dataesr/scientific-paragraphs-categorization huggingface dataset:
To consider a paleo-topography as acceptable, besides producing a rockslide volume within 20 to 26. 5km 3 , its hillslopes must be stable according to the criterion de ned for the Annapurna region. For each randomly generated paleo-topography, we thus apply the same procedure described in the previous section (Extended Data g. 7), and derive the distribution of the minimal FoS values. For the high relief of the Annapurnas, and j = 35°, all FoS values were found to be >=1 for a cohesion value C=2MPa. Based on this cut-off, any paleo-topography presenting FoS values lower than unity for C=2MPa is rejected. From the nal set of acceptable geometries, we calculate a mean topography, a distribution of volumes, of crest pro les and of paleo-summit elevations ( g. 3d and Extended Data g. 9). It has to be noted that the optimal ellipsoidal potential failures of the obtained paleo-topographies are shallower than the actual failure surface along present-day topography.
Acknowledgements: J. L. thanks  B. Sitaula  for his invaluable logistic help in the eld,  L. Bollinger  for his help during the helicopter ight in Sabche cirque and the numerous pictures he took,  Y. Gunzburger ,  F. Carraro Braga ,  M. Manas  and  P. Kumar  for initial discussions and modelling on slope stability of the paleo-summit. This study was funded by the  ANR Calimero  and the  INSU-Syster and INSU-Artemis  programs. P. G. V. acknowledges funding from the  French ANR-PIA  programme ( ANR-18-MPGA-0006 ). The Pleiades images were acquired in the framework of the  Isis collaborative program  between the  CNES  and  INSU. We thank the  LMC14 (Laboratoire de Mesure du Carbone-14 ), ARTEMIS national facility (LSCE ( CNRS-CEA-UVSQ)-IRD-IRSN-MC ) for the 14 C AMS results, and the  ASTER national facility (Cerege (CNRS ,  Univ Aix Marseille))  for the 36 Cl AMS results.
Non-invasive techniques to electrically stimulate the brain such as transcranial direct and alternating current stimulation (tDCS/tACS) are increasingly used in human neuroscience and offer potential new avenues to treat brain disorders. Previous research has shown that stimulation effects may depend on brain-states. However, this work mostly focused on experimentally induced brain-states over the course of several minutes. Besides such global, long-term changes in brain-states, previous research suggests, that the brain is likely to spontaneously alternate between states in sub-second ranges, which is much closer to the time scale at which it is generally believed to operate. Here, we utilized Hidden Markov Models (HMM) to decompose magnetoencephalography data obtained before and after tACS into spontaneous, transient brain-states with distinct spatial, spectral and connectivity profiles.
1 e ). The goal of the current study is to establish if differential effects of tACS on transient brain-states as outlined above exist, and to dissociate effects of tACS on oscillatory power from those on the occurrence of oscillatory activity. The existence of such transient brain-state dynamics would open a whole new perspective on tACS and brain stimulation data in general. In order to achieve our objectives, we adapted a recently proposed analysis pipeline utilizing Hidden Markov Models (HMMs) to decompose neural time-series data into distinct, transient brain-states  ( Baker et al. , 2014 ; Vidaurre et al. , 2016 Vidaurre et al. , , 2018b ) ). The analysis was carried out on two recently obtained tACS-magnetoencephalography (MEG) datasets  ( Kasten et al. , 2019 ). Due to the nature of the available data, we cannot yet resolve the intricacies of such transient brainstate dynamics, which, among other things, pertains the role of the frequency band or montage with which tACS is applied.
Participants All analyses in the current study were conducted on two pre-existing tACS-MEG datasets  ( Kasten et al. , 2019 ). The first one was carried out as a single-blind, between subject design on 40 participants (24 ± 3 years, 20 females) with participants randomly assigned to one out of two experimental groups (tACS vs. sham), while counterbalancing for participants' sex. The second experiment was performed as a singleblind within-subject design ( N = 19, 25 ± 3 years, 11 females), with participants receiving both stimulation conditions at random order across two experimental sessions scheduled on two separate days. Participants were right-handed according to the Edinburgh Handedness-Inventory  ( Oldfield, 1971 ) , had normal or corrected-to-normal vision, were nonsmokers, without history of neurological or psychiatric disease and medication-free at the day of the experiment.
