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REVIEW 3 major objections 5 minor 53 references

Graph Analysis of Neuronal-Culture Connectivity Derived from a Reservoir-Computing Model

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper claims that the reservoir-computed connectivity map of neuronal cultures can be read as an adjacency matrix, and that node centrality computed on it correlates with measured firing and bursting at each electrode.

desk verdict The simulation benchmark is solid and worth a look; the experimental validation is compromised by circularity and post-hoc selection. read the letter →

arxiv 2608.09773 v1 pith:3G7KVJK4 submitted 2026-08-10 q-bio.NC physics.comp-ph

Ilya Auslender , Giorgio Letti , Yasaman Heydari , Lorenzo Pavesi This is my paper · ORCID
classification q-bio.NCphysics.comp-ph
keywords neuronalculturesmicroelectrodearraysreservoircomputingconnectivityinferencegraphtheorycentralitymeasuresintrinsicmatrixnetworkneuroscience
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 the connectivity map inferred by a reservoir-computing model from microelectrode-array recordings—called the Intrinsic Connectivity Matrix (ICM)—can be treated as an effective adjacency matrix of the cultured neuronal network. The authors compute standard graph-theoretic centrality scores on that matrix and show that these scores correlate, at the level of individual electrodes, with measured spiking and bursting activity in both in-vitro cultures and simulated networks. They also show that agreement between the inferred ICM and the known ground-truth wiring of simulated networks is highest at an intermediate inhibition level and degrades as network complexity grows. If the interpretation holds, it gives experimentalists a way to measure network-level organization and node importance directly from spike recordings, without direct anatomical tracing.

What carries the argument

The central object is the Intrinsic Connectivity Matrix (ICM), denoted $T_0$, obtained by training a reservoir-computing model on instantaneous spike-rate sequences and then linearizing the trained operator while removing the influence of history; its entries are directed, signed weights (positive excitatory, negative inhibitory). The paper's operative identity is $T_0 \simeq A$, treating the ICM as an effective adjacency matrix for graph-theoretic analysis. The centrality measures computed on $T_0$ (in/out degree, Katz, eigenvector, PageRank) are the machinery that bridges structure and activity: they are the independent variables whose Pearson correlations with measured firing, bursting, and ISI statistics quantify topology–dynamics coupling. The preprocessing threshold $w'_{th}=0.2$ (Eq. 15) sparsifies noise-dominated weights before graph metrics are computed, and the confidence measure $\Gamma$ (Eq. 3) quantifies stability across reservoir initializations.

What would settle it

Simulate a ground-truth network whose adjacency matrix is known, train the RC model to obtain an ICM, then recompute the centrality–activity correlations after randomly permuting the entries of the ICM while preserving the distribution of edge weights and node degrees; if the permuted matrices yield correlations as strong as the unpermuted ones, the structural content of the ICM is not what drives the reported associations.

Watch

Extended reading notes

Core claim

Treating the reservoir-computed ICM as the adjacency matrix, $T_0 \simeq A$ (Eq. 13), the paper establishes that node centrality measures—effective and absolute in-degree, out-degree, Katz, eigenvector, and PageRank—computed on the inferred connectivity correlate with node-level observables such as average firing rate, bursting rate, and inter-spike-interval statistics, in both simulated and MEA-recorded cultures. Across the 40 simulated networks and 170 experimental recordings (49 used after filtering for data richness), the correlations are consistently positive and strongest for Katz centrality and in-degree measures, while burst duration shows only weak associations. The paper further reports that the ICM's fidelity to ground-truth connectivity is maximal at an intermediate inhibitory–excitatory ratio and that reservoir-computing model performance declines with increasing spectral radius. Consequently, the authors conclude that the graph-theoretic interpretation of the ICM both provides a scalable framework for functional network characterization and independently supports the validity of the reservoir-computing inference.

Load-bearing premise

The argument rests on the assumption that the inferred connectivity matrix reflects the culture's actual wiring rather than being an artifact of training on the very activity traces it is compared with.

Editorial extensions

If this is right

  • If $T_0 \simeq A$ holds, graph-theoretic descriptors of cultured networks can be computed from ordinary MEA recordings, giving a scalable summary of culture-level organization without invasive tracing.
  • Node centrality becomes a candidate predictor of local activity: electrodes high in in-degree or Katz centrality are expected to show higher firing and bursting rates, offering a structure-based readout for experiments.
  • The inhibition-balance result implies reservoir-computing connectivity inference is most reliable at intermediate inhibitory–excitatory ratios, so cultures outside that regime should be interpreted with caution.
  • The consistent structure–activity correlations in both simulations and experiments give independent support to the reservoir-computing inference model, extending its validity to datasets without ground-truth connectivity.

