dataesr/scientific-paragraphs-categorization huggingface dataset:
As shown in Fig. 8  , each atom type shows a distinct reduction in activity near the onset of the movement (at time = 0s) and an increase to baseline activity following the task. In addition, clear rebound behaviour is evident in the beta-type atoms, reflecting the post-movement beta rebound seen in traditional analyses (for example,  Bardouille et al. , 2019 ). This suggests that CDL reconstructs the expected brain responses. Finally, the right central mu atoms show a frequency profile that is distinctly different from the occipital and temporal alpha atoms, providing further confidence in the relationship between the CDL-detected waveforms and traditional analyses. The demographic composition of each cluster was assessed by comparing the age and sex distributions of the cluster to the distribution generated from the overall dataset using a Chi-squared test.
Clusters LT_alpha and LPostC_beta were found to have an age distribution that was significantly different from that of the overall dataset, with Chisquared values of 27. 47 (  = 0. 0012 ) and 36. 29 (  = 0. 000035 ), respectively. Both clusters had age distributions that were skewed towards older participants. Histograms showing the distributions of the two significant clusters compared to the overall dataset are presented in Fig. 9. No other clusters had age or sex distributions that were significantly different from that of the overall dataset. All clusters were examined for age-related changes in their component atom characteristics including peak frequency, activation sum (in the pre-movement and post-movement intervals), dipole position and orientation, and correlation of the  and  vectors to the mean atom's vectors were regressed with age for each task-related cluster.
Discussion In this work, a multi-channel data-driven CDL approach and unsupervised clustering method were successfully applied to the large openaccess Cam-CAN dataset to detect a set of prototypical, transient taskrelated atoms that occurred across many participants. The atom clusters that were generated had stereotypical patterns resembling known task-related brain activity, including occipital alpha and sensorimotor beta and mu. The spatial and temporal characteristics of each type of atom showed various age-related changes, with activation sum (driven by burst rate) showing the most prominent age-related effects across atom types. The results of this work suggest that several distinct types of sensorimotor and occipital transients are present in human MEG data, and that these transient bursts change in their rate of occurrence during task performance and throughout the normal ageing process.
In line with this hypothesis, two of the identified atom clusters resembled left sensorimotor beta transients, and one atom cluster resembled a right sensorimotor mu transient. The frequency bands and movement-related temporal behaviour associated with each of these atoms coincided with the features associated with sensorimotor beta and mu activity identified in classical average power analyses (as shown in Fig. 8  ). Given that the sensorimotor task used in this dataset was a right-handed unimanual button press, it was expected that contralateral (left) sensorimotor beta transients would be a dominant task-related atom type across many participants. An interesting finding of this analysis, however, was that two distinct clusters of contralateral sensorimotor beta transients emerged with slightly different representative waveforms and spatial topographies.
This suggests that young and old participants exhibit a larger number of lower power sensorimotor bursts than middle-aged participants, but that the increased burst rate is the primary factor driving an overall increased activation sum in young and old participants. Interestingly, the quadratic activation trends in the post-movement interval for the left pre-central beta cluster were not present in the left post-central beta cluster. This further demonstrates that the two beta clusters are distinct from one another, and vary differently with age. While this result differs from previous findings that found a decreasing linear trend in sensorimotor beta burst rate with age  ( Brady et al. , 2020 )  in the post-movement interval, it is interesting to note that quadratic trends with a vertex at approximately 60 years are a recurring theme in our age-related investigations of the Cam-CAN dataset (see  ( Brady et al.
Previous research has discussed the value of creating such a dictionary  ( Tal et al. , 2020 ) , and applying the methods described here to a large dataset of resting state data, such as that offered in the Cam-CAN dataset, would allow for such a set of transients to be realised. While CDL and the associated clustering methods presented here could be applied to any dataset regardless of size, the relatively small cluster sizes ( i. e. 25-40% of participants per cluster) reported here suggest that a top cluster analysis of a much smaller dataset would not yield particularly representative results. However, with access to a standard dictionary derived from a large dataset, template matching could be used to search small datasets for signals that have high similarity to the standard transients.