Electrical stimulation TACS was administered via two surface-conductive rubber electrodes positioned over locations Cz (7 × 5 cm) and Oz (4 × 4 cm) of the international 10-10 system via an electrically conductive, adhesive paste (ten20 paste, Weaver & Co, Aurora, CO, USA). The stimulation waveform was generated using a constant current stimulator (DC Stimulator Plus, Neuroconn, Illmenau, Germany) and remote-controlled via a digital-to-analog converter (NI-USB 6251, National Instruments, Austin, TX, USA) fed with data by a MATLAB script (MATLAB 2016a, The Math Works Inc. , Natick, MA, USA). Stimulation currents were guided into the MSR via the MRI extension-kit of the stimulator. Impedances were kept below 20 k Ω, including two 5 k Ω resistors inside the stimulation cables. Participants received 20 min of active tACS or sham stimulation (30 s of tACS at the beginning of the stimulation period) at their individual -frequency (IAF).
IAF was determined from a 3 min resting MEG obtained prior to the main experiment. 10 min of MEG were recorded directly before and after stimulation. To ensure participants remained attentive and kept their eyes open during the recording, they were asked to perform a simple visual change detection task. To this end, a white fixation-cross on gray background was rear-projected onto a screen (distance: ∼100 cm) inside the MSR. Participants had to manually respond to a 500 ms rotation of the cross by 45°, occurring at random intervals with a stimulus onset asynchrony of 10-110 s. Additional details on the experimental procedures, including debriefing and the assessment of adverse effects can be found in a previous publication on the data  ( Kasten et al. , 2019 ).
Preprocessing MEG preprocessing was performed in MATLAB 2019b using the fieldtrip toolbox  ( Oostenveld et al. , 2011 ). HMM training and state-wise frequency analysis was performed using the HMM-MAR toolbox ( https: //github. com/OHBA-analysis/HMM-MAR ). Statistical analysis was carried out in R 3. 6. 1 (The R Core Team, Vienna, Austria) running on R-Studio (RStudio Team, PBC, Boston, MA, USA). Statistical functions provided by the fieldtrip toolbox were utilized to compute clusterpermutation statistics  ( Maris and Oostenveld, 2007 ). In a first step, spatio-temporal signal-space-seperation (tSSS) was applied to the data to suppress external interferences and correct for headmovements during the recording  ( Nenonen et al. , 2012 ; Taulu et al. , 2005 ; Taulu and Simola, 2006 ). TSSS was applied using MaxFilter TM v2.
The regions correspond to the ROIs used in  Vidaurre et al. (2018b ). A weight-matrix was used to project data into brain-space for visualization purposes. A multivariate correction for spatial-leakage  ( Colclough et al. , 2015 )  was applied using the ROInets toolbox ( https://github. com/OHBA-analysis/MEG-ROI-nets ). The correction reduces artificial correlations between adjacent virtual channels, while resembling the original data as close as possible. Such correlations are known to bias connectivity estimates and can hamper HMM training. A conceptual overview of the analysis pipeline is provided in Fig. 2.
The standard approach for training an HMM with a fixed number of states and unknown transition and emission probabilities is the Baum-Welch algorithm -also referred to as the Forward-Backward algorithm  ( Baum et al. , 1970 ). The algorithm estimates both the emission and transition probabilities by starting off with an initial estimate and then iteratively optimizing both probability matrices. As this requires a complete sequential forward-and backward pass through the entire concatenated data of all subjects, which is demanding in terms of memory usage and computation times, we opted to run the algorithm with a recently developed stochastic inference procedure implemented in the HMM-MAR toolbox. In contrast, to traditional approaches using variational inference or maximum likelihood, stochastic inference allows to perform HMM training on large datasets Fig.
2018a  ). In line with previous work, we ran stochastic inference with a batch size of M = 5. Once the tran-sition and emission probabilities are estimated, a state probability sequence , indicating the probability of each state being active at each timepoint, can be computed along with the most likely state sequence ( Fig. 2  ). These form the basis for subsequent analyses characterizing each state's relative occurrence, dwell time and switching rate, as well as it is frequency content (see next section). We followed the analysis framework described by Vidaurre et al. (2018b ) using a time-delay-embedded HMM (TDE-HMM) trained on the concatenated ROI time series of all participants. This variant of the HMM, uses a Gaussian observation model with zero mean to model the data over a certain time window, effectively utilizing the data autocovariance across regions.
