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REVIEW 4 major objections 4 minor 53 references

Population rate coding in recurrent neuronal networks with undetermined-type neurons

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A recurrent network whose neurons can send both excitatory and inhibitory synapses represents time-varying stimuli in population firing rate with peak correlation above 0.92 and outperforms a fixed-type E/I network.

desk verdict A competent but modest parameter study of a random E/I edge-coloring network, whose stated biological motivation (co-release) is not actually implemented; the encoding trends are plausible but the paper overclaims the model's relationship to co-release. read the letter →

arxiv 1908.03886 v1 pith:GRVQVPW4 submitted 2019-08-11 q-bio.NC

Hao Si , Xiaojuan Sun This is my paper · ORCID
classification q-bio.NC MSC 92C2092B20
keywords populationratecodingrecurrentneuronalnetworkundetermined-typeneuronsexcitatory-inhibitorybalanceHodgkin-Huxleymodelco-releaseencodingfidelitysynapticstrengthratio
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 tries to establish that a recurrent spiking network in which a neuron's outgoing synapses are randomly typed excitatory or inhibitory rather than the neuron itself being typed can faithfully represent a time-varying stimulus in its population firing rate, and does so better than a traditional determined-type network. It reports an optimal working point: intermediate recurrent probability near Prc = 0.1 and a moderate ratio of inhibitory to excitatory synaptic strength, roughly 15 < R < 40, give the highest encoding fidelity, with peak correlation values above 0.92. The same intermediate-tuning pattern appears for background noise, excitatory synaptic strength, and synaptic time constant, where moderate noise, moderate excitatory strength, and fast synapses all help. A sympathetic reader would care because the result suggests that receptor-determined and co-released synaptic polarity, a physiologically observed arrangement, can be a workable architectural principle for rate coding rather than a biological detail to be averaged away.

What carries the argument

The key machinery is the undetermined-type assignment rule: each synapse is independently labelled excitatory with probability 0.8 or inhibitory with probability 0.2, so synaptic sign is treated as a property of the activated receptor rather than of the presynaptic neuron. The argument is carried by the ratio R = g_inh/g_exc, which controls whether the recurrent population is in an excitation-dominated or inhibition-dominated regime, together with the recurrent probability Prc, which fixes how many mixed-sign feedback paths exist. The encoding quality Q, defined as the maximum of the cross-correlation between the input signal and the population firing rate, is the measure that exposes the optimum: Q is high only when R, Prc, noise, and excitatory strength place the population in an intermediate dynamical state rather than at either extreme.

What would settle it

Run the identical encoding protocol on a matched network in which inhibitory postsynaptic effects are delivered only by a fixed set of 20 inhibitory neurons, keeping the same number of excitatory and inhibitory synapses, and compare Q; if the undetermined network no longer shows higher encoding fidelity, the paper's central comparison fails. Similarly, if allowing one presynaptic neuron to excite and inhibit the same postsynaptic cell causes Q to drop below the paper's exclusion rule, the biological motivation would be contradicted.

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Extended reading notes

Core claim

The central discovery is that population rate coding survives and is sharpened by removing the assumption that each neuron has a fixed excitatory or inhibitory type. In the proposed undetermined-type network, each recurrent connection is independently assigned as excitatory with probability 0.8 or inhibitory with probability 0.2, so one presynaptic neuron may excite some postsynaptic targets and inhibit others. Using the maximum correlation Q between a half-wave-rectified Gaussian input and the population firing rate as the measure of encoding quality, the paper finds Q reaches values above 0.92 for intermediate inhibitory-to-excitatory strength ratios (about 15 < R < 40) and recurrent probability near 0.1. The optimal values of noise intensity, excitatory synaptic strength, and synaptic time constant are likewise intermediate, meaning the network encodes best in a state that is neither too excitable nor too suppressed. Under matched parameters, this undetermined network attains higher Q than a conventional network with 80 excitatory and 20 inhibitory neurons, which the paper takes as evidence that co-release of excitatory and inhibitory receptors is a plausible and beneficial coding mechanism.

