Claims 14
From the paper High-Degree Neurons Feed Cortical Computations · claims file · checked 2026-11-06: ready
- data-recordings
The analysis used 25 recordings of somatosensory cortex cultures, with 7735 neurons in total after removing neurons with fewer than 100 spikes in the 60 min recording, an average of 309.4 neurons per recording and an average firing rate of 2.10 Hz.
only recordings from cortex were used in this analysis (number of recordings: 25 ... neurons with less than 100 spikes in the 60 minute recording (firing rate < 0.028 Hz) were removed from the analysis. Spike sorting yielded spike times for each neuron (7735 total neurons) with a resolution of 50 μs. The average firing rate for each neuron was 2.10 Hz and each recording had an average of 309.4 neurons
Materials and Methods, Experimental System, paragraph 1How it will be judged
Counted from the dataset's spike times. The paper says the 100-spike threshold was applied; whether the deposited neurons already passed it is for the author to find, and the counts are reported both as deposited and after applying it. Open, how the rate is taken; readings (a) spikes over the recording length of each recording, (b) spikes over 60 min. Reproduced when all four values are within tolerance under one reading.
- fig4ac-te-lognormal
The significant TE connection weights, raw and normalized, are roughly log-normally distributed at both time scales and vary over several orders of magnitude.
Similar to these studies, we found a roughly log-normal distribution of significant TE weights ... both TE and normalized TE values varied broadly over several orders of magnitude
Results, Connection Weight and Degree Distributions, paragraphs 2 and 3; Figure 4A and 4CHow it will be judged
TE and significance as in M-TE and M-SIG. The paper does not say whether Fig 4A and 4C use the full networks or the sub-networks; readings (f) and (s) of M-SUB, both reported. Per time scale, raw and normalized TE binned into 100 logarithmically spaced bins (Results, paragraph 3) and fit with a log-normal probability mass function with an extra normalization factor (Eq 21, not in the text read; the reading is a Gaussian in log TE times a factor alpha), by nonlinear least squares, per recording and on the average over recordings. The paper gives no goodness-of-fit threshold. Reading fixed here, reproduced when, for both time scales and both raw and normalized TE, the fit on the average distribution has R2 of at least 0.9 and the 1st and 99th percentiles of the significant TE values differ by at least a factor of 100 (two orders of magnitude); R2 and the spread are reported for every recording.
- fig4bd-heavy-tailed-degree
The total degree distributions are heavy-tailed, with many more high-degree neurons than in random networks with the same numbers of neurons and connections.
the degree distributions indicate that the real data contained many more high-degree neurons than would be expected in a random network
Results, Connection Weight and Degree Distributions, paragraph 4; Figure 4B and 4DHow it will be judged
Networks as in M-TE, M-SIG and M-SUB. Random networks made by placing binary connections with uniform probability among the same number of neurons with the same number of connections (paragraph 4), with the same sampling as the real data (Fig 4 legend), so under reading (s) one random network per sub-network. Distributions of total degree averaged over recordings, per time scale. The paper gives no measure of the tail. Reading fixed here, reproduced when, at both time scales, the fraction of neurons whose total degree exceeds the 99.9th percentile of the random networks' total degree is at least 10 times 0.001 (and the largest real degree exceeds the largest random one). The fraction is reported for every reading of M-TE and M-SUB.
- fig4bd-out-tail-longer
The in-degree distribution has a shorter tail than the out-degree distribution, so there are more high out-degree neurons than high in-degree neurons.
note that the in-degree distribution had a shorter tail than the out-degree distribution, indicating that there were more high out-degree neurons than there were high in-degree neurons
Figure 4B and 4D legendHow it will be judged
Networks as in fig4bd-heavy-tailed-degree. The paper gives no measure of the tail. Reading fixed here, reproduced when, at both time scales, the 99th percentile of out-degree is larger than that of in-degree and the largest out-degree is larger than the largest in-degree, pooled over recordings; a one-sided Wilcoxon signed-rank test over recordings of the 99th percentiles is reported as well.
- fig5b-out-degree-positive
Most recordings show a positive correlation between a transmitter's out-degree and the synergy computed by its receivers.
the majority of recordings exhibited positive correlations between transmitter out-degree and computation
Results, Degree and Computation, paragraph 1; Figure 5BHow it will be judged
As fig5a-in-degree-uncorrelated, with the transmitter's out-degree. Reproduced when more than half of the correlations are positive and the binomial probability of that many positives or more under p = 0.5 is below 0.05 (alpha a reading; the paper names none), over both time scales pooled, as the panel pools them (M-CORR); each time scale alone is reported. Partially reproduced when a majority is positive but not significant.
- fig5ab-correlations-beyond-null
Nearly all the per-recording degree and synergy correlations lie beyond a null of randomized degree and computation pairings, whose correlations sit near zero.
