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REVIEW 3 major objections 6 minor 68 references

Does the brain behave like a (complex) network? I. Dynamics

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Mapping the brain as a network does not make it one.

desk verdict A careful conceptual review that usefully frames networkness via four conditions, but its dynamics-only criterion is too narrow on its own admissions and the paper is a synthesis rather than a new result. read the letter →

arxiv 2412.15711 v2 pith:IRFZMQ2N submitted 2024-12-20 q-bio.NC cond-mat.dis-nnnlin.AO

D. Papo , J.M. Buldú This is my paper · ORCID
classification q-bio.NCcond-mat.dis-nnnlin.AO MSC 05C8237N2592B20
keywords braindynamicsnetworknesscomplexnetworksquencheddisordersynchronisationcriticalitystructure-dynamicsrelationshipfunctionalconnectivity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that applying graph theory to brain anatomy and activity is not the same as showing that the brain works as a network. The real question is whether network properties count: whether the topology, geometry, and disorder of a reconstructed graph demonstrably shape brain dynamics. The paper defines networkness as a property that must be earned through dynamic relevance, and reviews evidence across synchronisation, criticality, activity spreading, and pattern formation to ask where that condition is met. A fair reading is that descriptive network measures are only as meaningful as the dynamics they can explain, and that networkness is scale- and phenomenon-specific.

What carries the argument

The central object is the notion of networkness, defined by whether a system's behaviour can be reduced to its network structure without loss of information and by whether the structure's properties influence dynamics. The paper's analytical tools are the quenched/annealed disorder distinction, the master stability function and Kuramoto synchronisation framework, epidemic spreading models with absorbing-state transitions, and the concept of frustration; each is used to test where topology makes a dynamical difference.

What would settle it

A decisive observation would be a brain phenomenon whose dynamics remain unchanged when the reconstructed connectivity matrix is randomly rewired while node dynamics, inputs, and recording scales are held fixed; such invariance would show that the specific network topology does not count for that phenomenon.

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Extended reading notes

Core claim

The central claim is that networkness is not an automatic consequence of measuring connectivity; a brain system genuinely behaves as a network only when its network structure makes a causal dynamical difference. The paper grounds this in conditions for reducibility to a network (connectedness, discretisability, structure preservation, intrinsicality) and in a distinction between quenched disorder, the static anatomical connectivity, and annealed disorder, the activity-induced connectivity. It then surveys dynamical processes—synchronisation, criticality, epidemic spreading, frustration, topological transitions—to locate where network structure changes the physics rather than merely labelling it. The conclusion is that the brain may be describable as a network at some scales and for some phenomena, but that networkness is a scale- and phenomenon-specific achievement, not a generic property of brain tissue.

Load-bearing premise

The analysis assumes that 'bare dynamics' can be meaningfully separated from function and that dynamic relevance is the right criterion for judging networkness, since Section 1 explicitly sets aside the brain's ability to perform tasks.

Editorial extensions

If this is right

  • Purely descriptive graph metrics such as clustering, small-worldness, and modularity do not, by themselves, demonstrate that the brain is a network.
  • Network structure should be treated as a hypothesis that can fail at specific scales: a graph may be a useful data-compression device without being the brain's operating principle.
  • Brain criticality studies gain a sharper prediction: if hierarchical modular topology is the cause of scale-free avalanches, then perturbing modular structure should alter critical exponents, not just the descriptive statistics.
  • The quenched/annealed distinction gives a concrete way to decide whether anatomy or activity-induced coupling is the load-bearing structure for a given dynamical phenomenon.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If dynamic relevance is the right criterion, then task-driven or functional contexts may be where networkness becomes visible; a dynamics-only review may understate networkness that is function-dependent, a possibility the paper brackets at the outset.
  • Networkness may be a graded property: the same brain region could behave as a network for one dynamical process, such as synchronisation, and as a continuous field for another, such as ephaptic coupling, so the question would shift from 'is the brain a network?' to 'for which processes and at which scales is it one?'
  • A testable extension of the review's framework is to compare perturbation-response predictions of network models with continuum neural-field models on the same data; wherever the predictions diverge, the network representation either earns or loses its claim to dynamic relevance.
  • The conceptual apparatus could transfer to other biological and social systems that use graph descriptions, such as gene-regulatory or ecological networks, where the same gap between descriptive structure and operating principle may appear.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. This paper, the first part of a two-part review, argues that representing brain anatomy and activity as a complex network does not by itself imply that the brain actually operates as a network. It introduces the notion of 'networkness' as the property that network characteristics are consequential, reviews conditions for a system's reducibility to a network structure (connectedness, discretisability, structure preservation, intrinsicality), and examines a wide range of dynamical evidence—activity spreading, synchronisation, criticality and cascade models, frustration, and the effects of quenched versus annealed disorder—to assess when network structure demonstrably affects brain dynamics. The paper explicitly restricts Part I to bare, task-independent dynamics and defers genuinely functional analysis to a companion paper.

