Pith. sign in

REVIEW 4 major objections 3 minor 1 cited by

Distinct weak asymmetric interactions shape human brain functions as probability fluxes

T0 review · 4 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper claims that the human brain switches between tasks by making small, task-specific changes to the directional (antisymmetric) part of the couplings between brain regions, while the strong mutual (symmetric) couplings stay essential

desk verdict A genuinely new inference method with a plausible empirical story, but the central claim about task-dependent antisymmetric interactions is not yet established because the fitted matrices come without error bars. read the letter →

arxiv 2508.20961 v1 pith:W6CRPBYG submitted 2025-08-28 physics.bio-ph cond-mat.dis-nncond-mat.stat-mechphysics.data-anq-bio.NC

Yoshiaki Horiike , Shin Fujishiro This is my paper · ORCID
classification physics.bio-phcond-mat.dis-nncond-mat.stat-mechphysics.data-anq-bio.NC
keywords probabilityfluxnonequilibriumsteadystateasymmetricIsingmodelbrokendetailedbalancefMRIbraindynamicsenergy-efficientcomputationtask-dependentconnectivity
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

The paper argues that the human brain performs its many cognitive and motor functions not by raising its energy consumption, but by subtly modifying the directional part of the interaction network among brain regions. Analysing fMRI data from 590 adults at rest and during seven tasks, the authors find that the probability flux—the imbalance between forward and backward state transitions—forms a distinct pattern for each task, with circulating fluxes that indicate a nonequilibrium steady state. They fit an asymmetric Ising spin model to these fluxes and report that the symmetric part of the inferred interaction matrix is strong and similar across tasks, while the antisymmetric part is weak and task-dependent. The fitted model reproduces the observed flux patterns for most tasks (Pearson correlation above 0.7, working memory at 0.53), and fixing the interaction across tasks destroys the reconstruction. The claim is therefore that human brain function is a sequence of state transitions controlled by a small set of directional couplings.

What carries the argument

The key object is the probability flux on the hypercube of binarized brain states, defined as the difference between the forward and backward joint transition rates; its nonzero value is the microscopic signature of broken detailed balance. The inference machinery is an asymmetric Ising spin model, in which each of seven coarse-grained cortical clusters is a binary variable and the transition rate between states differing by one spin flip is taken to be the Arrhenius rate k exp[-beta sigma_i (sum_j J_ij sigma_j + h_i)]. The interaction matrix is decomposed into symmetric and antisymmetric parts, J_s = (J + J^T)/2 and J_a = (J - J^T)/2; the antisymmetric part is what generates the circulating

What would settle it

Generate synthetic time series from a 7-spin asymmetric Ising model with a known antisymmetric interaction matrix, run the paper's full inference pipeline on those series, and check whether the recovered antisymmetric part matches the known matrix. A mismatch would show that the task-dependent antisymmetric couplings inferred from fMRI are artifacts of applying a symmetric-derivation transition rate to asymmetric interactions.

Watch

Extended reading notes

Core claim

The central discovery claimed is that the functional identity of a brain state is carried by the antisymmetric part of the interaction matrix between seven coarse-grained cortical clusters. The symmetric (mutual) couplings are strong and nearly task-invariant; the antisymmetric (directional) couplings are visibly smaller and differ from task to task. This decomposition is obtained by inferring an asymmetric Ising spin system from the estimated transition rates and then writing the interaction matrix as J = J_s + J_a. The reconstructed probability fluxes match the empirical ones with r > 0.7 for seven of the eight conditions, and the match is lost when the interaction is forced to be task-ind

Load-bearing premise

The load-bearing premise is that the transition-rate formula used to infer the interactions—derived under the assumption of symmetric, reversible (detailed-balance) couplings—remains valid when the couplings are allowed to be asymmetric; if that extrapolation is wrong, the task-dependent directional couplings could be artifacts of the fitting procedure rather than properties of the brain.

Editorial extensions

If this is right

  • If the claim holds, task switching in the brain is a change in directional couplings, not in overall activation cost, giving a concrete mechanism for energy-efficient computation.
  • The probability-flux pattern becomes a functional observable: distinct tasks map to distinct flux cycles, so flux diagrams could be used to identify which cognitive operation is being performed.
  • The symmetric interaction scaffold can be treated as a fixed backbone, and only a small antisymmetric component needs to vary to produce task-specific dynamics; the model's success with task-dependent J and failure with task-independent J is direct evidence for this separation.
  • The same probability-flux inference method can be applied to other high-dimensional many-body time series to expose asymmetric interactions and nonequilibrium structure beyond the brain.

Reading between the lines

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

  • A testable extension is that targeted perturbation of a single directional coupling should alter the corresponding flux cycle without changing the symmetric backbone; this follows from the paper's mechanism but goes beyond its correlational analysis.
  • The working-memory failure (r = 0.53) hints that pairwise asymmetric interactions are not enough for at least one task; higher-order interactions or non-Markovian transitions might be needed, which the paper acknowledges as a future direction.
  • If the energy cost of changing couplings scales with their magnitude, the small antisymmetric values imply that the brain can store a large repertoire of task-specific directional modifications at near-zero metabolic overhead—a quantitative version of the paper's energy-efficiency intuition.
  • Because the transition-rate formula used for inference was derived under symmetric detailed balance, a rigorous nonequilibrium derivation of the same rate is the cleanest way to confirm whether the inferred antisymmetric structure is real; until then it should be read as conditional on that extrapolation.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 3 minor

Summary. The authors analyze public HCP fMRI data (590 subjects; rest plus seven tasks), coarse-grain 100 cortical parcels into 7 clusters by hierarchical clustering, binarize the time series into Ising states, and estimate hypercubic probability fluxes. They then infer an asymmetric Ising model from the empirical single-spin-flip transition rates using an Arrhenius-type rate formula, decompose the inferred interaction matrix into symmetric and antisymmetric parts, and report that the symmetric part is strong and task-independent while the antisymmetric part is weak and task-dependent (Fig. 4). The fitted model is used to reconstruct probability fluxes; Pearson correlations with the empirical fluxes are r = 0.53–0.96 (Fig. 5). The authors conclude that brain function is carried by task-dependent, subtle modifications of antisymmetric interactions, which may explain the brain's low task-related energy overhead.