The TDE-HMM is sensitive to changes in power and phase-locking while being able to deal with a relatively large number of channels  ( Vidaurre et al. , 2018b ). We chose a TDE-HMM with an observation window of 15 samples centered around each t and working in PCA-space with 84 components (explaining ∼68% of the variance in both datasets). This forces the model to return a common set of states across the whole dataset. To avoid that the model assigns states based on inter-individual differences between subjects, ROI time-series were standardized (z-transformed) within each subject and the dipole-signambiguity of individual time-series was resolved using the approach presented in  Vidaurre et al. (2018b ). After the training, we visually confirmed that each state was present in each subject (Supplementary Figs.
𝑟𝑒𝑙. 𝑐ℎ𝑎𝑛𝑔𝑒 = 𝐴 -𝐵 𝐵 where A is IAF band power after tACS or sham stimulation, and B is IAF band power in the baseline recording. To test if effects on state power are specific to the -frequency range, we repeated the analysis for the neighboring individual -(IAF-7 Hz -IAF-3 Hz) and -band (IAF + 4 Hz -IAF + 20 Hz). It should be noted that, while this control analysis can serve to assess if the response to -tACS is specific to the -band, it does not allow to determine if the response in the -band is specific to -tACS (or of similar effects could be achieved by stimulation in other frequency bands). The latter would require the inclusion of additional stimulation frequency conditions, which are not available for the current dataset. In addition, we ran the frequency analysis on the ROI time series without weighting by states to test for non-state resolved effects of tACS in the second dataset.
Statistical analyses The power change in the -band (IAF ± 2 Hz) with respect to baseline, averaged over all 42 ROIs, as well as the change in fractional occupancy and other state characteristics (dwell times, interval times) were assessed using repeated measures ANOVAs with factors STIMU-LATION (2-levels, tACS vs. sham, dataset 1: between-subject, dataset 2: within-subject) and STATE (4-levels, within-subject in both datasets). Greenhouse-Geisser corrected p -values are reported if sphericity was violated. Partial  2 is reported as a measure of effect size: η 2 = 𝑆𝑆 𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 𝑆 𝑆 𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 + 𝑆 𝑆 𝑑𝑒𝑚𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 To resolve in which states tACS led to a larger power increase relative to baseline as compared to sham, relative power changes in each state of all 42 ROIs were submitted to non-parametric random permutation cluster t-tests (two-sided; dataset 1: independent samples, dataset 2: dependent samples), using 10,000 randomizations and Monte-Carlo estimates for p -values.
Results replicate in validation data The HMM analysis on the second dataset returned states with spatiospectral profiles similar to the ones obtained in the first dataset ( Fig. 5  ). Like our results in the first dataset, the states seem to reflect visual, sensori-motor and DMN activity as well as a negative activation state. Again, we assessed the effect of tACS on power in the individual band (IAF ± 2 Hz) using a repeated measures ANOVA with the withinsubject factors STIMULATION (2-levels; tACS vs. sham) and STATE (4-levels). The analysis yielded significant effects of STIMULATION (F 1,18 = 9. 06, p =. 008,  2 = 0. 06) and STATE (F 3,54 = 5. 05, p =. 013,  2 = 0. 02). Importantly, the STIMULATION * STATE interaction again reached significance (F 3,54 = 6. 88, p =. 004,  2 = 0. 02), replicating the differential effect of tACS across states found in the first dataset ( Fig.
6 a, b ). To assess which states were affected by stimulation, we subsequently performed two-sided non-parametric random permutation cluster t-tests for dependent samples comparing the power increase during stimulation and sham in each state. Tests yielded a significant cluster in state 4 (p cluster =. 004, df = 18, Fig. 6 c ) as well as a trend in state 3 (p cluster =. 07, df = 18, trend not shown in cluster maps). No effects were found in the other states (all p cluster >. 46, df = 18, Supplementary Table  3 ). Noteworthy, state 4 in this dataset shows strong similarities with state 2 from dataset 1 ( Fig. 3  second column, Fig. 5  fourth column), which was the only state showing a significant effect to tACS in the previous analysis ( Fig. 4  ). Again, we did not find evidence for effects of tACS in the neighboring -(IAF-7 Hz -IAF-3 Hz) and -band (IAF + 4 Hz -IAF + 20 Hz; Supplementary Table  4 ).
