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Distinct timescales of population coding across cortex

Abstract

The cortex represents information across widely varying timescales1,2,3,4,5. For instance, sensory cortex encodes stimuli that fluctuate over few tens of milliseconds6,7, whereas in association cortex behavioural choices can require the maintenance of information over seconds8,9. However, it remains poorly understood whether diverse timescales result mostly from features intrinsic to individual neurons or from neuronal population activity. This question remains unanswered, because the timescales of coding in populations of neurons have not been studied extensively, and population codes have not been compared systematically across cortical regions. Here we show that population codes can be essential to achieve long coding timescales. Furthermore, we find that the properties of population codes differ between sensory and association cortices. We compared coding for sensory stimuli and behavioural choices in auditory cortex and posterior parietal cortex as mice performed a sound localization task. Auditory stimulus information was stronger in auditory cortex than in posterior parietal cortex, and both regions contained choice information. Although auditory cortex and posterior parietal cortex coded information by tiling in time neurons that were transiently informative for approximately 200 milliseconds, the areas had major differences in functional coupling between neurons, measured as activity correlations that could not be explained by task events. Coupling among posterior parietal cortex neurons was strong and extended over long time lags, whereas coupling among auditory cortex neurons was weak and short-lived. Stronger coupling in posterior parietal cortex led to a population code with long timescales and a representation of choice that remained consistent for approximately 1 second. In contrast, auditory cortex had a code with rapid fluctuations in stimulus and choice information over hundreds of milliseconds. Our results reveal that population codes differ across cortex and that coupling is a variable property of cortical populations that affects the timescale of information coding and the accuracy of behaviour.

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Figure 1: Imaging AC and PPC responses during a sound localization task.
Figure 2: Encoding and decoding stimulus and choice information in AC and PPC.
Figure 3: PPC populations were more coupled than AC populations.
Figure 4: Coupling is associated with a longer timescale of population codes for choice in PPC.

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Acknowledgements

We thank S. Chettih and M. Minderer for developing the cell selection software, and J. Assad, J. Drugowitsch, O. Mazor, and members of our laboratories for comments on the manuscript. We also thank the Research Instrumentation Core at Harvard Medical School. This work was supported by a Burroughs-Wellcome Fund Career Award at the Scientific Interface, the Searle Scholars Program, the New York Stem Cell Foundation, the Armenise-Harvard Foundation, the Alfred P. Sloan Research Foundation, a NARSAD Brain and Behavior Research Young Investigator Award, National Institutes of Health grants from the National Institute of Mental Health BRAINS program (R01-MH107620) and the National Institute of Neurological Disorders and Stroke (R01-NS089521), the Autonomous Province of Trento (Grandi Progetti ATTEND), and the Fondation Bertarelli. C.A.R. is a Life Sciences Research Foundation Simons Fellow. C.D.H. is a New York Stem Cell Foundation Robertson Neuroscience Investigator.

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Authors and Affiliations

Authors

Contributions

C.A.R. and C.D.H. conceived the project and designed the experiments. All authors contributed to the development of the concepts presented in the paper. C.A.R. performed the experiments. All authors designed the data analysis approaches. C.A.R. and C.D.H. conceived the application of the GLM and coupling approaches. E.P. and S.P. conceived information and consistency measures and modelling approaches. C.A.R. and E.P. performed the data analysis. C.A.R. and C.D.H. wrote the manuscript with contributions from E.P. and S.P. All authors contributed to the content and writing of the Supplementary Information.

Corresponding authors

Correspondence to Stefano Panzeri or Christopher D. Harvey.

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The authors declare no competing financial interests.