Load-bearing premise

The load-bearing assumption is that randomly labelling each outgoing synapse as excitatory or inhibitory in a fixed 4:1 ratio, and never letting the same presynaptic neuron give both signs to the same postsynaptic cell, is a fair stand-in for receptor-determined co-release; if the real biological rule for synaptic sign differs, the reported encoding advantage belongs to the random-labelling rule rather than to the biology it is meant to capture.

Editorial extensions

If this is right

  • Population firing rate can remain a high-fidelity code even when individual neurons have no fixed excitatory or inhibitory identity, as long as the collective mix of synapses is balanced.
  • Encoding quality is non-monotonic in inhibitory strength: both too-weak and too-strong inhibitory feedback degrade the population code, so an intermediate E/I balance is required for faithful encoding.
  • Sparse recurrence around Prc = 0.1 is better than dense recurrence for this rate-coding task, suggesting that too many recurrent connections wash out the stimulus-related signal.
  • Moderate background noise and fast synaptic kinetics improve fidelity, while strong noise and slow synapses degrade it.
  • At identical parameters, the undetermined-type network outperforms the standard fixed 80/20 E/I network, implying that receptor-determined synaptic polarity is a rational modeling choice for population rate coding.

Reading between the lines

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

  • If the random-sign assignment is interpreted as receptor-determined polarity, the model predicts that target-specific differences in receptor expression, rather than presynaptic cell type, determine whether a connection excites or inhibits; this could be tested by comparing networks with different correlations between target identity and synapse sign.
  • The optimum near Prc = 0.1 may reflect a balance between averaging over many neurons and preserving stimulus transients: denser recurrence smooths away fast signal changes, while very sparse recurrence leaves too little shared activity to encode reliably.
  • A natural extension the paper does not simulate is true co-release, where one presynaptic neuron simultaneously excites and inhibits the same postsynaptic cell; whether opposing conductances cancel or sharpen the code is an open question that could raise or lower the reported advantage.
  • The 80/20 excitatory-to-inhibitory ratio is fixed throughout; testing sensitivity to other ratios, such as 70/30 or 90/10, would show whether the qualitative optimum is tied to the biological balance or is an artifact of the chosen 4:1 mix.
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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

4 major / 4 minor

Summary. The manuscript studies population-rate coding in a recurrent Hodgkin-Huxley network in which each directed recurrent synapse is randomly assigned an excitatory (80%) or inhibitory (20%) sign independently of the presynaptic neuron's identity, which the authors call an 'undetermined-type' network. The stimulus is a half-wave-rectified Ornstein-Uhlenbeck process, and the encoding quality Q is the maximal correlation between the stimulus and the population firing rate at an optimal lag. Parameter scans over the I/E strength ratio R, recurrent probability Prc, noise intensity D, excitatory strength gexc, and synaptic time constant reveal an optimal regime around Prc ≈ 0.1 and 15 < R < 40 with Q above 0.9. The paper concludes that this undetermined network encodes better than a standard fixed-E/I network and interprets this as evidence that co-release of excitatory and inhibitory receptors should be considered.

Significance. If the computational results hold, the paper provides a systematic computational demonstration that edge-level random E/I sign assignment can be as good as or better than source-determined E/I assignment for population-rate encoding in recurrent Hodgkin-Huxley networks. The parameter sweeps are extensive and the qualitative inverted-U dependencies are coherent. The significance is, however, limited by the mismatch between the implemented model and the claimed biological motivation, and by the absence of quantitative uncertainty in the comparison to the determined network. The work would be a solid contribution if presented as a study of 'random-sign' or 'undetermined-type' connectivity rather than as evidence for co-release.

