrano

arXiv:2403.12663
(2024)

⇕ abstract

# Feature-aware ultra-low dimensional reduction of real networks

Robert Jankowski, Pegah Hozhabrierdi, MariĆ”n BoguĆ±Ć”, and M. Ćngeles Serrano

arXiv:2401.09368
(2024)

⇕ abstract

# Feature-enriched network geometry explains graph-structured data

Roya Aliakbarisani, M. Ćngeles Serrano, and MariĆ”n BoguĆ±Ć”

arXiv:2307.14198
(2023)

⇕ abstract

# Measuring spatial distances in causal sets via causal overlaps

MariĆ”n BoguĆ±Ć” and Dmitri Krioukov

Physical Review D
110
024008
(2024)

⇕ abstract

# Random graphs and real networks with weak geometric coupling

Jasper van der Kolk, M. Ćngeles Serrano, and MariĆ”n BoguĆ±Ć”

Physical Review Research
6
013337
(2024)

⇕ abstract

⇕ suppl. files

# Geometric renormalization of weighted networks

Muhua Zheng, Guillermo GarcĆa-PĆ©rez, MariĆ”n BoguĆ±Ć”, and M. Ćngeles Serrano

Communications Physics
7
97
(2024)

⇕ abstract

# D-Mercator: multidimensional hyperbolic embedding of real networks

Robert Jankowski, Antoine Allard, MariĆ”n BoguĆ±Ć”, and M. Ćngeles Serrano

Nature Communications
14
7585
(2023)

⇕ abstract

⇕ suppl. files

# Geometric description of clustering in directed networks

Antoine Allard, M. Ćngeles Serrano, and MariĆ”n BoguĆ±Ć”

Nature Physics
https://doi.org/10.1038/s41567-023-02246-6
(2023)

⇕ abstract

⇕ suppl. files

# Emergence of geometric Turing patterns in complex networks

Jasper van der Kolk, Guillermo GarcĆa-PĆ©rez, Nikos E. Kouvaris, M. Ćngeles Serrano, and MariĆ”n BoguĆ±Ć”

Physical Review X
13
021038
(2023)

⇕ abstract

⇕ suppl. files

# Non-Markovian epidemic spreading on temporal networks

Lilei Han, Zhaohu Lin, Qingqing Yin, Ming Tang, Shuguang Guan, and MariĆ”n BoguĆ±Ć”

Chaos Solitons and Fractals
173
113664
(2023)

⇕ abstract

# Detecting the ultra low dimensionality of real networks

Pedro Almagro, MariĆ”n BoguĆ±Ć”, and M. Ćngeles Serrano

Nature Communications
13
6096
(2022)

⇕ abstract

⇕ suppl. files

⇕ media coverage

# An anomalous topological phase transition in spatial random graphs

Jasper van der Kolk, M. Ćngeles Serrano, and MariĆ”n BoguĆ±Ć”

Communications Physics
5
245
(2022)

⇕ abstract

⇕ suppl. files

# The Shortest Path to Network Geometry

M. Ćngeles Serrano and MariĆ”n BoguĆ±Ć”

Elements in Structure and Dynamics of Complex Networks. Cambridge University Press
(2021)

⇕ abstract

# Network geometry

MariĆ”n BoguĆ±Ć”, Ivan Bonamassa, Manlio De Domenico, Shlomo Havlin, Dmitri Krioukov, and M. Ćngeles Serrano

Nature Reviews Physics
3
114 135
(2021)

⇕ abstract

# Scaling up real networks by geometric branching growth

Muhua Zheng, Guillermo GarcĆa-PĆ©rez, MariĆ”n BoguĆ±Ć”, and M. Ćngeles Serrano

Proc. Nat. Acad. Sci.
118(21)
e2018994118
(2021)

⇕ abstract

# Small worlds and clustering in spatial networks

MariĆ”n BoguĆ±Ć”, Dmitri Krioukov, Pedro Almagro, and M. Ćngeles Serrano

Physical Review Research
2
023040
(2020)

⇕ abstract

# Quantifying Human Engagement into Playful Activities

David Reguera, Pol Colomer-de-SimĆ³n, IvĆ”n Encinas, Manel Sort, Jan Wedekind, and MariĆ”n BoguĆ±Ć”