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Reviewer Information Nature thanks J. Pillow and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Figure 1 Sound frequency tuning in AC neurons.

a, Mean responses (maximum relative spike rate across the 1 s sound presentation) to sinusoid amplitude-modulated pure tones in example AC neurons. These tones were presented to passively listening mice after the task. a.u., arbitrary units. b, Histogram of sound responsive cells’ best frequencies, the frequency of the maximum response for each neuron (n = 206 neurons, unresponsive neurons were not included). cf, Information about the sound stimulus category and the mouse’s choice in the task were compared between neurons that were untuned or tuned for sound stimulus frequency as measured in a. Significant tuning was defined by comparing the frequency selectivity index (ymaxymean)/(ymax + ymean), where ymax is the mean response to the best frequency, and ymean is the mean response to the other frequencies, with the frequency selectivity index calculated with shuffled trial identities. Frequency-tuned and untuned neurons did not contain significantly different amounts of information about the stimulus category or choice in the task (P > 0.5, rank-sum test). g, h, In a subset of imaging experiments (n = 3), we played the same sound location stimuli as in the task, in a similar repeating pattern as mice experienced during task trials (three consecutive stimulus repeats). Trial-averaged responses to sound location stimuli measured during the task (left) and during passive listening (right) contexts. Line colours indicate the sound location (see i). Bottom row: tuning curves measured as the average maximal relative spike rate during the sound presentation at each sound location in task (left) and passive (right) contexts. i, Sound location colour legend, which applies to g and h. j, Cumulative distributions of sound location selectivity indices (LSI: (ymaxymean)/(ymax + ymean), where ymax is the mean response to the best location, and ymean is the mean response to the other locations) measured in AC and PPC neurons during the task (solid lines) and passive listening (dashed lines). AC cells had significantly higher LSIs than PPC cells (P < 0.001, rank-sum test), and AC cells had significantly higher LSIs in the passive context than the active context (P < 0.001, signed-rank test; AC: n = 329; PPC: n = 386). k, Sound stimulus category information during the task in neurons untuned or tuned for sound location, determined by comparing LSIs in real and shuffled data during passive listening. Neurons with significant sound location tuning had more information about the sound location stimulus category (left versus right), P < 0.001, rank-sum test. l, Cumulative distributions of sound category information for neurons tuned and untuned for sound location (using LSI significance). m, Choice information in neurons untuned or tuned for the sound location. n, Cumulative distributions of choice information for neurons tuned and untuned for the sound location (using LSI significance). Location-selective neurons had similar distributions of choice information (P > 0.5, rank-sum test). o, Mean response of all neurons across each stimulus repeat during the task (left) and passive (right) contexts, from the subset of imaging experiments with identical passive and active stimuli (n = 117 neurons). Responses to sound repeat 1 tended to be higher than responses to repeats 2 and 3 (P < 0.001, signed-rank test). p, Histograms of the stimulus repeat during which cells had their maximal responses during task (left) and passive listening (right) contexts. q, Z-scored, trial-averaged activity of all AC neurons with three stimulus repeats in the passive context, sorted by time of peak mean activity and aligned to the time of the first sound onset. Responses during the task (left) and passive listening (right) were sorted by the time of peak response during the task. White vertical lines show the onset times of the first, second, and third sound stimulus repeats. Task trials with more or fewer than three repeats were excluded. The overall temporal pattern of activation across the AC population appeared similar in the two contexts, with a subset of neurons responding during the first sound stimulus presentation, and other neurons responding later, with some responses appearing to depend on subsequent sound stimulus repeats. Many neurons did not appear obviously responsive to the sound stimuli used in the task. Data are, in a, g, h, o, mean ± s.e.m.

Extended Data Figure 2 GLM components, fit quality, and model fit examples.

