Paper Citation Record · LEDGER

GradNet: A Gradient-Based Framework for Optimal Network Science

As of 15 August 2026, this Paper Citation Record lists 69 of 69 outbound references and 2 inbound Pith citation observations for arXiv:2603.09197.

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

pith.paper-citation-record.v1
2603.09197 v2

Coverage vector

measured 69 of 69 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-15T12:10:14.223144Z

measured 71 of 71 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-14T07:48:34.056063Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

69 of 69 outbound references displayed

verified exact0
verified fuzzy0
unresolved69
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1008ab01-2499-4aec-9af8-7cedd16e1067 · outbound

This paper cites Statistical mechanics of complex networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Statistical mechanics of complex networks,

Reference 1

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Observation cd27a535-926e-4bd2-a27e-34870b253455 · outbound

This paper cites Newman,��.

GradNet: A Gradient-Based Framework for Optimal Network Science Newman,��

Reference 2

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Observation 2491693e-ec0d-4768-82a1-edeb12a92ffa · outbound

This paper cites The structure and function of complex networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science The structure and function of complex networks,

Reference 3

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Observation a10ef7ef-efb6-4fec-bd9f-a9f17c2f31d5 · outbound

This paper cites Complex networks: Structure and dynamics,.

GradNet: A Gradient-Based Framework for Optimal Network Science Complex networks: Structure and dynamics,

Reference 4

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Observation 68924b3d-b792-4497-8f0a-e1fc57f4a298 · outbound

This paper cites Synchronization in complex networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Synchronization in complex networks,

Reference 5

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Observation b4cf7315-49ba-4e98-a99e-86311f6d81ca · outbound

This paper cites Barrat, M.

GradNet: A Gradient-Based Framework for Optimal Network Science Barrat, M

Reference 6

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Observation 2df3df3a-3a5a-4229-a0ec-063566f4e9fc · outbound

This paper cites Epidemic processes in complex networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Epidemic processes in complex networks,

Reference 7

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Observation c93325e4-14db-4fb6-bea0-0fe93988db72 · outbound

This paper cites On random graphs i,.

GradNet: A Gradient-Based Framework for Optimal Network Science On random graphs i,

Reference 8

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Observation ba7bc9c8-7fee-447f-a124-29649886b26f · outbound

This paper cites Collective dynamics of ‘small- world’networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Collective dynamics of ‘small- world’networks,

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-15T12:10:14.223144Z

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Observation 2231c2c0-cdbc-4dc9-aea8-ebed32bf23ee · outbound

This paper cites Highly optimized tolerance: Robustness and design in complex systems,.

GradNet: A Gradient-Based Framework for Optimal Network Science Highly optimized tolerance: Robustness and design in complex systems,

Reference 10

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Observation 93c9fcb9-19a5-47a6-9711-e2f18b448987 · outbound

This paper cites Size and form in efficient transportation networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Size and form in efficient transportation networks,

Reference 11

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Observation 46b62248-97c9-4d9d-ae4e-419825e20ce7 · outbound

This paper cites Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems,.

GradNet: A Gradient-Based Framework for Optimal Network Science Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems,

Reference 12

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Observation 590705ca-e084-40b9-818a-109e522d7a45 · outbound

This paper cites Fluctuations and redundancy in optimal transport networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Fluctuations and redundancy in optimal transport networks,

Reference 13

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Observation 204d3c9a-c4c8-40a6-b2b9-124b4ea42e37 · outbound

This paper cites Optimization in complex networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Optimization in complex networks,

Reference 14

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Observation 63d3889e-a723-484e-9559-f5ba0828a788 · outbound

This paper cites The best is yet to come,.