Sci. Rep
10
4145
(2020)

⇕ abstract

⇕ suppl. files

# Mercator: uncovering faithful hyperbolic embeddings of complex networks

Guillermo GarcĆa-PĆ©rez, Antoine Allard, M. Ćngeles Serrano and MariĆ”n BoguĆ±Ć”

New Journal of Physics
21
123033
(2019)

⇕ abstract

⇕ suppl. files

# The interconnected wealth of nations: Shock propagation on global trade-investment multiplex networks

Michele Starnini, MariĆ”n BoguĆ±Ć”, and M. Ćngeles Serrano

Sci. Rep
9
13079
(2019)

⇕ abstract

# Memory-induced complex contagion in epidemic spreading

Xavier R. Hoffmann and MariĆ”n BoguĆ±Ć”

New Journal of Physics
21
033034
(2019)

⇕ abstract

# Multiscale unfolding of real networks by geometric renormalization

Guillermo GarcĆa-PĆ©rez, MariĆ”n BoguĆ±Ć”, and M. Ćngeles Serrano

Nature Physics
14
583-589
(2018)

⇕ abstract

⇕ suppl. files

⇕ media coverage

# Soft communities in similarity space

Guillermo GarcĆa-PĆ©rez, M. Ćngeles Serrano, and MariĆ”n BoguĆ±Ć”

J. Stat. Phys.
https://doi.org/10.1007/s10955-018-2084-z
(2018)

⇕ abstract

# Dynamical properties of the herding voter model with and without noise

Liudmila Rozanova and MariĆ”n BoguĆ±Ć”

Physical Review E
96
012310
(2017)

⇕ abstract

# Geometric correlations mitigate the extreme vulnerability of multiplex networks against targeted attacks

Kaj-Kolja Kleineberg, Lubos Buzna, Fragkiskos Papadopoulos, MariĆ”n BoguĆ±Ć”, and M. Ćngeles Serrano

Physical Review Letters
118
218301
(2017)

⇕ abstract

⇕ suppl. files

# Equivalence between non-Markovian and Markovian dynamics in epidemic spreading processes

Michele Starnini, James P. Gleeson, and MariĆ”n BoguĆ±Ć”

Physical Review Letters
118
128301
(2017)

⇕ abstract

⇕ suppl. files

# The geometric nature of weights in real complex networks

Antoine Allard, M. Ćngeles Serrano, Guillermo GarcĆa-PĆ©rez, and MariĆ”n BoguĆ±Ć”

Nature Communications
8
14103
(2017)

⇕ abstract

⇕ suppl. files

⇕ media coverage

# Hidden geometric correlations in real multiplex networks

Kaj-Kolja Kleineberg, MariĆ”n BoguĆ±Ć”, M. Ćngeles Serrano, and Fragkiskos Papadopoulos

Nature Physics
12
1076 1081
(2016)

⇕ abstract

⇕ suppl. files

# The hidden hyperbolic geometry of international trade: World Trade Atlas 1870-2013

Guillermo GarcĆa-PĆ©rez, MariĆ”n BoguĆ±Ć”, Antoine Allard, and M. Ćngeles Serrano

Scientific Reports
6
33441
(2016)

⇕ abstract

⇕ suppl. files

⇕ media coverage

# Competition between global and local online social networks

Kaj-Kolja Kleineberg and MariĆ”n BoguĆ±Ć”

Scientific Reports
6
25116
(2016)

⇕ abstract

⇕ suppl. files

# Digital Ecology: Coexistence and domination among interacting networks

Kaj-Kolja Kleineberg and MariĆ”n BoguĆ±Ć”

Scientific Reports
5
10268
(2015)

⇕ abstract

# Regulation of burstiness by network-driven activation

Guillermo GarcĆa-PĆ©rez, MariĆ”n BoguĆ±Ć”, and M. Ćngeles Serrano

Scientific Reports
5
9714
(2015)

⇕ abstract

# The lifespan method as a tool to study criticality in absorbing-state phase transitions

AngĆ©lica S. Mata, MariĆ”n BoguĆ±Ć”, Claudio Castellano, and Romualdo Pastor-Satorras