a, Time course of the behaviour variables included in the GLM during an example trial, in which the sound stimulus was played from location 1 (−90°) and the mouse turned left at the T-intersection to receive a reward. Each predictor was convolved with a set of basis functions (Methods, examples in bd). b, Generic set of basis functions that were convolved with behaviour variables and events, extending backwards and forwards in time to model a neuron’s response to, and prediction of, events. The density, temporal extent, and width of basis functions were tailored to each behavioural variable (Methods). c, Example set of basis functions used for sound onset for each of eight locations. These basis functions are shown before convolving with a vector that specifies sound onset time as a time series of zeros and ones (as shown in a). d, Example set of basis functions defined spatially along the extent of the stem of the T-maze, which were positive only when the mouse made a left turn in that trial. e, Example field of view showing GCaMP6 expression in PPC. f, Mean activity across all AC (red) and PPC (blue) cells, across all trials. Shading indicates s.e.m; n = 7 datasets for AC and PPC. g, Uncoupled encoding model performance measured using trial-averaged responses and predictions, quantified as explained variance. Each thin line is the distribution from a single dataset (n = 7 AC datasets, n = 7 PPC datasets). Thick lines indicate mean distributions across datasets. AC versus PPC: P > 0.1, rank-sum test. h, Uncoupled encoding model performance measured as the fraction of additional explained deviance compared with the null model on frame-by-frame activity (Methods). Each thin line is the distribution from a single dataset. Thick lines indicate mean distributions across datasets. AC versus PPC: P < 0.05, rank-sum test. Note that explained deviance is calculated over single imaging frames and single trials in the test dataset (not on averaged data), and, because of trial-to-trial variability of neuron responses, does not approach perfect prediction (1.0). i, Histograms of distributions of total beta score (the sum of the absolute value of beta coefficients) in fitted models across all AC and PPC neurons, for predictors in three categories: (1) sound, (2) running, and (3) position/choice (turn direction in the maze). For ease of display, identically zero values were ignored when making the histograms. AC neurons tended to have stronger weights for predictors related to the sound stimulus (P < 0.001, rank-sum test), while PPC neurons tended to have stronger weights for predictors related to position/choice (P < 0.05, rank-sum test). j, k, Relationship of predictor weights within single neurons in AC and PPC. For each neuron, a score within each predictor category was calculated as the sum of the absolute value of coefficients (‘total beta’). Clustering was used to reveal functional groups of neurons tuned to different sets of parameters (see Supplementary Information). Different clusters are indicated with different colours. Note that clustering was performed separately on AC and PPC data, hence the clusters obtained for AC are not related to those for PPC. ln, Fitted model components’ gain43 for variables related to running speed, position in the maze and turn direction, and sound location (exp(βX), right, where β is the fitted coefficient, and X is the task predictor convolved with the basis functions), during the various epochs of the trial. Data are mean ± s.e.m. o, Timescales of task predictors. A single exponential was fitted to the autocorrelation of each of the 419 task predictors used in the uncoupled model, to estimate each variable’s timescale of variability. Across all AC (red, n = 329) and PPC (blue, n = 386) neurons, the mean coefficient magnitude fitted by the model for each task predictor was compared with the decay time constant, to determine whether the longer coding timescale in PPC could be explained by neurons in PPC responding preferentially to variables with longer timescales of variability. Even for task variables with longer timescales, AC tended to have greater coefficients (P < 0.001, rank-sum test). It was thus unlikely that the longer coding timescales that we measured in PPC were due to its modulation by task variables with long timescales. Data are mean ± s.e.m. p, Example AC responses and model predictions. Trial-averaged responses of example AC neurons during the sound stimulus presentation in correct (black) and error (grey) test trials (left) and the model’s predicted responses in data that were left out (right). All responses were normalized to the maximum response across all trial conditions (y axis scale) and aligned to the time of the first sound stimulus onset. Each row is the trial-averaged response or prediction for trials of one of the eight sound location conditions. Neurons with model-fitted performance across the spectrum are included, from poorly fitted (25th percentile), to very well fitted (99th percentile). q, Same as p, for PPC.

Extended Data Figure 3 Choice probability and behavioural relevance of sensory information.