GradNet: A Gradient-Based Framework for Optimal Network Science The best is yet to come,

Reference 15

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Observation f02cb43f-80cb-4310-910c-efb0632ce820 · outbound

This paper cites Phase transitions in pareto optimal complex networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Phase transitions in pareto optimal complex networks,

Reference 16

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Observation a9a39bee-9913-42a0-8cc6-0ba5e4726514 · outbound

This paper cites Mitigation of malicious attacks on networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Mitigation of malicious attacks on networks,

Reference 17

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Observation d530b739-6cd3-42fa-b57c-c40138a0916e · outbound

This paper cites Onion-like network topology enhances robustness against malicious attacks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Onion-like network topology enhances robustness against malicious attacks,

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-15T12:10:14.223144Z

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Observation fc4db9db-4331-4cf3-ab70-02daa9f10030 · outbound

This paper cites Enhancing network robustness against malicious attacks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Enhancing network robustness against malicious attacks,

Reference 19

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Observation d3b271a9-9441-4bff-80a1-fbd19aed4bef · outbound

This paper cites Smart rewiring for network robustness,.

GradNet: A Gradient-Based Framework for Optimal Network Science Smart rewiring for network robustness,

Reference 20

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Observation 09873de5-7a2d-4c5e-959e-03296cdc3690 · outbound

This paper cites Improving the robustness of complex networks with preserving community structure,.

GradNet: A Gradient-Based Framework for Optimal Network Science Improving the robustness of complex networks with preserving community structure,

Reference 21

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Observation 77d6b94c-c1ca-417c-9507-ac2eeede9afe · outbound

This paper cites Optimizing network robustness by edge rewiring: a general framework,.

GradNet: A Gradient-Based Framework for Optimal Network Science Optimizing network robustness by edge rewiring: a general framework,

Reference 22

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Observation 01da7ca7-3f27-4318-b87e-e5cc1a2d0c10 · outbound

This paper cites Optimizing network robustness via krylov subspaces,.

GradNet: A Gradient-Based Framework for Optimal Network Science Optimizing network robustness via krylov subspaces,

Reference 23

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Observation b11f4aa5-ddbe-4a85-b6a7-2e13cee7df43 · outbound

This paper cites Network synchronization, diffusion, and the paradox of heterogeneity,.

GradNet: A Gradient-Based Framework for Optimal Network Science Network synchronization, diffusion, and the paradox of heterogeneity,

Reference 24

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Observation 088e51ee-4023-4d76-8c04-cfabae1d505f · outbound

This paper cites Entangled networks, synchronization, and optimal network topology,.

GradNet: A Gradient-Based Framework for Optimal Network Science Entangled networks, synchronization, and optimal network topology,

Reference 25

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Observation d570745b-996a-48a4-a691-48f2245e5867 · outbound

This paper cites Efficient rewirings for enhancing synchronizability of dynamical networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Efficient rewirings for enhancing synchronizability of dynamical networks,

Reference 26

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Observation 586a7fdf-5deb-4b07-8cfe-ad6dadd1cb37 · outbound

This paper cites Evolving enhanced topologies for the synchronization of dynamical complex networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Evolving enhanced topologies for the synchronization of dynamical complex networks,

Reference 27

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Observation e18b474d-7380-4f82-8a92-140e05b0e2c6 · outbound

This paper cites Synchronization of heterogeneous oscillators under network modifications: Perturbation and optimization of the synchrony alignment function,.

GradNet: A Gradient-Based Framework for Optimal Network Science Synchronization of heterogeneous oscillators under network modifications: Perturbation and optimization of the synchrony alignment function,

Reference 28

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Observation 69f67d1b-faa6-489e-82c6-827d82a34ab3 · outbound

This paper cites Emergent topology of optimal networks for synchrony,.

GradNet: A Gradient-Based Framework for Optimal Network Science Emergent topology of optimal networks for synchrony,

Reference 29

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Observation 63c3216d-c144-49d0-a915-b7c41a6bea23 · outbound

This paper cites Fastest mixing markov chain on a graph,.

GradNet: A Gradient-Based Framework for Optimal Network Science Fastest mixing markov chain on a graph,

Reference 30

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Observation 2979d6b2-92cb-4235-9c23-0bbf6e089231 · outbound

This paper cites Approximation algorithms for reducing the spectral radius to control epidemic spread,.

GradNet: A Gradient-Based Framework for Optimal Network Science Approximation algorithms for reducing the spectral radius to control epidemic spread,

Reference 31

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Observation 9e805d59-5656-4ee7-b4ac-b446bd75ecb9 · outbound

This paper cites Met: A fast algorithm for minimizing propagation in large graphs with small eigen-gaps,.