Physical Review E
91
052117
(2015)

⇕ abstract

# Emergence of Soft Communities from Geometric Preferential Attachment

Konstantin Zuev, MariĆ”n BoguĆ±Ć”, Ginestra Bianconi, and Dmitri Krioukov

Scientific Reports
5
9421
(2015)

⇕ abstract

# Escaping the avalanche collapse in self-similar multiplexes

M. Ćngeles Serrano, Lubos Buzna, and MariĆ”n BoguĆ±Ć”

New Journal of Physics
17
053033
(2015)

⇕ abstract

# Follow the Leader: Herding Behavior in Heterogeneous Populations

Guillem Mosquera-DoĆ±ate and MariĆ”n BoguĆ±Ć”

Physical Review E
91
052804
(2015)

⇕ abstract

⇕ media coverage

# Quantifying randomness in real networks

Chiara Orsini, Marija M. Dankulov, Pol Colomer-de-SimĆ³n, Almerima Jamakovic, Priya Mahadevan, Amin Vahdat, Kevin E. Bassler, ZoltĆ”n Toroczkai, MariĆ”n BoguĆ±Ć”, Guido Caldarelli, Santo Fortunato, and Dmitri Krioukov

Nature Communications
6
8627
(2015)

⇕ abstract

⇕ suppl. files

# Double percolation phase transition in clustered complex networks

Pol Colomer-de-SimĆ³n and MariĆ”n BoguĆ±Ć”

Physical Review X
4
041020
(2014)

⇕ abstract

# Simulating non-Markovian stochastic processes

MariĆ”n BoguĆ±Ć”, Luis F. Lafuerza, RaĆŗl Toral, and M. Ćngeles Serrano

Physical Review E
90
042108
(2014)

⇕ abstract

# Cosmological networks

MariĆ”n BoguĆ±Ć”, Maksim Kitsak, and Dmitri Krioukov

New Joural of Physics
16
093031
(2014)

⇕ abstract

# Complex architecture of primes and natural numbers

Guillermo GarcĆa-PĆ©rez, M. Ćngeles Serrano, and MariĆ”n BoguĆ±Ć”

Physical Review E
90
022806
(2014)

⇕ abstract

⇕ media coverage

# Evolution of the digital society reveals balance between viral and mass media influence

Kaj-Kolja Kleineberg and MariĆ”n BoguĆ±Ć”

Physical Review X
4
031046
(2014)

⇕ abstract

⇕ suppl. files

# Nature of the Epidemic Threshold for the Susceptible-Infected-Susceptible Dynamics in Networks

MariĆ”n BoguĆ±Ć”, Claudio Castellano, and Romualdo Pastor-Satorras

Physical Review Letters
111
068701
(2013)

⇕ abstract

⇕ suppl. files

# Deciphering the global organization of clustering in real complex networks

Pol Colomer-de-SimĆ³n, M. Ćngeles Serrano, Mariano G. BeirĆ³, J. Ignacio Alvarez-Hamelin, MariĆ”n BoguĆ±Ć”

Scientific Reports
3
2517
(2013)

⇕ abstract

⇕ suppl. files

# Epidemic spreading on interconnected networks

Anna Saumell-Mendiola, M. Ćngeles Serrano, and MariĆ”n BoguĆ±Ć”

Physical Review E
86
026106
(2012)

⇕ abstract

⇕ media coverage

# Popularity versus similarity in growing networks

Fragkiskos Papadopoulos, Maksim Kitsak, M. Ćngeles Serrano, MariĆ”n BoguĆ±Ć”, and Dmitri Krioukov

Nature
489
537-540
(2012)

⇕ abstract

⇕ suppl. files

⇕ media coverage

# Network Cosmology

Dmitri Krioukov, Maksim Kitsak, Robert S. Sinkovits, David Rideout, David Meyer, MariĆ”n BoguĆ±Ć”

Scientific Reports
2
793
(2012)

⇕ abstract

⇕ suppl. files

⇕ media coverage

# Uncovering the hidden geometry behind metabolic networks

M. Ćngeles Serrano, MariĆ”n BoguĆ±Ć”, and Francesc SaguĆ©s

Molecular BioSystems
8
843-850
(2012)