major comments (4)
  1. [Section 2.1 and Section 4] The implemented network assigns each recurrent connection an independent 80/20 E/I sign and explicitly states that one postsynaptic neuron never receives both E and I from the same presynaptic neuron; this is a per-synapse sign model, not a co-release model in which one terminal activates both receptor classes on the same target. Consequently, the abstract's and conclusion's claim that the results make it 'rational to consider the co-release of inhibitory and excitatory receptors' is not supported by the simulation. Please either simulate co-release explicitly or replace the co-release interpretation with the more modest claim about random, undetermined-type sign assignment, and add a sensitivity analysis for the 4:1 E/I ratio.
  2. [Section 3.3, Fig. 10] The central claim that the undetermined network outperforms the determined network is presented without error bars, trial counts, or statistical testing, and the figure legend in 10(b) is internally inconsistent ('gexc=0.08 gexc=0.1 gexc=0.08 gexc=1'). Given that the stated differences are small (roughly 0.85-0.9), the reader cannot assess whether the advantage is reliable. Please report mean ± SD over at least the 10 trials used elsewhere and state the exact parameters for both models.
  3. [Section 2.4, Eqs. (7)-(8)] There is an inconsistency in how the population firing rate is defined: Eq. (7) sets Δt=1 ms, while the correlation in Eq. (8) is computed with a 10 ms window sliding by 1 ms. Also, Eq. (7) as written gives spikes/ms, but Fig. 2 labels the ordinate in Hz. Since Q is a correlation coefficient it is invariant to this scale, but the manuscript should state the exact time bin used to generate the figures and provide the conversion factor; otherwise the simulations are not fully reproducible.
  4. [Section 3.2.2, Fig. 7] The text states that 'the product of R and gexc has a positive relationship with the encoding quality,' but the surrounding discussion and the figure indicate a non-monotonic (inverted-U) relationship, with both too-large and too-small inhibitory strength reducing Q. Please correct this statement to reflect the described optimum at intermediate values of R*gexc.
minor comments (4)
  1. [Throughout] There are numerous typos and cross-reference errors, including 'thses', 'hypthesis', 'In other word', and a reference to 'Fig. 5(b)' that should be 'Fig. 6(b)'.
  2. [Section 2.4.3, Eq. (10)] The synchronization measure k_{i,j} is not normalized by the number of time bins, and this quantity is never used in the Results; please either correct the formula or remove it to avoid confusing an undefined measure.
  3. [Section 3.1] The phrase 'the relationship of Q versus Prc around R≈0.1' appears to be a typo for 'Q versus R around Prc≈0.1,' since the curves shown in Fig. 4(c) are Q versus R for fixed values of Prc.
  4. [Section 3.3, Fig. 10(b)] The legend text 'gexc=1' is presumably a typo for 'gexc=0.1'; this should be corrected because the comparison of synaptic strength is a central element of the argument.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the encoding-quality results are direct simulation outputs, and the E/I-sign assignment and co-release motivation raise model-validity concerns, not circularity.

full rationale

The paper's central derivation is simulation-based: it constructs a Hodgkin-Huxley recurrent network, defines population firing rate and encoding fidelity Q as the maximum correlation between input and population rate, and then sweeps parameters R, Prc, D, gexc, and synaptic time constants, comparing against a fixed-E/I network. No parameter is fitted to an external target, and no 'prediction' is derived from fitted values; every Q value is a direct simulated output. The optimal ranges of R and Prc are read from the same parameter sweeps used to formulate the conclusions, but this is standard exploratory reporting of simulation surfaces rather than a reduction of a predicted quantity to an input by construction. The paper does state post hoc parameter choices such as 'we choose Prc = 0.12 cause that it is a compromise of the previous two cases' and 'proves the rationality of the parameter D = 1 that we selected before,' but these are selections reported after inspecting the sweeps, not fitted inputs disguised as predictions. The biological motivation regarding receptor-determined synaptic polarity and co-release is not actually implemented as co-release: Section 2.1 randomly assigns each connection as excitatory (80%) or inhibitory (20%) and explicitly avoids a postsynaptic neuron receiving both excitatory and inhibitory synapses from the same presynaptic neuron, and the Conclusion concedes the model is 'still not very biological enough.' This is a modeling-validity and interpretation limitation, not a circular derivation. There are no load-bearing self-citations, no imported uniqueness theorems, and no renaming of a known empirical result as a new organizational principle. The comparison with the determined E/I network is an independent baseline simulation. Therefore, under the stated rules requiring a specific reduction or fitted-parameter-as-prediction, no circularity is present; the appropriate score is 0.

