Paper Citation Record · LEDGER

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation

As of 9 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2607.10439.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2607.10439 v2

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measured 34 of 34 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-02T07:19:37.914735Z

measured 34 of 34 standing notices

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34 of 34 outbound references displayed

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Outbound references

Observation d5357f11-7ec1-4b03-97ac-396d84291805 · outbound

This paper cites Oxford University Press, New York, 2006.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Oxford University Press, New York, 2006

Reference 1

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Observation 8ba06753-86ba-4dc0-829b-ad5b09587da1 · outbound

This paper cites A review of classification algorithms for EEG-based brain–computer interfaces: a 10 year update.Journal of Neural Engineering, 15(3):031005, 2018.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation A review of classification algorithms for EEG-based brain–computer interfaces: a 10 year update.Journal of Neural Engineering, 15(3):031005, 2018

Reference 2

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Observation 8bfb8107-8af5-4a5c-9e4d-8e3cec91582f · outbound

This paper cites Hamiltonian neural networks.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Hamiltonian neural networks

Reference 3

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Observation 807d6bf0-05f7-4664-b281-ed32fc6c1a45 · outbound

This paper cites Zhong, Biswadip Dey, and Amit Chakraborty.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Zhong, Biswadip Dey, and Amit Chakraborty

Reference 4

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Observation 3d7d5ec6-6269-4f5f-87f8-9af35909bec6 · outbound

This paper cites Port-Hamiltonian systems theory: An introductory overview.Foundations and Trends in Systems and Control, 1(2–3):173–378, 2014.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Port-Hamiltonian systems theory: An introductory overview.Foundations and Trends in Systems and Control, 1(2–3):173–378, 2014

Reference 5

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Observation 22c6a452-9bb7-4513-af98-ce788bf170cc · outbound

This paper cites Strogatz.Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Strogatz.Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering

Reference 6

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Observation 7bf4f9d6-aa0e-437b-bf95-b5ba3402b302 · outbound

This paper cites Springer, Berlin, 1984.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Springer, Berlin, 1984

Reference 7

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Observation 0a472c80-271c-41b1-a44d-9f22722f5326 · outbound

This paper cites Fronto-parietal EEG coherence in theta and upper alpha reflect central executive functions of working memory.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Fronto-parietal EEG coherence in theta and upper alpha reflect central executive functions of working memory

Reference 8

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Observation 860fb14b-702e-4aef-a625-3295e3a48c0e · outbound

This paper cites The theta-gamma neural code.Neuron, 77(6):1002–1016, 2013.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation The theta-gamma neural code.Neuron, 77(6):1002–1016, 2013

Reference 9

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Observation 5b4f4a97-5453-4e7c-a522-533f3c550473 · outbound

This paper cites Jirsa, and Anthony R.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Jirsa, and Anthony R

Reference 10

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Observation be98b7cf-81e3-4cbb-b9db-1a77b051c457 · outbound

This paper cites Dynamic models of large-scale brain activity.Nature Neuroscience, 20(3):340–352, 2017.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Dynamic models of large-scale brain activity.Nature Neuroscience, 20(3):340–352, 2017

Reference 11

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Observation a57795a9-53b6-4764-b98c-9b331d89ef07 · outbound

This paper cites Morrison.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Morrison

Reference 12

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Observation 7c454dc4-4db3-41a5-9e91-c20d55b49c17 · outbound

This paper cites ¨Ottinger.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation ¨Ottinger

Reference 13

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Observation 5b7e0f02-d9b0-4173-ac5c-93d2447fef60 · outbound

This paper cites Wiley-Interscience, Hoboken, NJ, 2005.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Wiley-Interscience, Hoboken, NJ, 2005

Reference 14

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Observation 7272b64a-b073-4e3f-877f-514bdf76f746 · outbound

This paper cites The fluctuation-dissipation theorem.Reports on Progress in Physics, 29(1):255– 284, 1966.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation The fluctuation-dissipation theorem.Reports on Progress in Physics, 29(1):255– 284, 1966

Reference 15

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Observation 7567d096-d44d-4d04-b0a0-ca6d5558e135 · outbound

This paper cites McFarland, Thilo Hinterberger, Niels Birbaumer, and Jonathan R.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation McFarland, Thilo Hinterberger, Niels Birbaumer, and Jonathan R

Reference 16

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Observation e3f61fa3-7191-4fd4-9d22-adb274b3a2b5 · outbound

This paper cites Goldberger, Luis A.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Goldberger, Luis A