This would provide an opportunity for fast and efficient identification of a variety of transient bursts, regardless of the dataset size. The CDL approach described here also lends itself well to applications where an external synchronisation signal ( i. e. a task) is not present in the data. In the current work, we were interested in detecting taskrelated transients that were comparable to those detected by existing methods to help validate the efficacy of our methods. However, CDL is also well-suited for detecting transient signals that are not related to a task, because it can detect transient signals throughout electrophysiological data without reliance on task-related timestamps. This makes CDL an ideal tool for resting-state applications, and burst-based neurofeedback applications (see  Karvat et al.
This insight would have been lost had a different method that required a-priori specification of frequency bands been used. The clustering methods applied in this work allowed us to investigate data-driven transient bursts at the group level for the first time, which opened up the possibility of studying age-related trends in a large dataset. This work therefore afforded us with the unique opportunity to gain rich information about the age-related changes in these various transient burst types, and provided convincing evidence that burst rate was the primary factor driving these age-related changes. The methods developed in the current work provide a framework that other researchers can use in the future to detect transient bursts at the group level and further our collective understanding of human neuromagnetic transients.
Data and Code Availability Statement Data were obtained from the CamCAN repository (available at https://www. cam-can. org/index. php?content = dataset ). MEG processing was completed in the Python programming environment (v. 3. 7. 7), using the MNE-Python library (v. 0. 23. 0). Python code for this analysis is available at https://github. com/tbardouille/ camcan _ CSC _ beta.
Acknowledgments/Funding Data collection and sharing for this project was provided by the  Cambridge Centre for Ageing and Neuroscience (Cam-CAN ). Cam-CAN data collection funding was provided by the  UK Biotechnology and Biological Sciences Research Council  (grant number  BB/H008217/1 ), together with support from the  UK Medical Research Council  and  University of Cambridge, UK. Research presented in this paper was funded in part by the  Natural Sciences and Engineering Research Council of Canada Discovery Grant  (grant number  RGPIN-2018-05470 ), the  ANR grants BrAIN  (grant number  ANR-20-CHIA-0016 ) and  AI-Cog  (grant number  ANR-20-IADJ-0002 ). Scholarship support for this project was provided by the  Natural Sciences and Engineering Research Council of Canada and Dalhousie University.
Presynaptic fiber volleys (PFVs) and field excitatory postsynaptic potentials (fEPSPs) were evoked at 0. 1 Hz by the electrical stimulation of Schaffer collaterals and commissural fibers located in the stratum radiatum. The NMDARs-mediated component was isolated from slices perfused with low magnesium aCSF (0. 1 mM to relieve NMDARs of their Mg 2+ blockade) and supplemented with NBQX (10 µM). The slope of three successive PFVs and fEPSPs was averaged using WinLTP ® software 2. 30  [50, 51]. To evaluate the level of NMDAR activation, an index of synaptic efficacy (Ise) corresponding to the fEPSP/PFV ratio was plotted against increasing stimulus intensities (400 and 500 µA). The effects of successive application of SB-271046 with increased concentrations (0. 1 µM, 1 µM, and 10 µM) in the control or bicuculline-supplemented aCSF (10 µM) were evaluated by comparing Ise before and 15 min after the addition of the drug to the medium.
After the evaluation of the effective dose of SB-271046 on NMDARs' activation, the effects on basal synaptic transmission and synaptic plasticity were assessed using extracellular recordings obtained with a Multi-Electrodes array (MEA2100, Multi-Channel System, 60MEA200/30iR-Ti 8*8, Reutlingen, Germany). The recording chamber was equipped with 60 recording electrodes (30 µm diameter with 200 µm spacing). To assess basal neurotransmission, fEPSPs also evoked in the CA1 area by stimulation of the Schaffer collaterals/commissural fibers were measured using LTP director software ® 1. 4 (Multi-Channel Systems MCS). Input-output (I/O) curves were obtained with voltage currents ranging from 3000 to 5000 mV. The paired-pulse facilitation (PPF) of basal synaptic transmission was investigated through paired electrical stimulation with an interstimulus interval of 30 ms.