Assumptions & free parameters 8 free parameters · 6 assumptions · 1 invented entities

The central result rests on a set of hand-chosen model parameters and on the modeling premise that random E/I sign assignment captures receptor-determined synaptic action. No external data are fitted, but the 4:1 ratio and the avoidance of same-target co-release are load-bearing and unvalidated assumptions.

free parameters (8)
  • E:I connection ratio = 4:1 (80% excitatory, 20% inhibitory)
    Set in Sec. 2.1 without citation or sensitivity analysis; the undetermined network's behavior depends on it.
  • Excitatory synaptic strength gexc = 0.102 default; scanned 0.008 to 0.16
    Hand-selected default; the optimal range is read from the same Q surface used to draw conclusions (Sec. 3.2.2).
  • I/E strength ratio R = scanned 0-80; optimal around 15-40
    Central control parameter; the 'optimal range' claim is derived from the simulated Q values (Sec. 3.1).
  • Recurrent probability Prc = 0.12 default; scanned 0.02-0.8
    Default chosen as a compromise from the Q landscape; optimal near 0.1 is one of the findings (Sec. 3.1).
  • Noise intensity D = 1 default; scanned 0.1-2
    Default chosen as a compromise from the D-R map; intermediate D is claimed optimal (Sec. 3.2.1).
  • Synaptic time constants tau_exc, tau_inh = 0.3 ms, 0.6 ms; ratio 2
    Fixed; part of the claim that small tau improves encoding (Sec. 3.2.3).
  • External stimulus parameters (K, A, tau_c) = K=15, A=200, tau_c=80 ms
    Hand-set inputs adopted from prior works; not scanned, so the conclusions may depend on this choice (Sec. 2.3).
  • Network size N = 100
    No finite-size analysis, so finite-size effects are unquantified (Sec. 2.1).
assumptions (6)
  • domain assumption Hodgkin-Huxley equations with specified conductances describe the neurons
    Sec. 2.2, Eq. (1); standard model but treated as valid for the coding question without calibration.
  • ad hoc to paper Random directed connectivity with independent E/I sign at each edge approximates receptor-determined synaptic function
    Sec. 2.1; the central modeling premise, not derived from data and not the same as co-release at a shared synapse.
  • domain assumption Maximum input-population-rate correlation Q is an adequate measure of encoding quality
    Sec. 2.4.2; standard but ignores information-theoretic capacity, spike timing, and single-trial variability.
  • domain assumption Half-wave rectified Ornstein-Uhlenbeck current represents the stimulus
    Sec. 2.3; borrowed from prior studies, no validation against recorded inputs.
  • ad hoc to paper Avoiding E and I synapses from the same presynaptic neuron onto the same postsynaptic neuron does not alter the essential co-release phenomenon
    Sec. 2.1; stated for simplicity, but the paper's conclusion about co-release depends on this simplification.
  • ad hoc to paper The 4:1 E/I connection ratio is physiologically appropriate
    Sec. 2.1; no citation or sensitivity analysis supports this specific ratio.
invented entities (1)
  • Undetermined-type neuron with randomly assigned outgoing synaptic signs
    purpose: Enables one neuron to excite some targets and inhibit others, mimicking receptor-dependent synaptic action
    The paper provides no falsifiable handle that distinguishes this abstraction from a fixed-E/I network other than the simulation comparison itself; actual co-release at the same synapse is explicitly avoided, so the link to biology is indirect.

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Cite this review

Pith. "Pith review of Population rate coding in recurrent neuronal networks with undetermined-type neurons." pith.science (2026). https://pith.science/paper/GRVQVPW4

@misc{pith2026190803886,
  author       = {Pith},
  title        = {Pith review of: Population rate coding in recurrent neuronal networks with undetermined-type neurons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GRVQVPW4}},
  note         = {Machine review of arXiv:1908.03886}
}
read the original abstract

Neural coding is a key problem in neuroscience, which can promote people's understanding of the mechanism that brain processes information. Among the classical theories of neural coding, the population rate coding has been studied widely in many works. Most computational studies considered the neurons and the corresponding presynaptic synapses as pre-determined excitatory or inhibitory types. According to physiological evidence, however, that the real effect of a synapse is inhibitory or excitatory is determined by the type of the activated receptors. The co-release of excitatory and inhibitory receptors in the same synapse exists widely in the brain. In this paper, we study the population rate coding in recurrent neuronal networks with undetermined neurons and synapses, different from the traditional works, in which one neuron can perform either excitatory or inhibitory effect to the corresponding postsynaptic neurons. We find such neuronal networks can encode the stimuli information in population firing rate well. We find that intermediate recurrent probability together with moderate Inhibitory-Excitatory strength ratio can enhance the encoding performance. Suitable combinations of the previous two parameters with the noise intensity, the excitatory synaptic strength and the synaptic time constant have promoting effects on the performance of population rate coding. Finally, we compare the performance of population rate coding between the traditional (determined) model and ours, and we find that it is rational to consider the co-release of inhibitory and excitatory receptors.