Nearly all correlations were likely to be significant given the proximity of the null model correlations (no correlation) to zero (null model consisted of randomized degree/computation pairings) (N null = 400)
Figure 5A and 5B legendHow it will be judged
For each correlation of fig5a-in-degree-uncorrelated and fig5b-out-degree-positive, null correlations from random permutations of degree against synergy within the same recording and time scale. N null = 400 against N data = 40 gives 10 permutations per correlation, the reading taken. The paper gives no rule for significance. Reading fixed here, a correlation is beyond the null when its absolute value exceeds the 99th percentile of the absolute null correlations pooled over all 400; reproduced when at least 90% of correlations in each panel are beyond the null.
- fig5cd-pooled-trends
Pooled over all neuron groups and recordings, synergy shows no trend with receiver in-degree and rises with transmitter out-degree, at both time scales.
These trends were also observed in distributions of all neuron groups combined across all recordings for the two time scales of interest
Results, Degree and Computation, paragraph 1; Figure 5C and 5DHow it will be judged
Synergy values of all triples pooled over recordings, grouped by degree, with only degrees having 20 or more neuron groups kept (Fig 5 legend), the median per degree. The paper gives no test. Reading fixed here, Spearman correlation of the per-degree medians with degree; reproduced when, at both time scales, it is positive with p < 0.05 for out-degree and is not significantly positive for in-degree.
- fig6-information-gain-not-rising
The information gained by adding inputs to a neuron, a bound on its highest-order synergy, stays constant or decreases with the number of inputs at both time scales; exponential fits to the medians give small negative exponents, one with a 95% range overlapping zero.
we found that the information gain remained constant or decreased with added number of inputs ... Both fits produced small negative exponent values, one of which had an error overlapping zero
Results, Degree and Computation, paragraph 2; Figure 6How it will be judged
Information gain (Eq 12, not in the text read) read from Methods, Multivariate Transfer Entropy and Computation, last two paragraphs, as the TE from all n inputs jointly to I minus the TE from n - 1 of them, averaged over the n choices of the input left out. Open, whether it is normalized; the paper normalizes the PID terms by H(I_F) but does not say so for Fig 6; readings (u) normalized by H(I_F), (v) raw bits. For each receiver and n, all combinations of n of its inputs or 100 sampled combinations, whichever is smaller, averaged per neuron; n up to 6. Open, the first n; readings (a) n from 2 to 6, (b) n from 1 to 6. Network readings as in M-TE, M-SIG and M-SUB. Medians over neurons, pooled over recordings, fit with A exp(k n) by nonlinear least squares with a 95% confidence interval for k (Fig 6 legend). Reproduced when, at both time scales, k is negative and its interval does not lie wholly above zero (the legend's "Both fits produced small negative exponent values"); partially reproduced when no interval lies wholly above zero but a k is positive (gain constant, not decreasing); not reproduced when either time scale has an interval wholly above zero.
- table1-pid-examples
On the example distributions of Table 1, the PID multivariate TE finds synergy only in the synergistic and the synergistic and redundant examples; mutual information misses the hidden self interaction, and interaction information misses simultaneous synergy and redundancy and unique information.
Synergy is only found in the Synergistic Interaction example and the Synergistic and Redundant Interaction example
Materials and Methods, Multivariate Transfer Entropy and Computation, paragraphs 5 and 6; Figure 2 and Table 1How it will be judged
A computation on the joint distributions printed in Table 1, using no recorded data. PID terms as in M-PID, MI as Eq 1 and interaction information II(J_P; K_P; I_F) as the standard difference of conditional and unconditional mutual informations (Eq 11, not in the text read). The table's entries are rounded to four digits, so each column is renormalized to sum to 1 and values within 0.001 bits of zero count as zero. Reproduced when synergy is above 0.001 bits in exactly those two examples; in the hidden self interaction MI(J_P; I_F) is above zero while TE and every PID term are zero (MI does not separate J from the drive by I's own past); in the synergistic and redundant example II is zero while synergy and redundancy are not; and in the single and redundant example the unique information of J is above zero while the absolute value of II equals the redundancy (II does not reflect the unique information).
- fig7c-degree-modified-rule-matches
In a two-layer feedforward model, degree-modified and firing-rate-modified Hebbian rewiring rules qualitatively reproduce the degree and synergy correlations of the real data, the degree-modified rule more closely, while a pure Hebbian rule and random wiring do not.
Both the degree-modified and firing rate modified Hebbian rules qualitatively matched the degree vs. computation correlation results seen in the real data ... The degree-modified rule was closer than the firing rate modified rule ... the purely Hebbian rule and the random network produced correlation results that were qualitatively very different from the real data
Results, Feedforward Network Model, paragraph 3; Figure 7CHow it will be judged
A simulation with the parameters of Materials and Methods, Feedforward Network Model (20 binary neurons per layer; firing probability a sigmoid of input current with alpha about 0.023 and beta about 4.6, read as p = 1 / (1 + exp(beta - alpha I)), which gives rare firing at I = 0 and p = 0.5 at I = I_con N_Neurons = 200; I_con = 10; 80 connections; rewiring by 500 runs of statistics then one swap, repeated 80 times; 100 models per type). The currents from the binary signal (Eqs 16 to 19), the form of the score (Eq 20) and the fitted scores (Eqs 22 and 23) are not in the text read and must be taken from the version of record's equations before analysis. Degree and synergy correlations of the models computed as in M-PID and M-CORR on the model's states, one in-degree and one out-degree correlation per model (Fig 7C, light dots are individual models). The model's runs are independent and have no past, so the PID cannot be conditioned on the receiver's past as M-PID is. The paper does not say how it was computed in the model; reading, the PID of the states of two connected input neurons about the output neuron's state in the same run, over runs at least as many as the 500 used for rewiring, with the count reported. Fig 7C shows means and standard deviations; reading fixed here, a model type matches when its mean in-degree and mean out-degree correlations both lie within the real data's mean plus or minus one standard deviation. Reproduced when the degree-modified and firing-rate-modified types match, the degree-modified mean is nearer the real means (Euclidean distance over the two correlations, also a reading), and the Hebbian and random types do not match.