Significance. The paper's central thesis is important because it challenges the widespread, often implicit reification of network representations in neuroscience: rather than asking whether network measures exist, it asks whether network properties make a difference to brain dynamics or function. The manuscript is commendably cautious and self-aware, explicitly flagging conflicting evidence (e.g., Morrell et al. 2021 on external inputs generating apparent criticality, and reports of non-universal epidemic-model predictions), listing caveats about model ingredients, and repeatedly indicating that many structure-dynamics questions remain open. It also provides a valuable conceptual framework—time-scale separation between node dynamics, network dynamics, and processes on networks; quenched versus annealed disorder; the role of topology, geometry, and dimension—that will likely be pedagogically useful for the field. However, the central conceptual notion of 'networkness' is not given a crisp operational definition, and the paper's conclusion is explicitly conditioned on a companion paper that is not yet available.

major comments (3)
  1. [§1, §3.3, §4] The abstract states that the paper 'first define(s) the meaning of networkness,' but §2.1 lists four conditions (connectedness, discretisability, structure preservation, intrinsicality) without stating whether they are individually necessary, jointly sufficient, or simply desiderata, and §2.2.1 introduces two 'elements' (coupling strength and the coupling matrix) without formally connecting them to the §2.1 conditions. Section 3 then identifies 'dynamic relevance of network structure' as 'signs of networkness' without an explicit bridge between that sign and the earlier conditions. As a result, the central claim—that network properties count only when they demonstrably affect dynamics—lacks a testable criterion that a reader could apply to a concrete system. Please state the intended definition precisely (e.g., 'a network property is genuinely network-like iff removing or altering it changes an observable dynamical or functional quantity') and clarify the logical status of the §2.1 conditions relative to that criterion.
  2. [§1, §3.3, §4] The paper restricts Part I to 'bare dynamics' (§1) and explicitly concedes that 'most key issues associated with annealed brain network structure ... are better treated in a genuinely functional rather than in a purely dynamical framework' (§3.3). This concession means that the abstract's general negative thesis—that a complex network representation 'does not entail that the brain actually works as a network'—is here supported only for the dynamical domain, not for the functional domain that is listed in the abstract as part of what makes network properties 'count.' The paper should state in the abstract and in the concluding remarks that the dynamical analysis provides at most a sufficient condition for networkness, not a necessary one, and that a full verdict awaits the companion paper. Without this qualification, the reader may over-interpret the title and abstract as settling the entire networkness question.
  3. [§1, §3.3, §4] The manuscript depends on the unpublished companion paper (Papo and Buldú, in preparation) for the formal definition and examination of 'genuine functional brain activity' and for key aspects of annealed structure (§1, §3.3, and §4). This dependence makes the present contribution incomplete as a standalone argument: the 'meaning of networkness' promised in the abstract is not fully delivered until the companion appears. Please either include a concise statement of the functional criteria in the concluding remarks, or cite a published, preprint, or otherwise accessible version of the companion paper; without this, the reader cannot assess whether the functional evidence might reverse or qualify the dynamical conclusions.
minor comments (6)
  1. [General] The paper is very long and dense; it would benefit from a short 'definitions and scope' box or a glossary collecting the many technical terms (networkness, quenched versus annealed disorder, locality, frustration, self-averaging) that are introduced at various points and used throughout.
  2. [§2.2.1] There is a typo in 'Morevoer' in the paragraph on the coupling factor σ; please correct.
  3. [§3.2.4] The word 'non-equilbirium' should be 'non-equilibrium' in the paragraph on the meaning of observed structure.
  4. [§3.4.2] The word 'parametres' is a non-standard spelling; 'parameters' is intended.
  5. [§Quenched network structure and brain criticality] The phrase 'exstinguished by fluctuations' should be 'extinguished by fluctuations.'
  6. [§3.2.2, equation numbering] Equation [8.2] is labeled in a way that may confuse readers; please renumber it as a separate equation (e.g., [9]) and adjust subsequent references.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: the networkness criterion is a stipulated conceptual frame, not a fitted prediction, self-cited uniqueness result, or derivation from its own inputs.