a, Red: AC neurometric curve computed from the performance of a sound location decoder (Supplementary Information). Dark grey: psychometric curve for mice from AC imaging sessions. Session-averaged psychometric and neurometric curves were positively correlated (r = 0.93, P < 0.001). Data are mean ± s.e.m. b, Intersection information above chance levels in AC neurons. The amount of intersection information per cell above chance level was 0.2% ± 0.1% in AC (larger than zero with P < 0.0001, paired signed-rank test). c, Conditional choice information plotted against stimulus information for all single AC cells. Stimulus information was computed without discounting the correlation between stimulus and choice (Spearman’s r = 0.33, P < 0.001; Supplementary Information). df, Same as ac, except for PPC. d, Session-averaged psychometric and neurometric curves were positively correlated (r = 0.99, P < 0.001). e, Intersection information above chance levels in PPC neurons was 0.7% ± 0.2% (P < 0.0001, paired signed-rank test). f, Spearman’s r = 0.43, P < 0.001. g, Cumulative conditional choice information, computed by the performance of a choice decoder assuming knowledge of all GLM predictors not directly related to choice (Supplementary Information). Cumulative conditional choice information was significant in both AC and PPC (AC: P < 0.05, PPC: P < 0.001, one-tailed t-test on the value of the choice information at the moment of the turn). Red, AC; blue, PPC; data are mean ± s.e.m. h, i, Total single-cell conditional choice information, computed as the maximum of the cumulative conditional choice information for each cell in AC and PPC. jl, Same as gi, quantifying the performance of the conditional choice decoder as a model-based choice probability19. j, Population choice probability was significantly larger than 0.5 in both AC and PPC at the last aligned time frame (P < 0.001, one-tailed t-test). k, Mean single-cell choice probability 0.537 ± 0.005 (larger than 0.5, P < 0.001, t-test). l, Mean single-cell choice probability 0.536 ± 0.006 (larger than 0.5, P < 0.001, t-test).

Extended Data Figure 4 Decoder controls.

a, Grey: behaviour performance during single imaging sessions used in all analyses. Overall behaviour performance did not correlate with the number of choice-selective neurons in the AC (r = −0.34, P > 0.1) or PPC (r = 0.38, P > 0.1) populations. Red, blue: single-session neurometric curves using a sound location decoder in AC, PPC, respectively (same as in Extended Data Fig. 3a, d and Supplementary Information). The r value in each panel reports the correlation coefficient between the neurometric and psychometric curves. *P < 0.05; **P < 0.01; ***P < 0.001; one-tailed test with a null hypothesis that correlation is not higher than chance. b, Left: z-scored trial-averaged activity of all AC neurons with >0.06 bits of stimulus information, sorted by time of peak mean activity, aligned to trial events as in Fig. 1d, e. Right: instantaneous stimulus category information in the same neurons. The scale bar showing time below the top right panel applies to all panels be and gj. c, Left: z-scored, trial-averaged activity of all AC neurons with ≤0.06 bits of stimulus information. Right: instantaneous stimulus category information in the same neurons. d, Left: z-scored, trial-averaged activity of all AC neurons with >0.06 bits of choice information, sorted by time of peak mean activity. Right: instantaneous choice information for the same cells. e, Left: z-scored, trial-averaged activity of all AC neurons with ≤0.06 bits of choice information, sorted by time of peak mean activity. Right: instantaneous choice information for the same cells. f, Information about stimulus category (left, magenta) and choice (right, magenta) averaged across all AC neurons with ≥0.06 bits of information, as a function of the time from the peak. Normalized, aligned activity in all cells (dashed line) and informative cells (solid red line) are superimposed. gk, Same as bf, for PPC cells. ln, Information about the exact location of the sound stimulus. l, The cumulative population decoder was used on subsets of trials from only two sound locations such that there were equal numbers of trials from each location and no other locations were present. The data are shown for a comparison of locations 6 and 8. Note that locations 6 and 8 are part of the same category and indicate the same correct choice in the task. m, Maximum cumulative information calculated as in l for other location pairs belonging to the same stimulus category (left or right). All imaging experiments were performed in the left hemisphere, so AC had higher information about contralateral sound stimulus locations. Data are mean ± s.e.m. n, Diagram showing the sound location arrangements for location pairs compared in decoders in l and m. o, Choice information in all datasets. Green bars: choice information that could be extracted from sound location owing to an uneven distribution of errors across sound locations. This was a concern, because more errors occurred at sound locations close to the midline (Fig. 1c), and perhaps location tuning could have led to an aberrant choice of information measurement. Light red (AC) and light blue (PPC): maximum instantaneous choice information in neuronal population activity. Dark red (AC) and dark blue (PPC): total cumulative choice information in neuronal population activity. The uneven distribution of error trials across sound locations was not sufficient to explain choice information in AC or PPC.

