---
_id: '14739'
abstract:
- lang: eng
text: Attempts to incorporate topological information in supervised learning tasks
have resulted in the creation of several techniques for vectorizing persistent
homology barcodes. In this paper, we study thirteen such methods. Besides describing
an organizational framework for these methods, we comprehensively benchmark them
against three well-known classification tasks. Surprisingly, we discover that
the best-performing method is a simple vectorization, which consists only of a
few elementary summary statistics. Finally, we provide a convenient web application
which has been designed to facilitate exploration and experimentation with various
vectorization methods.
acknowledgement: "The work of Maria-Jose Jimenez, Eduardo Paluzo-Hidalgo and Manuel
Soriano-Trigueros was supported in part by the Spanish grant Ministerio de Ciencia
e Innovacion under Grants TED2021-129438B-I00 and PID2019-107339GB-I00, and in part
by REXASI-PRO H-EU project, call HORIZON-CL4-2021-HUMAN-01-01 under Grant 101070028.
The work of\r\nMaria-Jose Jimenez was supported by a grant of Convocatoria de la
Universidad de Sevilla para la recualificacion del sistema universitario español,
2021-23, funded by the European Union, NextGenerationEU. The work of Vidit Nanda
was supported in part by EPSRC under Grant EP/R018472/1 and in part by US AFOSR
under Grant FA9550-22-1-0462. \r\nWe are grateful to the team of GUDHI and TEASPOON
developers, for their work and their support. We are also grateful to Streamlit
for providing extra resources to deploy the web app\r\nonline on Streamlit community
cloud. We thank the anonymous referees for their helpful suggestions."
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Dashti
full_name: Ali, Dashti
last_name: Ali
- first_name: Aras
full_name: Asaad, Aras
last_name: Asaad
- first_name: Maria-Jose
full_name: Jimenez, Maria-Jose
last_name: Jimenez
- first_name: Vidit
full_name: Nanda, Vidit
last_name: Nanda
- first_name: Eduardo
full_name: Paluzo-Hidalgo, Eduardo
last_name: Paluzo-Hidalgo
- first_name: Manuel
full_name: Soriano Trigueros, Manuel
id: 15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8
last_name: Soriano Trigueros
orcid: 0000-0003-2449-1433
citation:
ama: Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M.
A survey of vectorization methods in topological data analysis. IEEE Transactions
on Pattern Analysis and Machine Intelligence. 2023;45(12):14069-14080. doi:10.1109/tpami.2023.3308391
apa: Ali, D., Asaad, A., Jimenez, M.-J., Nanda, V., Paluzo-Hidalgo, E., & Soriano
Trigueros, M. (2023). A survey of vectorization methods in topological data analysis.
IEEE Transactions on Pattern Analysis and Machine Intelligence. IEEE. https://doi.org/10.1109/tpami.2023.3308391
chicago: Ali, Dashti, Aras Asaad, Maria-Jose Jimenez, Vidit Nanda, Eduardo Paluzo-Hidalgo,
and Manuel Soriano Trigueros. “A Survey of Vectorization Methods in Topological
Data Analysis.” IEEE Transactions on Pattern Analysis and Machine Intelligence.
IEEE, 2023. https://doi.org/10.1109/tpami.2023.3308391.
ieee: D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, and M. Soriano
Trigueros, “A survey of vectorization methods in topological data analysis,” IEEE
Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 12.
IEEE, pp. 14069–14080, 2023.
ista: Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros
M. 2023. A survey of vectorization methods in topological data analysis. IEEE
Transactions on Pattern Analysis and Machine Intelligence. 45(12), 14069–14080.
mla: Ali, Dashti, et al. “A Survey of Vectorization Methods in Topological Data
Analysis.” IEEE Transactions on Pattern Analysis and Machine Intelligence,
vol. 45, no. 12, IEEE, 2023, pp. 14069–80, doi:10.1109/tpami.2023.3308391.
short: D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, M. Soriano
Trigueros, IEEE Transactions on Pattern Analysis and Machine Intelligence 45 (2023)
14069–14080.