Significance. If the central claim is established, the paper would offer a physically interpretable, low-energy mechanism for task switching and would extend probability-flux analysis to whole-cortex human fMRI data. The authors make useful methodological contributions: flux-based rather than static-correlation analysis, robustness checks across cluster numbers, binarization schemes, and Glauber rates, and a task-independent interaction control. The public HCP dataset is appropriate. However, the central mechanistic claims currently rest on an acknowledged extrapolation of the transition-rate formula to asymmetric interactions and on fitted parameters without uncertainty quantification; the validation against empirical fluxes is in-sample. The significance of the work is therefore conditional on these points being resolved.

major comments (4)
  1. [Methods, 'Infering Ising spin system from transition rates', Eq. (27)] The Arrhenius transition rate in Eq. (27) is derived from the detailed-balance condition with a symmetric interaction matrix. The text states: 'We assume the symmetric interaction matrix to derive equation (26) but we apply the result to the asymmetric interaction matrix.' This extrapolation is load-bearing for the central claim. For J ≠ J^T, the pseudo-Hamiltonian is not a true energy and the reverse-rate ratio implied by Eq. (27) does not correspond to a canonical stationary distribution; the inferred antisymmetric part βJ^(a) is therefore a direct product of this heuristic. Please derive the asymmetric rate from a consistent nonequilibrium model or validate the inference on synthetic data with a known asymmetric interaction matrix before interpreting βJ^(a) as a brain property.
  2. [Fig. 4c and Eqs. (28)–(29)] The central claim that the antisymmetric interaction is task-dependent is made by visual comparison of point estimates. No standard errors, confidence intervals, or significance tests are reported for βJ or βh. Since Eq. (28) defines a linear least-squares problem, the covariance of βJ is in principle available; alternatively, the bootstrap used for the flux analysis could be extended to the inference. This is essential because the antisymmetric entries are an order of magnitude smaller than the symmetric entries (color scales −0.1..0.1 vs −1..1 in Fig. 4), so the apparent cross-task differences may be sampling noise. The central conclusion is a comparative claim about fitted matrices, and comparative claims require uncertainty quantification.
  3. [Fig. 5 and 'To validate our inferred model'] The reported correlations (r = 0.53–0.96) are in-sample: the probability fluxes are reconstructed from model parameters fitted to the empirical transition rates of the same task. This measures goodness-of-fit, not predictive success. The task-independent interaction control (Extended Data Figs. 9–10) is more informative, but it is not a formal statistical test. Please add out-of-sample evaluation (e.g., split-half or cross-validation) or a null-model significance test of the improvement from task-dependent interactions. The working-memory result (r = 0.53) is acknowledged, but the interpretation of the remaining correlations as validation needs to be calibrated against the in-sample nature of the comparison.
  4. [Methods: 'Spatial coarse-graining...' and 'Temporal coarse graining...'] The number of clusters (7) is set by manually choosing a dendrogram threshold, and the binarization is one of three possible transformations. Extended Data Figs. 3–5 show robustness for the probability-flux diagrams, but not for the inferred interaction matrix βJ or external field βh. Because the inference operates on the 2^7 state space, these preprocessing choices are load-bearing for the structural claim. Please report the inferred symmetric/antisymmetric matrices for alternative cluster numbers and binarization schemes, or quantify the sensitivity in some other way.
minor comments (3)
  1. [Data availability / Code availability] Both sections contain placeholder text ('TBA' and 'zenodo.0000000'). Actual data and code links must be provided for reproducibility.
  2. [Methods heading] The heading 'Infering Ising spin system from transition rates' contains a typo; it should read 'Inferring'.
  3. [Supplementary Fig. S1e] The reported correlation (r = 0.691, p = 0.058) is not significant at the 0.05 level; the text should state this explicitly rather than implying a relation.

Circularity Check

1 steps flagged · score 6.0 of 10

The 'predicted' probability fluxes in Fig. 5 are an in-sample fit to the same transition rates used to infer the model, so the reported correlations measure goodness-of-fit rather than predictive validation.

  1. fitted input called prediction [Introduction (last paragraph); Results, 'THE STRUCTURAL ORIGIN OF TASK-DEPENDENT IRREVERSIBLE DYNAMICS' (Fig. 5); Methods, 'Infering Ising spin system from transition rates', Eqs. (28)-(29)]
    "Finally, we confirm that our model captures the task-dependent dynamics observed in the data by comparing the predicted dynamics from the Ising spin system with the empirical data. ... To validate our inferred model, we reconstruct the probability flux and compare it with the original data. ... the two sets of probability fluxes are correlated (Pearson coefficient larger than 0.7) except for the working memory task."

    Equation (28) fits βJ, βh, and A by minimizing the squared difference between the model log transition rates and the empirical log transition rates over all single-spin-flip transitions. Those same empirical transition rates are the input to the empirical probability flux via Eq. (4). Figure 5 then correlates the flux computed from the fitted model with the empirical flux from the identical dataset. The reported r = 0.53-0.96 is therefore an in-sample goodness-of-fit statistic, not a predictive success: the 'predicted dynamics' are generated by parameters fitted to the very transition rates being compared. The task-dependent antisymmetric interaction is also a fitted parametrization of the same transition-rate asymmetries, so the flux correlation does not independently confirm the mechanis

full rationale

The paper's central mechanistic claim—that tasks differ by subtly modifying the antisymmetric part of an inferred interaction matrix—is a descriptive model fit, not a circular derivation: the interaction matrices and their symmetric/antisymmetric decompositions are new quantities extracted from the data, and the authors do not derive them from the conclusion. There is no load-bearing self-citation: ref. 49 (Horiike & Fujishiro) is used only for the PCA hypercube projection method, and the data/code self-citation (ref. 72) is not part of the argument. The main circularity concern is the validation step: the model is fitted to empirical transition rates (Eq. 28) and then 'predicted' fluxes (Fig. 5) are compared with fluxes computed from those same rates. This is a fitted-input-called-prediction pattern; it partially inflates the support for the model. However, the paper is honest that this is a reconstruction rather than an out-of-sample forecast, and the central interaction-matrix comparison (Fig. 4) has independent content. The stated assumption that a symmetric-interaction Arrhenius rate (Eq. 26) is applied to an asymmetric interaction matrix is a correctness/robustness limitation, not circularity, and the lack of uncertainty quantification on the small antisymmetric entries is a statistical gap, not a circular step. On balance, the circularity is partial and localized to the flux-validation claim, giving a score of 6.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on several fitted quantities: per-task asymmetric interaction matrices (42 entries), external fields (7), a rate constant, and the choice of coarse-graining. The Arrhenius rate extrapolation to asymmetric matrices is a notable ad hoc modeling step. No new physical entities are introduced beyond the model parameters themselves.