Data Analysis Analyses were performed with R ® software 4. 2. 0 and GraphPad ® Prism 8. 3. The assessment of normality of the data distribution was performed using the Shapiro test and the homogeneity of variances with Levene's test. When data were normally distributed, two-way analysis of variance (ANOVAs with repeated measures or not) were used for group comparisons, and data are expressed as mean + standard error of the mean (SEM). Otherwise, data are expressed in median ± interquartile. To assess drugs effects, paired t-tests (for data normally distributed) or Wilcoxon paired tests (for data not normally distributed) were used. A significant difference was admitted in all cases when p was below 0. 05.
Data Analysis Analyses were performed with R ® software 4. 2. 0 and GraphPad ® Prism 8. 3. Th sessment of normality of the data distribution was performed using the Shapiro tes the homogeneity of variances with Levene's test. When data were normally distrib two-way analysis of variance (ANOVAs with repeated measures or not) were use group comparisons, and data are expressed as mean + standard error of the mean (S Otherwise, data are expressed in median ± interquartile. To assess drugs effects, pai tests (for data normally distributed) or Wilcoxon paired tests (for data not normally tributed) were used. A significant difference was admitted in all cases when p was b 0. 05.
Spatiotemporal dynamics in simulated data In this section we present the results of numerical simulations with 3D realistic brain geometry using software SimNIBS  [31]. This tool allows modelling of transcranial direct current stimulation (tDCS) with stimulating electrodes located at the scalp. The model uses Poisson equation  [32]. Since this equation is linear, it is thus possible to use it for modelling of transcranial alternating current stimulation (tACS) with several simultaneously acting time-dependent sources  [31]. Numerical implementation is presented in Supplementary Materials B. In numerical simulations, we use 30 electrodes including 3 tACS electrodes and 27 electrodes registering EEG. We consider two stimulating electrodes and one return electrode, where stimulation observes the conservation of charges, that is, the sum of injected currents is equal to zero at any given time point.
Optical flow patterns in simulated data Depending on the phase and frequency in the simulated data, we observe standing waves, out-ofphase standing waves and modulated waves. In the case of standing waves, as from the earlier analysis, we can expect that sources and sinks have the same location in this ideal configuration. Furthermore, in analytical approximation, they coincide with the maxima and minima of the potential distribution. For the generated data, there is a number of stages of data processing which could influence the result. Let us recall that 30 signals were simulated as they would have been recorded at the scalp. These signals were then projected onto a circular domain, as is done for the real EEG data. However, the same signals were used to generate optical flow patterns with some other transformations (see Supplementary Materials, A).
Optical flow patterns in EEG data Results of Section 2 allow us to interpret EEG dynamics as standing waves, out-of-phase standing waves, and modulated waves. Analysis of optical flow patterns in Appendix D suggests that such regimes satisfy Properties 1 and 2. In the previous section, these properties were verified for the simulated data. We will now verify them for the real EEG data. The EEG data for all 16 subjects and 270 trials are included in the analyses. The numbers of sources and sinks are approximately the same, similar to the number of spirals-in and spirals-out (Figure  6 ). Source/sink patterns occur about 3% more than spiral-type patterns. However, saddles have the largest share of the identified patterns -about 45% of the total number of patterns. Similar to the simulated data, the number of saddles was approximately equal to the total number of the other two patterns (sources and sinks).
