European Training Network on Grey-Box Models for Safe and Reliable Intelligent Mobility Systems

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Deliverables

15 PhD degrees awarded

15 PhD degrees awarded (between M44 – M53)

Second peer reviewed paper by all ESRs
First peer reviewed paper by all ESRs

First peer reviewed paper by the ESRs

USD2022 special GREYDIENT session

Special GREYDIENT session during ISMA-USD2022

Symposium

GREYDIENT symposium, as described in the proposal

Pitch videos

By the end of the project, 30 ESR pitch videos will be uploaded to YouTubeMonthly after M18 to M48

2 Overview movies

2 overview movies of the project: one at M8, another at M46

8 Newsletters

During the project, 8 newsletters will be distributed.Specifically, they will be distributed in months 6, 12, 18, 24, 30, 36, 42, 48

Project website

Project website general info and recruitment

Publications

Exploring multi-fidelity noisy data: Methods and real-world examples

Author(s): Katerina Giannoukou, Paolo Ascia, Stefano Marelli, Fabian Duddeck and Bruno Sudret
Published in: ISMA-USD Proceedings, 2024
Publisher: KU Leuven Department of Mechanical Engineering

Grey-Box Models for Cyber-Physical Systems Reliability, Safety and Resilience Assessment

Author(s): Juan-Pablo Futalef, Francesco Di Maio, Enrico Zio
Published in: Book of Extended Abstracts for the 32nd European Safety and Reliability Conference, 2023, Page(s) 2757-2764
Publisher: Research Publishing Services
DOI: 10.3850/978-981-18-5183-4_s20-05-564-cd

Near-real-time online process control using grey-box models

Author(s): Dodt, Miriam B.; Persoons, Augustin; Faes, Matthias G. R.; Moens, David
Published in: proceedings of the 14th International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP14), 2023, Issue 14, 2023
Publisher: Trinity College
DOI: 10.5281/zenodo.8255763

Grey-box Approach for the Prognostic and Health Management of Lithium-Ion Batteries

Author(s): Francesco Cancelliere, Sylvain Girard, Jean-Marc Bourinet, Matteo Broggi
Published in: Annual Conference of the PHM Society, Issue 15, 2023, ISSN 2325-0178
Publisher: PHM Society
DOI: 10.36001/phmconf.2023.v15i1.3506

Determination of the random spatial variation of the bending stiffness in composite materials

Author(s): Gavallas, Panagiotis; Tsivolas, Eleftherios; Stefanou, George
Published in: EUROMECH Colloquium 642, 2024
Publisher: Sapienza University of Rome
DOI: 10.5281/zenodo.14033483

First-passage Probability Estimation of Stochastic Dynamic Systems by a Parametric Approach

Author(s): Chen Ding, Chao Dang, Matteo Broggi, Michael Beer
Published in: 8th International Symposium on Reliability Engineering and Risk Management, Issue 4th - 7th September, 2022, 2023, Page(s) 40-46
Publisher: Research Publishing Services
DOI: 10.3850/978-981-18-5184-1_ms-01-175-cd

The effect of noise on reliability analysis

Author(s): Pires, Anderson; Moustapha, Maliki; id_orcid0000-0002-1138-4666; Marelli, Stefano; id_orcid0000-0002-9268-9014; Sudret, Bruno; id_orcid0000-0002-9501-7395
Published in: Proceedings of the 8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2022), Oslo, Norway, June 5-9, 2022, Issue 6, 2022, ISBN 9788412322286
Publisher: ECCOMAS
DOI: 10.5281/zenodo.14186841

Unsupervised Representation Learning of Complex Time Series for Maneuverability State Identification in Smart Mobility

Author(s): Lebese, Thabang
Published in: Proc. 16 th International Conference on Agents and Artificial Intelligence (ICAART 2024), 2024, Page(s) 12
Publisher: ICAART
DOI: 10.5281/zenodo.13735693

A Grey-Box Digital Twin-Based Approach for Risk Monitoring of Nuclear Power Plants