full rationale

The paper is a conceptual review and does not fit parameters, make quantitative predictions, or invoke a uniqueness theorem, so the main circularity patterns do not apply. Its central framing—'Asking whether the brain behaves as a network means asking whether network properties count'—is presented as a definitional stance rather than as a theorem derived from data. The subsequent focus on dynamic relevance is an explicitly chosen criterion ('Signs of brain networkness: dynamic relevance of network structure'), not a result that is claimed to follow from independent premises. The manuscript itself flags its scope limitation: Section 1 states that dynamics are treated 'divorced from considerations of neural systems’ ability to perform a given task,' and Section 3.3 concedes that key issues about annealed network structure 'are better treated in a genuinely functional rather than in a purely dynamical framework.' This is an incompleteness or narrowing of scope, not a circular reduction, because the paper does not pretend to settle the functional question from the dynamics-only criterion. Self-citations (e.g., Papo, 2019; Papo and Buldú, in preparation) are used to mark prior conceptual commitments and to defer functional analysis to a companion paper; they are not load-bearing evidence that forces the conclusion. The only residual concern is that defining 'genuinely behaves as a network' in terms of dynamic relevance makes the criterion somewhat stipulative, but stipulation is not circular derivation. Score 1 reflects the presence of minor, non-load-bearing self-citations rather than any circularity.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The paper introduces no fitted parameters and no invented entities. It does rest on three domain assumptions: dynamics can be treated separately from function; statistical mechanics provides the right criterion for networkness; and brain anatomy and dynamics can be represented as topological spaces with good covers. These are stated or implied in Sections 1 and 2.

assumptions (3)
  • domain assumption A system's networkness can be assessed from its dynamics alone, independent of function.
    The paper explicitly brackets function and treats dynamics in isolation (Section 1, 'we treat dynamics in a way that is divorced from considerations of neural systems' ability to perform a given task'). This is a substantive modeling choice.
  • domain assumption Statistical mechanics criteria, such as large-N emergence and self-averaging, are the appropriate yardstick for genuine networkness.
    Section 2.1.1 argues a small connected network would not be a genuine network 'in a statistical mechanical sense', importing a specific notion of what counts as a network.
  • domain assumption Brain anatomy and dynamics can be represented as topological spaces with well-behaved discretizations.
    Section 2 defines the brain as a topological space (N, tau) and invokes good covers, contractibility, and irreducible nodes to justify discretization. These are unproved background mathematical conditions.

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Cite this review

Pith. "Pith review of Does the brain behave like a (complex) network? I. Dynamics." pith.science (2026). https://pith.science/paper/IRFZMQ2N

@misc{pith2026241215711,
  author       = {Pith},
  title        = {Pith review of: Does the brain behave like a (complex) network? I. Dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IRFZMQ2N}},
  note         = {Machine review of arXiv:2412.15711}
}
read the original abstract

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.

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Works this paper leans on

68 extracted references · 63 canonical work pages

  1. [1]

    Meinhardt, H. (1972). A theory of biological pattern formation. Kybernetik 12, 30–39. Gilson, M., Tagliazucchi, E., and Cofré, R. (2023). Entropy production of multivariate Ornstein-Uhlenbeck processes correlates with consciousness levels in the human brain. Phys. Rev. E 107, 024121. Ginzburg, I., and Sompolinsky, H. (1994). Theory of correlations in stoc...

    work page 1972

  2. [6]

    Kubo, R. (1966). The fluctuation-dissipation theorem. Rep. Prog. Phys. 29, 255–284. Kujala, R., Glerean, E., Pan, R.K., Jääskeläinen, I.P., Sams, M., and Saramäki, J. (2016). Graph coarse-graining reveals differences in the module-level structure of functional brain networks. Eur. J. Neurosci. 44, 2673–2684. Kumar, A., Rotter, S., and Aertsen, A. (2008). ...

    work page 1966

  3. [8]

    Kaiser, M., and Hilgetag, C.C. (2004b). Spatial growth of real-world networks. Phys. Rev. E 69, 036103. Kaiser, M., Hilgetag, C.C, and van Ooyen, A. (2009). A simple rule for axon outgrowth and synaptic competition generates realistic connection lengths and filling fractions. Cereb. Cortex 19, 3001–3010. Kalisman, N., Silberberg, G., and Markram, H. (2005)...

    work page Pith review arXiv 2004

  4. [11]

