Claims 20
From the paper Self-organization of high-dimensional geometry of neural activity in culture · claims file · checked 2026-10-21: ready
- dishes-analysed
Seven dishes met the paper's inclusion rule (spontaneous activity observed continuously for more than 10 days) and were summarized.
Averaging data across seven dishes revealed that power law in PCA was consistently established around 15 DIV
Results, Self-organization of power law in PCA, paragraph 3; Methods, Data processing and principal component analysis, paragraph 1How it will be judged
Count the dishes in which recordings with activity above 0.03 Hz (reading S1 or S2) run continuously, without a day missing activity, over more than 10 days (Methods, Data processing, paragraph 1, "continuously observed for more than 10 days"). A count of dishes is exact; tolerance 0 for that reason.
- activity-onset
Spontaneous activity became detectable at about 2 to 3 DIV.
Spontaneous activity became detectable approximately 2 – 3 days in vitro (DIV)
Results, Self-organization of power law in PCA, paragraph 1How it will be judged
For each dish, the earliest DIV with a recording whose activity exceeds 0.03 Hz (readings S1, at least one electrode above 0.03 Hz, or S2). Reproduced when the median over dishes lies within the reported range 2 to 3 widened by 10% of each bound (1.8 to 3.3, the expected value and tolerance above). The paper gives no detection rule beyond the 0.03 Hz selection, which is used for that reason. If the dataset starts each dish later than this, the claim cannot be tested.
- fig1b-async-to-bursts
As the cultures matured, spiking changed from asynchronous firing to synchronous bursting.
During this transition from exponential to power-law decay, spiking activity evolved from asynchronous firing to synchronous bursting
Figure 1B; Results, Self-organization of power law in PCA, paragraphs 1 and 4How it will be judged
The paper shows this in raster plots only and defines no burst or synchrony measure. Readings, each over all recordings of all dishes against DIV, (a) the mean pairwise Pearson correlation of the 100 ms spike counts (the bins of the Methods), (b) the largest fraction of electrodes active within one 100 ms bin, as a share of electrodes. Reproduced when under each reading the Spearman correlation with DIV is positive with p < 0.05, and the dish median at 15 DIV and later exceeds that at 3 to 5 DIV. The test and threshold are a reading of "evolved" chosen here, as the paper gives none.
- fig1d-power-law-emerges
In early cultures the variance spectrum decays faster than a power function; as the culture matures it follows a power function, linear on log-log axes.
Initially, the variance spectrum decayed more rapidly than a power function. However, as the culture matured, the spectrum began to follow a power function, appearing linear on a bilogarithmic scale
Figure 1D; Results, Self-organization of power law in PCA, paragraph 2How it will be judged
Fit b per recording (fit readings F1 and F2). Reproduced when in a majority of the seven dishes the recordings of the first three recorded DIV have b at or above 0.1 and the recordings from 15 DIV on have b below 0.1. The 0.1 boundary is the paper's own threshold between its Exponential and Power-law groups (Results, Co-occurrence, paragraph 3). The first three DIVs, the 15 DIV boundary (from Results paragraph 3) and the majority of dishes are readings chosen here, as the paper gives no rule for Figure 1D.
- fig1e-example-dish
In the example dish the variance spectrum shifted from exponential to power-law decay around 10 DIV and stayed so to at least 19 DIV, with a power-law fit of exponent 1.30.
in this dish, the variance spectrum shifted from exponential decay to power-law decay around 10 DIV and remained stable at least until 19 DIV
Figure 1E and legend; Results, Self-organization of power law in PCA, paragraph 2How it will be judged
The example dish is not identified, and the paper does not say which spectra the red line of Figure 1E fits. The shift is the first DIV from which b stays below 0.1 (the paper's group threshold). The exponent is read as (a) the median of c over that dish's recordings from the shift to 19 DIV, (b) c fitted to the 19 DIV spectrum, (c) a pure power law fitted to all the dish's spectra from the shift on, pooled. Reproduced when at least one of the seven dishes has a shift within tolerance, b below 0.1 at every recording from the shift to 19 DIV, and an exponent within tolerance under one reading, with fit reading F1 or F2.