Reading between the lines

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

  • A natural null-model test would permute ICM edge weights or degrees and recompute centrality–activity correlations; if the null reproduces the observed correlations, the inferred matrix would be shown to carry no structure beyond the activity statistics used to train the model.
  • The framework is portable to higher-density recording systems and in-vivo large-scale electrophysiology, where the authors expect denser sampling to sharpen the centrality–activity link, but this is not tested in the paper.
  • The observation that evoked-response training yields smaller inferred networks suggests stimulus-driven activity highlights a different subgraph than spontaneous activity; an explicit comparison of graph metrics between the two training conditions could reveal whether the effective connectivity is state-dependent.
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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 / 5 minor

Summary. The paper proposes a pipeline that takes the Intrinsic Connectivity Matrix (ICM) inferred by a reservoir-computing (RC) model from multichannel MEA recordings, treats the ICM as an effective adjacency matrix (T0 ≈ A, Eq. 13), and computes graph-theoretic centralities whose relationships with node- and culture-level activity measures are then examined. The authors first benchmark the RC inference against known ground-truth adjacency matrices in NEST simulations, studying how inhibitory balance and spectral radius affect inference accuracy, and then report correlations between centrality measures and firing/burst/ISI statistics in both simulations and experimental MEA recordings. The claimed contribution is a scalable graph-theoretic characterization of neuronal cultures and, at the same time, a validation of the RC-based connectivity inference.

Significance. The in silico benchmarking against ground-truth adjacency matrices (Section 3.2, Table 2, Fig. 2) is a genuine strength: it provides controlled evidence about when the linearized ICM approximates the structural connectivity, and it is independent of the experimental circularity discussed below. The application of established centrality measures to MEA-derived connectivity is also potentially useful for moving beyond electrode-wise activity summaries. However, the paper's central validation claim—that the experimental centrality–activity correlations support the RC inference and the T0 ≈ A assumption—is not yet established because the ICM is trained on the same spike-rate traces that supply the dependent variables. A surrogate-data control is needed before the experimental correlations can be interpreted as evidence for the inferred connectivity. With that control added, this would be a valuable contribution to functional network analysis of in vitro cultures.

major comments (3)
  1. [§2.6, Eq. (13); §3.4, Fig. 6] The central experimental claim is not supported as it stands because of circularity. The ICM T0 is obtained by training the RC model on the instantaneous spike-rate sequences of each recording, and the dependent variables (AFR, ABR, μISI, σISI) are computed from the same recordings. Any learned operator that reproduces the training traces must encode per-electrode firing statistics, so centrality measures derived from T0 will be correlated with those statistics even if T0 carries no genuine cross-electrode structural information. The observation in Fig. 6A that ICM-based centralities correlate with firing rate more strongly than ground-truth-based centralities is the expected signature of this imprinting, not evidence that T0 ≈ A. The authors themselves note in Section 4.6 that some correlations 'may appear mathematically expected from an analytical perspective,' which is precisely the unresolved issue. To validate the experimental claim, the authors should add a surrogate-data null control: for example, train the RC model on temporally shuffled or phase-randomized ISR traces that preserve each electrode's rate and spectral statistics but destroy cross-electrode structure, and show that the Fig. 6B correlations disappear or become significantly weaker. Alternatively, they could compare against a null model that preserves node-strength and degree distributions while randomizing edge placement. Without such a control, the experimental correlations in Fig. 6 do not validate the RC inference.
  2. [§2.6.1, Eq. (15)] The threshold w'_th = 0.2 is selected via F1-score analysis on simulations (Section 3.2) and then applied unchanged to experimental ICMs. Simulations use Izhikevich/NEST networks with known ground truth, while experimental recordings are noisier and may have a different effective connectivity scale, so a threshold optimized in silico need not be appropriate for the experimental data. Because the threshold directly determines which edges survive and therefore affects all downstream centrality measures, the authors should (i) justify the transferability of the threshold to experimental data, and (ii) report a sensitivity analysis of the Fig. 6 correlations over a range of thresholds (for example, 0.1–0.3) to show that the conclusions do not hinge on this specific choice.
  3. [§3.4, Fig. 6B] The experimental dataset used for Fig. 6B is a post-hoc selection of 49 out of 170 recordings based on the data-richness parameter q, and the reported correlations are not corrected for multiple comparisons across six centrality measures and several observables. The selection criterion is itself correlated with RC model performance, and the paper states that weaker correlations were associated with low q; retaining only high-q recordings therefore inflates the apparent strength of the effect. The authors should report the full 170-recording analysis or explicitly show how the correlations vary with q rather than filtering, justify the selection before presenting the correlations, and provide multiple-comparison-corrected confidence intervals or p-values (for example, FDR or permutation-based) for any claim of 'statistically robust associations.'
minor comments (5)
  1. [§2.4] The sentence 'We focus on the some common measures reported in many MEA measurements studies' contains a typo; 'the some' should read 'some'.
  2. [Fig. 6 caption] The caption contains a typo: 'buttom right' should be 'bottom right.'
  3. [§2.7.1] The reference to the DLP stimulation system appears as 'DLP system []' with an empty citation; this should either be completed or removed.
  4. [Table 2] The missing entries in the 'Full Excitatory' row for inhibitory metrics are explained only after the table; using an explicit 'N/A' or en-dash with a table note would be clearer.
  5. [§3.2.1, Fig. 3C] The gamma-like fit 'ax^p e^{-qx}' is introduced without defining the parameters or reporting the fit uncertainty; adding confidence intervals or the fitted parameter values would make the claimed optimal inhibition regime more quantitative.