    Saichev, A.I., and Sornette, D. (2011). Generating functions and stability study of multivariate self-excited epidemic processes. Eur. Phys. J. B 83, 271–282. Salinas, E., and Sejnowski, T.J. (2001). Correlated neuronal activity and the flow of neural information. Nat. Rev. Neurosci. 2, 539–550. Salnikov, V., Cassese, D., and Lambiotte, R. (2018). Simplici...

    work page 2011

  5. [12]

    Goh, K.I., Kahng, B., and Kim, D. (2001). Spectra and eigenvectors of scale-free networks. Phys. Rev. E 64, 051903. Gollo, L.L., and Breakspear, M. (2014a). The frustrated brain: from dynamics on motifs to communities and networks. Philos. Trans. R. Soc. B 369, 20130532. Gollo, L.L., Mirasso, C., Sporns, O., and Breakspear, M. (2014b). Mechanisms of zero-...

    work page 2001

  6. [13]

    Li, D, and Zhou, C. (2011). Organization of anti-phase synchronization pattern in neural networks: what are the key factors? Front. Syst. Neurosci. 5,

    work page 2011

  7. [15]

    Weninger, L., Srivastava, P., Zhou, D., Kim, J.Z., Cornblath, E.J., Bertolero, M.A., Habel, U., Merhof, D., and Bassett, D.S. (2022). Information content of brain states is explained by structural constraints on state energetics. Phys. Rev. E 106, 014401. Wernicke, C. (1874). Der aphasische Symptomencomplex. Eine psychologische Studie auf anatomischer Bas...

    work page 2022

  8. [30]

    Wang, X.J., and Buzsáki, G. (1996). Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J. Neurosci. 16, 6402–6413. Wang, X.J., and Kennedy, H. (2016). Brain structure and dynamics across scales: in search of rules. Curr. Opin. Neurobiol. 37, 92–98. Watanabe, T., and Masuda, N. (2010). Enhancing the spectral gap of netwo...

    work page 1996

Show all 68 references
  1. [42]

    Yang, D.P., Zhou, H.J., and Zhou, C. (2017). Co-emergence of multi-scale cortical activities of irregular firing, oscillations and avalanches achieves cost-efficient information capacity. PLoS Comput. Biol. 13, e1005384. Yeh, F.C., Tang, A., Hobbs, J.P., Hottowy, P., Dabrowski...

    2017

  2. [44]

    Roxin, A., Riecke, H., and Solla, S.A. (2004). Self-sustained activity in a small-world network of excitable neurons. Phys. Rev. Lett. 92, 198101. Royer, J., Bernhardt, B.C., Larivière, S., Gleichgerrcht, E., Vorderwülbecke, B.J., Vulliémoz, S., and Bonilha, L. (2022). Epileps...

    2004

  3. [45]

    and Shannahoff-Khalsa, D

    Papo, D., Bucolo, M., Dimitriadis, S.I., Onton, J.A., Philippu, A. and Shannahoff-Khalsa, D. (2023). Editorial: Advances in brain dynamics in the healthy and psychiatric disorders. Front. Psychiatry 14, 1284670. Papo, D., and Buldú, J.M. (2019). Brain synchronizability, a fals...

    2023

  4. [64]

    West, B.J., Geneston, E.L., and Grigolini, P. (2008). Maximizing information exchange between complex networks. Phys. Rep. 468, 1–99. Weyl, H. (1952), Symmetry. Princeton University Press. Whalen, A. J., Brennan, S.N., Sauer, T.D., and Schiff, S.J. (2015). Observability and co...

    2008

  5. [72]

    Pernice, V., Staude, B., Cardanobile, S., and Rotter, S. (2011). How structure determines correlations in neuronal networks. PLoS Comput. Biol. 7, e1002059. Pernice, V., Staude, B., Cardanobile, S., and Rotter, S. (2012). Recurrent interactions in spiking networks with arbitra...

    2011

  6. [87]

    Sandhu, R., Georgiou, T., Reznik, E., Zhu, L., Kolesov, I., Senbabaoglu, Y., and Tannenbaum, A. (2015). Graph curvature for differentiating cancer networks. Sci. Rep. 5, 12323. Santos, E., Schöll, M., Sánchez-Porras, R., Dahlem, M.A., Silos, H., Unterberg, A., Dickhaus, H., an...

    2015

  7. [90]

    Novikov, E., Novikov, A., Shannahoff-Khalsa, D., Schwartz, B., and Wright, J. (1997). Phys. Rev. E 56, R2387–R2389. Nunez, P.L. (2000). Toward a quantitative description of large-scale neocortical dynamic function and EEG. Behav. Brain Sci. 23, 371–398. O’Byrne, J., and Jerbi,...