Figures

Figures reproduced from arXiv: 1908.03886 by the authors.

Figure 1
Figure 1. The illustration of the recurrent network. The light blue circles denote the neurons whose total number is [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. (a) A glimpse that the effect of R on the encoding quality Q. The coding quality in the first layer as a function of the I/E synaptic strength ratio R. The encoding quality has a better performance as R locates in a moderate range. Prc = 0.1, D = 1, g exc = 0.102, τ exc = 0.3, τinh = 0.6. (b)(c)(d) The typical results of population firing rate encoding from the same stimuli injected into the recurrent network. From … view at source ↗
Figure 3
Figure 3. Encoding quality Q depending on R and Prc. The color code denotes the coding quality with dark blue being the best cases. In the parameter space of R and Prc it seems that Q takes higher values below the black dashed curve(noted as blue area) while smaller values above the dashed curve(noted as white area). In the blue area, especially around Prc = 0.1, the quality Q has a clear tendency to increase first and then d… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Statistical results and samples of data from the e [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Encoding quality depending on D and R. The color denotes the encoding quality and red denotes higher Q. We slice three cases of D = 0.7, 1, 1.2 in the left part with different color and plot the corresponding curve of Q vs. R in the right part. Prc = 0.12, g exc = 0.10…
Figure 6
Figure 6. Figure 6: Statistics of the data from the effects of noise intensity on the population rate coding. (a) The orange line denotes the mean values of Q vs. R under different D. The orange bar denotes the corresponding SD. The curve shows the same trends that lower Q for lower R and…
Figure 7
Figure 7. Figure 7: Encoding quality depending on g exc and R. The color decodes the encoding quality and the orange color denotes higher Q. Q takes higher values in the area between the two black dashed parallel lines but lower values out of the area especially in the upper right corner.…
Figure 8
Figure 8. Figure 8: The effects of synaptic time constant on the population rate coding. The color decodes the encoding quality and the blue color denotes higher Q. Prc = 0.12, D = 1, g exc = 0.102. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: Effects of synaptic strength and noise intensity on the encoding quality in determined EI model. (a) The noise intensity has a similar effect with us on the encoding quality that too weak and strong noise depress the population rate coding while intermediate noise faci…
Figure 10
Figure 10. Figure 10: Comparison of synaptic strength and noise intensity on the encoding quality in two models. (a) The red color denotes the determined [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

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Works this paper leans on

53 extracted references · 38 canonical work pages

  1. [1]

    R. C. deCharms, A. Zador, Neural representation and the cortical code, Annual Review of Neuroscience 23 (1) (2000) 613–647, pMID: 10845077. doi:10.1146/annurev.neuro.23.1.613

    work page doi:10.1146/annurev.neuro.23.1.613 2000

  2. [2]

    W. T. Newsome, K. H. Britten, J. A. Movshon, Neuronal correlates of a perceptual decision, Nature 341 (1989) 52–54. doi:10.1038/ 341052a0

    work page 1989

  3. [3]

    Georgopoulos, M

    A. Georgopoulos, M. Taira, A. Lukashin, Cognitive neurophysiology of the motor cortex, Science 260 (5104) (1993) 47–52. doi:10.1126/ science.8465199

    work page 1993

  4. [4]

    M. N. Shadlen, W. T. Newsome, Noise, neural codes and cortical organization, Current Opinion in Neurobiology 4 (4) (1994) 569 – 579. doi:https://doi.org/10.1016/0959-4388(94)90059-0

    work page doi:10.1016/0959-4388(94)90059-0 1994

  5. [5]

    Marsalek, C

    P. Marsalek, C. Koch, J. H. R. Maunsell, On the relationship between synaptic input and spike output jitter in individual neurons., Proceedings of the National Academy of Sciences of the United States of America 94 2 (1997) 735–40. doi:10.1073/pnas.94.2.735

    work page doi:10.1073/pnas.94.2.735 1997

  6. [6]