- fig1f-transition-15div
Across seven dishes the exponential decay rate of the variance spectrum is large early in development and falls as the culture matures, so that the power law in PCA is established around 15 DIV.
Averaging data across seven dishes revealed that power law in PCA was consistently established around 15 DIV ... The exponential decay rate, which quantifies the degree of exponential decay, was large in the early stages of development, indicating a dominance of exponential decay. As the culture matured, the decay rate decreased, reflecting a shift toward power-law decay
Figure 1F (left); Results, Self-organization of power law in PCA, paragraph 3How it will be judged
Fit b per recording (F1 and F2). The decrease holds when the Spearman correlation of b with DIV over all recordings is negative. "Established" is read as the first DIV from which b stays below 0.1 (the paper's group threshold), taken as (a) on the 3-day moving average over DIV of b pooled over dishes (the thick line of Figure 1F), (b) per dish, the median over dishes. Reproduced when b decreases with DIV and the DIV is within tolerance under one reading.
- fig1f-exponent-1p2
Once established, the power-law exponent of the variance spectrum stabilized at about 1.2.
The powerlaw exponent stabilized at approximately 1.2
Figure 1F (right); Results, Self-organization of power law in PCA, paragraph 3How it will be judged
The exponent c of the fit, over recordings after the transition DIV found in fig1f-transition-15div. Readings (a) the median of c over those recordings, (b) the 3-day moving average of c at the last DIV. Reproduced when the value is within tolerance under one reading, with fit reading F1 or F2.
- fig1d-shuffle
Temporal shuffling leaves the variance spectrum unchanged early in development but, once the power law has emerged, disrupts it and returns it to exponential decay.
During the initial development period, shuffling did not alter the variance spectra. However, after the emergence of the power law in PCA, shuffling significantly disrupted the power law, reverting them to exponential decay
Figure 1D, dashed lines and legend; Results, Self-organization of power law in PCA, paragraph 4How it will be judged
Shuffle each recording as in the Figure 1D legend and fit b to the original and the shuffled spectra (F1 and F2). The paper reports no test. Early recordings are those in the Exponential group (b at or above 0.1); late ones those in the Power-law group. Reproduced when (i) in early recordings the median ratio of shuffled to original b lies within 0.9 to 1.1 (the registry's default 10%), and (ii) in late recordings the shuffled b is at or above 0.1 in a majority and exceeds the original b, with a one-sided Wilcoxon signed-rank test over recordings at p < 0.05. The test and the 10% band are readings of "did not alter" and "significantly" chosen here, as the paper gives none; the effect sizes are reported.
- fig2b-spatial-structure
Early in development (3 DIV) all PCs correspond to a few scattered electrodes; in mature cultures (15 DIV) dominant PCs correspond to localized clusters of electrodes, while minor PCs remain on globally distributed, sporadic electrodes.
In the early stages of development(3 DIV), all PCs corresponded to a small number of scattered electrodes. However, as the culture matured (15 DIV), dominant PCs began to correspond to localized clusters of electrodes, while minor PCs remained associated with globally distributed, sporadic electrodes
Figure 2B; Results, Self-organization of spatial structure of PCs, paragraph 2How it will be judged
Shown as maps of PC weights; judged with the paper's own measure. Reproduced when fig2c-locality-spectrum is reproduced and, in a majority of dishes at 15 DIV (or the nearest recorded DIV), the mean locality of the first 10 PCs exceeds that of the last 10, while at 3 DIV it does not exceed it by more than 10%. The 10-PC groups follow the window of the Figure 2C moving average; the groups, the majority and the 10% band are readings chosen here, as the paper judges Figure 2B by eye.
- fig2c-locality-spectrum
The locality spectrum (the number of electrodes with local Moran's I above threshold, against PC index) is flat early in development and becomes steeper as the culture matures.