Thus, spatiotemporal dynamics of EEG data characterized by brain micro-states are determined by the change of brain sources, but the underlying regimes (patterns) are not yet identified. We consider in this work some of these regimes determined by phases and frequencies of brain sources. Regimes determined by phases and frequencies of brain sources. Since spatiotemporal dynamics in EEG data is complex and depends on many factors, one needs to first identify some basic spatiotemporal regimes. We have shown here that the phase and frequency of the signal, for a given EEG signal frequency band (e. g. , alpha) give rise to certain regimes in the spatiotemporal dynamics induced by brain sources and their interactions. For the case of single positive and negative poles (source and sink), only standing waves are possible.
1). Table  S2  contains the formulas being used. The intensity at C5 (return electrode) was adjusted in order to satisfy (Eq S4). The algorithm above always allows computing the voltages at all points of the grid. Extracting the voltages at a small number of electrodes on the scalp surface is necessary in order to create a dataset with parameters comparable to experimental EEG data. Coordinates of 30 electrodes were chosen from the list of 76 items provided with the example dataset  [44]. Their coordinates (3D) were used for estimating the tACS voltages (by using the voltage at the closest point of the grid as an estimation of the voltage at an electrode).
Moreover, the reduction proposed assumes a reflection symmetry of the network to obtain the given form. This, however, seems limiting in particular in the case where each perceptual decision recruits different sensory modalities. Here we propose a straightforward one-dimensional non-linear form to address these limitations: the non-linear Drift-Diffusion Model (nl-DDM). It recreates double-well-like dynamics from an evidence-accumulation perspective, without assuming reflection symmetry. We show its validity and compare its fitting performances to these of the DDM. We first provide a formal description of the nl-DDM, relating it to the DDM. Then, we fit them on two human behavior datasets: one that was already published  (Wagenmakers et al. , 2008)  where participants classified words into two categories (existing vs.
Results In this paper we introduce a model, the non-linear Drift-Diffusion Model (nl-DDM), that, similarly to the DDM, can be formulated through a Langevin equation. This model takes the form  = -(-)(-)(+)+(), where the decision variable follows an infinitesimal change of  during the time interval. More details on the formalism of this model can be found in the Methods section of this paper. We show that the nl-DDM performs better than the DDM in terms of fitting accuracy and theoretical predictions on behavior. To do that, we fitted both models on two datasets: a classification task we designed and a dataset published previously in  Wagenmakers et al. (2008). To provide more insight into the empirical meaning of the parameters beyond the formalism, we performed correlation analyses between nl-DDM and DDM parameters.
Behavioral results For decision-making analysis, it is helpful to obtain each participant's response times and decision accuracy, particularly for decision model fitting. We used two datasets in this paper. The section Data collection and processing describes these datasets in detail. They both consist of classification tasks performed by human participants. One of them is a dataset collected by  Wagenmakers et al. (2008) , in which participants had to assess whether a word presented on screen existed or not. The second one is a dataset not presented before, in which participants were shown visual stimuli on screen and had to classify them according to their type (either "face" or "number"). To ensure the correctness of both datasets in terms of behavioral measurements, we describe here the validation conducted on our dataset.
Analyses of the Wagenmakers' dataset are available in  Wagenmakers et al. (2008)  and are not discussed further here. First, we ruled out methodological artifacts, as we aimed at providing equiprobable stimuli for each participant. On average, participants were shown 49. 82 ± 2. 42% of "number+sound" stimuli, showing the quasi equiprobability of each stimulus. We then tested whether the experiment we designed led to similar responses across all participants by performing mixed-model ANOVAs on their response times and response accuracy for both stimulus-response mapping (betweensubject factor) and stimuli (within-subject factor). Across all participants and stimulus types, the mean response time is 535 ± 61 ms (mean ± standard deviation,  = 25), with an accuracy of 98. 59 ± 0. 95%. For the "face" stimulus, participants responded after 539 ± 56 ms with an average accuracy of 98.