free parameters (5)
  • Asymmetric interaction matrix beta*J (42 off-diagonal entries) = inferred per task
    Each off-diagonal element of the 7x7 interaction matrix is fit to the empirical transition rates via the loss function of Eq. (28); the matrix is generally asymmetric.
  • External field beta*h (7 entries) = inferred per task
    The external input vector is fit jointly with the interaction matrix; it varies across tasks.
  • Rate constant A = inferred per task
    The Arrhenius pre-factor A in Eq. (27) is a fitted scalar.
  • Number of clusters (7) = 7
    The dendrogram threshold for hierarchical clustering is chosen manually; robustness to 4, 5, 6 clusters is checked in Extended Data Fig. 4.
  • Binarization scheme = static transformation
    The main-text figures use the static transformation; dynamic and curve transformations are shown in Extended Data Fig. 5, but the choice itself is one of several possible.
assumptions (6)
  • domain assumption The dynamics are a continuous-time Markov process.
    Invoked in Methods for probability flux analysis and in the master equation (Eq. 18); the authors call it 'the reasonable first step' and consider higher-order Markov processes as a future direction.
  • domain assumption The probability distribution is stationary over the scanning period.
    Assumed for flux estimation (Eq. 3-4) and checked via Eq. (13) in Extended Data Fig. 1, but the check is a histogram rather than a formal test.
  • domain assumption Pairwise interactions are sufficient.
    The Ising model includes only pairwise terms; the paper notes that higher-order interactions might improve the working-memory reconstruction.
  • domain assumption Single-spin-flip dynamics.
    Transition rates are set to zero for states differing by more than one spin flip, which restricts the state-space connectivity.
  • ad hoc to paper The symmetric-derived Arrhenius rate (Eq. 27) applies to asymmetric interaction matrices.
    The Methods explicitly state the formula is derived for symmetric interactions but applied to asymmetric ones; this is a load-bearing extrapolation.
  • domain assumption Coarse-graining into 7 clusters preserves the qualitative dynamics.
    The clusters are derived from correlation-based hierarchical clustering and compared with known functional clusters; the authors list this as the first assumption in the Conclusion.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Distinct weak asymmetric interactions shape human brain functions as probability fluxes." pith.science (2026). https://pith.science/paper/W6CRPBYG

@misc{pith2026250820961,
  author       = {Pith},
  title        = {Pith review of: Distinct weak asymmetric interactions shape human brain functions as probability fluxes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W6CRPBYG}},
  note         = {Machine review of arXiv:2508.20961}
}
read the original abstract

The functional computation of the human brain arises from the collective behaviour of the underlying neural network. The emerging technology enables the recording of population activity in neurons, and the theory of neural networks is expected to explain and extract functional computations from the data. Thermodynamically, a large proportion of the whole-body energy is consumed by the brain, and functional computation of the human brain seems to involve high energy consumption. The human brain, however, does not increase its energy consumption with its function, and most of its energy consumption is not involved in specific brain function: how can the human brain perform its wide repertoire of functional computations without drastically changing its energy consumption? Here, we present a mechanism to perform functional computation by subtle modification of the interaction network among the brain regions. We first show that, by analyzing the data of spontaneous and task-induced whole-cerebral-cortex activity, the probability fluxes, which are the microscopic irreversible measure of state transitions, exhibit unique patterns depending on the task being performed, indicating that the human brain function is a distinct sequence of the brain state transitions. We then fit the parameters of Ising spin systems with asymmetric interactions, where we reveal that the symmetric interactions among the brain regions are strong and task-independent, but the antisymmetric interactions are subtle and task-dependent, and the inferred model reproduces most of the observed probability flux patterns. Our results indicate that the human brain performs its functional computation by subtly modifying the antisymmetric interaction among the brain regions, which might be possible with a small amount of energy.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Nonreciprocal Blume-Capel Model with Antisymmetric Single-Ion Anisotropies

    cond-mat.stat-mech 2025-12 conditional novelty 6.0 of 10

    In a nonreciprocal Blume-Capel magnet, an antisymmetric single-ion anisotropy suppresses oscillatory dynamics and restores a static ordered phase belonging to the 2D Ising universality class.

Reference graph

Works this paper leans on

88 extracted references · 38 canonical work pages · cited by 1 Pith paper

  1. [1]

    author author J. J. \ Hopfield ,\ title title Neurons, Dynamics and Computation , \ https://doi.org/10.1063/1.881412 journal journal Phys. Today \ volume 47 ,\ pages 40--46 ( year 1994 ) NoStop

    doi:10.1063/1.881412 1994

  2. [2]

    author author J. J. \ Hopfield ,\ title title Brain, neural networks, and computation , \ https://doi.org/10.1103/RevModPhys.71.S431 journal journal Rev. Mod. Phys. \ volume 71 ,\ pages S431--S437 ( year 1999 ) NoStop

    doi:10.1103/revmodphys.71.s431 1999

  3. [3]

    author author P. S. \ Churchland \ and\ author T. J. \ Sejnowski ,\ @noop title The Computational Brain ,\ edition twenty-fifth anniversary \ ed.,\ Computational Neuroscience Series\ ( publisher The MIT Press ,\ year 2017 ) NoStop

