Temporal coding of reward-guided choice in the posterior parietal cortex

Temporal coding of reward-guided choice in the posterior parietal cortex Hawellek Wong Pesaran

Tag layer of the DHSS Meta-Tagging Project. The article text is reproduced from the staged copy named in sourceDesc and is not altered; the tags are held separately in standOff so that overlapping and nested spans are preserved.

Temporal coding of reward-guided choice in the posterior parietal cortex 2016 Proceedings of the National Academy of Sciences of the United States of America 10.1073/pnas.1606479113 Hawellek2016-temporal-coding-of-reward-guided-choice-in-t Hawellek2016-temporal-coding-of-reward-guided-choice-in-t.txt, the project's staged copy 0f51fc22dbcf1c3a47673c6a38899fb871fdc08c not-redistributable neuroscience

the paper's own words

the tag layer; a sentence written by the tagger about the paper, always anchored to a quotation but not itself a quotation

0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them whether the information a parietal neuron's firing rate carries about an upcoming choice depends on when in the ongoing population rhythm the spikes occur Quotation withheld because this record is not cleared for redistribution. whether and how the coding of decisions depends on the temporally structured firing of parietal neurons Quotation withheld because this record is not cleared for redistribution. choice information is modulated by beta and gamma phase, and for beta it peaks at a different phase from the spike count, so information and excitability come apart Quotation withheld because this record is not cleared for redistribution. mechanism Quotation withheld because this record is not cleared for redistribution. phase-dependent coding of choice in posterior parietal cortex Quotation withheld because this record is not cleared for redistribution. electrophysiology electrophysiology Quotation withheld because this record is not cleared for redistribution. mechanisms An asymmetric interplay of excitation and inhibition within the beta cycle produces an uninformative upswing and an informative downswing of spiking duplicate of: mechanisms[3] Quotation withheld because this record is not cleared for redistribution. mechanisms Beta rhythms are tuned to large-scale network communication rather than local processing, which is why choice information becomes separated in time from local excitability Quotation withheld because this record is not cleared for redistribution. mechanisms Downstream ensembles read out the two rhythms with different integration windows, beta's extending past the moment of peak synchronous input to catch the later information peak Quotation withheld because this record is not cleared for redistribution. beta spiking is proposed to come from an asymmetric interplay of excitation and inhibition, giving an uninformative upswing and an informative downswing at similar spike counts Quotation withheld because this record is not cleared for redistribution. the two bands are read as two network scales, gamma as local bottom-up processing and beta as top-down linkage to a larger cortical network status: the paper's own words: may reflect Quotation withheld because this record is not cleared for redistribution. downstream ensembles may integrate over different windows in the two bands, with the beta window reaching past peak synchrony to the later information peak Quotation withheld because this record is not cleared for redistribution. theta may regulate the faster scales, since theta phase predicts beta and gamma amplitude Quotation withheld because this record is not cleared for redistribution. parietal spiking may multiplex decision signals into a beta and a gamma channel Quotation withheld because this record is not cleared for redistribution. Mutual information estimates could have been inflated at phase bins containing few spikes; the authors re-ran the analysis with stratified spike counts. what this limits: every mutual-information value: MI ESTIMATION MAY HAVE BEEN BIASED BY THE DIFFERING SPIKE COUNTS AT DIFFERENT PHASES OF ACTIVITY Quotation withheld because this record is not cleared for redistribution. How the beta-band dissociation between spiking and information is generated, and how downstream populations could read it out, is left open. what this limits: the mechanism behind the beta dissociation: it RAISES QUESTIONS ABOUT HOW THE ACTIVITY CAN BE GENERATED AND HOW OTHER NEURONAL POPULATIONS CAN DECODE SUCH ACTIVITY EFFICIENTLY Quotation withheld because this record is not cleared for redistribution. how such a code is generated and how any downstream population could read it efficiently is left open duplicate of: limitations[1] · what this limits: the same scope as limitations[1] - generation and readout both open Quotation withheld because this record is not cleared for redistribution. the proposed source of the beta dissociation - the beta to gamma phase difference - was tested and did not correlate with it what this limits: the paper's own candidate explanation, which it tested and rejected: WE OBSERVED NO CORRELATION BETWEEN THE BETA-GAMMA PHASE DIFFERENCE AND THE MOMENT OF THE BETA CHOICE-MI Quotation withheld because this record