Fitting on data The fitting of parameters was performed using the PyDDM  (Shinn et al. , 2020b)  Python toolbox for both the nl-DDM and the DDM, minimizing the negative log-likelihood function. As participants in our experiment were shown two types of stimuli, we fitted a model per participant for each model type, resulting in 25 DDM and 25 nl-DDM fitted. In addition, 17 × 2 models of each type were computed for the Wagenmakers dataset (17 participants × 2 conditions = 34 models). Since the two datasets did not use the same number of parameters for each model, we performed a pairwise comparison of loss values over the models. To remove the possible effect of outliers, for which fitting would have failed, we removed the models for which the loss values were above the mean loss + standard deviation over all models.
18,  = 2. 241,  = 0. 015,  = 0. 324,  = 48). We computed the Bayesian Information Criterion (BIC) for each model to establish a comparison of model performance that takes into account the sample size and number of parameters necessary for each model. This is indeed necessary when comparing performance across datasets, since the number of conditions, and hence of parameters needed, is different. We observed that the nl-DDM fitted response time data significantly better than the DDM even when accounting for the number of parameters (Figure  6 , (47) = 2. 18,  = 2. 207,  = 0. 016,  = 0. 319).
Note that we only took into account our dataset for parameter comparison, and while fitting the models to this set, we assumed that the starting points followed a uniform distribution spanning the entire decision interval [-, ] for the nl-DDM, while we took a shorter interval for the DDM to avoid border effects. This difference in assumptions for the starting point distribution was compensated by fitting a non-decision time in the nl-DDM and taking the same value when fitting the DDM. We first empirically show the relation between the parameters within the nl-DDM. We observe a strong negative correlation between  the boundary and  the time constant. This corresponds to their similar effect on the attractiveness of the correct response. Increasing either will make the decision more attractive, so to keep the same attractiveness of the correct response, if one increases, the other should decrease.
We took in both cases a uniform distribution, but while fitting our dataset, we assumed that this distribution spanned the whole decision space for the nl-DDM, while it was an interval [ 0 -  ,  0 +   ] ⊆ [-, ] for the DDM, with ± the decision boundaries of the DDM. By doing so, we wanted to show that with fewer degrees of freedom, our model could fit behavioral data better than the DDM. The DDM assumes a global bias towards either boundary transcribed in the position of the starting point distribution within the decision interval. Variability in the starting point enables faster error responses  (Ratcliff and Rouder, 1998). In our model, that could also be achieved by including starting point variability similarly to the DDM, that is by defining an interval [𝑥 0 -𝑠 𝑧 , 𝑥 0 + 𝑠 𝑧 ] ⊆ [-𝑎, 𝑎], with ± the decision boundaries of the nl-DDM.
It is the strategy that we have implemented while fitting the Wagenmakers' dataset. However, this would have been an issue when comparing the two models as the starting point distributions fitted by the DDM and the nl-DDM did not necessarily match. The most striking consequence of such a mismatch is the difference between the nondecision times of the two models. Indeed, the non-decision time of the nl-DDM would be close to the minimum response time displayed by a participant. At the same time, it would be smaller in the DDM, as the displacement of the decision variable from the bias to either decision boundary in the absence of noise is not instantaneous. To minimize this effect, we have also fitted the variability of the non-decision time for the Wagenmakers' dataset, although introducing such variability in one model and not the other made the two models less comparable.
Classification task with different sensory modalities We first tested the quality of the nl-DDM by fitting it to data we collected. 25 (11 female, 14 male) healthy right-handed participants aged 27. 72 ± 8. 96 (mean ± standard deviation) with normal or corrected-to-normal vision and hearing took part in a perceptual classification task experiment. EEG brain activity was also recorded (not reported here). The experiment was performed under A sound accompanied images of numbers to suppress any ambiguity. Participants were instructed to respond using their right hand. To control for possible differences in motor response speeds between the two fingers, one group of participants ( = 15) was instructed to report faces with a left click and numbers with a right click ("face is left button" stimulus-response mapping), while the other ( = 10) was given the opposite instruction ("face is right button" stimulus-response mapping).