    2017

  4. [4]

    author author D. S. \ Bassett \ and\ author M. S. \ Gazzaniga ,\ title title Understanding complexity in the human brain , \ https://doi.org/10.1016/j.tics.2011.03.006 journal journal Trends Cognit. Sci. \ volume 15 ,\ pages 200--209 ( year 2011 ) NoStop

    work page doi:10.1016/j.tics.2011.03.006 2011

  5. [5]

    author author T. R. \ Insel , author S. C. \ Landis ,\ and\ author F. S. \ Collins ,\ title title The NIH BRAIN Initiative , \ https://doi.org/10.1126/science.1239276 journal journal Science \ volume 340 ,\ pages 687--688 ( year 2013 ) NoStop

    work page doi:10.1126/science.1239276 2013

  6. [6]

    author author L. A. \ Jorgenson , author W. T. \ Newsome , author D. J. \ Anderson , author C. I. \ Bargmann , author E. N. \ Brown , author K. Deisseroth , author J. P. \ Donoghue , author K. L. \ Hudson , author G. S. F. \ Ling , author P. R. \ MacLeish , author E. Marder , author R. A. \ Normann , author J. R. \ Sanes , author M. J. \ Schnitzer , autho...

    arXiv 2014

  7. [7]

    author author T. J. \ Sejnowski , author P. S. \ Churchland ,\ and\ author J. A. \ Movshon ,\ title title Putting big data to good use in neuroscience , \ https://doi.org/10.1038/nn.3839 journal journal Nat. Neurosci. \ volume 17 ,\ pages 1440--1441 ( year 2014 ) NoStop

    work page doi:10.1038/nn.3839 2014

  8. [8]

    Yuste ,\ title title From the neuron doctrine to neural networks , \ https://doi.org/10.1038/nrn3962 journal journal Nat

    author author R. Yuste ,\ title title From the neuron doctrine to neural networks , \ https://doi.org/10.1038/nrn3962 journal journal Nat. Rev. Neurosci. \ volume 16 ,\ pages 487--497 ( year 2015 a ) NoStop

    doi:10.1038/nrn3962 2015

Show all 88 references
  1. [9]

    Panzeri , author M

    author author S. Panzeri , author M. Moroni , author H. Safaai ,\ and\ author C. D. \ Harvey ,\ title title The structures and functions of correlations in neural population codes , \ https://doi.org/10.1038/s41583-022-00606-4 journal journal Nat. Rev. Neurosci. \ volume 23 ,\...

    2022 doi

  2. [10]

    author author D. S. \ Bassett \ and\ author O. Sporns ,\ title title Network neuroscience , \ https://doi.org/10.1038/nn.4502 journal journal Nat. Neurosci. \ volume 20 ,\ pages 353--364 ( year 2017 ) NoStop

    2017 doi

  3. [11]

    author author C. W. \ Lynn \ and\ author D. S. \ Bassett ,\ title title The physics of brain network structure, function and control , \ https://doi.org/10.1038/s42254-019-0040-8 journal journal Nat. Rev. Phys. \ volume 1 ,\ pages 318--332 ( year 2019 ) NoStop

    2019 doi

  4. [12]

    author author J. W. \ Mink , author R. J. \ Blumenschine ,\ and\ author D. B. \ Adams ,\ title title Ratio of central nervous system to body metabolism in vertebrates: Its constancy and functional basis , \ https://doi.org/10.1152/ajpregu.1981.241.3.R203 journal journal Am. J....

    1981 doi

  5. [13]

    author author M. A. \ Hofman ,\ title title Energy Metabolism , Brain Size and Longevity in Mammals , \ https://doi.org/10.1086/413544 journal journal Q. Rev. Biol. \ volume 58 ,\ pages 495--512 ( year 1983 ) NoStop

    1983 doi

  6. [14]

    author author D. F. \ Rolfe \ and\ author G. C. \ Brown ,\ title title Cellular energy utilization and molecular origin of standard metabolic rate in mammals , \ https://doi.org/10.1152/physrev.1997.77.3.731 journal journal Physiol. Rev. \ volume 77 ,\ pages 731--758 ( year 19...

    1997 doi

  7. [15]

    author author C. W. \ Kuzawa , author H. T. \ Chugani , author L. I. \ Grossman , author L. Lipovich , author O. Muzik , author P. R. \ Hof , author D. E. \ Wildman , author C. C. \ Sherwood , author W. R. \ Leonard ,\ and\ author N. Lange ,\ title title Metabolic costs and ev...

    2014 doi

  8. [16]

    author author C. W. \ Lynn , author E. J. \ Cornblath , author L. Papadopoulos , author M. A. \ Bertolero ,\ and\ author D. S. \ Bassett ,\ title title Broken detailed balance and entropy production in the human brain , \ https://doi.org/10.1073/pnas.2109889118 journal journal...

    2021 doi

  9. [17]

    Sanz Perl , author H

    author author Y. Sanz Perl , author H. Bocaccio , author C. Pallavicini , author I. P \'e rez-Ipi \ n a , author S. Laureys , author H. Laufs , author M. Kringelbach , author G. Deco ,\ and\ author E. Tagliazucchi ,\ title title Nonequilibrium brain dynamics as a signature of ...

    2021 doi

  10. [18]

    author author M. E. \ Raichle \ and\ author D. A. \ Gusnard ,\ title title Appraising the brain's energy budget , \ https://doi.org/10.1073/pnas.172399499 journal journal Proc. Natl. Acad. Sci. \ volume 99 ,\ pages 10237--10239 ( year 2002 ) NoStop

    2002 doi

  11. [19]

    author author M. E. \ Raichle ,\ title title The Brain 's Dark Energy , \ https://doi.org/10.1126/science.1134405 journal journal Science \ volume 314 ,\ pages 1249--1250 ( year 2006 ) NoStop

    2006 doi

  12. [20]

    author author M. E. \ Raichle \ and\ author M. A. \ Mintun ,\ title title Brain Work and Brain Imaging , \ https://doi.org/10.1146/annurev.neuro.29.051605.112819 journal journal Annu. Rev. Neurosci. \ volume 29 ,\ pages 449--476 ( year 2006 ) NoStop

    2006

  13. [21]

    Balasubramanian ,\ title title Brain power , \ https://doi.org/10.1073/pnas.2107022118 journal journal Proc

    author author V. Balasubramanian ,\ title title Brain power , \ https://doi.org/10.1073/pnas.2107022118 journal journal Proc. Natl. Acad. Sci. \ volume 118 ,\ pages e2107022118 ( year 2021 ) NoStop

    2021 doi

  14. [22]

    author author W. B. \ Levy \ and\ author V. G. \ Calvert ,\ title title Communication consumes 35 times more energy than computation in the human cortex, but both costs are needed to predict synapse number , \ https://doi.org/10.1073/pnas.2008173118 journal journal Proc. Natl....