date_created: 2024-01-08T09:59:46Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2024-01-08T10:11:46Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1109/tpami.2023.3308391
file:
- access_level: open_access
checksum: 465c28ef0b151b4b1fb47977ed5581ab
content_type: application/pdf
creator: dernst
date_created: 2024-01-08T10:09:14Z
date_updated: 2024-01-08T10:09:14Z
file_id: '14740'
file_name: 2023_IEEEToP_Ali.pdf
file_size: 2370988
relation: main_file
success: 1
file_date_updated: 2024-01-08T10:09:14Z
has_accepted_license: '1'
intvolume: ' 45'
issue: '12'
keyword:
- Applied Mathematics
- Artificial Intelligence
- Computational Theory and Mathematics
- Computer Vision and Pattern Recognition
- Software
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '12'
oa: 1
oa_version: Published Version
page: 14069-14080
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_identifier:
eissn:
- 1939-3539
issn:
- 0162-8828
publication_status: published
publisher: IEEE
quality_controlled: '1'
status: public
title: A survey of vectorization methods in topological data analysis
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 45
year: '2023'
...
---
_id: '12128'
abstract:
- lang: eng
text: We introduce a machine-learning (ML) framework for high-throughput benchmarking
of diverse representations of chemical systems against datasets of materials and
molecules. The guiding principle underlying the benchmarking approach is to evaluate
raw descriptor performance by limiting model complexity to simple regression schemes
while enforcing best ML practices, allowing for unbiased hyperparameter optimization,
and assessing learning progress through learning curves along series of synchronized
train-test splits. The resulting models are intended as baselines that can inform
future method development, in addition to indicating how easily a given dataset
can be learnt. Through a comparative analysis of the training outcome across a
diverse set of physicochemical, topological and geometric representations, we
glean insight into the relative merits of these representations as well as their
interrelatedness.
acknowledgement: 'C P acknowledges funding from Astex through the Sustaining Innovation
Program under the Milner Consortium. B C acknowledges resources provided by the
Cambridge Tier-2 system operated by the University of Cambridge Research Computing
Service funded by EPSRC Tier-2 capital Grant EP/P020259/1. F A F acknowledges funding
from the Swiss National Science Foundation (Grant No. P2BSP2_191736). '
article_number: '040501'
article_processing_charge: No
article_type: original
author:
- first_name: Carl
full_name: Poelking, Carl
last_name: Poelking
- first_name: Felix A
full_name: Faber, Felix A
last_name: Faber
- first_name: Bingqing
full_name: Cheng, Bingqing
id: cbe3cda4-d82c-11eb-8dc7-8ff94289fcc9
last_name: Cheng
orcid: 0000-0002-3584-9632
citation:
ama: 'Poelking C, Faber FA, Cheng B. BenchML: An extensible pipelining framework
for benchmarking representations of materials and molecules at scale. Machine
Learning: Science and Technology. 2022;3(4). doi:10.1088/2632-2153/ac4d11'
apa: 'Poelking, C., Faber, F. A., & Cheng, B. (2022). BenchML: An extensible
pipelining framework for benchmarking representations of materials and molecules
at scale. Machine Learning: Science and Technology. IOP Publishing. https://doi.org/10.1088/2632-2153/ac4d11'
chicago: 'Poelking, Carl, Felix A Faber, and Bingqing Cheng. “BenchML: An Extensible
Pipelining Framework for Benchmarking Representations of Materials and Molecules
at Scale.” Machine Learning: Science and Technology. IOP Publishing, 2022.
https://doi.org/10.1088/2632-2153/ac4d11.'
ieee: 'C. Poelking, F. A. Faber, and B. Cheng, “BenchML: An extensible pipelining
framework for benchmarking representations of materials and molecules at scale,”
Machine Learning: Science and Technology, vol. 3, no. 4. IOP Publishing,
2022.'
ista: 'Poelking C, Faber FA, Cheng B. 2022. BenchML: An extensible pipelining framework
for benchmarking representations of materials and molecules at scale. Machine
Learning: Science and Technology. 3(4), 040501.'