Author(s): Leonardo Miqueles, Ibrahim Ahmed, Francesco Di Maio, Enrico Zio
Published in: Proceedings of the 32nd European Safety and Reliability Conference (ESREL 2022), Issue 28th of August – 1st of September, 2022, 2022
Publisher: Research Publishing

A new scheme combining adaptive Kriging with adaptative variance-reduction using Gaussian mixture importance sampling

Author(s): Persoons, Augustin; Wei, Pengfei; Bogaerts, Lars; Moens, David; Broggi, Matteo; Beer, Michael
Published in: USD 2022, Issue 3, 2023
Publisher: KU Leuven Mecha(tro)nic System Dynamics (LMSD) department
DOI: 10.5281/zenodo.7568688

A parallel Bayesian interval optimization approach for static analysis of structures with interval uncertainties

Author(s): Chen Ding, Chao Dang, Matteo Broggi, Michael Beer
Published in: 14th International Conference on Applications of Statistics and Probability in Civil Engineering, Issue 9th - 13th of July 2023, 2023
Publisher: Trinity College Dublin
DOI: 10.5281/zenodo.10220655

A SELF-LEARNING DIGITAL TWIN FOR PROCESS CONTROL OF FAST PROCESSES UNDER UNCERTAINTY

Author(s): Miriam B. Dodt, Augustin Persoons, Matthias G. R. Faes, David Moens
Published in: Proceedings of the 5th International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2019), 5th International Conference on Uncertainty Quantification in Computational Sciences and Engineering, 2023
Publisher: Institute of Structural Analysis and Antiseismic Research National Technical University of Athens
DOI: 10.7712/120223.10352.19909

Management of a free-floating electrical scooters fleet

Author(s): Cancelliere Francesco; Girard Sylvain
Published in: Congrès Lambda Mu 23 « Innovations et maîtrise des risques pour un avenir durable, 2022
Publisher: Institut pour la Maîtrise des Risques
DOI: 10.5281/zenodo.8090807

Random Field Modeling of the Mechanical Properties of Graphene Nano-platelets

Author(s): Panagiotis Gavallas, Dimitrios Savvas, George Stefanou
Published in: 14th International Conference on Applications of Statistics and Probability in Civil Engineering, Issue 9th - 13th July 2023, 2023
Publisher: Trinity College Dublin
DOI: 10.5281/zenodo.10906215

A transfer learning framework for crashworthiness analysis based on sphere projection and PointNN

Author(s): Giada Colella, Volker A. Lange, and Fabian Duddeck
Published in: ISMA-USD proceedings, 2024
Publisher: KU Leuven Department of Mechanical Engineering

Multifidelity surrogate modelling with noisy grey-box models

Author(s): Giannoukou, Aikaterini; Marelli, Stefano; id_orcid0000-0002-9268-9014; Sudret, Bruno; id_orcid0000-0002-9501-7395
Published in: MASCOT-NUM Annual Meeting 2022, Clermont Ferrand, France, June 7-9, 2022, 2022
Publisher: MascotNum
DOI: 10.3929/ethz-b-000588908

Separable Physics-Informed Neural Networks for Robust Inverse Quantification in Solid Mechanics

Author(s): Bonnet Eymard, Damien; Persoons, Augustin; Faes, Matthias G.R.; Moens, David
Published in: Proceedings of the The 9th International Symposium on Reliability Engineering and Risk Management (ISRERM 2024), Issue 9, 2025
Publisher: RESEARCH PUBLISHING
DOI: 10.5281/zenodo.14039660

QUANTIFYING THE EPISTEMIC UNCERTAINTY LINKED TO THE DEVELOPMENT PROCESS OF AN EARLY-STAGE COMPONENT FOR CRASHWORTHINESS

Author(s): Paolo Ascia, Matthias G. R. Faes, Fabian Duddeck
Published in: Proceedings of the 5th International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2019), 5th International Conference on Uncertainty Quantification in Computational Sciences and Engineering, 2023, Page(s) 466-477
Publisher: Institute of Structural Analysis and Antiseismic Research National Technical University of Athens
DOI: 10.7712/120223.10350.19704