    2021 doi

  15. [23]

    author author D. C. \ Van Essen , author S. M. \ Smith , author D. M. \ Barch , author T. E. \ Behrens , author E. Yacoub ,\ and\ author K. Ugurbil ,\ title title The WU-Minn Human Connectome Project : An overview , \ https://doi.org/10.1016/j.neuroimage.2013.05.041 journal jo...

    2013 doi

  16. [24]

    author author D. M. \ Barch , author G. C. \ Burgess , author M. P. \ Harms , author S. E. \ Petersen , author B. L. \ Schlaggar , author M. Corbetta , author M. F. \ Glasser , author S. Curtiss , author S. Dixit , author C. Feldt , author D. Nolan , author E. Bryant , author ...

    2013

  17. [25]

    Hassabis , author D

    author author D. Hassabis , author D. Kumaran , author C. Summerfield ,\ and\ author M. Botvinick ,\ title title Neuroscience- Inspired Artificial Intelligence , \ https://doi.org/10.1016/j.neuron.2017.06.011 journal journal Neuron \ volume 95 ,\ pages 245--258 ( year 2017 ) NoStop

    2017 doi

  18. [26]

    author author D. H. \ Wolpert , author J. Korbel , author C. W. \ Lynn , author F. Tasnim , author J. A. \ Grochow , author G. Karde s , author J. B. \ Aimone , author V. Balasubramanian , author E. De Giuli , author D. Doty , author N. Freitas , author M. Marsili , author T. ...

    2024

  19. [27]

    Mehonic \ and\ author A

    author author A. Mehonic \ and\ author A. J. \ Kenyon ,\ title title Brain-inspired computing needs a master plan , \ https://doi.org/10.1038/s41586-021-04362-w journal journal Nature \ volume 604 ,\ pages 255--260 ( year 2022 ) NoStop

    2022 doi

  20. [28]

    author author F. H. C. \ Crick ,\ title title Thinking about the Brain , \ https://doi.org/10.1038/scientificamerican0979-219 journal journal Sci. Am. \ volume 241 ,\ pages 219--232 ( year 1979 ) NoStop

    1979 doi

  21. [29]

    Von Neumann \ and\ author R

    author author J. Von Neumann \ and\ author R. Kurzweil ,\ @noop title The Computer & the Brain ,\ edition 3rd \ ed.\ ( publisher Yale University Press ,\ year 2012 ) NoStop

    2012

  22. [30]

    author author W. S. \ McCulloch \ and\ author W. Pitts ,\ title title A logical calculus of the ideas immanent in nervous activity , \ https://doi.org/10.1007/BF02478259 journal journal Bull. Math. Biophys. \ volume 5 ,\ pages 115--133 ( year 1943 ) NoStop

    1943 doi

  23. [31]

    author author P. W. \ Anderson ,\ title title More Is Different : Broken symmetry and the nature of the hierarchical structure of science. \ https://doi.org/10.1126/science.177.4047.393 journal journal Science \ volume 177 ,\ pages 393--396 ( year 1972 ) NoStop

    1972 doi

  24. [32]

    Feder ,\ title title The brain is big science , \ https://doi.org/10.1063/PT.3.2207 journal journal Phys

    author author T. Feder ,\ title title The brain is big science , \ https://doi.org/10.1063/PT.3.2207 journal journal Phys. Today \ volume 66 ,\ pages 20--22 ( year 2013 ) NoStop

    2013 doi

  25. [33]

    Yuste \ and\ author G

    author author R. Yuste \ and\ author G. M. \ Church ,\ title title The new century of the brain , \ https://www.jstor.org/stable/26039815 journal journal Sci. Am. \ volume 310 ,\ pages 38--45 ( year 2014 ) NoStop

    2014

  26. [34]

    Rubinov ,\ title title Neural networks in the future of neuroscience research , \ https://doi.org/10.1038/nrn4042 journal journal Nat

    author author M. Rubinov ,\ title title Neural networks in the future of neuroscience research , \ https://doi.org/10.1038/nrn4042 journal journal Nat. Rev. Neurosci. \ volume 16 ,\ pages 767--767 ( year 2015 ) NoStop

    2015 doi

  27. [35]

    Yuste ,\ title title On testing neural network models , \ https://doi.org/10.1038/nrn4043 journal journal Nat

    author author R. Yuste ,\ title title On testing neural network models , \ https://doi.org/10.1038/nrn4043 journal journal Nat. Rev. Neurosci. \ volume 16 ,\ pages 767--767 ( year 2015 b ) NoStop

    2015 doi

  28. [36]

    author author W. J. \ Sidis ,\ @noop title The Animate and the Inanimate \ ( publisher Independent publisher ,\ year 2021 ) NoStop

    2021

  29. [37]

    o dinger , author E. Schr \

    author author E. Schr \"o dinger , author E. Schr \"o dinger ,\ and\ author E. Schr \"o dinger ,\ https://www.cambridge.org/core/product/identifier/9781107295629/type/book title What Is Life? The Physical Aspect of the Living Cell ; with, Mind and Matter ; & Autobiographical S...