mla: 'Poelking, Carl, et al. “BenchML: An Extensible Pipelining Framework for Benchmarking
Representations of Materials and Molecules at Scale.” Machine Learning: Science
and Technology, vol. 3, no. 4, 040501, IOP Publishing, 2022, doi:10.1088/2632-2153/ac4d11.'
short: 'C. Poelking, F.A. Faber, B. Cheng, Machine Learning: Science and Technology
3 (2022).'
date_created: 2023-01-12T12:02:21Z
date_published: 2022-11-17T00:00:00Z
date_updated: 2023-08-04T08:49:53Z
day: '17'
ddc:
- '000'
department:
- _id: BiCh
doi: 10.1088/2632-2153/ac4d11
external_id:
isi:
- '000886534000001'
file:
- access_level: open_access
checksum: 8930d4ad6ed9b47358c6f1a68666adb6
content_type: application/pdf
creator: dernst
date_created: 2023-01-23T10:42:04Z
date_updated: 2023-01-23T10:42:04Z
file_id: '12343'
file_name: 2022_MachLearning_Poelking.pdf
file_size: 13814559
relation: main_file
success: 1
file_date_updated: 2023-01-23T10:42:04Z
has_accepted_license: '1'
intvolume: ' 3'
isi: 1
issue: '4'
keyword:
- Artificial Intelligence
- Human-Computer Interaction
- Software
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
publication: 'Machine Learning: Science and Technology'
publication_identifier:
issn:
- 2632-2153
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/capoe/benchml
scopus_import: '1'
status: public
title: 'BenchML: An extensible pipelining framework for benchmarking representations
of materials and molecules at scale'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 3
year: '2022'
...
---
_id: '12134'
abstract:
- lang: eng
text: Standard epidemic models exhibit one continuous, second order phase transition
to macroscopic outbreaks. However, interventions to control outbreaks may fundamentally
alter epidemic dynamics. Here we reveal how such interventions modify the type
of phase transition. In particular, we uncover three distinct types of explosive
phase transitions for epidemic dynamics with capacity-limited interventions. Depending
on the capacity limit, interventions may (i) leave the standard second order phase
transition unchanged but exponentially suppress the probability of large outbreaks,
(ii) induce a first-order discontinuous transition to macroscopic outbreaks, or
(iii) cause a secondary explosive yet continuous third-order transition. These
insights highlight inherent limitations in predicting and containing epidemic
outbreaks. More generally our study offers a cornerstone example of a third-order
explosive phase transition in complex systems.
acknowledgement: We acknowledge support from the Volkswagen Foundation under Grant
No. 99720 and the German Federal Ministry for Education and Research (BMBF) under
Grant No. 16ICR01. This research was supported by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2068—390729961—Cluster
of Excellence Physics of Life of TU Dresden.
article_number: 04LT02
article_processing_charge: No
article_type: original
author:
- first_name: Georg
full_name: Börner, Georg
last_name: Börner
- first_name: Malte
full_name: Schröder, Malte
last_name: Schröder
- first_name: Davide
full_name: Scarselli, Davide
id: 40315C30-F248-11E8-B48F-1D18A9856A87
last_name: Scarselli
orcid: 0000-0001-5227-4271
- first_name: Nazmi B
full_name: Budanur, Nazmi B
id: 3EA1010E-F248-11E8-B48F-1D18A9856A87
last_name: Budanur
orcid: 0000-0003-0423-5010
- first_name: Björn
full_name: Hof, Björn
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
- first_name: Marc
full_name: Timme, Marc
last_name: Timme
citation:
ama: 'Börner G, Schröder M, Scarselli D, Budanur NB, Hof B, Timme M. Explosive transitions
in epidemic dynamics. Journal of Physics: Complexity. 2022;3(4). doi:10.1088/2632-072x/ac99cd'
apa: 'Börner, G., Schröder, M., Scarselli, D., Budanur, N. B., Hof, B., & Timme,
M. (2022). Explosive transitions in epidemic dynamics. Journal of Physics:
Complexity. IOP Publishing. https://doi.org/10.1088/2632-072x/ac99cd'
chicago: 'Börner, Georg, Malte Schröder, Davide Scarselli, Nazmi B Budanur, Björn
Hof, and Marc Timme. “Explosive Transitions in Epidemic Dynamics.” Journal
of Physics: Complexity. IOP Publishing, 2022. https://doi.org/10.1088/2632-072x/ac99cd.'