A Classification Problem Formulation for the Reliability Assessment of End-To-End Communication Among Cyber Devices in Cyber-Physical Systems

Author(s): Juan-Pablo Futalef, Francesco Di Maio, Enrico Zio
Published in: 8th International Conference on System Reliability and Safety, 2024
Publisher: IEEE

AN UNIFIED ENRICHMENT STRATEGY FOR RELIABILITY-BASED DESIGN OPTIMIZATION USING ADAPTIVE KRIGING AND ZERO-ORDER ALGORITHMS

Author(s): Alessio Faraci, Pierre Beaurepaire, Nicolas Gayton
Published in: Proceedings of the 5th International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2019), 5th International Conference on Uncertainty Quantification in Computational Sciences and Engineering, 2023, Page(s) 478-485
Publisher: Institute of Structural Analysis and Antiseismic Research National Technical University of Athens
DOI: 10.7712/120223.10351.19782

New insights on reliability analysis for stochastic simulators using surrogate models

Author(s): Anderson V. Pires, Maliki Moustapha, Stefano Marelli, Bruno Sudret
Published in: ISMA-USD proceedings, 2024
Publisher: KU Leuven
DOI: 10.5281/zenodo.14187066

Enhancing Reliability-Based Design Optimization through adaptive Kriging and gradient-free optimization

Author(s): Faraci, Alessio; Beaurepaire, Pierre; Gayton, Nicolas
Published in: ISMA-USD proceedings, 2024
Publisher: KU Leuven Department of Mechanical Engineering
DOI: 10.5281/zenodo.14207477

Physics-Informed Neural Networks to propagate random field properties of composite materials

Author(s): Bonnet Eymard, Damien; Persoons, Augustin; Gavallas, Panagiotis; Moens, David; Faes, Matthias G.R.; Stefanou, George
Published in: ISMA-USD 2024, Issue 4, 2024
Publisher: KU Leuven Mecha(tro)nic System Dynamics (LMSD) department
DOI: 10.5281/zenodo.13907104

Enhanced Scenario Generation for Integrated-Power and Telecommunication Infrastructures Using the RESTART Sampling Technique

Author(s): Juan-Pablo Futalef, Francesco Di Maio, Enrico Zio
Published in: 6th International Conference on System Reliability and Safety, 2022
Publisher: IEEE

A multifidelity framework for grey-box modelling of automated welding processes

Author(s): Dodt, Miriam Beatrice; Bogaerts, Lars; Persoons, Augustin; Matthias G.R., Faes; Moens, David
Published in: Proceedings of ISMA2024 International Conference on Noise and Vibration Engineering USD2024 International Conference on Uncertainty in Structural Dynamics, Issue 19, 2024
Publisher: KU Leuven Department of Mechanical Engineering LMSD (Mecha(tro)nic System Dynamics)

Enhancing development flexibility: a grey-box strategy for adapting to unforeseen adverse conditions

Author(s): Ascia, Paolo; Duddeck, Fabian
Published in: Proceedings of ISMA/USD2024, 2024, Page(s) 1-14
Publisher: ISMA/USD
DOI: 10.5281/zenodo.13933792

A finite element model of component solution space for early stage design uncertainties

Author(s): Ascia, Paolo; Kaps, Arne; Daub, Marco; Burmberger, Lukas; Duddeck, Fabian
Published in: Proceedings of the ISMA/USD2022 conference, 2022, Page(s) 4678-4686
Publisher: ISMA/USD
DOI: 10.5281/zenodo.7584546

Introducing efficient structural reliability methods for stochastic simulators

Author(s): Pires, Anderson V.; Moustapha, Maliki; id_orcid0000-0002-1138-4666; Marelli, Stefano; id_orcid0000-0002-9268-9014; Sudret, Bruno; id_orcid0000-0002-9501-7395
Published in: SIAM Conference on Uncertainty Quantification (UQ 2024). Searchable Abstract Document, Issue 11, 2024
Publisher: SIAM

Grey-box multifidelity surrogate modelling to combine noisy measurements and computer simulations