Circularity Check

2 steps flagged · score 7.0 of 10

Fig. 6 centrality–activity correlations are trained-data imprinting, not independent validation of Eq. (13); a surrogate-data null control is missing.

  1. fitted input called prediction [Sec. 2.2–2.3 (training), Eq. (13) (T0 as adjacency), Sec. 3.4 / Fig. 6 (centrality–activity correlations)]
    "Another outcome of the model was the inference of the network's connectivity map. This was achieved by linearizing the operator in Eq.(2) and removing the influence of previous time steps on the connectivity. We therefore defined the resulting matrix as the Intrinsic Connectivity Matrix (ICM), denoted by T0... We evaluated several node centrality measures, namely in- and out-degree, Katz, eigenvector, and PageRank centralities, against node-level activity metrics computed for each node."

    T0 is derived from an RC model trained to minimize loss on the same instantaneous-spike-rate sequences from which AFR, ABR, and ISI observables are computed. Eq. (13) promotes this fitted linearized operator to an adjacency matrix, and Sec. 3.4 correlates T0-based centralities with those same observables as support for the RC inference. If the learned operator merely recodes per-electrode firing statistics (e.g., in-degree sums inferred incoming weights, which inherit the fitted rate structure), the correlations are expected by construction and carry no information about whether T0 approximates structural connectivity A. Fig.

  2. self citation load bearing [Sec. 2.6, Eq. (13)]
    "A central working hypothesis of this study is to treat the ICM as an effective adjacency matrix and to apply graph-theoretic measures to T0 in order to characterize structural properties of the culture. This assumption is supported by previous validation [26], where simulations performed with NEST demonstrated that the inferred ICM exhibits, on average, high accuracy when benchmarked against the ground-truth adjacency matrix... we adopt the approximation T0 ≃ A."

    For the experimental culture data there is no ground-truth adjacency matrix, so Eq. (13) is the load-bearing bridge that turns the fitted T0 into a structure whose centralities can be 'validated' against activity. The stated support for this bridge is a self-citation to the authors' prior paper [26], which used the same RC training procedure; that prior validation is not independently re-derived here. Although Sec. 3.2 provides an in-house NEST benchmark of T0 vs. A, that benchmark cannot justify the experimental centrality-activity correlations, which remain entangled with the training data. Section 4.6 concedes that some correlations 'may appear mathematically expected from an analytical perspective,' precisely the unresolved point.

full rationale

The experimental half of the validation loop is circular: the same recordings supply both the training data for the RC model and the dependent variables (AFR, ABR, ISI) against which T0-derived centralities are correlated. Consequently, the Fig. 6 associations do not independently establish that T0 approximates the structural adjacency matrix A; they are equally consistent with T0 having recoded per-electrode firing statistics during training. The in-silico benchmark in Section 3.2/Table 2 is genuinely independent and valuable, which prevents a score of 8–10, but it validates T0 against ground-truth A in simulations and does not rescue the experimental claim. The paper's own observation that ICM-based correlations are often higher than ground-truth-based correlations (Fig. 6A) is the expected signature of this imprinting, and Section 4.6 explicitly acknowledges that some correlations 'may appear mathematically expected from an analytical perspective.' A rate-matched surrogate or permutation control, in which electrode identities or training traces are shuffled, would be needed to determine whether the reported associations reflect genuine cross-electrode structure or simply training-data imprinting. For these reasons the central experimental validation is partially circular, and the self-citation in Eq. (13) is load-bearing for the experimental interpretation, yielding a score of 7.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claim rests on treating the RC-inferred ICM as an adjacency matrix and on the stability of correlations computed from it. Key free parameters include the threshold, hyperparameters, and phenomenological fit parameters. No new physical entities are introduced. The most fragile assumption is the independence between the inferred connectivity and the activity measures used for correlation.