DMN state disproportionally drives global tACS effect Our results so far suggest that one out of our four transient brainstates is most susceptible to tACS. But does this state also drive the tACS effect on a global level? To address this question, we revisited the global (i. e. , non-state-solved) tACS effect in the within-subject dataset. We computed non-state-resolved power spectra from our ROI time se- ries and computed the pre-to post-stimulation power increase in the individual -band and submitted the resulting data to a dependent samples random-permutation cluster test. The test confirmed a global effect of tACS in the data (p cluster =. 006, df = 18; Fig. 7 a-c ). Importantly, the global cluster shows a substantial spatial overlap with the cluster found in the DMN state (state 4) in the second dataset, with 12 out of 18 significant ROIs in the global cluster overlapping ( Fig.
Discussion In the current study, we aimed to reveal the role of hidden, spontaneous brain-state dynamics on aftereffects of tACS. To this end, we adapted a novel analysis framework to decompose neural time series data into brain-states using Hidden Markov Models  ( Baker et al. , 2014 ; Vidaurre et al. , 2018b Vidaurre et al. , , 2016 ) ). These states are characterized by distinct spatial, spectral and connectivity profiles and reflect known networks of human brain activity. The approach further allowed us to gain insights to the nature of changes underlying the increase in spectral power often associated with tACS  ( Kasten et al. , 2016 ; Veniero et al. , 2015 ; Zaehle et al. , 2010 ). Our results suggest that tACS distinctly and consistently modulated -power within the same state across both datasets, which we identified as most likely reflecting DMN activity.
We did not find evidence for such an effect in other states. Further analyses in our within-subject dataset suggest that the effect in the DMN state substantially overlaps with the tACS effect seen on a global level and seems to be the most significant driving force of the global effect. This significant contribution of the state occurs despite the fact that the state is active for only ∼12% of the total time. We did not find evidence that the time spent in any of the states was modulated by tACS, or that the stimulation gave rise to entirely new brain-states. Overall this finding confirms the general assumption that tACS indeed affects the power of oscillatory activity but not how frequently this activity occurs. TACS is generally considered a subthreshold stimulation approach. As such, it is believed to be capable of modulating pre-existing oscillatory activity, but not of inducing new oscillatory activity.
, 2013 ; Kasten and Herrmann, 2017 ). Unfortunately, neither of these explanations can fully account for our findings of a susceptible, high -power DMN state and an unsusceptible high -power visual state. This may indicate that our current perspectives on the state-dependency of tACS effects may be too simplistic. To what extent other features of brain-states such as the number of brain regions involved, their connectivity profiles, the duration for which the state is active, the nature of the underlying information processing or subtle differences in the underlying activity patterns might play a role remains largely elusive and may deserve consideration in future studies. Noteworthy, the DMN state most affected by tACS in both datasets happens to be the state that was active for the least amount of time, while exhibiting the most widespread activation and connectivity profile.
, 2018b ). However, such more detailed descriptions of the data come at the cost of a larger number of multiple comparisons that have to be taken into account and may hamper statistical power. In addition, an overall more complex pattern of results may be more difficult to interpret. The results at hand were obtained from a re-analysis of two existing datasets  ( Kasten et al. , 2019 ). Consequently, the current results cannot be interpreted as an independent replication of the aftereffect of tACS, but rather provides a different point of view on the underlying tACSinduced oscillatory changes already demonstrated in this dataset. Further, the datasets only provide data for one stimulation montage and frequency along with a sham control. This precludes definitive conclusions about the frequency specificity of tACS and how it might relate to brainstate dynamics based on the current findings.
It is generally believed that tACS elicits its effects in a frequency specific manner, i. e. only modulates oscillations within the frequency band at which it is applied. Indeed several studies report frequency specific effects of stimulation on behavioral tasks or MEP measures  ( Feurra et al. , 2013 ; Kasten et al. , 2020 ; Wöstmann et al. , 2018 ). Testing frequency specificity in the context of tACS aftereffects is however challenging and time consuming, as each additional stimulation condition (i. e. , frequency) included in the protocol requires an additional recording session (or experimental group) increasing the burden of measurements for both participants and experimenters. We therefore refrained from including more stimulation conditions when the data was originally acquired. While the state-dependent effect of our -tACS seems to be limited to the -band, it cannot be ruled out that stimulation at other frequencies would have had the same effect.