is not cleared for redistribution. the primary modulation statistic assumes a single concentration across phase bins and cannot see multimodal modulation, so a second statistic had to be run what this limits: the modulation-strength statistic: THE MEAN RESULTANT LENGTH R ASSUMES A UNIMODAL CONCENTRATION ... IT IS INSENSITIVE TO MORE COMPLEX FORMS OF MODULATION SUCH AS MULTIMODAL MODULATIONS - so the analysis was REPEATED using entropy-based permutation statistics Quotation withheld because this record is not cleared for redistribution. MI is positively biased for smaller samples and spuriously high for phase bins with few spikes, and spike counts differ across phases, so MI had to be reestimated with the counts equal across phase bins what this limits: the same scope as limitations[0], with the correction reported: WE REESTIMATED MI WHILE STRATIFYING SPIKE COUNTS TO BE EQUAL ACROSS PHASE BINS ... THE PATTERN ... PERSISTED Quotation withheld because this record is not cleared for redistribution. the unit of analysis is mixed: 149 units of which only 45 are single units, the rest multiunit what this limits: what a 'unit' means in every count here: 149 UNITS [97 ... (31 SINGLE UNITS AND 66 MULTIUNITS) FOR MONKEY C AND 52 (14 SINGLE UNITS AND 38 MULTIUNITS) FOR MONKEY R] Quotation withheld because this record is not cleared for redistribution. gamma coherence depended on how far apart the two electrodes were, which is read as gamma being more local rather than as a recording artefact what this limits: the spatial reach of the gamma result: THE DISTANCE BETWEEN THE ELECTRODE TIPS OF THE RECORDING PAIRS INFLUENCED THE SFC, comparing pairs at a median separation of 1.07 mm against the farther half Quotation withheld because this record is not cleared for redistribution. the MI between the spiking of a neuron and the movement condition, in or out of the response field Quotation withheld because this record is not cleared for redistribution. the trigonometric moment of a phase histogram, which is how the temporal concentration of spiking is measured in detail Quotation withheld because this record is not cleared for redistribution. PAC and N to M phase-phase locking, imported to ask how the three time scales relate Quotation withheld because this record is not cleared for redistribution. a fitted psychometric function relating the reward difference between the two shapes to the probability of choosing one Quotation withheld because this record is not cleared for redistribution. the whole analysis repeated while STRATIFYING the number of spikes at each phase bin eliminates: spike count as the driver of mutual information - MI rises with the amount of data, so a phase bin with more spikes would show more MI whether or not the phase carries anything · outcome (stated by the tagger, no quotation): held Quotation withheld because this record is not cleared for redistribution. THE ESTIMATOR'S OWN BIAS WOULD HAVE PRODUCED THE RESULT: mutual information runs high on small samples, the number of spikes differs from phase bin to phase bin, so phase-dependent information is exactly what a biased estimator would manufacture here Quotation withheld because this record is not cleared for redistribution. and it is answered twice over - each bin's estimate is restricted to the smallest bin's sample size, and spikes in excess of that minimum are deleted at random and the estimate repeated a thousand times Quotation withheld because this record is not cleared for redistribution. INFORMATION AND RATE ARE NOT THE SAME QUANTITY: in the beta band the spike count is symmetric about its preferred phase while the information is not, and the two peak at different times Quotation withheld because this record is not cleared for redistribution. so a rate-based reading of this code would place the information at the wrong moment - and in the gamma band, where the two do coincide, it would be right Quotation withheld because this record is not cleared for redistribution. THE NULL IS THE FINDING: removing the spike count's prediction leaves the beta information still modulated but flattens the gamma information entirely, so the same control analysis reports independence in one band and dependence in the other Quotation withheld because this record is not cleared for redistribution. THE HEADLINE STATISTIC NAMES ITS OWN BLIND SPOT: the resultant length assumes one concentration across phase bins and is insensitive to multimodal modulation, which is why an entropy measure is run beside it Quotation withheld because this record is not cleared for redistribution. A UNIT HERE IS TWO DIFFERENT KINDS OF OBJECT: 45 single units and 104 multiunits, and every count in the paper is reported split rather than pooled Quotation withheld because this record is not cleared for redistribution. and 'coherent' is a label produced by a threshold - a unit qualifies if any one of 59 frequency bins passes, and where two electrodes were available the one with more significant bins was kept Quotation withheld because this record is not cleared for redistribution. THEY TEST THEIR OWN PROPOSED MECHANISM AND IT FAILS: the beta to gamma phase difference looked like it could produce the dissociation, and the correlation