free parameters (7)
  • ICM threshold w'_th = 0.2
    Set by F1-score analysis on simulated networks (Sec. 2.6.1) and applied to experimental ICMs; a hand-chosen cutoff that determines which edges enter the graph analysis.
  • Reservoir dimension multiplier m = 5
    Chosen as a practical compromise between representational richness and computational cost (Sec. 2.3); affects ICM quality.
  • Memory parameter alpha = optimized in [0.1, 0.9]
    Optimized to maximize connectivity confidence Gamma (Sec. 2.3); inherited from prior model.
  • Katz damping alpha_K = not stated
    Distance cost factor in Katz centrality (Eq. 5); value not reported, affects centrality values.
  • PageRank damping alpha_p = not stated
    Damping factor in PageRank (Eq. 7); standard value presumably used but not reported.
  • Gain parameter g = not reported
    Effective network gain in the exponential gain model approximately e^{g Delta w} (Sec. 3.3), fitted to simulation and experimental data.
  • Gamma-like fit parameters a, p, q = fitted
    Phenomenological fit a x^p e^{-qx} for performance vs inhibition (Sec. 3.2.2), fitted to the data.
assumptions (5)
  • domain assumption ICM is an effective adjacency matrix (T0 approximately equal to A)
    Stated in Sec. 2.6, Eq. (13); all graph-theoretic analysis depends on this identification.
  • domain assumption Linearized RC model captures leading-order causal interactions
    Required for the ICM to reflect structure; acknowledged in Sec. 2.2 and 4.1 as an approximation.
  • domain assumption Training data are sampled from the same dynamics used for validation and correlation
    The ICM and the dependent variables come from the same recordings, so independence of the two domains is assumed, not established.
  • standard math Standard graph centrality definitions and their convergence conditions
    Katz, eigenvector, and PageRank definitions (Eqs. 5-7) rely on standard results, e.g., convergence for alpha less than or equal to 1/rho(A).
  • domain assumption Node-level observations are statistically independent for Pearson correlation
    Correlations pool node-level data across electrodes within cultures, but nearby electrodes are spatially correlated; this independence is assumed in significance testing.

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Cite this review

Pith. "Pith review of Graph Analysis of Neuronal-Culture Connectivity Derived from a Reservoir-Computing Model." pith.science (2026). https://pith.science/paper/3G7KVJK4

@misc{pith2026260809773,
  author       = {Pith},
  title        = {Pith review of: Graph Analysis of Neuronal-Culture Connectivity Derived from a Reservoir-Computing Model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3G7KVJK4}},
  note         = {Machine review of arXiv:2608.09773}
}
read the original abstract

Graph-theoretical analysis offers a principled framework for quantifying emergent dynamics in neuronal cultures. Here, we present an analytical pipeline for inferring network-level properties of in vitro cortical cultures from multichannel electrophysiological recordings. The approach builds on a recently proposed Reservoir Computing (RC) framework (Auslender et al., 2025), which enables direct extraction of an Intrinsic Connectivity Map (ICM) from neural activity. We interpret the ICM as an effective adjacency matrix and apply graph-theoretic centrality measures to quantify node- and edge-level contributions to the culture's collective dynamics. We systematically evaluate both local and global graph metrics and examine their relationships with experimentally measured activity features, including firing rates and network-level descriptors. To validate the inference procedure, we also simulate the experimental environment, enabling controlled benchmarking of the RC-derived connectivity against a known ground-truth adjacency matrix and assessment of model performance as a function of graph structure. Our results demonstrate statistically robust associations, of varying strength, between graph-theoretic measures and experimentally observed activity patterns. These findings additionally support the validity of the RC-based connectivity inference and establish a scalable, data-driven framework for functional network characterization in neuronal culture systems.

Figures

Figures reproduced from arXiv: 2608.09773 by the authors.