Acknowledgments This research was supported by the  Neuroimaging Unit of the Carl von Ossietzky University Oldenburg  funded by grants of from the  German Research Foundation  (  3T MRI INST 184/152-1 FUGG  and  MEG INST 184/148-1 FUGG  ). Christoph S. Herrmann was supported by a grant of the  German Research Foundation (Deutsche Forschungsgemeinschaft, DFG)  under Germany's Excellence Strategy -EXC 2177/1 -Project  ID 390895286.
Combining Planck and SPT Cluster Likelihoods In order to combine Planck and SPT cluster likelihoods, it is necessary to take into account the overlapping area of the observed sky and the clusters in common between the two catalogs. We choose to modify the Planck likelihood. In particular, we perform a split in the redshift of the entire likelihood. For z 0. 25, where we do not have cluster data from the SPT-SZ survey, we rely on the original version for the Planck likelihood. For z > 0. 25, we modify the Planck likelihood, removing the part of the sky also observed by the SPT-SZ survey and the clusters in common with the SPT-SZ catalog. Hereafter, we refer to this new Planck redshift-splitted likelihood as "PvSPLIT". With this choice, we can therefore treat the two Planck and SPT cluster likelihoods independently.
Sampling Recipe For the cosmological analysis, we make use of the complete SPT likelihood, described in Section 2. 1. In particular, we rely  on the combination of the SPT-selected clusters with their detection significance and redshift, together with the WL and X-ray follow-up data, where available. Following the definition in  Bocquet et al. (2019) , we refer to this data set as "SPTcl" (SPT-SZ + WL + Y X ). For the Planck part of the likelihood, we use the PvSPLIT version described in the previous section. We adopt the parameterization for the scaling relations described in Equations (  14 ) and (15). In this analysis, we want to test the capability of the Planck +SPT combination to constrain the Planck scaling relation parameters. For this reason, we do not consider the original X-ray+WL calibration reported in Table  2  when analyzing Planck data.
Mass Evaluation We now describe the approach we use to provide a new evaluation of true Planck cluster masses, M 500. We follow the discussion in Planck  Collaboration et al. (2016b). We start from the Planck cluster observable, the signal-to-noise ratio q, and evaluate P(M 500 |q), which represents the conditional probability that a cluster with a given signal-to-noise ratio q has a mass M 500. Following the Bayes theorem, this probability is defined as ( | ) ( | ) ( ) ( ) µ P M q P q M P M , 1 8 500 500 500 where the first term is the conditional probability of the data (the signal-to-noise ratio q), given the model (the cluster mass M 500 ), and the second term is the mass probability distribution. The latter is related to the mass function dN dM 500 , such that ( ) | ( ) ò ¢ = ¢ P M dN dM dM dN dM.
Cosmological and Scaling Relation Parameters The results presented in this analysis are obtained by combining the full SPT likelihood with the new Planck likelihood, presented in Section 2 and 3, SPTcl + PvSPLIT. When discussing our results, we focus on the constraints for the cosmological parameters Ω m and σ 8 and for the Planck scaling relation parameters ( ) b 1 SZ and α SZ. We start by comparing the results for the SPTcl + PvSPLIT baseline combination with constraints obtained when considering the SPT data and Planck data alone. We stress that, when providing results for Planck data alone, we are actually considering the combination of cluster counts with measurements of BAO  (Beutler et al. 2011 (Beutler et al. , 2012;; Ross et al. 2015; Alam et al. 2017 ), together with constraints on the baryon density Ω b h 2 from big bang nucleosynthesis (BBN hereafter).
We also consider the full calibration of the scaling relation parameters (as reported in Table  2 ), following the analysis in Planck  Collaboration et al. (2016b). In this work, we simply perform a new analysis using the MultiNest sampler, within the cosmoSIS package, in order to provide consistent results. This data set combination is labeled as "PvFULL. " We report the constraints on cosmological and scaling relation parameters in Table  4. We show the 68% confidence level (CL hereafter) constraints for all the parameters. In the triangular plot in Figure  2  we show the one-dimensional and two-dimensional probability distributions for the cosmological and scaling relation parameters for the main comparison between the baseline SPTcl + PvSPLIT and the original PvFULL and SPTcl analysis.