is absent Quotation withheld because this record is not cleared for redistribution. claim_type: existence a second reading DIFFERING from the recorded value. Recorded: mechanism — note: a second reading, verbatim-verified, disagreeing with the value on the record. Not applied - a person decides. Quotation withheld because this record is not cleared for redistribution. method: spike-field coherence and phase-binned mutual information between firing and choice, with the spike-count prediction regressed out to give an orthogonal information measure, and cross-frequency coupling between the three bands a second reading DIFFERING from the recorded value. Recorded: electrophysiology — note: a second reading, verbatim-verified, disagreeing with the value on the record. Not applied - a person decides. Quotation withheld because this record is not cleared for redistribution. phenomenon: phase-of-firing coding: the same firing rate carries different amounts of information about a decision depending on the phase of the surrounding rhythm a second reading DIFFERING from the recorded value. Recorded: phase-dependent coding of choice in posterior parietal cortex — note: a second reading, verbatim-verified, disagreeing with the value on the record. Not applied - a person decides. Quotation withheld because this record is not cleared for redistribution. builds-on → the body of evidence linking firing-rate information to ongoing population dynamics in cortex (refs 35, 40-48) Quotation withheld because this record is not cleared for redistribution. builds-on → recent accounts positing that beta and gamma activity reflect different network-level processes (refs 31, 49-52) Quotation withheld because this record is not cleared for redistribution. builds-on → previous reports on the impact of temporal structure on firing-rate encoding in primate cortex (refs 47, 48) Quotation withheld because this record is not cleared for redistribution. extends → work showing that coherently active parietal ensembles predict reaction times and movement choices better than incoherent neurons Quotation withheld because this record is not cleared for redistribution. supports → primate visual cortex work in which gamma enhances selectivity around peak excitability Quotation withheld because this record is not cleared for redistribution. supports → prefrontal working-memory work in which information about sequential objects arrives at different beta phases Quotation withheld because this record is not cleared for redistribution. supports → the account in which gamma reflects local bottom-up processing and beta top-down linkage across a larger cortical scale Quotation withheld because this record is not cleared for redistribution. qualifies → its own explanation of the beta dissociation, by testing the beta to gamma phase difference against it and finding no relationship differs in: THE AXIS IS THE REFERENCE RHYTHM. 'Beta-gamma phase-phase coupling could contribute to the temporal localization of the choice-MI with respect to the beta [rhythm].' The paper qualifies its own account by naming what the localisation is measured AGAINST - a self-qualification, which is the rarer and more careful use of this type. CORRECTED AT: the quote originally ended at 'could contribute to the temporal localization of the choice-MI' - THE HYPOTHESIS HALF OF THE SPAN. The paper then rejects it: 'However, we observed no correlation between the beta-gamma phase difference and the moment of the beta choice-MI phase histogram on a single-spike LFP level.' The target already said 'finding no relationship', so the row's prose was right and its EVIDENCE recorded the possibility rather than the finding. Widened through the reversal. Quotation withheld because this record is not cleared for redistribution. builds-on → the view that theta-band activity regulates activity on faster time scales Quotation withheld because this record is not cleared for redistribution. choice-MI —distinct-from→ spike count choice-MI spike count differs in: THE AXIS IS SYMMETRY AROUND THE PREFERRED PHASE. 'Quotation withheld.' Both quantities are measured against the same reference phase; only one is distributed evenly about it, which is what dissociates the information from the firing that carries it. · strength of the relation: 1 · note: THE RESULT: in the beta band the two histograms have significantly different moments, so information and firing peak at different times in the cycle Quotation withheld because this record is not cleared for redistribution. beta activity —causes→ choice-MI beta activity choice-MI strength of the relation: 1 · note: peak-to-trough modulation of 15.3 percent, with the information raised on the downswing and lowered on the upswing Quotation withheld because this record is not cleared for redistribution. gamma activity —causes→ choice-MI gamma activity choice-MI strength of the relation: 1 · note: AND HERE THEY COINCIDE: no difference between the moments of information and spike count, so the same rhythm behaves differently in the two bands Quotation withheld because this record is not cleared for redistribution. beta activity —contrasted-with→ gamma activity beta activity gamma activity strength of the relation: 1 · note: the entire claim is a comparison of two bands measured in the same spikes at the same time Quotation withheld because this record is not cleared for redistribution. spike count —distinct-from→ beta activity spike count beta activity strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but beta activity 'independently correlated' with spike counts and choice encoding; distinct-from is loose. Quotation withheld because this record is not cleared for redistribution. stratifying —operationalised-as→ spike count stratifying spike count strength of the relation: 1 · note: spikes in excess of the smallest bin are deleted at random and the estimate repeated a thousand times - data discarded on purpose to equalise the samples Audit 2026-09-28: DOUBTFUL - read against its span and kept, but spike counts were stratified per phase bin; operationalised-as is loose. Quotation withheld because this record is not cleared for redistribution. mutual information —operationalised-as→ movement choice mutual information movement choice strength of the relation: 1 · note: 101 of 149 units carried significant choice information in the firing rate before any phase is considered Quotation withheld because this record is not cleared for redistribution. single units —distinct-from→ multiunits single units multiunits strength of the relation: 1 · note: 45 against 104, and every percentage in the paper is reported for the two classes separately instead of pooled Quotation withheld because this record is not cleared for redistribution. single units —operationalised-as→ spike waveforms single units spike waveforms strength of the relation: 1 · note: k-means over-clustering in a three-dimensional feature space, manual merging, and acceptance only where the cluster stayed clear of the multiunit cloud for a whole 100 second window Quotation withheld because this record is not cleared for redistribution. theta activity —part-of→ temporal structure theta activity temporal structure strength of the relation: 1 · note: three scales that respond differently to the same event: theta constant, beta down, gamma up Quotation withheld because this record is not cleared for redistribution. phase–phase coupling —distinct-from→ choice-MI phase–phase coupling choice-MI differs in: NOT MIS-TYPED - I HAD READ ONLY THE FIRST TWO SENTENCES. The span raises the possibility and then rejects it: 'Beta-gamma phase-phase coupling COULD CONTRIBUTE to the temporal localization of the choice-MI ... HOWEVER, WE OBSERVED NO CORRELATION BETWEEN THE BETA-GAMMA PHASE DIFFERENCE AND THE MOMENT OF THE BETA CHOICE-MI PHASE HISTOGRAM ON A SINGLE-SPIKE LFP LEVEL.' THE AXIS IS WHETHER THE PHASE DIFFERENCE PREDICTS THE CHOICE-MI MOMENT, and the evidence for the distinction is a NULL - the polarity gap again, in a row I had queued for retraction. · strength of the relation: 1 · note: THEY TEST THEIR OWN PROPOSED MECHANISM AND IT FAILS: the beta to gamma phase difference looked like it could produce the dissociation, and the circular correlation is flat Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but NO CORRELATION was found between the beta-gamma phase difference and the choice-MI moment; distinct-from rests on a null result. Quotation withheld because this record is not cleared for redistribution. choice-MI —distinct-from→ baseline epoch choice-MI baseline epoch strength of the relation: 1 · note: the effect is absent before the targets appear and absent in coherent units that carry no choice information - two places it should not be, and is not Quotation withheld because this record is not cleared for redistribution. trigonometric moment —operationalised-as→ spike count trigonometric moment spike count strength of the relation: 1 · note: the spike histogram's moment is indistinguishable from its preferred phase, which is what makes it symmetric and the information histogram's asymmetry meaningful Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the trigonometric moment describes the temporal concentration OF spiking across phase bins; operationalised-as is loose. Quotation withheld because this record is not cleared for redistribution. temporal structure —causes→ decision temporal structure decision strength of the relation: 1 · note: stated as a hypothesis before any measurement Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span states a hypothesis; causes states it as a finding. Quotation withheld because this record is not cleared for redistribution. mutual information mutual information Quotation withheld because this record is not cleared for redistribution. permutation test permutation test Quotation withheld because this record is not cleared for redistribution. false discovery rate correction false discovery rate correction Quotation withheld because this record is not cleared for redistribution. familywise error correction familywise error correction Quotation withheld because this record is not cleared for redistribution. Rayleigh test (circular uniformity) Rayleigh test (circular uniformity) Quotation withheld because this record is not cleared for redistribution. Watson-Williams test Watson-Williams test Quotation withheld because this record is not cleared for redistribution. Fisher's