Figure 1
Figure 1. Schematic pipeline of the present study. Electrophysiological signals emerge from in-vitro or in-silico neuronal networks (simulated in NEST [31]), from which spatio-temporal activity patterns are preprocessed and quantitative observables (e.g., firing rate) are extracted. The preprocessed data are further transformed into training samples for the RC model, which infers the Intrinsic Connectivity Matrix (ICM), denot… view at source ↗
Figure 2
Figure 2. Connectivity inference by the RC model via the Intrinsic Connectivity Matrix (ICM). (A–C) Predicted vs. ground-truth structural weights for all 40 simulated networks, grouped by inhibitory–excitatory ratio: (A) fully excitatory, η < 0.1 (14 720 edges; 9 networks); (B) low inhibition, 0.1 ≤ η < 0.5 (12 928 edges; 23 networks); (C) high inhibition, η ≥ 0.5 (17 728 edges; 8 networks). For each network, weights were nor… view at source ↗
Figure 2
Figure 2. B 0.922 0.798 0.441 0.796 (0.27) 0.482 (−0.17) 0.95 0.692 High Inhibition, η ≥ 0.5, [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figures from the paper (4 more)
Figure 3
Figure 3. Figure 3: Effect of global graph measures on RC-model performance. (A) Pearson correlation map between ground-truth graph measures (vertical axis) and RC-model performance metrics (horizontal axis) for both NEST simulations and MEA experiments. (B) ICM confidence (Γ) does not ne…
Figure 4
Figure 4. Figure 4: Dependence of culture-level observables on global connectivity properties. (A) Pearson correlation map between ground-truth graph measures (vertical axis) and culture observables (horizontal axis) for both NEST simulations and MEA experiments. (B)–(C) Mean firing rate …
Figure 5
Figure 5. Figure 5: Example map of an analyzed neuronal culture obtained from a MEA experiment. The 8 × 8 grid corresponds to a MEA chip with 60 electrodes (64 positions excluding the four corner sites), where each pixel represents an electrode and, correspondingly, a node in the network.…
Figure 6
Figure 6. Figure 6: Pearson correlations between node centrality measures and node-level observables. (A) NEST simulation data; (B) MEA experimental dataset—49 selected recordings (out of 170 total) with the highest data-richness parameter q, previously shown to correlate with Reservoir C…

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Works this paper leans on

53 extracted references · 27 canonical work pages

  1. [36]

    From structure to activity: Using centrality measures to predict neuronal activity,

    J. M. Fletcher and T. Wennekers, “From structure to activity: Using centrality measures to predict neuronal activity,”International Journal of Neural Systems, vol. 28, no. 02, p. 1 750 013, 2018, PMID: 28076982.DOI: 10 . 1142 / S0129065717500137eprint: https : / / doi . org / 10 . 1142 / S0129065717500137. [Online]. Available:https://doi.org/10.1142/S0129...

    work page doi:10.1142/s0129065717500137 2018

  2. [1]

    E. R. Kandel, J. H. Schwartz, T. M. Jessell, S. A. Siegelbaum, and A. J. Hudspeth,Principles of Neural Science, 5th ed. New York: McGraw-Hill, 2013

    work page 2013

  3. [2]

    Network neuroscience,

    D. S. Bassett and O. Sporns, “Network neuroscience,”Nature Neuroscience, vol. 20, no. 3, pp. 353–364, 2017. DOI:10.1038/nn.4502

    doi:10.1038/nn.4502 2017

  4. [3]

    Neuronal graphs: A graph theory primer for microscopic, functional networks,

    C. J. Nelson and S. Bonner, “Neuronal graphs: A graph theory primer for microscopic, functional networks,” Frontiers in Neural Circuits, 2021.DOI:10.3389/fncir.2021.662882

    arXiv 2021

  5. [4]

    The economy of brain network organization,

    E. Bullmore and O. Sporns, “The economy of brain network organization,”Nature Reviews Neuroscience, vol. 13, no. 5, pp. 336–349, 2012.DOI:10.1038/nrn3214

    doi:10.1038/nrn3214 2012

  6. [5]

    Complex brain networks: Graph theoretical analysis of structural and functional systems,

    E. Bullmore and O. Sporns, “Complex brain networks: Graph theoretical analysis of structural and functional systems,”Nature Reviews Neuroscience, vol. 10, no. 3, pp. 186–198, 2009.DOI:10.1038/nrn2575

    doi:10.1038/nrn2575 2009

  7. [6]

    Complex network measures of brain connectivity: Uses and interpretations,

    M. Rubinov and O. Sporns, “Complex network measures of brain connectivity: Uses and interpretations,” NeuroImage, vol. 52, no. 3, pp. 1059–1069, 2010.DOI:10.1016/j.neuroimage.2009.10.003

    doi:10.1016/j.neuroimage.2009.10.003 2010

  8. [7]

    The hubs of the human connectome are generally implicated in the anatomy of brain disorders,

    N. A. Crossley et al., “The hubs of the human connectome are generally implicated in the anatomy of brain disorders,”Brain, vol. 137, no. 8, pp. 2382–2395, 2014.DOI:10.1093/brain/awu132

    work page doi:10.1093/brain/awu132 2014

Show all 53 references
  1. [8]

    Micro-connectomics: Probing the organization of neuronal networks at the cellular scale,

    M. Schröter, O. Paulsen, and E. T. Bullmore, “Micro-connectomics: Probing the organization of neuronal networks at the cellular scale,”Nature Reviews Neuroscience, vol. 18, pp. 131–146, 2017.DOI: 10.1038/nrn. 2016.182