    M. C. W. van Rossum, G. G. Turrigiano, S. B. Nelson, Fast propagation of firing rates through layered networks of noisy neurons, Journal of Neuroscience 22 (5) (2002) 1956–1966. doi:10.1523/JNEUROSCI.22-05-01956.2002

    work page arXiv 2002

  7. [7]

    M. E. Mazurek, M. N. Shadlen, Limits to the temporal fidelity of cortical spike rate signals, Nature Neuroscience 5 (2002) 463–471. doi: 10.1038/nn836

    work page doi:10.1038/nn836 2002

  8. [8]

    Aertsen, M

    A. Aertsen, M. Diesmann, M. Gewaltig, Propagation of synchronous spiking activity in feedforward neural networks, Journal of Physiology- Paris 90 (3) (1996) 243 – 247. doi:https://doi.org/10.1016/S0928-4257(97)81432-5

    work page doi:10.1016/s0928-4257(97)81432-5 1996

Show all 53 references
  1. [9]

    Riehle, S

    A. Riehle, S. Gr ¨un, M. Diesmann, A. Aertsen, Spike synchronization and rate modulation di fferentially involved in motor cortical function, Science 278 (5345) (1997) 1950–1953. doi:10.1126/science.278.5345.1950

    1997

  2. [10]

    Diesmann, M.-O

    M. Diesmann, M.-O. Gewaltig, A. Aertsen, Stable propagation of synchronous spiking in cortical neural networks, Nature 402 (1999) 529–

    1999

  3. [11]

    Litvak, H

    V . Litvak, H. Sompolinsky, I. Segev, M. Abeles, On the transmission of rate code in long feedforward networks with excitatory–inhibitory balance, Journal of Neuroscience 23 (7) (2003) 3006–3015. doi:10.1523/JNEUROSCI.23-07-03006.2003

    2003

  4. [12]

    T. P. V ogels, L. F. Abbott, Signal propagation and logic gating in networks of integrate-and-fire neurons, Journal of Neuroscience 25 (46) (2005) 10786–10795. doi:10.1523/JNEUROSCI.3508-05.2005

    2005 doi

  5. [13]

    Masuda, K

    N. Masuda, K. Aihar, Bridging rate coding and temporal spike coding by e ffect of noise, Phys. Rev. Lett. 88 (2002) 248101. doi:10.1103/ PhysRevLett.88.248101

    2002

  6. [14]

    Masuda, K

    N. Masuda, K. Aihara, Duality of rate coding and temporal coding in multilayered feedforward networks, Neural Computation 15 (2003) 103–125. doi:10.1162/089976603321043711

    2003 doi

  7. [15]

    Masuda, K

    N. Masuda, K. Aihara, Dual coding and e ffects of global feedback in multilayered neural networks, Neurocomputing 58-60 (2004) 33 – 39, computational Neuroscience: Trends in Research 2004. doi:https://doi.org/10.1016/j.neucom.2004.01.019

    2004 doi

  8. [16]

    R. M. Bruno, B. Sakmann, Cortex is driven by weak but synchronously active thalamocortical synapses, Science 312 (5780) (2006) 1622–

    2006

  9. [17]

    Kumar, S

    A. Kumar, S. Rotter, A. Aertsen, Spiking activity propagation in neuronal networks: reconciling di fferent perspectives on neural coding, Nature Reviews Neuroscience 11 (2010) 615–627. doi:10.1038/nrn2886

    2010 doi

  10. [18]

    E. D. Adrian, The basis of sensation, W W Norton and Co, 1928. doi:10.1016/0166-2236(92)90361-B . 12

    1928 doi

  11. [19]

    Kostal, P

    L. Kostal, P. Lansky, J.-P. Rospars, Review article: Neuronal coding and spiking randomness, European Journal of Neuroscience 26 (10) (2007) 2693–2701. doi:10.1111/j.1460-9568.2007.05880.x

    2007

  12. [20]

    M. N. Shadlen, W. T. Newsome, The variable discharge of cortical neurons: Implications for connectivity, computation, and information coding, Journal of Neuroscience 18 (10) (1998) 3870–3896. doi:10.1523/JNEUROSCI.18-10-03870.1998