Initially, the locality spectrum was flat, but as culture matured, it became steeper
Figure 2C; Results, Self-organization of spatial structure of PCs, paragraph 3How it will be judged
Locality spectra and slopes as in the opening comment (readings M1 and M2, L1 and L2). Steeper means a more negative slope (dominant PCs more local). The sign is read from the definition of locality, as the text gives no slope values and Figure 2D was not read. Reproduced when the Spearman correlation of the locality slope with DIV, over all recordings, is negative with p < 0.05, and the median slope at 3 to 5 DIV is closer to zero than that at 15 DIV and later. The test is a reading of "became steeper", which the paper does not test.
- fig2d-locality-slope
The slope of the locality spectrum confirms that spatial structure emerges progressively and is absent in the initial stages of development.
analysis of the slope of the locality spectrum confirmed the progressive emergence of spatial structure, which was absent during the initial stages of development
Figure 2D; Results, Self-organization of spatial structure of PCs, paragraph 3How it will be judged
As fig2c-locality-spectrum, on the 3-day moving average of the slope over DIV (Figure 2D, blue line). Reproduced when the moving average is near zero at the first recorded DIVs (its magnitude below 10% of its most negative value) and falls over DIV, without returning to zero once below half of its most negative value. The 10% and half bounds are readings chosen here of "absent" and "progressive", as the paper gives no number or test.
- fig2d-shuffle-locality
Temporal shuffling, which removes inter-electrode correlations, disrupts the spatial structure of PCs; the locality spectrum becomes nearly independent of PC index.
applying a circular shift to data with an established spatial structure, which removed inter-electrode correlations, disrupted the structure ... the locality spectrum became nearly independent of the PC indices
Figure 2D, dashed line; Results, Self-organization of spatial structure of PCs, paragraph 4How it will be judged
Shuffle as in the Figure 1D legend. Data with established structure are read as (a) recordings from 15 DIV on, (b) recordings in the PCA Power-law group. Reproduced when, under each of M1 and M2 and L1 and L2, the median shuffled slope has a magnitude below 10% of the median original slope and the shuffled slopes are less negative than the original ones by a one-sided Wilcoxon signed-rank test at p < 0.05. "Nearly independent" and the test are readings chosen here, as the paper gives no number or test.
- fig3c-avalanches-emerge
Across seven dishes the cascade size distribution shifted from exponential to power-law decay at about 15 DIV, with a power exponent of about 1.5.
Data summarized from seven dishes show that the distribution shifted from an exponential decay to a power-law decay at approximately 15 DIV, with an exponent around 1.5
Figure 3C; Results, Co-occurrence of power law in PCA and neuronal avalanches, paragraph 2How it will be judged
Cascades and sizes as in the opening comment (readings A1 and A2), fit over sizes 1 to 128 (F1 and F2), per recording. The shift DIV is read as in fig1f-transition-15div, on the avalanche b with the same 0.1 boundary, (a) on the pooled 3-day moving average, (b) per dish, the median. The exponent is the median c over recordings after the shift. Reproduced when both values are within tolerance under one reading. The 0.1 boundary for avalanches is carried over from the PCA groups; the paper gives none for avalanches.
- fig3ef-groups-cooccur
Recordings classified by the PCA decay rate alone (Power-law group, b below 0.1) show both power laws, while the Exponential group shows neither.
Interestingly, although these groups were categorized based solely on the power law in PCA, regardless of the power law in the neuronal avalanches, it was clearly observed that both phenomena appeared in the Power-law group ( Fig. 3E ). In contrast, neither power law was observed in the Exponential group
Figure 3E and 3F; Results, Co-occurrence of power law in PCA and neuronal avalanches, paragraph 3How it will be judged
Groups by PCA b with the paper's threshold 0.1, a method value used as given. The panels show representative recordings. Readings, (a) per recording, the avalanche b is lower in the Power-law group than in the Exponential group (one-sided Mann-Whitney U, p < 0.05, a test chosen here) and the median avalanche b is below 0.1 in the Power-law group and at or above 0.1 in the Exponential group; (b) the cascade size distribution pooled over all recordings of each group, fitted, has b below 0.1 for the Power-law group and at or above 0.1 for the Exponential group. Reproduced when one reading holds under the fit and size readings.