GradNet: A Gradient-Based Framework for Optimal Network Science Met: A fast algorithm for minimizing propagation in large graphs with small eigen-gaps,

Reference 32

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Observation de79c08f-b82f-47d0-9f7c-f6fba6590ec6 · outbound

This paper cites Distributed topology manipulation to control epidemic spreading over networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Distributed topology manipulation to control epidemic spreading over networks,

Reference 33

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Observation 5e9a4ce5-f822-4a97-81fb-61870bd7b7cd · outbound

This paper cites Optimizing controllability of complex networks by minimum structural perturbations,.

GradNet: A Gradient-Based Framework for Optimal Network Science Optimizing controllability of complex networks by minimum structural perturbations,

Reference 34

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Observation b3055bdd-4c9d-48af-9dda-4076ec13412d · outbound

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GradNet: A Gradient-Based Framework for Optimal Network Science Network design for controllability metrics,

Reference 35

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Observation 53f810b1-c65b-4b14-8f49-aa0eb91cd946 · outbound

This paper cites Growing well-connected graphs,.

GradNet: A Gradient-Based Framework for Optimal Network Science Growing well-connected graphs,

Reference 36

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Observation e22c944e-d728-4ec9-beb2-45fee1eb9142 · outbound

This paper cites Minimizing effective resistance of a graph,.

GradNet: A Gradient-Based Framework for Optimal Network Science Minimizing effective resistance of a graph,

Reference 37

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This paper cites Symmetry breaking in optimal transport networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Symmetry breaking in optimal transport networks,

Reference 38

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Observation c5072867-b563-487a-8dea-d212bef5ba23 · outbound

This paper cites Optimal design of spatial distribution networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Optimal design of spatial distribution networks,

Reference 39

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GradNet: A Gradient-Based Framework for Optimal Network Science Master stability functions for synchro- nized coupled systems,

Reference 40

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GradNet: A Gradient-Based Framework for Optimal Network Science Epidemic spreading in real networks: An eigenvalue viewpoint,

Reference 41

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This paper cites Optimal network topologies: expanders, cages, ramanujan graphs, entangled networks and all that,.

GradNet: A Gradient-Based Framework for Optimal Network Science Optimal network topologies: expanders, cages, ramanujan graphs, entangled networks and all that,

Reference 42

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Observation 90d8ab03-70d3-4fd7-b300-2b4e72da46b2 · outbound

This paper cites Spectral measure of structural robustness in complex networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Spectral measure of structural robustness in complex networks,

Reference 43

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GradNet: A Gradient-Based Framework for Optimal Network Science Optimal synchronization of complex networks,

Reference 44

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GradNet: A Gradient-Based Framework for Optimal Network Science Graph neural networks with adaptive structures,

Reference 45

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GradNet: A Gradient-Based Framework for Optimal Network Science Aro-gnn: Adaptive relation-optimized graph neural networks,

Reference 46

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This paper cites Automatic differentiation in machine learning: a survey,.

GradNet: A Gradient-Based Framework for Optimal Network Science Automatic differentiation in machine learning: a survey,

Reference 47

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Observation 3520cb87-e9d9-4b63-aa55-fe97ac01a3f2 · outbound

This paper cites Gradnet: A python package for optimal network science,.

GradNet: A Gradient-Based Framework for Optimal Network Science Gradnet: A python package for optimal network science,

Reference 48

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GradNet: A Gradient-Based Framework for Optimal Network Science Algebraic connectivity of graphs,

Reference 49

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GradNet: A Gradient-Based Framework for Optimal Network Science Old and new results on algebraic connectivity of graphs,

Reference 50

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GradNet: A Gradient-Based Framework for Optimal Network Science Maximum algebraic connectivity augmentation is np-hard,

Reference 51

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GradNet: A Gradient-Based Framework for Optimal Network Science Optimal robust network design: Formulations and algorithms for maximizing algebraic connec- tivity,

Reference 52

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GradNet: A Gradient-Based Framework for Optimal Network Science ¨Uber die abgrenzung der eigenwerte einer matrix,

Reference 53

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This paper cites International symposium on mathematical problems in theoretical physics,.

GradNet: A Gradient-Based Framework for Optimal Network Science International symposium on mathematical problems in theoretical physics,

Reference 54

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This paper cites From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators,.