Reference 17

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Observation 77d931b2-e919-4ea5-b3f3-5cbff50cd0c4 · outbound

This paper cites Identifying true brain interaction from EEG data using the imaginary part of coherency.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Identifying true brain interaction from EEG data using the imaginary part of coherency

Reference 18

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Observation afad3c0f-c138-4ca9-8c63-1ec72e5586ee · outbound

This paper cites Stam, Guido Nolte, and Andreas Daffertshofer.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Stam, Guido Nolte, and Andreas Daffertshofer

Reference 19

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Observation 11287be7-fecc-4f57-8dc5-cd3513cb753f · outbound

This paper cites an unresolved cited work.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Unresolved cited work

Reference 20

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Observation 745983f1-0724-4b06-b128-4c2909cf69bf · outbound

This paper cites Pascual-Marqui, Dietrich Lehmann, Martha Koukkou, Kieko Kochi, Peter Anderer, Bernd Saletu, Hideki Tanaka, Koichi Hirata, E.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Pascual-Marqui, Dietrich Lehmann, Martha Koukkou, Kieko Kochi, Peter Anderer, Bernd Saletu, Hideki Tanaka, Koichi Hirata, E

Reference 21

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Observation af1e6db3-001a-47c0-949a-bc8c08764b0c · outbound

This paper cites Knock, M.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Knock, M

Reference 22

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Observation af15b7cc-b919-49c2-a342-f7300a67460d · outbound

This paper cites Resting-state functional connectivity emerges from structurally and dynamically shaped slow fluctuations.Journal of Neuroscience, 33(27):11239–11252, 2013.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Resting-state functional connectivity emerges from structurally and dynamically shaped slow fluctuations.Journal of Neuroscience, 33(27):11239–11252, 2013

Reference 23

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Observation d61ab591-6964-48f0-ba6b-0e5348c57f98 · outbound

This paper cites Jansen and Vincent G.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Jansen and Vincent G

Reference 24

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Observation f7367994-3a06-4f61-b7b3-8d01c8fd55f0 · outbound

This paper cites A recurrent network mechanism of time integration in perceptual decisions.Journal of Neuroscience, 26(4):1314–1328, 2006.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation A recurrent network mechanism of time integration in perceptual decisions.Journal of Neuroscience, 26(4):1314–1328, 2006

Reference 25

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Observation 7a0eb349-7929-4993-9e43-328932709860 · outbound

This paper cites Beggs and Dietmar Plenz.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Beggs and Dietmar Plenz

Reference 26

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Observation 2348ce61-85a3-4a72-a8db-a51ba0e2e531 · outbound

This paper cites Nikouline, J.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Nikouline, J

Reference 27

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Observation 95717659-f357-488d-a247-ed3d5f7cc2ab · outbound

This paper cites The frontier of simulation-based inference.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation The frontier of simulation-based inference

Reference 28

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Observation 0ff0bdbe-56f6-42e2-8c59-bd3fdc03c630 · outbound

This paper cites Peterson, Paroma Varma, Priyadarshini Sebastian, Richard Gao, Torben Noto, Antonio H.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Peterson, Paroma Varma, Priyadarshini Sebastian, Richard Gao, Torben Noto, Antonio H

Reference 29

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Observation 4f49c101-ba28-4bf0-a00e-5372a536b419 · outbound

This paper cites Casali, Olivia Gosseries, Mario Rosanova, M´ elanie Boly, Simone Sarasso, Karina R.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Casali, Olivia Gosseries, Mario Rosanova, M´ elanie Boly, Simone Sarasso, Karina R

Reference 30

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Observation 2dd7140f-4f61-4a2a-9afd-4dd7ce157a35 · outbound

This paper cites Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems

Reference 31

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Observation 2cecf220-b7da-4998-a35d-1773c766493c · outbound

This paper cites Saturnino.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Saturnino

Reference 32

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Observation 96fc485e-cee8-42ba-b63f-5bcbae06fefb · outbound

This paper cites Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M

Reference 33

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Observation c0be6a45-555d-41f1-b86e-62fda05311bd · outbound

This paper cites The non-invasive Berlin Brain-Computer Interface: Fast acquisition of effective perfor- mance in untrained subjects.NeuroImage, 37(2):539–550, 2007.

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation The non-invasive Berlin Brain-Computer Interface: Fast acquisition of effective perfor- mance in untrained subjects.NeuroImage, 37(2):539–550, 2007

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-02T07:19:37.914735Z

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