    2017 doi

  2. [9]

    Contributions and challenges for network models in cognitive neuroscience,

    O. Sporns, “Contributions and challenges for network models in cognitive neuroscience,”Nature Neuroscience, vol. 17, no. 5, pp. 652–660, 2014.DOI:10.1038/nn.3690

    2014 doi

  3. [10]

    The human connectome: A structural description of the human brain,

    O. Sporns, G. Tononi, and R. Kötter, “The human connectome: A structural description of the human brain,” PLoS Computational Biology, vol. 1, no. 4, e42, 2005.DOI:10.1371/journal.pcbi.0010042

    2005 doi

  4. [11]

    The wu-minn human connectome project: An overview,

    D. C. Van Essen, S. M. Smith, D. M. Barch, T. E. J. Behrens, E. Yacoub, and K. Ugurbil, “The wu-minn human connectome project: An overview,”NeuroImage, vol. 80, pp. 62–79, 2013.DOI: 10.1016/j.neuroimage. 2013.05.041

    2013 doi

  5. [12]

    The connectomics of brain disorders,

    A. Fornito, A. Zalesky, and M. Breakspear, “The connectomics of brain disorders,”Nature Reviews Neuroscience, vol. 16, no. 3, pp. 159–172, 2015.DOI:10.1038/nrn3901

    2015 doi

  6. [13]

    Diestel,Graph Theory, 5th ed

    R. Diestel,Graph Theory, 5th ed. Berlin: Springer, 2017.DOI:10.1007/978-3-662-53622-3

    2017 doi

  7. [14]

    Newman,Networks: An Introduction

    M. Newman,Networks: An Introduction. Oxford: Oxford University Press, 2010

    2010

  8. [15]

    From simple graphs to the connectome: Networks in neuroimaging,

    O. Sporns, “From simple graphs to the connectome: Networks in neuroimaging,”Neuroimage, vol. 62, no. 2, pp. 881–886, 2012.DOI:10.1016/j.neuroimage.2011.08.085 20 APREPRINT- AUGUST11, 2026

    2012 doi

  9. [17]

    Distributed network interactions and their emergence in developing neocortex,

    G. B. Smith, B. Hein, D. E. Whitney, D. Fitzpatrick, and M. Kaschube, “Distributed network interactions and their emergence in developing neocortex,”Nature Neuroscience, vol. 21, no. 11, pp. 1600–1608, 2018.DOI: 10.1038/s41593-018-0247-5

    2018 doi

  10. [18]

    What we can do and what we cannot do with fmri,

    N. K. Logothetis, “What we can do and what we cannot do with fmri,”Nature, vol. 453, no. 7197, pp. 869–878, 2008.DOI:10.1038/nature06976

    2008 doi

  11. [19]

    Large-scale recording of neuronal ensembles,

    G. Buzsáki, “Large-scale recording of neuronal ensembles,”Nature Neuroscience, vol. 7, no. 5, pp. 446–451, 2004.DOI:10.1038/nn1233

    2004 doi

  12. [20]

    The big and the small: Challenges of imaging the brain’s circuits,

    J. W. Lichtman and W. Denk, “The big and the small: Challenges of imaging the brain’s circuits,”Science, vol. 334, no. 6056, pp. 618–623, 2011.DOI:10.1126/science.1209168

    2011 doi

  13. [22]

    Multi-electrode array technologies for neuroscience and cardiology,

    M. E. Spira and A. Hai, “Multi-electrode array technologies for neuroscience and cardiology,”Nature Nanotech- nology, vol. 8, no. 2, pp. 83–94, 2013.DOI:10.1038/nnano.2012.265

    2013 doi

  14. [23]

    Revealing neuronal function through micro- electrode array recordings,

    M. Obien, K. Deligkaris, T. Bullmann, D. Bakkum, and U. Frey, “Revealing neuronal function through micro- electrode array recordings,”Frontiers in Neuroscience, vol. 8, p. 423, 2015.DOI: 10.3389/fnins.2014.00423

    2015

  15. [24]

    Multiscale functional connectivity estimation on low-density neuronal cultures recorded by high-density cmos microelectrode arrays,

    A. Maccione, M. Garofalo, T. Nieus, M. Tedesco, L. Berdondini, and S. Martinoia, “Multiscale functional connectivity estimation on low-density neuronal cultures recorded by high-density cmos microelectrode arrays,” Journal of Neuroscience Methods, vol. 207, no. 2, pp. 161–171,...