- figs1-classified-by-avalanches
A similar co-occurrence is seen when recordings are classified by their neuronal avalanches.
A similar co-occurrence was also observed when data were classified based on the neuronal avalanches (Fig. S1)
Figure S1, cited in Results, Co-occurrence of power law in PCA and neuronal avalanches, paragraph 3How it will be judged
Figure S1 and its legend are not in the text read, so the threshold on the avalanche b is not known. The reading is the same threshold as the PCA groups, 0.1, on the avalanche b, with readings (a) and (b) of fig3ef-groups-cooccur applied with the roles of the two decay rates swapped. A different threshold in the supplement could change the outcome; the claim is open on that point until the supplement is read.
- figs2-shuffle-breaks-cooccurrence
The co-occurrence of the two power laws is easily disrupted by temporal shuffling, reflecting that the two phenomena are not inherently associated.
This co-occurrence is notable because it is easily disrupted by temporal shuffling, reflecting that these phenomena are inherently unassociated (Fig. S2)
Figure S2, cited in Results, Co-occurrence of power law in PCA and neuronal avalanches, paragraph 3; Discussion, paragraph 2How it will be judged
Figure S2 and its legend are not in the text read, so neither the shuffle applied to the avalanche analysis nor the measure of disruption is known. Readings, on recordings of the Power-law group shuffled as in the Figure 1D legend, (a) the shuffled data keep avalanche b below 0.1 while their PCA b is at or above 0.1 (the Discussion says sequences with avalanches but no power law in PCA are easy to construct), in a majority of recordings; (b) over all recordings, the correlation of fig3d-decay-rates-correlated computed on shuffled data is not positive with p < 0.05. The claim is open on this point until the supplement is read; where the readings disagree it is blocked as methods_underspecified.
- no-temporal-structure
The cultures did not show the in vivo temporal structure of PCs, in which dominant PCs have longer time scales than minor PCs.
This temporal structure is characterized by dominant PCs exhibiting longer time scales, while minor PCs exhibit shorter time scales. However, our study using the dissociated neuronal culture was unable to replicate such a temporal structure
Discussion, paragraph 4How it will be judged
A claim of absence, but the paper names no measure or test. Readings, on recordings from 15 DIV on, (a) the time scale of each PC's projection as the lag at which its autocorrelation (100 ms bins) first falls below 1/e, (b) the integral of the positive part of that autocorrelation; the claim holds when the Spearman correlation of time scale with PC rank is not negative with p < 0.05 in a majority of recordings. As the paper names no test, the outcome is reported under both readings, and the claim is blocked as methods_underspecified where they disagree.
- fig4d-cauchy-model-power-law
In the binary threshold network with heavy-tailed (Cauchy) connections, the variance spectrum decays exponentially for weak connections and becomes a power law at the critical point, with exponent 1.56, where neuronal avalanches also occur.
The variance spectrum exhibited an exponential decay when the typical connection strength was sufficiently smaller than the critical point. However, as the connection strength increased, the spectrum transitioned to a power-law decay at the critical point. ... The power-law exponent at the critical state was 1.56
Figure 4C and 4D; Results, Heavy-tailed connectivity is important for the co-occurrence, paragraph 4How it will be judged
A simulation, not a test on the recorded data. The Methods give the threshold theta 1, connection probability 0.01, the critical point at g 1, and Gaussian or Cauchy weights of strength g, but the network size N, the scaling of the distributions with g (the formulas are lost from the text), the run length, the initial state and inputs, and how model activity is binned for PCA are not given. Cannot be specified from the text read; recorded so the finding is covered.
- fig4d-gaussian-model-no-power-law
Networks with Gaussian connections, which lack neuronal avalanches, show no power law in PCA at any connection strength.
In contrast, Gaussian networks, which fails to reproduce neuronal avalanches, were also unable to reproduce a power law in PCA at any connection strength
Figure 4C and 4D; Results, Heavy-tailed connectivity is important for the co-occurrence, paragraph 4How it will be judged
A simulation, not a test on the recorded data; unspecified as for fig4d-cauchy-model-power-law. Recorded so the finding is covered.
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