⇕ abstract

⇕ suppl. files

# Clustering of random scale-free networks

Pol Colomer-de-SimĆ³n and MariĆ”n BoguĆ±Ć”

Physical Review E
86
026120
(2012)

⇕ abstract

# Measuring the evolution of contemporary western popular music

JoĆ”n SerrĆ , Ćlvaro Corral, MariĆ”n BoguĆ±Ć”, MartĆn Haro and Josep Lluis Arcos

Scientific Reports
2
521
(2012)

⇕ abstract

⇕ suppl. files

⇕ media coverage

# Percolation in self-similar networks

M. Ćngeles Serrano, Dmitri Krioukov, and MariĆ”n Boguna

Physical Review Letters
106
048701
(2011)

⇕ abstract

# Sustaining the Internet with hyperbolic mapping

BoguĆ±Ć”, M; Papadopoulos, F; Krioukov, D

Nature Communications
1
62
(2010)

⇕ abstract

⇕ suppl. files

⇕ media coverage

# Hyperbolic geometry of complex networks

Krioukov, D; Papadopoulos, F; Kitsak, M; Vahdat, A; Boguna, M

Physical Review E
82
36106
(2010)

⇕ abstract

# Curvature and temperature of complex networks

Krioukov, D; Papadopoulos, F; Vahdat, A; Boguna, M

Physical Review E
80
35101
(2009)

⇕ abstract

# Navigability of complex networks

Boguna, M; Krioukov, D; Claffy, KC

Nature Physics
5
74-80
(2009)

⇕ abstract

⇕ suppl. files

⇕ media coverage

# Navigating Ultrasmall Worlds in Ultrashort Time

Boguna, M; Krioukov, D

PHYSICAL REVIEW LETTERS
102
58701
(2009)

⇕ abstract

⇕ media coverage

# Extracting the multiscale backbone of complex weighted networks

Serrano, MA; Boguna, M; Vespignani, A

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
106
6483-6488
(2009)

⇕ abstract

⇕ suppl. files

# Langevin approach for the dynamics of the contact process on annealed scale-free networks

Boguna, M; Castellano, C; Pastor-Satorras, R

PHYSICAL REVIEW E
79
36110
(2009)

⇕ abstract

# Self-similarity of complex networks and hidden metric spaces

Serrano, MA; Krioukov, D; Boguna, M

PHYSICAL REVIEW LETTERS
100
78701
(2008)

⇕ abstract

⇕ suppl. files

# Approximating PageRank from in-degree

Fortunato, S; Boguna, M; Flammini, A; Menczer, F

ALGORITHMS AND MODELS FOR THE WEB-GRAPH. LECTURE NOTES IN COMPUTER SCIENCE
4936
59-71
(2008)

⇕ abstract

# Decoding the Structure of the WWW: A Comparative Analysis of Web Crawls

Serrano, MA; Maguitman, A; BoguĆ±a, M; Fortunato, S; Vespignani, A

ACM TRANSACTIONS ON THE WEB
1
10
(2007)

⇕ abstract

# Patterns of dominant flows in the world trade web

M. Ćngeles Serrano, MariĆ”n Boguna, and Alessandro Vespignani

J. Econ. Interac. Coord.
DOI 10.1007/s11403-007-0026-y
(2007)

⇕ abstract

# On Local Estimations of PageRank: A Mean Field Approach

Santo Fortunato, MariĆ”n BoguĆ±Ć”, Alessandro Flammini, and Filippo Menczer

Internet Mathematics
4
245-266
(2007)

⇕ abstract

# Modeling the Internet

Serrano, MA; Boguna, M; Diaz-Guilera, A

EUROPEAN PHYSICAL JOURNAL B
50
249-254
(2006)

⇕ abstract

# Correlations in weighted networks

Serrano, MA; Boguna, M; Pastor-Satorras, R

PHYSICAL REVIEW E
74
55101
(2006)

⇕ abstract

# Clustering in complex networks. I. General formalism

Serrano, MA; Boguna, M

PHYSICAL REVIEW E
74
56114
(2006)