    1998

  13. [21]

    Gerstner, Population dynamics of spiking neurons: Fast transients, asynchronous states, and locking, Neural Comput

    W. Gerstner, Population dynamics of spiking neurons: Fast transients, asynchronous states, and locking, Neural Comput. 12 (1) (2000) 43–89. doi:10.1162/089976600300015899

    2000 doi

  14. [22]

    Kandel, J

    E. Kandel, J. Schwartz, T. Jessell, Principles of Neural Science, Prentice-Hall International edit, Elsevier, 1991

    1991

  15. [23]

    Brunel, V

    N. Brunel, V . Hakim, Fast global oscillations in networks of integrate-and-fire neurons with low firing rates, Neural Computation 11 (7) (1999) 1621–1671. doi:10.1162/089976699300016179

    1999 doi

  16. [24]

    B. W. Knight, Dynamics of encoding in neuron populations: Some general mathematical features, Neural Computation 12 (3) (2000) 473–

    2000

  17. [25]

    Dayan, L

    P. Dayan, L. F. Abbott, Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, The MIT Press, 2005

    2005

  18. [26]

    Masuda, B

    N. Masuda, B. Doiron, A. Longtin, K. Aihara, Coding of temporally varying signals in networks of spiking neurons with global delayed feedback, Neural Computation 17 (2005) 2139–2175. doi:10.1162/0899766054615680

    2005 doi

  19. [27]

    S. Wang, C. Zhou, Information encoding in an oscillatory network, Phys. Rev. E 79 (2009) 061910. doi:10.1103/PhysRevE.79.061910

    2009 doi

  20. [28]

    D. Guo, C. Li, Population rate coding in recurrent neuronal networks with unreliable synapses, Cognitive Neurodynamics 6 (1) (2012) 75–87. doi:10.1007/s11571-011-9181-x

    2012 doi

  21. [29]

    van Vreeswijk, H

    C. van Vreeswijk, H. Sompolinsky, Chaos in neuronal networks with balanced excitatory and inhibitory activity, Science 274 (5293) (1996) 1724–1726. doi:10.1126/science.274.5293.1724

    1996

  22. [30]

    Salinas, T

    E. Salinas, T. J. Sejnowski, Correlated neuronal activity and the flow of neural information, Nature Reviews Neuroscience 2 (2001) 539–550. doi:10.1038/35086012

    2001 doi

  23. [31]

    Brunel, Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons, Journal of Computational Neuroscience 8 (3) (2000) 183–208

    N. Brunel, Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons, Journal of Computational Neuroscience 8 (3) (2000) 183–208. doi:10.1023/A:1008925309027

    2000 doi

  24. [32]

    Mehring, U

    C. Mehring, U. Hehl, M. Kubo, M. Diesmann, A. Aertsen, Activity dynamics and propagation of synchronous spiking in locally connected random networks, Biological Cybernetics 88 (2003) 395–408. doi:10.1007/s00422-002-0384-4

    2003 doi

  25. [33]

    Teramae, T

    J.-n. Teramae, T. Fukai, Local cortical circuit model inferred from power-law distributed neuronal avalanches, Journal of Computational Neuroscience 22 (3) (2007) 301–312. doi:10.1007/s10827-006-0014-6

    2007 doi

  26. [34]

    Kremkow, A

    J. Kremkow, A. Aertsen, A. Kumar, Gating of signal propagation in spiking neural networks by balanced and correlated excitation and inhibition, Journal of Neuroscience 30 (47) (2010) 15760–15768. doi:10.1523/JNEUROSCI.3874-10.2010

    2010 doi

  27. [35]

    Kumar, S

    A. Kumar, S. Rotter, A. Aertsen, Conditions for propagating synchronous spiking and asynchronous firing rates in a cortical network model, Journal of Neuroscience 28 (20) (2008) 5268–5280. doi:10.1523/JNEUROSCI.2542-07.2008

    2008 doi

  28. [36]

    T. P. V ogels, L. F. Abbott, Gating multiple signals through detailed balance of excitation and inhibition in spiking networks, Nature Neuro- sciencedoi:10.1038/nn.2276

    doi

  29. [37]