    1997

  8. [100]

    Lifshitz, I.M. (1964). The energy spectrum of disordered systems. Adv. Phys. 13, 483–536. Lifshitz, I.M. Gredeskul, S.A., and Pastur, A.L. (1988). Introduction to the theory of disordered systems. Wiley, New York. Lindner, B. (2022). Fluctuation-dissipation relations for spiki...

    1964

  9. [107]

    Papo, D., Zanin, M., Pineda, J.A., Boccaletti, S., and Buldú, J.M. (2014c). Brain networks: great expectations, hard times, and the big leap forward. Philos. Trans. R. Soc. B 369, 20130525. Paradisi, P., Cesari, R., Contini, D., Donateo, A., and Palatella, L. (2009). Character...

    2014

  10. [110]

    41 Kaiser, M., and Hilgetag, C.C. (2004a). Modelling the development of cortical systems networks. Neurocomputing 58–60, 297–302. Kaiser, M., and Hilgetag, C.C. (2010). Optimal hierarchical modular topologies for producing limited sustained activation of neural networks. Front...

    2004

  11. [111]

    Markov, N.T., Ercsey-Ravasz, M., Van Essen, D.C., Knoblauch, K., Toroczkai, Z., and Kennedy, H. (2013). Cortical high-density counterstream architectures. Science 342, 1238406. Markram, H., Lübke, J., Frotscher, M., and Sakmann, B. (1997a). Physiology and anatomy of synaptic c...

    2013

  12. [112]

    Papo, D. (2019). Gauging functional brain activity: from distinguishability to accessibility. Front. Physiol. 10,

    2019

  13. [115]

    Trousdale, J., Hu, Y., Shea-Brown, E., and Josić, K. (2012). Impact of network structure and cellular response on spike time correlations. PLoS Comput. Biol. 8, e1002408. Tsodyks, M., Uziel, A., and Markram, H. (2000). Synchrony generation in recurrent networks with frequency-...

    2012

  14. [123]

    understands

    Lambiotte, R., Rosvall, M., and Scholtes, I. (2019). From networks to optimal higher-order models of complex systems. Nat. Phys. 15, 313–320. Landau, I.D., Egger, R., Dercksen, V.J., Oberlaender, M., and Sompolinsky, H. (2016). The impact of structural heterogeneity on excitat...

    2019

  15. [166]

    Higgins, P.J. (1971). Categories and groupoids. Nostrand Reinhold. Hilgetag, C.C., and Goulas, A. (2020). ‘Hierarchy’in the organization of brain networks. Philos. Trans. R. Soc. B 375, 20190319. Hinrichsen, H. (2000). Non-equilibrium critical phenomena and phase transitions i...

    1971

  16. [167]

    Kastner, M., and Schnetz, O. (2008). Phase transitions induced by saddle points of vanishing curvature. Phys. Rev. Lett. 100, 160601. Kauffman, L.H. (2006). Formal knot theory. Courier Corporation. Kennedy, H., Knoblauch, K., and Toroczkai, Z. (2013) Why data coherence and qua...

    2008 arXiv

  17. [169]

    Stepanyants, A., Hof, P.R., and Chklovskii, D.B. (2002). Geometry and structural plasticity of synaptic connectivity. Neuron 34, 275–288. Stern, M., Istrate, N., and Mazzucato, L. (2022). A reservoir of timescales in random neural networks. arXiv:2110.09165. Stern, M., Sompoli...

    2002 arXiv

  18. [178]

    Zimmern, V. (2020). Why brain criticality is clinically relevant: a scoping review. Front. Neural Circuits 14,

    2020

  19. [182]

    Motter, A.E., and Timme, M. (2018). Antagonistic phenomena in network dynamics. Annu. Rev. Condens. Matter Phys. 9,

    2018

  20. [196]

    Timme, M. (2006). Does dynamics reflect topology in directed networks? Europhys. Lett. 76,

    2006

  21. [200]

    Mézard, M., Parisi, G., and Virasoro, M.A. (1987). Spin glass theory and beyond. World Scientific, Singapore. Millán, A.P., Gori, G., Battiston, F., Enss, T., and Defenu, N. (2021a). Complex networks with tuneable spectral dimension as a universality playground. Phys. Rev. Res....

    1987

  22. [259]

    Song, C., Havlin, S., and Makse, H.A. (2006). Origins of fractality in the growth of complex networks. Nat. Phys. 2, 275–281. Song, C., Wang, P., and Makse, H. (2008). A phase diagram for jammed matter. Nature 453, 629–632. Song, S., Sjöström, P.J., Reigl, M., Nelson, S., and ...