ieee: 'G. Börner, M. Schröder, D. Scarselli, N. B. Budanur, B. Hof, and M. Timme,
“Explosive transitions in epidemic dynamics,” Journal of Physics: Complexity,
vol. 3, no. 4. IOP Publishing, 2022.'
ista: 'Börner G, Schröder M, Scarselli D, Budanur NB, Hof B, Timme M. 2022. Explosive
transitions in epidemic dynamics. Journal of Physics: Complexity. 3(4), 04LT02.'
mla: 'Börner, Georg, et al. “Explosive Transitions in Epidemic Dynamics.” Journal
of Physics: Complexity, vol. 3, no. 4, 04LT02, IOP Publishing, 2022, doi:10.1088/2632-072x/ac99cd.'
short: 'G. Börner, M. Schröder, D. Scarselli, N.B. Budanur, B. Hof, M. Timme, Journal
of Physics: Complexity 3 (2022).'
date_created: 2023-01-12T12:03:43Z
date_published: 2022-10-25T00:00:00Z
date_updated: 2023-02-13T09:15:13Z
day: '25'
ddc:
- '530'
department:
- _id: BjHo
doi: 10.1088/2632-072x/ac99cd
file:
- access_level: open_access
checksum: 35c5c5cb0eb17ea1b5184755daab9fc9
content_type: application/pdf
creator: dernst
date_created: 2023-01-24T07:24:37Z
date_updated: 2023-01-24T07:24:37Z
file_id: '12350'
file_name: 2022_JourPhysics_Boerner.pdf
file_size: 1006106
relation: main_file
success: 1
file_date_updated: 2023-01-24T07:24:37Z
has_accepted_license: '1'
intvolume: ' 3'
issue: '4'
keyword:
- Artificial Intelligence
- Computer Networks and Communications
- Computer Science Applications
- Information Systems
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
publication: 'Journal of Physics: Complexity'
publication_identifier:
issn:
- 2632-072X
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Explosive transitions in epidemic dynamics
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2022'
...
---
_id: '12147'
abstract:
- lang: eng
text: Continuous-time neural networks are a class of machine learning systems that
can tackle representation learning on spatiotemporal decision-making tasks. These
models are typically represented by continuous differential equations. However,
their expressive power when they are deployed on computers is bottlenecked by
numerical differential equation solvers. This limitation has notably slowed down
the scaling and understanding of numerous natural physical phenomena such as the
dynamics of nervous systems. Ideally, we would circumvent this bottleneck by solving
the given dynamical system in closed form. This is known to be intractable in
general. Here, we show that it is possible to closely approximate the interaction
between neurons and synapses—the building blocks of natural and artificial neural
networks—constructed by liquid time-constant networks efficiently in closed form.
To this end, we compute a tightly bounded approximation of the solution of an
integral appearing in liquid time-constant dynamics that has had no known closed-form
solution so far. This closed-form solution impacts the design of continuous-time
and continuous-depth neural models. For instance, since time appears explicitly
in closed form, the formulation relaxes the need for complex numerical solvers.
Consequently, we obtain models that are between one and five orders of magnitude
faster in training and inference compared with differential equation-based counterparts.