Author(s): Giannoukou, Katerina; Marelli, Stefano; id_orcid0000-0002-9268-9014; Sudret, Bruno; id_orcid0000-0002-9501-7395
Published in: MASCOT-NUM 2023 Conference, Le Croisic, France, April 3-6, 2023, 2023
Publisher: Mascot-Num
DOI: 10.3929/ethz-b-000638593

Comparison of state of the art sampling-based Bayesian Updating techniques

Author(s): M. B. Dodt, M. Kitahara, M. Broggi, M. Beer
Published in: 8th International Symposium on Reliability Engineering and Risk Management, 2023, Page(s) 59-66
Publisher: Research Publishing Services
DOI: 10.3850/978-981-18-5184-1_ms-02-146-cd

ENHANCING TRANSFER LEARNING FOR CRASHWORTHINESS STUDIES UNDER LOW DATA AVAILABILITY THROUGH SPHERE PROJECTION

Author(s): Giada Colella, Volker A. Lange, Fabian Duddeck
Published in: Proceedings of the 5th International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2019), 5th International Conference on Uncertainty Quantification in Computational Sciences and Engineering, 2023, Page(s) 453-465
Publisher: Institute of Structural Analysis and Antiseismic Research National Technical University of Athens
DOI: 10.7712/120223.10349.19593

Accuracy of physics informed neural network used to model the elastic response of a material

Author(s): D. Bonnet-Eymard, A. Persoons, M. Faes and D. Moens
Published in: ISMA-USD proceedings, 2022
Publisher: KU Leuven Department of Mechanical Engineering
DOI: 10.5281/zenodo.7566341

Surrogate-based reliability analysis for noisy models

Author(s): Pires, Anderson; Moustapha, Maliki; id_orcid0000-0002-1138-4666; Marelli, Stefano; id_orcid0000-0002-9268-9014; Sudret, Bruno; id_orcid0000-0002-9501-7395
Published in: 14th International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP14), Issue 1, 2023
Publisher: Trinity College Dublin
DOI: 10.3929/ethz-b-000638957

Review on Python Toolboxes for Kriging Surrogate Modelling

Author(s): Alessio Faraci, Pierre Beaurepaire, Nicolas Gayton
Published in: Book of Extended Abstracts for the 32nd European Safety and Reliability Conference, 2023, Page(s) 854-861
Publisher: Research Publishing Services
DOI: 10.3850/978-981-18-5183-4_r16-08-037

Active learning in grey-box models for near-real-time online monitoring of dynamic processes

Author(s): Dodt, Miriam B.; Persoons, Augustin; Faes, Matthias G.R.; Moens, David
Published in: ISMA/USD proceedings, Issue 2, 2022
Publisher: KU Leuven, Department of Mechanical Engineering
DOI: 10.5281/zenodo.7568690

Constructing confidence and prediction intervals for multifidelity surrogate models involving noisy data

Author(s): Giannoukou, Katerina; Marelli, Stefano; id_orcid0000-0002-9268-9014; Sudret, Bruno; id_orcid0000-0002-9501-7395
Published in: 5th International Conference on Uncertainty Quantification in Computational Science and Engineering (UNCECOMP 2023), Athens Greece, June 12-14, 2023, 2023
Publisher: UNCECOMP
DOI: 10.3929/ethz-b-000638592

Extending multi-fidelity surrogate modelling to stochastic simulators

Author(s): Giannoukou, Katerina; Marelli, Stefano; id_orcid0000-0002-9268-9014; Sudret, Bruno; id_orcid0000-0002-9501-7395
Published in: SIAM Conference on Uncertainty Quantification (UQ 2024), 2024
Publisher: SIAM

Defining what is a probability of failure for systems modelled by stochastic simulators

Author(s): Pires, Anderson; Moustapha, Maliki; id_orcid0000-0002-1138-4666; Marelli, Stefano; id_orcid0000-0002-9268-9014; Sudret, Bruno; id_orcid0000-0002-9501-7395
Published in: Proceedings of the 5th International Conference on Uncertainty Quantification in Computational Science and Engineering (UNCECOMP 2023), Athens, Greece, June 12-14, 2023, Athens, Greece, June 12-14, 2023, Issue 14, 2023
Publisher: UNCECOMP
DOI: 10.3929/ethz-b-000638960