Extended Data Figure 5 Coupling and Pearson’s correlations across contexts.

a, The coupled model was fitted using random subpopulations of 37 neurons (the number of neurons in the smallest dataset) 100 times in all AC and PPC datasets. Cumulative distributions of performance of the coupled model using all subsamples of AC (red) and PPC (blue) datasets show that all PPC datasets still had greater coupling than all AC datasets (P < 0.01, rank-sum test), even when using smaller numbers of neurons. b, c, Cumulative distributions of the coupling index in AC (red) and PPC (blue), measured during passive listening and the ‘no task/stimulus’ context. d, Cumulative distributions of partial Pearson’s correlations (Methods) during the pre-turn period of the task in AC (red) and PPC (blue). Consistent with the higher coupling indices measured in PPC (Fig. 3d), correlations were higher in PPC than AC (P < 0.001, Kolmogorov–Smirnov test). e, Cumulative distributions of partial Pearson’s correlations during passive listening to the stimulus sets used in the task in AC (red) and PPC (blue) datasets. PPC was more correlated than AC, even when the mouse was not engaged in a task (P < 0.001; Kolmogorov–Smirnov test). f, Cumulative distributions of partial Pearson’s correlations measured in the ‘no task/stimulus’ context in AC (red) and PPC (blue). Again, PPC was more correlated than AC, in the absence of task or sound stimulus presentations (P < 0.001, Kolmogorov–Smirnov test). g, Cumulative distributions of Pearson’s correlations measured in the ‘no task/stimulus’ context when the mice were stationary (not running) on the ball (AC versus PPC: P < 0.001, Kolmogorov–Smirnov test). h, Cumulative distributions of mean relative spike rates in AC (0.24 ± 0.14 arbitrary units, mean ± s.e.m.) and PPC (0.45 ± 0.18 arbitrary units). AC versus PPC: P < 0.001, Kolmogorov–Smirnov test. i, Coupling index versus mean relative firing rate measured during the pre-turn period of the task. Each dot is one neuron. Because coupling and firing rate were not positively correlated (AC: r = −0.020; PPC: r = 0.007; P > 0.25), it is unlikely that higher firing rates in PPC caused an artefactual increase in correlation and coupling relative to AC. j, Partial Pearson’s correlations, computed across trials for time lags spanning 0 to over 1 s in AC (red) and PPC (blue), over all data, during the task. ***P < 0.001, rank-rum test on the average partial Pearson’s correlation across lags smaller than 0.5 s. Data are mean ± s.e.m. across cell pairs. k, Partial Pearson’s correlations in AC populations, computed separately for correct (red) and error (pink) trials, for pre-turn data. Data are mean ± s.e.m across cell pairs. l, Same as k, for PPC (dark blue, correct trials; light blue, error trials). ***P < 0.001, rank-sum test on the average partial Pearson’s correlation across lags smaller than 0.5 s. m, Partial Pearson’s correlations in the pre-turn (red) and post-turn (pink) trial epochs in AC populations. Data are mean ± s.e.m across cell pairs. n, Same as m, for PPC. ***P < 0.001, rank-sum test on the average partial Pearson’s correlation across lags smaller than 0.5 s.

Extended Data Figure 6 Using the cell–cell model to test possible contributions of task features to coupling.

To help exclude the possibility that coupling parameters simply allowed the model to explain behavioural correlates not included in the uncoupled model, rather than neuron–neuron correlations, we removed all the task predictors from our model to create a cell–cell model that only had coupling predictors. We reasoned that if the model could misattribute common drive to neurons by behaviour variables, then the cell–cell model should be able to take on the uncoupled model’s prediction of responses to task parameters. We estimated an upper bound on the bleed-through of task variables to coupling parameters by comparing the cell–cell model dcxc with dcdu, the increase in model performance when including coupling predictors in addition to the task predictors. If the coupling predictors could explain all of the responses related to the task predictors, dcxc would far exceed the coupling value. a, b, Performance of a version of the encoding model with only the activity of other neurons as predictors and no task predictors (cell–cell model) compared with coupling (performance of coupled model − performance of uncoupled model) in AC (a) and PPC (b). c, Comparing cumulative distributions of coupling in AC (red line) and PPC (blue line) with our estimates of an upper bound on the extent to which coupling could be explained entirely by task-related variables (black lines). Note that the coupling distribution in AC cells (red line) was mostly restricted to values less than the upper bound on coupling explainable by task-related variables, while coupling in many PPC neurons (blue line) exceeded it (P < 0.01, rank-sum test). These results suggest that the higher level of coupling measured in PPC is unlikely to be due to shared common inputs to PPC neurons relating to task variables.