More importantly, in contrast to ordinary differential equation-based continuous
networks, closed-form networks can scale remarkably well compared with other deep
learning instances. Lastly, as these models are derived from liquid networks,
they show good performance in time-series modelling compared with advanced recurrent
neural network models.
acknowledgement: This research was supported in part by the AI2050 program at Schmidt
Futures (grant G-22-63172), the Boeing Company, and the United States Air Force
Research Laboratory and the United States Air Force Artificial Intelligence Accelerator
and was accomplished under cooperative agreement number FA8750-19-2-1000. The views
and conclusions contained in this document are those of the authors and should not
be interpreted as representing the official policies, either expressed or implied,
of the United States Air Force or the U.S. Government. The U.S. Government is authorized
to reproduce and distribute reprints for Government purposes, notwithstanding any
copyright notation herein. This work was further supported by The Boeing Company
and Office of Naval Research grant N00014-18-1-2830. M.T. is supported by the Poul
Due Jensen Foundation, grant 883901. M.L. was supported in part by the Austrian
Science Fund under grant Z211-N23 (Wittgenstein Award). A.A. was supported by the
National Science Foundation Graduate Research Fellowship Program. We thank T.-H.
Wang, P. Kao, M. Chahine, W. Xiao, X. Li, L. Yin and Y. Ben for useful suggestions
and for testing of CfC models to confirm the results across other domains.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Ramin
full_name: Hasani, Ramin
last_name: Hasani
- first_name: Mathias
full_name: Lechner, Mathias
id: 3DC22916-F248-11E8-B48F-1D18A9856A87
last_name: Lechner
- first_name: Alexander
full_name: Amini, Alexander
last_name: Amini
- first_name: Lucas
full_name: Liebenwein, Lucas
last_name: Liebenwein
- first_name: Aaron
full_name: Ray, Aaron
last_name: Ray
- first_name: Max
full_name: Tschaikowski, Max
last_name: Tschaikowski
- first_name: Gerald
full_name: Teschl, Gerald
last_name: Teschl
- first_name: Daniela
full_name: Rus, Daniela
last_name: Rus
citation:
ama: Hasani R, Lechner M, Amini A, et al. Closed-form continuous-time neural networks.
Nature Machine Intelligence. 2022;4(11):992-1003. doi:10.1038/s42256-022-00556-7
apa: Hasani, R., Lechner, M., Amini, A., Liebenwein, L., Ray, A., Tschaikowski,
M., … Rus, D. (2022). Closed-form continuous-time neural networks. Nature Machine
Intelligence. Springer Nature. https://doi.org/10.1038/s42256-022-00556-7
chicago: Hasani, Ramin, Mathias Lechner, Alexander Amini, Lucas Liebenwein, Aaron
Ray, Max Tschaikowski, Gerald Teschl, and Daniela Rus. “Closed-Form Continuous-Time
Neural Networks.” Nature Machine Intelligence. Springer Nature, 2022. https://doi.org/10.1038/s42256-022-00556-7.
ieee: R. Hasani et al., “Closed-form continuous-time neural networks,” Nature
Machine Intelligence, vol. 4, no. 11. Springer Nature, pp. 992–1003, 2022.
ista: Hasani R, Lechner M, Amini A, Liebenwein L, Ray A, Tschaikowski M, Teschl
G, Rus D. 2022. Closed-form continuous-time neural networks. Nature Machine Intelligence.
4(11), 992–1003.
mla: Hasani, Ramin, et al. “Closed-Form Continuous-Time Neural Networks.” Nature
Machine Intelligence, vol. 4, no. 11, Springer Nature, 2022, pp. 992–1003,
doi:10.1038/s42256-022-00556-7.