exact test Fisher's exact test Quotation withheld because this record is not cleared for redistribution. circular correlation circular correlation Quotation withheld because this record is not cleared for redistribution. linear regression linear regression Quotation withheld because this record is not cleared for redistribution. bootstrap bootstrap Quotation withheld because this record is not cleared for redistribution. confidence interval confidence interval Quotation withheld because this record is not cleared for redistribution. maximum likelihood estimation maximum likelihood estimation Quotation withheld because this record is not cleared for redistribution. psychometric function fitting psychometric function fitting Quotation withheld because this record is not cleared for redistribution. multitaper spectral estimation multitaper spectral estimation Quotation withheld because this record is not cleared for redistribution. principal component analysis principal component analysis Quotation withheld because this record is not cleared for redistribution. k-means clustering k-means clustering Quotation withheld because this record is not cleared for redistribution. mutual information mutual information Quotation withheld because this record is not cleared for redistribution. permutation tests permutation tests Quotation withheld because this record is not cleared for redistribution. Rayleigh tests Rayleigh tests Quotation withheld because this record is not cleared for redistribution. Watson–Williams tests Watson–Williams tests Quotation withheld because this record is not cleared for redistribution. Fisher’s exact test Fisher’s exact test Quotation withheld because this record is not cleared for redistribution. circular correlation circular correlation Quotation withheld because this record is not cleared for redistribution. false-discovery rate false-discovery rate Quotation withheld because this record is not cleared for redistribution. linear regression linear regression Quotation withheld because this record is not cleared for redistribution. Most recorded parietal units carried significant information about the animal's upcoming choice in their firing rate. Quotation withheld because this record is not cleared for redistribution. How much choice information a neuron's spiking carried depended on the phase of beta and gamma field activity, but not on theta phase. Quotation withheld because this record is not cleared for redistribution. For beta activity, choice information peaked at a different phase from spike count, on the downswing of the cycle. Quotation withheld because this record is not cleared for redistribution. For gamma activity, by contrast, choice information and spike count peaked at the same phase. Quotation withheld because this record is not cleared for redistribution. Once spike count was regressed out, gamma phase no longer modulated choice information, showing the gamma effect was not independent of excitability. Quotation withheld because this record is not cleared for redistribution. Gamma activity appeared more spatially local than theta or beta activity. Quotation withheld because this record is not cleared for redistribution. The three rhythms responded differently to the onset of the decision: theta unchanged, beta reduced, gamma enhanced. Quotation withheld because this record is not cleared for redistribution. Beta activity sits at the hub of cross-frequency interactions, coupled to theta by PAC and to gamma by phase-phase coupling. Quotation withheld because this record is not cleared for redistribution. 101 units (68%) carried significant choice information in their firing rate Quotation withheld because this record is not cleared for redistribution. spiking was coherent with the nearby field at three separate scales - theta, beta and gamma - which responded differently to the choice event Quotation withheld because this record is not cleared for redistribution. beta coherence and power both fell during the choice epoch Quotation withheld because this record is not cleared for redistribution. gamma spike-field coherence, but not LFP power, rose during the choice epoch Quotation withheld because this record is not cleared for redistribution. units coherent in one band were more often coherent in another than chance allows, across all three pairings Quotation withheld because this record is not cleared for redistribution. preferred phases clustered on the downswing and trough and did not shift between baseline and choice Quotation withheld because this record is not cleared for redistribution. choice information varied with beta and gamma phase but not with theta phase Quotation withheld because this record is not cleared for redistribution. and the same conclusion followed from a modulation entropy that makes fewer distributional assumptions Quotation withheld because this record is not cleared for redistribution. beta spike counts were symmetric about the preferred phase, with a peak-to-trough modulation of 13.6 percent Quotation withheld because this record is not cleared for redistribution. THE DISSOCIATION: beta choice information was asymmetric, peaked on the downswing, and its moment differed significantly from