    1992

  30. [38]

    author author M. E. \ Raichle ,\ title title The Brain 's Dark Energy , \ https://www.jstor.org/stable/26001942 journal journal Sci. Am. \ volume 302 ,\ pages 44--49 ( year 2010 ) NoStop

    2010

  31. [39]

    Zhang \ and\ author M

    author author D. Zhang \ and\ author M. E. \ Raichle ,\ title title Disease and the brain's dark energy , \ https://doi.org/10.1038/nrneurol.2009.198 journal journal Nat. Rev. Neurol. \ volume 6 ,\ pages 15--28 ( year 2010 ) NoStop

    2009 doi

  32. [40]

    Schaefer , author R

    author author A. Schaefer , author R. Kong , author E. M. \ Gordon , author T. O. \ Laumann , author X.-N. \ Zuo , author A. J. \ Holmes , author S. B. \ Eickhoff ,\ and\ author B. T. T. \ Yeo ,\ title title Local- Global Parcellation of the Human Cerebral Cortex from Intrinsi...

    2018 doi

  33. [41]

    author author R. K. P. \ Zia \ and\ author B. Schmittmann ,\ title title A possible classification of nonequilibrium steady states , \ https://doi.org/10.1088/0305-4470/39/24/L04 journal journal J. Phys. A: Math. Gen. \ volume 39 ,\ pages L407--L413 ( year 2006 ) NoStop

    2006 doi

  34. [42]

    author author R. K. P. \ Zia \ and\ author B. Schmittmann ,\ title title Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states , \ https://doi.org/10.1088/1742-5468/2007/07/P07012 journal journal J. Stat. Mech: Theory E...

    2007 doi

  35. [43]

    Battle , author C

    author author C. Battle , author C. P. \ Broedersz , author N. Fakhri , author V. F. \ Geyer , author J. Howard , author C. F. \ Schmidt ,\ and\ author F. C. \ MacKintosh ,\ title title Broken detailed balance at mesoscopic scales in active biological systems , \ https://doi.o...

    2016 doi

  36. [44]

    author author K. G. \ Wilson ,\ title title Problems in Physics with many Scales of Length , \ https://doi.org/10.1038/scientificamerican0879-158 journal journal Sci. Am. \ volume 241 ,\ pages 158--179 ( year 1979 ) NoStop

    1979 doi

  37. [45]

    Meshulam , author J

    author author L. Meshulam , author J. L. \ Gauthier , author C. D. \ Brody , author D. W. \ Tank ,\ and\ author W. Bialek ,\ title title Coarse Graining , Fixed Points , and Scaling in a Large Population of Neurons , \ https://doi.org/10.1103/PhysRevLett.123.178103 journal jou...

    2019 doi

  38. [46]

    author author D. M \"u llner ,\ title title Modern hierarchical, agglomerative clustering algorithms , \ https://doi.org/10.48550/arXiv.1109.2378 journal journal arXiv \ ( year 2011 ),\ 10.48550/arXiv.1109.2378 NoStop

    2011 doi arXiv

  39. [47]

    author author B. T. \ Thomas Yeo , author F. M. \ Krienen , author J. Sepulcre , author M. R. \ Sabuncu , author D. Lashkari , author M. Hollinshead , author J. L. \ Roffman , author J. W. \ Smoller , author L. Z \"o llei , author J. R. \ Polimeni , author B. Fischl , author H...

    2011

  40. [48]

    author author I. T. \ Jolliffe ,\ @noop title Principal Component Analysis ,\ edition 2nd \ ed.,\ Springer Series in Statistics\ ( publisher Springer ,\ year 2002 ) NoStop

    2002

  41. [49]

    Horiike \ and\ author S

    author author Y. Horiike \ and\ author S. Fujishiro ,\ title title Orthogonal Projections of Hypercubes , \ https://doi.org/10.48550/arXiv.2501.10257 journal journal arXiv \ ( year 2025 a ),\ 10.48550/arXiv.2501.10257 NoStop

    2025 doi

  42. [50]

    Schnakenberg ,\ title title Network theory of microscopic and macroscopic behavior of master equation systems , \ https://doi.org/10.1103/RevModPhys.48.571 journal journal Rev

    author author J. Schnakenberg ,\ title title Network theory of microscopic and macroscopic behavior of master equation systems , \ https://doi.org/10.1103/RevModPhys.48.571 journal journal Rev. Mod. Phys. \ volume 48 ,\ pages 571--585 ( year 1976 ) NoStop

    1976 doi

  43. [51]

    author author T. L. \ Hill ,\ @noop title Free Energy Transduction and Biochemical Cycle Kinetics \ ( publisher Springer-Verlag ,\ year 1989 ) NoStop

    1989

  44. [52]

    Toulouse ,\ title title Theory of the frustration effect in spin glasses: I , \ https://doi.org/10.1142/9789812799371_0009 journal journal Commun

    author author G. Toulouse ,\ title title Theory of the frustration effect in spin glasses: I , \ https://doi.org/10.1142/9789812799371_0009 journal journal Commun. Phys. \ volume 2 ,\ pages 115--119 ( year 1977 ) NoStop

    1977 doi

  45. [53]

    author author R. J. \ Glauber ,\ title title Time- Dependent Statistics of the Ising Model , \ https://doi.org/10.1063/1.1703954 journal journal J. Math. Phys. \ volume 4 ,\ pages 294--307 ( year 1963 ) NoStop

    1963 doi

  46. [54]

    Foster \ and\ author D

    author author M. Foster \ and\ author D. Scheinost ,\ title title Brain states as wave-like motifs , \ https://doi.org/10.1016/j.tics.2024.03.004 journal journal Trends Cognit. Sci. \ volume 28 ,\ pages 492--503 ( year 2024 ) NoStop

    2024 doi

  47. [55]

    author author D. L. \ Barack \ and\ author J. W. \ Krakauer ,\ title title Two views on the cognitive brain , \ https://doi.org/10.1038/s41583-021-00448-6 journal journal Nat. Rev. Neurosci. \ volume 22 ,\ pages 359--371 ( year 2021 ) NoStop

    2021 doi

  48. [56]

    Seifert ,\ title title Stochastic thermodynamics, fluctuation theorems and molecular machines , \ https://doi.org/10.1088/0034-4885/75/12/126001 journal journal Rep

    author author U. Seifert ,\ title title Stochastic thermodynamics, fluctuation theorems and molecular machines , \ https://doi.org/10.1088/0034-4885/75/12/126001 journal journal Rep. Prog. Phys. \ volume 75 ,\ pages 126001 ( year 2012 ) NoStop