Transfer learning for metamodel construction to enable uncertainty quantifications in crash design based on scarce data availability

Author(s): Giada Colella, Volker A. Lange, and Fabian Duddeck
Published in: ISMA-USD proceedings, 2022
Publisher: KU Leuven Department of Mechanical Engineering

An Importance Function to Generate Scenarios for Training a Grey-Box Model for the Computational Risk Assessment of Cyber-Physical Systems

Author(s): Juan-Pablo Futalef, Francesco Di Maio, Enrico Zio
Published in: Proceeding of the 33rd European Safety and Reliability Conference, 2023, Page(s) 2130-2137
Publisher: Research Publishing Services
DOI: 10.3850/978-981-18-8071-1_p684-cd

Time-Varying Statistics of Oscillators Endowed with Fractional Derivative Elements

Author(s): Yi Luo, Pol Spanos
Published in: 14th International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP14), Issue 9th - 13th of July, 2023, 2023
Publisher: Trinity College Dublin
DOI: 10.5281/zenodo.13904692

Response statistics of composite structures with stochastic material properties based on microstructure

Author(s): George Stefanou, Dimitrios Savvas, Panagiotis Gavallas, Iason Papaioannou
Published in: ISMA-USD proceedings, 2022
Publisher: KU Leuven Department of Mechanical Engineering

Unsupervised Representation Learning for Smart Transportation

Author(s): Thabang Lebese, Cécile Mattrand, David Clair, Jean-Marc Bourinet, François Deheeger
Published in: Lecture Notes in Computer Science, Advances in Intelligent Data Analysis XXII, 2024, Page(s) 15-27, ISBN 978-3-031-58553-1
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-58553-1_2

Mechanical properties of graphene nanoplatelets containing random structural defects

Author(s): Panagiotis Gavallas, Dimitrios Savvas, George Stefanou
Published in: Mechanics of Materials, Issue 180, 2023, Page(s) 104611, ISSN 0167-6636
Publisher: Elsevier BV
DOI: 10.1016/j.mechmat.2023.104611

Robust design optimization of expensive stochastic simulators under lack-of-knowledge

Author(s): Conradus van Mierlo; Augustin Persoons; Matthias G. R. Faes; David Moens
Published in: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 2023, ISSN 2332-9025
Publisher: The American Society of Mechanical Engineers
DOI: 10.1115/1.4056950

Prognostic of lithium-ion batteries using a combination of physical modeling and hybrid multi-layer perceptron particle filter

Author(s): Francesco Cancelliere, Sylvain Girard, Jean-Marc Bourinet, Matteo Broggi
Published in: Energy Reports, Issue 12, 2024, Page(s) 5863-5874, ISSN 2352-4847
Publisher: Elsevier
DOI: 10.1016/j.egyr.2024.11.058

Estimation of Response Expectation Bounds under Parametric P-Boxes by Combining Bayesian Global Optimization with Unscented Transform

Author(s): Chen Ding, Chao Dang, Matteo Broggi, Michael Beer
Published in: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, Issue 10, 2024, ISSN 2376-7642
Publisher: American Society of Civil Engineers
DOI: 10.1061/ajrua6.rueng-1169

A dynamic importance function for accidental scenarios generation by RESTART in the computational risk assessment of cyber-physical infrastructures

Author(s): Juan-Pablo Futalef, Francesco Di Maio, Enrico Zio
Published in: Reliability Engineering & System Safety, Issue 253, 2024, Page(s) 110538, ISSN 0951-8320
Publisher: Elsevier BV
DOI: 10.1016/j.ress.2024.110538

Crashworthiness Analysis: Exploiting Information of Developed Products With Control Variates

Author(s): Giada Colella, Marcos A. Valdebenito, Fabian Duddeck, Volker A. Lange, Matthias Faes
Published in: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, Issue 10, 2024, ISSN 2332-9017
Publisher: ASME
DOI: 10.1115/1.4066079