the spike count's Quotation withheld because this record is not cleared for redistribution. removing the spike count's prediction left the beta information histogram still significantly modulated, so beta relates to firing and to encoding independently Quotation withheld because this record is not cleared for redistribution. in gamma the information and the spike count shared the same concentration, with no difference between their moments Quotation withheld because this record is not cleared for redistribution. AND THE SAME SUBTRACTION GIVES A NULL IN GAMMA: the orthogonal information was uniform across phase bins, so gamma's two correlations are not independent Quotation withheld because this record is not cleared for redistribution. the moment of gamma choice information differed significantly from the moment of beta choice information Quotation withheld because this record is not cleared for redistribution. THE ESTIMATOR'S OWN BIAS WOULD HAVE MADE THIS RESULT: information runs high at small samples and spike counts differ by phase bin, and the pattern survived equalising the spike counts Quotation withheld because this record is not cleared for redistribution. the equalisation deletes spikes at random down to the smallest bin and repeats the estimate a thousand times Quotation withheld because this record is not cleared for redistribution. and each bin's probabilities are estimated over the lowest sample count across bins, with bootstrapped resampling to that size Quotation withheld because this record is not cleared for redistribution. THE PRIMARY STATISTIC IS SAID TO BE BLIND TO SOMETHING: the resultant length assumes a single concentration across bins and cannot detect multimodal modulation Quotation withheld because this record is not cleared for redistribution. the pattern held for each animal separately and for units split by coherence band, firing rate, sulcal bank and electrode separation Quotation withheld because this record is not cleared for redistribution. and it was absent in the baseline epoch and in coherent units without choice information Quotation withheld because this record is not cleared for redistribution. theta phase showed no relationship to choice information even among units selected for significant theta coherence Quotation withheld because this record is not cleared for redistribution. coherence above 20 Hz was stronger between closer electrode tips, which is read as gamma being more local than theta or beta Quotation withheld because this record is not cleared for redistribution. the medial and lateral banks of the sulcus showed no difference in temporal structure Quotation withheld because this record is not cleared for redistribution. theta phase predicted beta and gamma amplitude, with the theta to beta coupling strongest Quotation withheld because this record is not cleared for redistribution. phase-phase coupling was strongest between beta and gamma, weaker between theta and beta, and absent between theta and gamma Quotation withheld because this record is not cleared for redistribution. THEY TEST THEIR OWN EXPLANATION AND IT FAILS: the beta to gamma phase difference did not correlate with the beta information moment Quotation withheld because this record is not cleared for redistribution. beta activity took a central role among three interrelated temporal modes, most prominently coupled to slower theta through PAC and to faster gamma through phase-phase coupling Quotation withheld because this record is not cleared for redistribution. A MIXED UNIT OF ANALYSIS: 149 units of which 45 are single units and 104 multiunits, with 186 field recordings alongside Quotation withheld because this record is not cleared for redistribution. single-unit status required the cluster to stay clear of the multiunit cloud across a whole 100 second window Quotation withheld because this record is not cleared for redistribution. spikes and field phases were always taken from different electrodes Quotation withheld because this record is not cleared for redistribution. trial-locked evoked potentials were regressed out of every trial before analysis Quotation withheld because this record is not cleared for redistribution. the family-wise correction was built against a named failure mode - a few large-effect frequencies dominating the maximum resample distribution and cutting its degrees of freedom Quotation withheld because this record is not cleared for redistribution. a unit counted as coherent if any one of the tested frequency bins passed Quotation withheld because this record is not cleared for redistribution. 