⇕ abstract

# Clustering in complex networks. II. Percolation properties

Serrano, MA; Boguna, M

PHYSICAL REVIEW E
74
56115
(2006)

⇕ abstract

# Percolation and Epidemic Thresholds in Clustered Networks

Serrano, MA; Boguna, M

PHYSICAL REVIEW LETTERS
97
88701
(2006)

⇕ abstract

# A model for noise effects on fibre tract trajectories in diffusion tensor imaging: theory and simulations

Boguna, M; Pajevic, S; Basser, PJ; Weiss, GH

NEW JOURNAL OF PHYSICS
7
24
(2005)

⇕ abstract

# Tuning clustering in random networks with arbitrary degree distributions

Serrano, MA; Boguna, M

PHYSICAL REVIEW E
72
36133
(2005)

⇕ abstract

# Diffusion-annihilation processes in complex networks

Catanzaro, M; Boguna, M; Pastor-Satorras, R

PHYSICAL REVIEW E
71
56104
(2005)

⇕ abstract

# Generalized percolation in random directed networks

Boguna, M; Serrano, MA

PHYSICAL REVIEW E
72
16106
(2005)

⇕ abstract

# Generation of uncorrelated random scale-free networks

Catanzaro, M; Boguna, M; Pastor-Satorras, R

PHYSICAL REVIEW E
71
27103
(2005)

⇕ abstract

# Competition and adaptation in an Internet evolution model

Serrano, MA; Boguna, M; Diaz-Guilera, A

PHYSICAL REVIEW LETTERS
94
38701
(2005)

⇕ abstract

# Conditional dynamics driving financial markets

Boguna, M; Masoliver, J

EUROPEAN PHYSICAL JOURNAL B
40
347-352
(2004)

⇕ abstract

# Cut-offs and finite size effects in scale-free networks

Boguna, M; Pastor-Satorras, R; Vespignani, A

EUROPEAN PHYSICAL JOURNAL B
38
205-209
(2004)

⇕ abstract

# Models of social networks based on social distance attachment

Boguna, M; Pastor-Satorras, R; Diaz-Guilera, A; Arenas, A

PHYSICAL REVIEW E
70
56122
(2004)

⇕ abstract

# Class of correlated random networks with hidden variables

Boguna, M; Pastor-Satorras, R

PHYSICAL REVIEW E
68
36112
(2003)

⇕ abstract

# Topology of the world trade web

Serrano, MA; Boguna, M

PHYSICAL REVIEW E
68
15101
(2003)

⇕ abstract

# Topology and correlations in structured scale-free networks

Vazquez, A; Boguna, M; Moreno, Y; Pastor-Satorras, R; Vespignani, A

PHYSICAL REVIEW E
67
46111
(2003)

⇕ abstract

# Absence of Epidemic Threshold in Scale-Free Networks with Degree Correlations

Boguna, M; Pastor-Satorras, R; Vespignani, A

PHYSICAL REVIEW LETTERS
90
28701
(2003)

⇕ abstract

# Epidemic spreading in correlated complex networks

Boguna, M; Pastor-Satorras, R

PHYSICAL REVIEW E
66
47104
(2002)

⇕ abstract

# Evaluation of rate constants for conformational transitions using single-molecule fluorescence spectroscopy

Berezhkovskii, AM; BoguĆ±a, M; Weiss, GH

CHEMICAL PHYSICS LETTERS
336
321-324
(2001)

⇕ abstract

# Rate constants for slow conformational transitions and their sampling errors using single-molecule fluorescence spectroscopy

BoguĆ±a, M; Berezhkovskii, AM; Weiss, GH

JOURNAL OF PHYSICAL CHEMISTRY A
105
4898-4901
(2001)

⇕ abstract

# Rate constants from uncorrelated single-molecule data

Boguna, M; Kullman, L; Bezrukov, SM; Berezhkovskii, AM; Weiss, GH

JOURNAL OF PHYSICAL CHEMISTRY B
105
6246-6250
(2001)

⇕ abstract

# A discrete formulation of the theory of sojourn times in a two-state system

Boguna, M; Masoliver, J; Weiss, GH

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
289
307-320
(2001)