    2012 doi

  49. [57]

    Van den Broeck ,\ title title Stochastic thermodynamics: A brief introduction , \ https://doi.org/10.3254/978-1-61499-278-3-155 journal journal Proc

    author author C. Van den Broeck ,\ title title Stochastic thermodynamics: A brief introduction , \ https://doi.org/10.3254/978-1-61499-278-3-155 journal journal Proc. Int. Sch. Phys.; ``Enrico Fermi'' \ volume 184 ,\ pages 155--193 ( year 2013 ) NoStop

    2013 doi

  50. [58]

    Peliti \ and\ author S

    author author L. Peliti \ and\ author S. Pigolotti ,\ @noop title Stochastic Thermodynamics: An Introduction \ ( publisher Princeton University Press ,\ year 2021 ) NoStop

    2021

  51. [59]

    author author N. Shiraishi ,\ https://doi.org/10.1007/978-981-19-8186-9 title An Introduction to Stochastic Thermodynamics : From Basic to Advanced ,\ edition 1st \ ed.,\ series Fundamental Theories of Physics Series \ No.\ number v.212 \ ( publisher Springer Singapore Pte. Li...

    2023 doi

  52. [60]

    Seifert ,\ https://doi.org/10.1017/9781009024358 title Stochastic Thermodynamics ,\ edition 1st \ ed.\ ( publisher Cambridge University Press ,\ year 2025 ) NoStop

    author author U. Seifert ,\ https://doi.org/10.1017/9781009024358 title Stochastic Thermodynamics ,\ edition 1st \ ed.\ ( publisher Cambridge University Press ,\ year 2025 ) NoStop

    2025 doi

  53. [61]

    Schneidman , author M

    author author E. Schneidman , author M. J. \ Berry , author R. Segev ,\ and\ author W. Bialek ,\ title title Weak pairwise correlations imply strongly correlated network states in a neural population , \ https://doi.org/10.1038/nature04701 journal journal Nature \ volume 440 ,...

    2006 doi

  54. [62]

    Masuda , author S

    author author N. Masuda , author S. Islam , author S. Thu Aung ,\ and\ author T. Watanabe ,\ title title Energy landscape analysis based on the Ising model: Tutorial review , \ https://doi.org/10.1371/journal.pcsy.0000039 journal journal PLOS Complex Syst. \ volume 2 ,\ pages ...

    2025 doi

  55. [63]

    Ganmor , author R

    author author E. Ganmor , author R. Segev ,\ and\ author E. Schneidman ,\ title title Sparse low-order interaction network underlies a highly correlated and learnable neural population code , \ https://doi.org/10.1073/pnas.1019641108 journal journal Proc. Natl. Acad. Sci. \ vo...

    2011 doi

  56. [64]

    Battiston , author E

    author author F. Battiston , author E. Amico , author A. Barrat , author G. Bianconi , author G. Ferraz De Arruda , author B. Franceschiello , author I. Iacopini , author S. K \'e fi , author V. Latora , author Y. Moreno , author M. M. \ Murray , author T. P. \ Peixoto , autho...

    2021 doi

  57. [65]

    author author T. M. \ Wong , author R. Preissl , author P. Datta , author M. Flickner , author R. Singh , author S. K. \ Esser , author E. McQuinn , author R. Appuswamy , author W. P. \ Risk ,\ and\ author H. D. \ Simon ,\ title title Ten to power 14 , \ https://scholar.google...

    2012

  58. [66]

    Gopnik ,\ title title Making AI More Human , \ https://www.jstor.org/stable/26172695 journal journal Sci

    author author A. Gopnik ,\ title title Making AI More Human , \ https://www.jstor.org/stable/26172695 journal journal Sci. Am. \ volume 316 ,\ pages 60--65 ( year 2017 ) NoStop

    2017

  59. [67]

    Bertolero , author D

    author author M. Bertolero , author D. S. \ Bassett ,\ and\ author M. R. \ Studios ,\ title title How matter becomes mind , \ https://www.jstor.org/stable/27265246 journal journal Sci. Am. \ volume 321 ,\ pages 26--33 ( year 2019 ) NoStop

    2019

  60. [68]

    Efron ,\ title title Bootstrap Methods : Another Look at the Jackknife , \ https://doi.org/10.1214/aos/1176344552 journal journal Ann

    author author B. Efron ,\ title title Bootstrap Methods : Another Look at the Jackknife , \ https://doi.org/10.1214/aos/1176344552 journal journal Ann. Stat. \ volume 7 ,\ pages 1--26 ( year 1979 ) NoStop

    1979

  61. [69]

    Gabrielli , author D

    author author A. Gabrielli , author D. Garlaschelli , author S. P. \ Patil ,\ and\ author M. \'A . \ Serrano ,\ title title Network renormalization , \ https://doi.org/10.1038/s42254-025-00817-5 journal journal Nat. Rev. Phys. \ volume 7 ,\ pages 203--219 ( year 2025 ) NoStop

    2025 doi

  62. [70]

    Bar-Joseph , author D

    author author Z. Bar-Joseph , author D. K. \ Gifford ,\ and\ author T. S. \ Jaakkola ,\ title title Fast optimal leaf ordering for hierarchical clustering , \ https://doi.org/10.1093/bioinformatics/17.suppl_1.S22 journal journal Bioinformatics \ volume 17 ,\ pages S22--S29 ( y...

    2001 doi

  63. [71]

    Kurths , author U

    author author J. Kurths , author U. Schwarz , author A. Witt , author R. Th . \ Krampe ,\ and\ author M. Abel ,\ title title Measures of complexity in signal analysis , \ in\ https://doi.org/10.1063/1.51037 booktitle AIP Conf . Proc . ,\ Vol.\ volume 375 \ ( publisher AIP ,\ y...