Extended Data Figure 7 Choice information redundancy.

a, b, Cumulative (dark lines) and instantaneous (light lines) choice information in AC (n = 7 datasets) and PPC (n = 7 datasets), aligned to the turn and averaged across datasets. Data are mean ± s.e.m. across datasets. c, Ratio of instantaneous to cumulative choice information in 1 s windows, relative to the time of the mouse’s turn in the maze. In PPC, instantaneous and cumulative information were similar before the turn. These results support our findings in Fig. 4, that information in PPC was consistent (in other words, redundant) across time before the mouse reported its choice by turning in the maze. Data are mean ± s.e.m across datasets. ***P < 0.001, z-test.

Extended Data Figure 8 Population scaling of information and consistency.

a, Scaling of total information content (maximum of cumulative information) with population size. Data are mean ± s.e.m. across datasets. Lines: analytical prediction from the random overlap model (Supplementary Information). b, Scaling of information consistency with population size, by measuring τ2 (the long timescale component of decoder consistency, as in Fig. 4f) while varying population sizes (Supplementary Information). Data are mean ± s.e.m. across datasets. While information in AC and PPC grew with increasing population size, the coding timescale remained constant in AC, but grew modestly in PPC.

Extended Data Figure 9 Simple generative model of sequential neuronal activity and the effect of shuffling on information content.

a, Schematic of simple model of choice tuning and statistical coupling between cells, expressed as a probabilistic graphical model. ‘Choice’ indicates the choice encoded by the neuronal population in any given trial, represents the activation of cell i, β is the strength of choice tuning, and γ1 and γ2 represent the strength of the statistical coupling of cell i to cell i − 1 and cell i − 2, respectively (Supplementary Information). b, Example of cell activity and decoded choice signal generated by the model for a batch of 20 trials encoding right choice. For each trial, the top row indicates the activity of left-preferring cells (black, active). The middle row indicates the activity of right-preferring cells. The bottom row indicates the choice decoded at each instant from the population activity (green, right; purple, left; Supplementary Information). Symbols on the right indicate whether the readout model implemented the correct choice. c, Temporal consistency computed across 105 trials, each composed of 50 time steps. Different shades of red (or blue) indicate different multiplicative scaling factors applied to both coupling parameters γi, ranging from 0 for no coupling to 1 for the values derived from experimental data in AC (or PPC). Dashed lines: consistency computed for shuffled data (superimposed with the solid lines corresponding to no coupling). d, Same as c, for the instantaneous choice information contained in the choice signal generated by the model, over the first ten time steps of the simulation. Note how cross-cell coupling enables accumulation of choice information. Note also how information in shuffled data is identical to the information in the unshuffled data. e, Temporal consistency for simulated PPC data, computed separately for behaviourally correct trials (solid line) and error trials (dashed line), as determined by the readout model described in Supplementary Information. f, Behavioural performance generated by the readout model (Supplementary Information) as a function of strength of the coupling in the model; 0 corresponds to no coupling, 1 to the value of the coupling parameters derived from the experimental data. g, Instantaneous stimulus information measured 1 s after the first stimulus onset, in real experimental data (red) and after disrupting coupling by shuffling the identities of trials of the same condition independently for each neuron (grey). Information was computed for random subpopulations of 37 cells and averaged across 48 such random selections. Circles represent individual datasets, bars represent the average across datasets, data represent mean ± s.e.m. h, Same as g, for cumulative information at the last aligned time point in a trial. i, Same as g, for choice information in both AC (red) and PPC (blue) at the moment of the turn. j, Same as i, for cumulative information at the last aligned time point in the trial.

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Runyan, C., Piasini, E., Panzeri, S. et al. Distinct timescales of population coding across cortex. Nature 548, 92–96 (2017). https://doi.org/10.1038/nature23020

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