GradNet: A Gradient-Based Framework for Optimal Network Science From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators,

Reference 55

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This paper cites Synchronization on small-world networks,.

GradNet: A Gradient-Based Framework for Optimal Network Science Synchronization on small-world networks,

Reference 56

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GradNet: A Gradient-Based Framework for Optimal Network Science Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?

Reference 57

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GradNet: A Gradient-Based Framework for Optimal Network Science On the topology of synchrony optimized networks of a kuramoto-model with non-identical oscillators,

Reference 58

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GradNet: A Gradient-Based Framework for Optimal Network Science An information flow model for conflict and fission in small groups,

Reference 59

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GradNet: A Gradient-Based Framework for Optimal Network Science Community detection in graphs,

Reference 60

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GradNet: A Gradient-Based Framework for Optimal Network Science Finding and evaluating community structure in networks,

Reference 61

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This paper cites Infer- ring the connectivity of coupled oscillators from time-series statistical similarity analysis,.

GradNet: A Gradient-Based Framework for Optimal Network Science Infer- ring the connectivity of coupled oscillators from time-series statistical similarity analysis,

Reference 62

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Observation e1a426d2-6000-4037-b910-e464d880168a · outbound

This paper cites Reconstruction of a random phase dynamics network from observations,.

GradNet: A Gradient-Based Framework for Optimal Network Science Reconstruction of a random phase dynamics network from observations,

Reference 63

Resolution: unresolved; no resolver link, observed 2026-07-15T12:10:14.223144Z

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Observation 55f875b7-809b-4137-bb85-d174ec5cd408 · outbound

This paper cites Inferring networks from time series: A neural approach,.

GradNet: A Gradient-Based Framework for Optimal Network Science Inferring networks from time series: A neural approach,

Reference 64

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Observation b90418cf-5e5e-46a6-8e52-5304641dfb5e · outbound

This paper cites The quantum internet,.

GradNet: A Gradient-Based Framework for Optimal Network Science The quantum internet,

Reference 65

Resolution: unresolved; no resolver link, observed 2026-07-15T12:10:14.223144Z

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Observation cd569d54-1040-4133-87d1-aa573dfeab2f · outbound

This paper cites Quantum internet: A vision for the road ahead,.

GradNet: A Gradient-Based Framework for Optimal Network Science Quantum internet: A vision for the road ahead,

Reference 66

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Observation 1f890e98-ca49-4d34-93c9-54701dd2d4c5 · outbound

This paper cites The path to scalable distributed quantum computing,.

GradNet: A Gradient-Based Framework for Optimal Network Science The path to scalable distributed quantum computing,

Reference 67

Resolution: unresolved; no resolver link, observed 2026-07-15T12:10:14.223144Z

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Observation 6b686aa6-ddf6-4c9d-b3de-170ce1a4875f · outbound

This paper cites Entanglement availability differentiation service for the quantum internet,.

GradNet: A Gradient-Based Framework for Optimal Network Science Entanglement availability differentiation service for the quantum internet,

Reference 68

Resolution: unresolved; no resolver link, observed 2026-07-15T12:10:14.223144Z

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Observation 44c94556-825e-4d4e-8d56-8188ceefc85a · outbound

This paper cites End-to-end capacities of a quantum communication network,.

GradNet: A Gradient-Based Framework for Optimal Network Science End-to-end capacities of a quantum communication network,

Reference 69

Resolution: unresolved; no resolver link, observed 2026-07-15T12:10:14.223144Z

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Pith citing papers

Observation b6cdf4c4-533b-4826-a6f7-50e6e0d12c57 · inbound

Mapping open quantum dynamics onto graphs cites this paper.

Mapping open quantum dynamics onto graphs GradNet: A Gradient-Based Framework for Optimal Network Science

Reference 44

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Observation 83d05cf4-7bd9-4a1f-a472-81e7eac32d9e · inbound

A Multi-Agent Framework for Zero-Dimensional Reduced-Order Model Planning cites this paper.

A Multi-Agent Framework for Zero-Dimensional Reduced-Order Model Planning GradNet: A Gradient-Based Framework for Optimal Network Science

Reference 14

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