    1996 doi

  64. [72]

    Horiike \ and\ author S

    author author Y. Horiike \ and\ author S. Fujishiro ,\ https://zenodo.org/records/0000000 title The data and code for the paper ` TBA ' , \ howpublished Zenodo ( year 2025 b ) NoStop

    2025

  65. [73]

    van Rossum \ and\ author F

    author author G. van Rossum \ and\ author F. L. \ Drake ,\ @noop title The Python Language Reference ,\ edition release 3.0.1 [repr.] \ ed.,\ series Python Documentation Manual / Guido van Rossum ; Fred L . Drake [Ed.] \ No.\ number Pt. 2 \ ( publisher Python Software Foundati...

    2010

  66. [74]

    Vos De Wael , author O

    author author R. Vos De Wael , author O. Benkarim , author C. Paquola , author S. Lariviere , author J. Royer , author S. Tavakol , author T. Xu , author S.-J. \ Hong , author G. Langs , author S. Valk , author B. Misic , author M. Milham , author D. Margulies , author J. Smal...

    2020 doi

  67. [75]

    Frostig , author M

    author author R. Frostig , author M. J. \ Johnson ,\ and\ author C. Leary ,\ title title Compiling Machine Learning Programs via High-Level Tracing , \ in\ https://hal.science/hal-05188750 booktitle SysML Conf . 2018 \ ( year 2019 ) NoStop

    2018

  68. [76]

    author author J. D. \ Hunter ,\ title title Matplotlib: A 2D Graphics Environment , \ https://doi.org/10.1109/MCSE.2007.55 journal journal Comput. Sci. Eng. \ volume 9 ,\ pages 90--95 ( year 2007 ) NoStop

    2007 doi

  69. [77]

    author author A. A. \ Hagberg , author D. A. \ Schult ,\ and\ author P. J. \ Swart ,\ title title Exploring network structure, dynamics, and function using NetworkX , \ in\ https://conference.scipy.org/proceedings/SciPy2008/paper_2/ booktitle Proc. 7th Python Sci . Conf . \ ( ...

    2008

  70. [78]

    author author R. D. \ Markello , author J. Y. \ Hansen , author Z.-Q. \ Liu , author V. Bazinet , author G. Shafiei , author L. E. \ Su \'a rez , author N. Blostein , author J. Seidlitz , author S. Baillet , author T. D. \ Satterthwaite , author M. M. \ Chakravarty , author A....

    2022 doi

  71. [79]

    Abraham , author F

    author author A. Abraham , author F. Pedregosa , author M. Eickenberg , author P. Gervais , author A. Mueller , author J. Kossaifi , author A. Gramfort , author B. Thirion ,\ and\ author G. Varoquaux ,\ title title Machine learning for neuroimaging with scikit-learn , \ https:...

    2014

  72. [80]

    author author S. K. \ Lam , author A. Pitrou ,\ and\ author S. Seibert ,\ title title Numba: A LLVM-based Python JIT compiler , \ in\ https://doi.org/10.1145/2833157.2833162 booktitle Proc. Second Workshop LLVM Compil . Infrastruct . HPC ,\ series and number LLVM '15 \ ( publi...

    2015

  73. [81]

    author author C. R. \ Harris , author K. J. \ Millman , author S. J. \ Van Der Walt , author R. Gommers , author P. Virtanen , author D. Cournapeau , author E. Wieser , author J. Taylor , author S. Berg , author N. J. \ Smith , author R. Kern , author M. Picus , author S. Hoye...

    2020

  74. [82]

    author author W. McKinney ,\ title title Data Structures for Statistical Computing in Python , \ in\ https://doi.org/10.25080/Majora-92bf1922-00a booktitle Python in Science Conference \ ( year 2010 )\ pp.\ pages 56--61 NoStop

    2010 doi

  75. [83]

    Pedregosa , author G

    author author F. Pedregosa , author G. Varoquaux , author A. Gramfort , author V. Michel , author B. Thirion , author O. Grisel , author M. Blondel , author P. Prettenhofer , author R. Weiss , author V. Dubourg , author J. Vanderplas , author A. Passos , author D. Cournapeau ,...

    2011

  76. [84]

    a ggstr \

    author author P. Virtanen , author R. Gommers , author T. E. \ Oliphant , author M. Haberland , author T. Reddy , author D. Cournapeau , author E. Burovski , author P. Peterson , author W. Weckesser , author J. Bright , author S. J. \ Van Der Walt , author M. Brett , author J....

    2020

  77. [85]

    Waskom ,\ title title Seaborn: Statistical data visualization , \ https://doi.org/10.21105/joss.03021 journal journal J

    author author M. Waskom ,\ title title Seaborn: Statistical data visualization , \ https://doi.org/10.21105/joss.03021 journal journal J. Open Source Softw. \ volume 6 ,\ pages 3021 ( year 2021 ) NoStop

    2021 doi

  78. [86]

    Kovesi ,\ title title Good Colour Maps : How to Design Them , \ https://doi.org/10.48550/arXiv.1509.03700 journal journal arXiv \ ( year 2015 ),\ 10.48550/arXiv.1509.03700 NoStop

    author author P. Kovesi ,\ title title Good Colour Maps : How to Design Them , \ https://doi.org/10.48550/arXiv.1509.03700 journal journal arXiv \ ( year 2015 ),\ 10.48550/arXiv.1509.03700 NoStop

    2015 doi arXiv

  79. [87]

    Van Den Broeck \ and\ author M

    author author C. Van Den Broeck \ and\ author M. Esposito ,\ title title Ensemble and trajectory thermodynamics: A brief introduction , \ https://doi.org/10.1016/j.physa.2014.04.035 journal journal Physica A \ volume 418 ,\ pages 6--16 ( year 2015 ) NoStop

    2014 doi

  80. [88]

    Kubo , author M

    author author R. Kubo , author M. Toda ,\ and\ author N. Hashitsume ,\ https://doi.org/10.1007/978-3-642-58244-8 title Statistical Physics II : Nonequilibrium Statistical Mechanics ,\ edition 2nd \ ed.,\ series Springer Series in Solid-State Sciences \ No.\ number v.31 \ ( pub...

    1998 doi

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.