16,123 trials from one monkey and 11,440 from the other entered the analysis Quotation withheld because this record is not cleared for redistribution. reward magnitudes for each shape held for 50 to 60 trials and then changed without warning Quotation withheld because this record is not cleared for redistribution. coherent unit coherent unit Quotation withheld because this record is not cleared for redistribution. orthogonal-MI orthogonal-MI Quotation withheld because this record is not cleared for redistribution. n:m phase-phase coupling n:m phase-phase coupling Quotation withheld because this record is not cleared for redistribution. modulation entropy modulation entropy Quotation withheld because this record is not cleared for redistribution. mutual information mutual information Quotation withheld because this record is not cleared for redistribution. orthogonal-MI orthogonal-MI Quotation withheld because this record is not cleared for redistribution. coherent coherent Quotation withheld because this record is not cleared for redistribution. stratifying stratifying Quotation withheld because this record is not cleared for redistribution. single units single units Quotation withheld because this record is not cleared for redistribution. LFP phase bin LFP phase bin Quotation withheld because this record is not cleared for redistribution. movement condition movement condition Quotation withheld because this record is not cleared for redistribution. reward magnitude reward magnitude Quotation withheld because this record is not cleared for redistribution. mutual information mutual information Quotation withheld because this record is not cleared for redistribution. spike-field coherence spike-field coherence Quotation withheld because this record is not cleared for redistribution. spike counts spike counts Quotation withheld because this record is not cleared for redistribution. trial-locked evoked potentials trial-locked evoked potentials Quotation withheld because this record is not cleared for redistribution. choice-MI choice-MI Quotation withheld because this record is not cleared for redistribution. spike count spike count Quotation withheld because this record is not cleared for redistribution. SFC SFC Quotation withheld because this record is not cleared for redistribution. phase phase Quotation withheld because this record is not cleared for redistribution. trigonometric moment trigonometric moment Quotation withheld because this record is not cleared for redistribution. 149 units — total number of recorded parietal units analyzed across the two monkeys Quotation withheld because this record is not cleared for redistribution. 101 units (68%) — number and share of units with significant choice mutual information during the choice epoch Quotation withheld because this record is not cleared for redistribution. 13.6% / 6.6 spikes/s — peak-to-trough modulation of spike count by beta phase, and the equivalent firing-rate swing Quotation withheld because this record is not cleared for redistribution. 15.3% — peak-to-trough modulation of choice mutual information by beta phase Quotation withheld because this record is not cleared for redistribution. 6.2% — peak-to-trough modulation of spiking by gamma phase (about three spikes/s) Quotation withheld because this record is not cleared for redistribution. 12.3% — peak-to-trough modulation of choice mutual information by gamma phase Quotation withheld because this record is not cleared for redistribution. 16,123 trials (monkey C) and 11,440 trials (monkey R) — number of choice-task trials contributed by each animal Quotation withheld because this record is not cleared for redistribution. 1.07 mm vs. 2.86 mm — median electrode-tip separation of the near and far halves of recording pairs, used to test locality of the rhythms Quotation withheld because this record is not cleared for redistribution. r = −0.063, P = 0.55 — circular correlation between beta-gamma phase difference and the moment of the beta choice-MI histogram (no relationship) Quotation withheld because this record is not cleared for redistribution. 13.6% — peak-to-trough modulation of the spike count by beta phase, about 6.6 spikes per second Quotation withheld because this record is not cleared for redistribution. 15.3% — peak-to-trough modulation of choice information by beta phase - a similar size to the spike modulation but at a different phase Quotation withheld because this record is not cleared for redistribution. 12.3% — peak-to-trough modulation of choice information by gamma phase, against 6.2 percent for the spike count Quotation withheld because this record is not cleared for redistribution. P = 0.30 — the gamma orthogonal-information null - the result that says gamma's two effects are not separable Quotation withheld because this record is not cleared for redistribution. r = −0.063 — the correlation between the beta-gamma phase difference and the moment of the beta choice-MI phase histogram, testing whether that coupling could contribute to the temporal localization of the choice-MI Quotation withheld because this record is not cleared for redistribution. 149 units — 45 single units and 104 multiunits from two monkeys, with 186 simultaneous field recordings Quotation withheld because this record is not cleared for redistribution. 101 units (68%) — units with significant choice information in the firing rate Quotation withheld because this record is not cleared for redistribution. 16,123 trials — trials from monkey C, against 11,440 from monkey R Quotation withheld because this record is not cleared for redistribution.

The full text of this article is not redistributable, so it is not included here. The evidence sentences are withheld with it; the tag layer and its grounding status remain. The article itself is at https://doi.org/10.1073/pnas.1606479113.