    2006 arXiv

  23. [351]

    Huttenlocher, P. (1979). Synaptic density in human frontal cortex—developmental changes and effects of aging. Brain Res. 163, 195–205. Ignaccolo, M., Latka, M., Jernajczyk, W., Grigolini, P., and West, B.J. (2010a). Dynamics of electroencephalogram entropy and pitfalls of scal...

    1979

  24. [367]

    Timme, M. (2007). Revealing network connectivity from response dynamics. Phys. Rev. Lett. 98, 224101. Tirabassi, G., Sevilla-Escoboza, R., Buldú, J.M., and Masoller, C. (2015). Inferring the connectivity of coupled oscillators from time-series statistical similarity analysis. ...

    2007

  25. [376]

    Perin, R., Berger, T.K., and Markram, H.A. (2011). A synaptic organizing principle for cortical neuronal groups. Proc. Natl. Acad. Sci. U.S.A. 108, 5419–5424. Pernice, V., Deger, M., Cardanobile, S., and Rotter, S. (2013). The relevance of network micro-structure for neural dy...

    2011

  26. [380]

    Kurchan, J. (2005). In and out of equilibrium. Nature 433, 222–225. Kuśmierz, Ł., Ogawa, S., and Toyoizumi, T. (2020). Edge of chaos and avalanches in neural networks with heavy-tailed synaptic weight distribution. Phys. Rev. Lett. 125, 028101. Lacasa, L., and Gómez-Gardeñes, ...

    2005

  27. [396]

    Hagmann, P., Cammoun, L., Gigandet, X., Meuli, R., Honey, C.J., Wedeen, V.J., and Sporns, O. (2008). Mapping the structural core of human cerebral cortex. PLoS Biol. 6, e159. Hahn, G., Ponce-Alvarez, A., Monier, C., Benvenuti, G., Kumar, A., Chavane, F., Deco, G., and Frégnac,...

    2008

  28. [420]

    Kuramoto, Y., and Battogtokh, D. (2002). Coexistence of coherence and incoherence in nonlocally coupled phase oscillators. Nonlinear Phenom. Complex Syst. 5,

    2002

  29. [463]

    Motter, A.E., Zhou, C., and Kurths, J. (2005). Network synchronization, diffusion, and the paradox of heterogeneity. Phys. Rev. E 71, 016116. Mulas, R., Kuehn, C., and Jost, J. (2020). Coupled dynamics on hypergraphs: master stability of steady states and synchronization. Phys...

    2005

  30. [544]

    K., de Candia, A., Sarracino, A., Herrmann, H

    Nandi, M. K., de Candia, A., Sarracino, A., Herrmann, H. J., and de Arcangelis, L. (2023). Fluctuation-dissipation relations in the imbalanced Wilson-Cowan model. Phys. Rev. E 107, 064307. Navas, A., Papo, D., Boccaletti, S., Del-Pozo, F., Bajo, R., Maestú, F., Martínez, J.H.,...

    2023

  31. [571]

    Schneidman, E., Berry, M.J., Segev, R., and Bialek, W. (2006). Weak pairwise correlations imply strongly correlated network states in a neural population. Nature, 440, 1007–1012. Schöll, E. (2016). Synchronization patterns and chimera states in complex networks: interplay of t...

    2006

  32. [591]

    and Bullmore, E.T

    Meunier, D., Lambiotte, R. and Bullmore, E.T. (2010). Modular and hierarchically modular organization of brain networks. Front. Neurosci. 4,

    2010

  33. [620]

    Jefferys, J.G., de la Prida, L.M., Wendling, F., Bragin, A., Avoli, M., Timofeev, I., and da Silva, F.H.L. (2012). Mechanisms of physiological and epileptic HFO generation. Prog. Neurobiol. 98, 250–264. Jin, S.H., Jeong, W., and Chung, C.K. (2015). Mesial temporal lobe epileps...

    2012

  34. [663]

    Ódor, G. (2008). Universality in nonequilibrium lattice systems: theoretical foundations. World Scientific. Ódor, G., Dickman, R., and Ódor, G. (2015). Griffiths phases and localization in hierarchical modular networks. Sci. Rep. 5, 14451. Ódor, G., Papp, I., Deng, S., and Kel...

    2008

  35. [694]

    Masuda, N., Porter, M.A., and Lambiotte, R. (2017). Random walks and diffusion on networks. Phys. Rep. 716, 1–58. Matkovič, A., Anticevic, A., Murray, J.D., and Repovš, G. (2023). Static and dynamic fMRI-derived functional connectomes represent largely similar information. Net...