    2012 doi

  16. [25]

    Network plasticity in cortical assemblies,

    M. Chiappalone, P. Massobrio, and S. Martinoia, “Network plasticity in cortical assemblies,”European Journal of Neuroscience, vol. 28, pp. 221–237, 2008.DOI:10.1111/j.1460-9568.2008.06259.x

    2008

  17. [26]

    Decoding neuronal networks: A reservoir computing approach for predicting connectivity and functionality,

    I. Auslender, G. Letti, Y . Heydari, C. Zaccaria, and L. Pavesi, “Decoding neuronal networks: A reservoir computing approach for predicting connectivity and functionality,”Neural Networks, vol. 184, p. 107 058, 2025,ISSN: 0893-6080.DOI: https://doi.org/10.1016/j.neunet.2024.10...

    2025

  18. [27]

    Model-free reconstruction of excitatory neuronal connectivity from calcium imaging signals,

    O. Stetter, D. Battaglia, J. Soriano, and T. Geisel, “Model-free reconstruction of excitatory neuronal connectivity from calcium imaging signals,”PLoS Computational Biology, vol. 8, no. 8, e1002653, 2012.DOI: 10.1371/ journal.pcbi.1002653

    2012

  19. [28]

    Transfer entropy—a model -free measure of effective con- nectivity for the neurosciences,

    R. Vicente, M. Wibral, M. Lindner, and G. Pipa, “Transfer entropy—a model -free measure of effective con- nectivity for the neurosciences,”Journal of Computational Neuroscience, vol. 30, pp. 45–67, 2011.DOI: 10.1007/s10827-010-0262-3

    2011 doi

  20. [29]

    A convolutional neural network for estimating synaptic connectivity from spike trains,

    D. Endo et al., “A convolutional neural network for estimating synaptic connectivity from spike trains,”Scientific Reports, vol. 11, no. 1, p. 12 087, 2021.DOI:10.1038/s41598-021-91244-w

    2021 doi

  21. [30]

    Functional connectivity in in vitro neuronal assemblies,

    D. Poli, V . P. Pastore, and P. Massobrio, “Functional connectivity in in vitro neuronal assemblies,”Frontiers in Neural Circuits, vol. 9, p. 57, 2015.DOI:10.3389/fncir.2015.00057

    2015

  22. [31]

    Nest (neural simulation tool),

    M.-O. Gewaltig and M. Diesmann, “Nest (neural simulation tool),”Scholarpedia, vol. 2, no. 4, p. 1430, 2007

    2007

  23. [32]

    Notes on regression and inheritance in the case of two parents,

    K. Pearson, “Notes on regression and inheritance in the case of two parents,”Proceedings of the Royal Society of London, vol. 58, pp. 240–242, 1895

  24. [33]

    Extremely rich repertoire of bursting patterns during the development of cortical cultures,

    D. A. Wagenaar, J. Pine, and S. M. Potter, “Extremely rich repertoire of bursting patterns during the development of cortical cultures,”BMC Neuroscience, vol. 7, p. 11, 2006.DOI:10.1186/1471-2202-7-11

    2006 doi

  25. [34]

    A self-adapting approach for the detection of bursts and network bursts in neuronal cultures,

    V . Pasquale, S. Martinoia, and M. Chiappalone, “A self-adapting approach for the detection of bursts and network bursts in neuronal cultures,”Journal of computational neuroscience, vol. 29, no. 1, pp. 213–229, 2010

    2010

  26. [35]

    Burst detection algorithms for the analysis of spatio-temporal patterns in cortical networks of neurons,

    M. Chiappalone, A. Novellino, I. Vajda, A. Vato, S. Martinoia, and J. van Pelt, “Burst detection algorithms for the analysis of spatio-temporal patterns in cortical networks of neurons,”Neurocomputing, vol. 65, pp. 653–662, 2005

    2005

  27. [37]

    A new status index derived from sociometric analysis,

    L. Katz, “A new status index derived from sociometric analysis,”Psychometrika, vol. 18, no. 1, pp. 39–43, 1953

    1953

  28. [38]

    Factoring and weighting approaches to status scores and clique identification,

    P. Bonacich, “Factoring and weighting approaches to status scores and clique identification,”Journal of Mathe- matical Sociology, vol. 2, no. 1, pp. 113–120, 1972.DOI:10.1080/0022250X.1972.9989806 21 APREPRINT- AUGUST11, 2026

    1972

  29. [39]

    Power and centrality: A family of measures,

    P. Bonacich, “Power and centrality: A family of measures,”American Journal of Sociology, vol. 92, no. 5, pp. 1170–1182, 1987.DOI:10.1086/228631

    1987 doi

  30. [40]

    The anatomy of a large-scale hypertextual web search engine,

    S. Brin and L. Page, “The anatomy of a large-scale hypertextual web search engine,”Computer Networks and ISDN Systems, vol. 30, no. 1–7, pp. 107–117, 1998.DOI:10.1016/S0169-7552(98)00110-X

    1998 doi

  31. [41]

    Simple model of spiking neurons,

    E. M. Izhikevich, “Simple model of spiking neurons,”IEEE Transactions on neural networks, vol. 14, no. 6, pp. 1569–1572, 2003

    2003

  32. [42]

    Which model to use for cortical spiking neurons?