Uncertainty-Aware Multifidelity Surrogate Modeling with Noisy Data

Author(s): Katerina Giannoukou, Stefano Marelli, Bruno Sudret
Published in: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, Issue 11, 2025, ISSN 2376-7642
Publisher: American Society of Civil Engineers (ASCE)
DOI: 10.1061/ajrua6.rueng-1441

The effect of random field parameter uncertainty on the response variability of composite structures

Author(s): George Stefanou; Dimitrios Savvas; Panagiotis Gavallas; Iason Papaioannou
Published in: Composites Part C: Open Access, Issue 3, 2022, ISSN 2666-6820
Publisher: Elsevier BV
DOI: 10.1016/j.jcomc.2022.100324

First-passage probability estimation of high-dimensional nonlinear stochastic dynamic systems by a fractional moments-based mixture distribution approach

Author(s): Chen Ding; Chao Dang; Marcos A. Valdebenito; Matthias G.R. Faes; Matteo Broggi; Michael Beer
Published in: Mechanical Systems and Signal Processing (2022), Issue 08883270, 2022, ISSN 0888-3270
Publisher: Academic Press
DOI: 10.48550/arxiv.2210.04715

Digital twins in safety analysis, risk assessment and emergency management

Author(s): Enrico Zio, Leonardo Miqueles
Published in: Reliability Engineering & System Safety, Issue 246, 2024, Page(s) 110040, ISSN 0951-8320
Publisher: Elsevier BV
DOI: 10.1016/j.ress.2024.110040

CNN-based prediction of microstructure-derived random property fields of composite materials

Author(s): Panagiotis Gavallas, George Stefanou, Dimitrios Savvas, Cécile Mattrand, Jean-Marc Bourinet
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 430, 2024, Page(s) 117207, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/j.cma.2024.117207

Reliability analysis for non-deterministic limit-states using stochastic emulators

Author(s): Anderson V. Pires, Maliki Moustapha, Stefano Marelli, Bruno Sudret
Published in: Structural Safety, Issue 117, 2025, Page(s) 102621, ISSN 0167-4730
Publisher: Elsevier BV
DOI: 10.1016/j.strusafe.2025.102621

Transfer learning for crash design

Author(s): Giada Colella, Volker A. Lange, Fabian Duddeck
Published in: Discover Mechanical Engineering, Issue 3, 2024, ISSN 2731-6564
Publisher: Springer
DOI: 10.1007/s44245-024-00059-2

Increasing design flexibility by manually adapting the solution space for crashworthiness

Author(s): Paolo Ascia, Volker A. Lange, Fabian Duddeck
Published in: Journal of Mathematics in Industry, Issue 13, 2023, ISSN 2190-5983
Publisher: Springer Verlag
DOI: 10.1186/s13362-023-00137-2

Sampling and active learning methods for network reliability estimation using K-terminal spanning tree

Author(s): Chen Ding, Pengfei Wei, Yan Shi, Jinxing Liu, Matteo Broggi, Michael Beer
Published in: Reliability Engineering & System Safety, Issue 250, 2024, Page(s) 110309, ISSN 0951-8320
Publisher: Elsevier BV
DOI: 10.1016/j.ress.2024.110309

Reliability analysis for data-driven noisy models using active learning

Author(s): Anderson V. Pires, Maliki Moustapha, Stefano Marelli, Bruno Sudret
Published in: Structural Safety, Issue 112, 2024, Page(s) 102543, ISSN 0167-4730
Publisher: Elsevier BV
DOI: 10.1016/j.strusafe.2024.102543

A new reliability method combining adaptive Kriging and active variance reduction using multiple importance sampling

Author(s): Augustin Persoons, Pengfei Wei, Matteo Broggi, Michael Beer
Published in: Structural and Multidisciplinary Optimization, Issue 66, 2023, ISSN 1615-147X
Publisher: Springer Verlag
DOI: 10.1007/s00158-023-03598-6

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