    2017 doi

  36. [749]

    Zhang, H., Watrous, A.J., Patel, A., and Jacobs, J. (2018). Theta and alpha oscillations are traveling waves in the human neocortex. Neuron 98, 1269–1281. Zhang, L., Motter, A.E., and Nishikawa, T. (2017). Incoherence-mediated remote synchronization. Phys. Rev. Lett. 118, 1741...

    2018

  37. [777]

    Kafashan, M., Palanca, B.J.A., and Ching, S. (2018). Dimensionality reduction impedes the extraction of dynamic functional connectivity states from fMRI recordings of resting wakefulness. J. Neurosci. Methods 293, 151–161. Kaiser, M., Görner, M., and Hilgetag, C.C. (2007). Cri...

    2018

  38. [823]

    Shi, Y.L., Zeraati, R., Levina, A., and Engel, T.A. (2023). Spatial and temporal correlations in neural networks with structured connectivity. Phys. Rev. Res. 5, 013005. Shinomoto, S., and Kuramoto, Y. (1986). Phase transitions in active rotator systems. Prog. Theor. Phys. 75,...

    2023

  39. [854]

    Ruiz-García, M., and Katifori, E. (2020). Topologically controlled emergent dynamics in flow networks. arXiv:2001.01811. Safari, A., Moretti, P., Diez, I., Cortes, J.M., and Muñoz, M.A. (2021). Persistence of hierarchical network organization and emergent topologies in models ...

    2020 arXiv

  40. [904]

    Simeon, G., Piella, G., Camara, O., and Pareto, D. (2022). Riemannian Geometry of Functional Connectivity Matrices for multi-site attention-deficit/hyperactivity disorder data harmonization. Front. Neuroinform. 16, 769274. Simhal, A.K., Carpenter, K.L., Nadeem, S., Kurtzberg, ...

    2022

  41. [925]

    Pastor-Satorras, R., and Vespignani, A. (2001). Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200–3203. Pearl, J. (1988). Probabilistic reasoning. In Intelligent systems: networks of plausible inference. Morgan Kaufmann. San Fransisco, CA, USA. Pecora, L.M.,...

    2001

  42. [1014]

    Topodynamics of metastable brains

    Paluš, M. (1996). Nonlinearity in normal human EEG: cycles, temporal asymmetry, nonstationarity and randomness, not chaos. Biol. Cybern. 75, 389–96. Pang, J.C., Aquino, K. M., Oldehinkel, M., Robinson, P.A., Fulcher, B.D., Breakspear, M., and Fornito, A. (2023). Geometric cons...

    1996 arXiv

  43. [1056]

    Roberts, J.A., Perry, A., Lord, A.R., Roberts, G., Mitchell, P.B., Smith, R.E., Calamante, F., and Breakspear, M. (2016). The contribution of geometry to the human connectome. Neuroimage 124, 379–393. Robinson, P.A. (2013). Discrete-network versus modal representations of brai...

    2016

  44. [1301]

    van den Heuvel, M.P., Kahn, R.S., Goñi, J., and Sporns, O. (2012). High-cost, high-capacity backbone for global brain communication. Proc. Natl. Acad. Sci. U.S.A. 109, 11372–11377. van den Heuvel, M.P., Mandl, R.C., Kahn, R.S., and Hulshoff Pol, H.E. (2009). Functionally linke...

    2012

  45. [1569]

    Voges, N., and Perrinet, L. (2010). Phase space analysis of networks based on biologically realistic parameters. J. Physiol. Paris 104, 51–60. Voges, N., Schüz, A., Aertsen, A., and Rotter, S. (2010). A modeler's view on the spatial structure of intrinsic horizontal connectivi...

    2010

  46. [1594]

    Stam, C.J. (2014). Modern network science of neurological disorders. Nat. Rev. Neurosci. 15, 683–695. Stam, C.J., and de Bruin, E.A. (2004). Scale‐free dynamics of global functional connectivity in the human brain. Hum. Brain Mapp. 22, 97–109. Stanley, M.L., Moussa, M.N., Paol...