    E. M. Izhikevich, “Which model to use for cortical spiking neurons?”IEEE transactions on neural networks, vol. 15, no. 5, pp. 1063–1070, 2004

    2004

  33. [43]

    Self-organization of in vitro neuronal assemblies drives to complex network topology,

    P. C. Antonello, T. F. Varley, J. Beggs, M. Porcionatto, O. Sporns, and J. Faber, “Self-organization of in vitro neuronal assemblies drives to complex network topology,”Elife, vol. 11, e74921, 2022

    2022

  34. [44]

    Measuring the accuracy of diagnostic systems,

    J. A. Swets, “Measuring the accuracy of diagnostic systems,”Science, vol. 240, no. 4857, pp. 1285–1293, 1988. DOI:10.1126/science.3287615

    1988 doi

  35. [45]

    The relationship between precision-recall and roc curves,

    J. Davis and M. Goadrich, “The relationship between precision-recall and roc curves,” inProceedings of the 23rd International Conference on Machine Learning, 2006, pp. 233–240.DOI:10.1145/1143844.1143874

    2006

  36. [46]

    C. J. van Rijsbergen,Information Retrieval. Butterworths, 1979

    1979

  37. [47]

    Evaluation: From precision, recall and f-measure to roc, informedness, markedness and correlation,

    D. M. W. Powers, “Evaluation: From precision, recall and f-measure to roc, informedness, markedness and correlation,”Journal of Machine Learning Technologies, vol. 2, no. 1, pp. 37–63, 2011

    2011

  38. [48]

    Optimal control of transient dynamics in balanced networks supports generation of complex movements,

    G. Hennequin, T. P. V ogels, and W. Gerstner, “Optimal control of transient dynamics in balanced networks supports generation of complex movements,”Neuron, vol. 82, no. 6, pp. 1394–1406, 2014.DOI: 10.1016/j. neuron.2014.04.045

    2014 doi

  39. [49]

    Memory traces in dynamical systems,

    S. Ganguli, D. Huh, and H. Sompolinsky, “Memory traces in dynamical systems,”Proceedings of the National Academy of Sciences, vol. 105, no. 48, pp. 18 970–18 975, 2008.DOI:10.1073/pnas.0804451105

    2008 doi

  40. [50]

    Paradoxical effects of external modulation of inhibitory interneurons,

    M. V . Tsodyks, W. E. Skaggs, T. J. Sejnowski, and B. L. McNaughton, “Paradoxical effects of external modulation of inhibitory interneurons,”Journal of Neuroscience, vol. 17, no. 11, pp. 4382–4388, 1997.DOI: 10.1523/ JNEUROSCI.17-11-04382.1997

    1997

  41. [51]

    Chaos in neuronal networks with balanced excitatory and inhibitory activity,

    C. van Vreeswijk and H. Sompolinsky, “Chaos in neuronal networks with balanced excitatory and inhibitory activity,”Science, vol. 274, no. 5293, pp. 1724–1726, 1996.DOI:10.1126/science.274.5293.1724

    1996

  42. [52]

    The asynchronous state in cortical circuits,

    A. Renart et al., “The asynchronous state in cortical circuits,”Science, vol. 327, no. 5965, pp. 587–590, 2010. DOI:10.1126/science.1179850

    2010 doi

  43. [53]

    Complex dynamics in recurrent cortical networks based on spatially realistic connec- tivities,

    N. V oges and L. Perrinet, “Complex dynamics in recurrent cortical networks based on spatially realistic connec- tivities,”Frontiers in Computational Neuroscience, vol. 6, p. 41, 2012.DOI:10.3389/fncom.2012.00041

    2012 arXiv

  44. [54]

    Generating coherent patterns of activity from chaotic neural networks,

    D. Sussillo and L. F. Abbott, “Generating coherent patterns of activity from chaotic neural networks,”Neuron, vol. 63, no. 4, pp. 544–557, 2009.DOI:10.1016/j.neuron.2009.07.018

    2009 doi

  45. [55]

    Technologies to study action potential propagation with a focus on hd-meas,

    V . Emmenegger, M. E. J. Obien, F. Franke, and A. Hierlemann, “Technologies to study action potential propagation with a focus on hd-meas,”Frontiers in cellular neuroscience, vol. 13, p. 457 375, 2019.DOI: 10.3389/fncel.2019.00159 22

    2019

Pith tools

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