- fig7b-connectivity-patterns
The pure Hebbian rule pools connections among the input neurons most correlated with the network-wide signal, the firing-rate-modified rule spreads them to less correlated input neurons, and the degree-modified rule spreads them almost uniformly across the input layer.
As expected, the purely Hebbian rule pooled connections between the most strongly correlated neurons ... The firing rate modified rule spread connections more broadly to input layer neurons less well correlated with the binary network-wide signal. Finally, the degree-modified rule ... spread connectivity almost uniformly across the input layer
Results, Feedforward Network Model, paragraph 2; Figure 7BHow it will be judged
The models of fig7c-degree-modified-rule-matches, connection probabilities averaged over 100 models. The paper gives no measure. Reading fixed here, the fraction of connections leaving the upper half of input-layer indices (the neurons more correlated with the binary signal); reproduced when it is ordered Hebbian above firing-rate-modified above degree-modified, and the degree-modified fraction is within 0.5 plus or minus 0.1.
- fig7d-degree-rule-highest-conditioned-mi
The pure Hebbian rule gives the highest mutual information between connected neurons, but conditioned on the network-wide binary signal the degree-modified rule gives the highest; it alone raises neuron-to-neuron communication while also reinforcing network-wide correlation.
Unsurprisingly, we found the largest mutual information in the purely Hebbian rule ... when we conditioned the mutual information on the binary network-wide correlation signal, we found that the degree-modified Hebbian rule produced the highest mutual information
Results, Feedforward Network Model, paragraph 4; Figure 7D and 7EHow it will be judged
The models of fig7c-degree-modified-rule-matches. Per model, the mean over connections of MI between the input and output neuron's states (Eq 1) and of MI conditioned on b(t). Open, the number of runs MI is estimated from; reading, a fresh set of runs at least as large as the 500 used for rewiring, with the count reported. Pairs of rules compared by two-sided Mann-Whitney tests across the 100 models with Benjamini-Hochberg FDR control (Fig 7D legend). Which pairs the legend marks with p < 0.001 is shown only in the figure, which could not be read. Reading fixed here, the significance requirement applies to the result the legend notes ("the degree-modified Hebbian model showed higher mutual information after the effects of the common binary signal were removed"). Reproduced when the Hebbian rule has the highest mean unconditioned MI, the degree-modified rule has the highest conditioned MI and is above each other rule at corrected p < 0.001, and the Hebbian and firing-rate-modified rules' conditioned MI is not significantly above the random model's (Fig 7E, the other rules "maintained or decreased neuron-to-neuron communication"). Every pairwise test is reported.
- figs1-larger-model
With 40 neurons per layer the model gives the same qualitative results, the degree-modified rule again raising neuron-to-neuron communication, though the Hebbian and firing-rate-modified rules give larger conditioned mutual information than in the small model.
As with the smaller model, the larger model produced computation correlation results similar to the results seem in the data for the degree-modified and firing-rate modified Hebbian rewiring rules, but not the pure Hebbian rewiring rule ... As in the smaller model, the degree-modified Hebbian rewiring rule reinforced network-wide activity and increased neuron-to-neuron communication
Results, Feedforward Network Model, paragraph 6; S1 FigHow it will be judged
As fig7c-degree-modified-rule-matches, fig7b-connectivity-patterns and fig7d-degree-rule-highest-conditioned-mi with N_Neurons = 40 (so 320 connections and 320 rewirings) and the larger model's score equations (Eq 23 and Eq 24, not in the text read). Eq 15 involves N_Neurons and "All other parameters and equations related to the model were used as defined above"; open whether alpha and beta were recomputed; readings (a) alpha and beta solved again from Eqs 14 and 15 with N_Neurons = 40, (b) alpha 0.023 and beta 4.6 kept. Reproduced when the correlation match of fig7c holds for the degree-modified and firing-rate-modified rules and not for the Hebbian rule, the connectivity ordering of fig7b-connectivity-patterns holds (S1B Fig "qualitatively identical"), the degree-modified rule's conditioned MI is above the random model's (Mann-Whitney, FDR, p < 0.001), and the Hebbian and firing-rate-modified rules' mean conditioned MI are larger than in the 20-neuron models.
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