    2014

  47. [1619]

    Zaslavsky, G.M. (2002). Chaos, fractional kinetics, and anomalous transport. Phys. Rep. 371, 461–580. Zelenyi, L.M., and Milovanov, A.V. (2004). Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics. Phys. Usp. 47,

    2002

  48. [2109]

    Pecora, L.M., Sorrentino, F., Hagerstrom, A.M., Murphy, T.E., and Roy, R. (2014). Cluster synchronization and isolated desynchronization in complex networks with symmetries. Nat. Commun. 5,

    2014

  49. [2198]

    Sethna, J.P., Dahmen, K.A., and Myers, C.R. (2001). Crackling noise. Nature 410, 242–250. Sethna, J.P. (2021). Statistical mechanics: entropy, order parameters, and complexity (Vol. 14). Oxford, U.K: Oxford University Press. Severino, F.P.U., Ban, J., Song, Q., Tang, M., Bianc...

    2001

  50. [2454]

    Shanker, O. (2007). Defining dimension of a complex network. Mod. Phys. Lett. B 21, 321–326. Shapiro, B. (1982). Renormalization-group transformation for the Anderson transition. Phys. Rev. Lett. 48,

    2007

  51. [2521]

    Moretti, P., and Zaiser, M. (2019). Network analysis predicts failure of materials and structures. Proc. Natl. Acad. Sci. U.S.A. 116, 16666–16668. Morone, F., Leifer, I., and Makse, H.A. (2020). Fibration symmetries uncover the building blocks of biological networks. Proc. Nat...

    2019

  52. [4079]

    Peliti, L. (1985). Path integral approach to birth-death processes on a lattice. J. Phys. 46, 1469–1483. Pennec, X. (2006). Intrinsic statistics on Riemannian manifolds: basic tools for geometric measurements. J. Math. Imaging Vis. 25, 127–154. Peraza, L.R., Díaz-Parra, A., Ke...

    1985

  53. [4086]

    small-world

    Miller, K.L., Alfaro-Almagro, F., Bangerter, N.K., Thomas, D.L., Yacoub, E., Xu, J., Bartsch, A.J., Jbabdi, S., Sotiropoulos, S.N., Andersson, J.L., and Griffanti, L. (2016). Multimodal population brain imaging in the UK Biobank prospective epidemiological study. Nat. Neurosci...

    2016

  54. [4747]

    Priesemann, V., and Shriki, O. (2018). Can a time varying external drive give rise to apparent criticality in neural systems? PLoS Comput. Biol. 14, e1006081. Puglisi, A., Sarracino. A, and Vulpiani, A. (2017). Temperature in and out of equilibrium: a review of concepts tools ...

    2018

  55. [5319]

    Litwin-Kumar, A, and Doiron, B. (2012). Slow dynamics and high variability in balanced cortical networks with clustered connections. Nat. Neurosci. 15, 1498–1505. Liu, Y., Dehmamy, N., and Barabási, A.L. (2021). Isotopy and energy of physical networks. Nat. Phys. 17, 216–222 L...

    2012

  56. [5515]

    Ng, B., Varoquaux, G., Poline, J.B., Greicius, M., and Thirion, B. (2015). Transport on Riemannian manifold for connectivity-based brain decoding. IEEE Trans. Med. Imaging 35, 208–216. Ng, B., Varoquaux, G., Poline, J.B., Thirion, B., Greicius, M.D., and Poston, K.L. (2017). D...

    2015

  57. [5990]

    Vincent, J.L., Patel, G.H., Fox, M.D., Snyder, A.Z., Baker, J.T., Van Essen, D.C., Zempel, J.M., Snyder, L.H., Corbetta, M., and Raichle, M.E. (2007). Intrinsic functional architecture in the anaesthetized monkey brain. Nature 447, 83-86. Vitelli, V., and Turner, A.M. (2004). ...

    2007

  58. [6175]

    Muñoz, M.A., Juhász, R., Castellano, C., and Ódor, G. (2010). Griffiths phases on complex networks. Phys. Rev. Lett. 105, 128701. Nakao, H., and Mikhailov, A.S. (2010). Turing patterns in network-organized activator-inhibitor systems. Nat. Phys. 6,

    2010

  59. [8462]

    Jones, M.S., Macdonald, K.D., Choi, B., Dudek, F.E., and Barth, D.S. (2000). Intracellular correlates of fast (200 Hz) electrical oscillations in rat somatosensory cortex. J. Neurophysiol. 84, 1505–1518. Jost, J. (1997). Compact Riemann surfaces. Springer-Verlag. Jost, J., and...

    2000

  60. [9910]

    Millán, A.P., Torres, J.J., and Bianconi, G. (2020). Explosive higher-order Kuramoto dynamics on simplicial complexes. Phys. Rev. Lett. 124, 218301. Millán, A.P., Torres, J.J., and Bianconi, G. (2019). Synchronization in network geometries with finite spectral dimension. Phys....

    2020

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.