⇕ abstract

# The asymptotic form of the probability density of sojourn times in randomly changing multistate systems

Boguna, M; Masoliver, J; Weiss, GH

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
284
13-22
(2000)

⇕ abstract

# Residence time densities for non-Markovian systems. (I). The two-state system

Boguna, M; Berezhkovskii, AM; Weiss, GH

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
282
475-485
(2000)

⇕ abstract

# Residence time densities for non-Markovian systems. (II). The N-state system

Boguna, M; Weiss, GH

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
282
486-494
(2000)

⇕ abstract

# Occupancy of a single site by many random walkers

Boguna, M; Berezhkovskii, AM; Weiss, GH

PHYSICAL REVIEW E
62
3250-3256
(2000)

⇕ abstract

# Continued fraction solution for the radiative transfer equation in three dimensions

Boguna, M; Porra, JM; Masoliver, J

PHYSICAL REVIEW E
61
6248-6254
(2000)

⇕ abstract

# Persistent random walk model for transport through thin slabs

Boguna, M; Porra, JM; Masoliver, J

PHYSICAL REVIEW E
59
6517-6526
(1999)

⇕ abstract

# Generalization of the persistent random walk to dimensions greater than 1

Boguna, M; Porra, JM; Masoliver, J

PHYSICAL REVIEW E
58
6992-6998
(1998)

⇕ abstract

# Properties of resonant activation phenomena

Boguna, M; Porra, JM; Masoliver, J; Lindenberg, K

PHYSICAL REVIEW E
57
3990-4002
(1998)

⇕ abstract

# Long-tailed trapping times and Levy flights in a self-organized critical granular system

Boguna, M; Corral, A

PHYSICAL REVIEW LETTERS
78
4950-4953
(1997)

⇕ abstract

# Isotropization time for non-Markovian CTRWs

Boguna, M; Porra, JM; Masoliver, J; Weiss, GH

PHYSICA A
230
149-155
(1996)

⇕ abstract

# Greedy Forwarding in Dynamic Scale-Free Networks Embedded in Hyperbolic Metric Spaces

Fragkiskos Papadopoulos, Dmitri Krioukov, Marian Boguna, and Amin Vahdat

IEEE INFOCOM, San Diego, CA, March 2010
(2010)

⇕ abstract

# Greedy Forwarding in Scale-Free Networks Embedded in Hyperbolic Metric Spaces

Dmitri Krioukov, Fragkiskos Papadopoulos, Marian Boguna, and Amin Vahdat

ACM SIGMETRICS Performance Evaluation Review
37
(2009)

⇕ abstract

# Weighted configuration model

Serrano, MA; Boguna, M

Science of Complex Networks: From Biology to the Internet and WWW. AIP CONFERENCE PROCEEDINGS
776
101-107
(2005)

⇕ abstract

# Epidemic spreading in complex networks with degree correlations

Boguna, M; Pastor-Satorras, R; Vespignani, A

STATISTICAL MECHANICS OF COMPLEX NETWORKS. LECTURE NOTES IN PHYSICS
625
127-147
(2003)

⇕ abstract

# Reaction-diffusion processes in scale-free networks

M. Catanzaro, M. BoguĆ±a, and R. Pastor-Satorras

Bolyai Society Mathematical Studies
18
203-237
(2008)

⇕ abstract

# Correlations in complex networks

M. Angeles Serrano, Marian BoguĆ±a, Romualdo Pastor-Satorras, and Alessandro Vespignani

World Scientific, Singapur
(2006)

⇕ abstract

# Book review: Random Networks for Communication. From Statistical Physics to Information Systems

BoguĆ±Ć”, M

Journal of Statistical Physics
135
585-586
(2009)

⇕ abstract

# Book Review: The Structure and Dynamics of Networks

M. BoguĆ±Ć”

Journal of Statistical Physics
DOI: 10.1007/s10955-006-9267-8
(2006)

⇕ abstract

# Book Review: Evolution of Networks. From Biological Nets to the Internet and WWW

M. BoguĆ±Ć”

Journal of Statistical Physics
114
1627-1628
(2004)

⇕ abstract