short: R. Hasani, M. Lechner, A. Amini, L. Liebenwein, A. Ray, M. Tschaikowski,
G. Teschl, D. Rus, Nature Machine Intelligence 4 (2022) 992–1003.
date_created: 2023-01-12T12:07:21Z
date_published: 2022-11-15T00:00:00Z
date_updated: 2023-08-04T09:00:10Z
day: '15'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1038/s42256-022-00556-7
external_id:
arxiv:
- '2106.13898'
isi:
- '000884215600003'
file:
- access_level: open_access
checksum: b4789122ce04bfb4ac042390f59aaa8b
content_type: application/pdf
creator: dernst
date_created: 2023-01-24T09:49:44Z
date_updated: 2023-01-24T09:49:44Z
file_id: '12355'
file_name: 2022_NatureMachineIntelligence_Hasani.pdf
file_size: 3259553
relation: main_file
success: 1
file_date_updated: 2023-01-24T09:49:44Z
has_accepted_license: '1'
intvolume: ' 4'
isi: 1
issue: '11'
keyword:
- Artificial Intelligence
- Computer Networks and Communications
- Computer Vision and Pattern Recognition
- Human-Computer Interaction
- Software
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 992-1003
project:
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
publication: Nature Machine Intelligence
publication_identifier:
issn:
- 2522-5839
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
link:
- relation: erratum
url: https://doi.org/10.1038/s42256-022-00597-y
scopus_import: '1'
status: public
title: Closed-form continuous-time neural networks
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 4
year: '2022'
...
---
_id: '9234'
abstract:
- lang: eng
text: In this paper, we present two new inertial projection-type methods for solving
multivalued variational inequality problems in finite-dimensional spaces. We establish
the convergence of the sequence generated by these methods when the multivalued
mapping associated with the problem is only required to be locally bounded without
any monotonicity assumption. Furthermore, the inertial techniques that we employ
in this paper are quite different from the ones used in most papers. Moreover,
based on the weaker assumptions on the inertial factor in our methods, we derive
several special cases of our methods. Finally, we present some experimental results
to illustrate the profits that we gain by introducing the inertial extrapolation
steps.
acknowledgement: 'The authors sincerely thank the Editor-in-Chief and anonymous referees
for their careful reading, constructive comments and fruitful suggestions that help
improve the manuscript. The research of the first author is supported by the National
Research Foundation (NRF) South Africa (S& F-DSI/NRF Free Standing Postdoctoral
Fellowship; Grant Number: 120784). The first author also acknowledges the financial
support from DSI/NRF, South Africa Center of Excellence in Mathematical and Statistical
Sciences (CoE-MaSS) Postdoctoral Fellowship. The second author has received funding
from the European Research Council (ERC) under the European Union’s Seventh Framework
Program (FP7 - 2007-2013) (Grant agreement No. 616160). Open Access funding provided
by Institute of Science and Technology (IST Austria).'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Chinedu
full_name: Izuchukwu, Chinedu
last_name: Izuchukwu
- first_name: Yekini
full_name: Shehu, Yekini
id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87
last_name: Shehu
orcid: 0000-0001-9224-7139
citation:
ama: Izuchukwu C, Shehu Y. New inertial projection methods for solving multivalued
variational inequality problems beyond monotonicity. Networks and Spatial Economics.
2021;21(2):291-323. doi:10.1007/s11067-021-09517-w
apa: Izuchukwu, C., & Shehu, Y. (2021). New inertial projection methods for
solving multivalued variational inequality problems beyond monotonicity. Networks
and Spatial Economics. Springer Nature. https://doi.org/10.1007/s11067-021-09517-w
chicago: Izuchukwu, Chinedu, and Yekini Shehu. “New Inertial Projection Methods
for Solving Multivalued Variational Inequality Problems beyond Monotonicity.”
Networks and Spatial Economics. Springer Nature, 2021. https://doi.org/10.1007/s11067-021-09517-w.
ieee: C. Izuchukwu and Y. Shehu, “New inertial projection methods for solving multivalued
variational inequality problems beyond monotonicity,” Networks and Spatial
Economics, vol. 21, no. 2. Springer Nature, pp. 291–323, 2021.
ista: Izuchukwu C, Shehu Y. 2021. New inertial projection methods for solving multivalued
variational inequality problems beyond monotonicity. Networks and Spatial Economics.
21(2), 291–323.
mla: Izuchukwu, Chinedu, and Yekini Shehu. “New Inertial Projection Methods for
Solving Multivalued Variational Inequality Problems beyond Monotonicity.” Networks
and Spatial Economics, vol. 21, no. 2, Springer Nature, 2021, pp. 291–323,
doi:10.1007/s11067-021-09517-w.
short: C. Izuchukwu, Y. Shehu, Networks and Spatial Economics 21 (2021) 291–323.
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title: New inertial projection methods for solving multivalued variational inequality
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