    Mayor, W

    J. Mayor, W. Gerstner, Transient information flow in a network of excitatory and inhibitory model neurons: Role of noise and signal autocor- relation, Journal of Physiology-Paris 98 (4) (2004) 417 – 428. doi:https://doi.org/10.1016/j.jphysparis.2005.09.009

    2004 doi

  30. [38]

    R. Han, J. Wang, H. Yu, B. Deng, X. Wei, Y . Qin, H. Wang, Intrinsic excitability state of local neuronal population modulates signal propagation in feed-forward neural networks, Chaos: An Interdisciplinary Journal of Nonlinear Science 25 (4) (2015) 043108. doi:10. 1063/1.4917014

    2015

  31. [39]

    Barral, X.-J

    J. Barral, X.-J. Wang, A. Reyes, Propagation of spike timing and firing rate in feedforward networks reconstituted in vitro, bioRxiv doi: 10.1101/151134

    doi

  32. [40]

    URL https://en.wikipedia.org/wiki/Neuron

    Wikipedia contributors, Neuron — Wikipedia, the free encyclopedia, [Online; accessed 26-August-2018] (2018). URL https://en.wikipedia.org/wiki/Neuron

    2018

  33. [41]

    Shrivastava, A

    A. Shrivastava, A. Triller, W. Sieghart, Gabaa receptors: Post-synaptic co-localization and cross-talk with other receptors, Frontiers in Cellular Neuroscience 5 (2011) 7. doi:10.3389/fncel.2011.00007

    2011 arXiv

  34. [42]

    Kantamneni, Cross-talk and regulation between glutamate and gabab receptors, Frontiers in Cellular Neuroscience 9 (2015) 135

    S. Kantamneni, Cross-talk and regulation between glutamate and gabab receptors, Frontiers in Cellular Neuroscience 9 (2015) 135. doi: 10.3389/fncel.2015.00135

    2015

  35. [43]

    A. L. Hodgkin, A. F. Huxley, Currents carried by sodium and potassium ions through the membrane of the giant axon of loligo, The Journal of Physiology 116 (4) (1952) 449–472. doi:10.1113/jphysiol.1952.sp004717

    1952 doi

  36. [44]

    Hansel, G

    D. Hansel, G. Mato, C. Meunier, Phase dynamics for weakly coupled hodgkin-huxley neurons, EPL (Europhysics Letters) 23 (5) (1993) 367. doi:10.1209/0295-5075/23/5/011

    1993 doi

  37. [45]

    X.-J. Wang, G. Buzs ´aki, Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model, Journal of Neuroscience 16 (20) (1996) 6402–6413. doi:10.1523/JNEUROSCI.16-20-06402.1996

    1996

  38. [46]

    S. Wang, W. Wang, F. Liu, Propagation of firing rate in a feed-forward neuronal network, Phys. Rev. Lett. 96 (2006) 018103.doi:10.1103/ PhysRevLett.96.018103

    2006

  39. [47]

    S. I. Thorpe, D. Fize, C. Marlot, Speed of processing in the human visual system, Nature 381 (1996) 520–522. doi:10.1038/381520a0

    1996 doi

  40. [48]

    S. J. Thorpe, A. Delorme, R. van Rullen, Spike-based strategies for rapid processing, Neural networks : the official journal of the International Neural Network Society 14 6-7 (2001) 715–25. doi:10.1016/S0893-6080(01)00083-1

    2001 doi

  41. [49]

    van Rullen, S

    R. van Rullen, S. J. Thorpe, Rate coding versus temporal order coding: What the retinal ganglion cells tell the visual cortex, Neural Compu- tation 13 (2001) 1255–1283. doi:10.1162/08997660152002852

    2001 doi

  42. [50]

    Gollisch, M

    T. Gollisch, M. Meister, Rapid neural coding in the retina with relative spike latencies, Science 319 (5866) (2008) 1108–1111. doi: 10.1126/science.1149639

    2008 doi

  43. [51]

    B. A. Olshausen, D. J. Field, Sparse coding of sensory inputs., Current opinion in neurobiology 14 4 (2004) 481–7. doi:10.1016/j.conb. 2004.07.007. 13

    2004 doi

  44. [518]

    doi:10.1162/089976600300015673

    doi

  45. [1627]

    doi:10.1126/science.1124593

    doi

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.