dataesr/scientific-paragraphs-categorization huggingface dataset:
This method for simulation of time series is implemented by Boore in Fortran  [28]. In order to generate time acceleration series for the numerical examples, we implemented the stochastic method in Matlab software  [29]. Parameters of the ground spectrum were taken as suggested values in reference  [22]  and summarized as indicated below: -the source E(M 0 , f ): is based on the source spectral shape AS00 (Atkinson and Silva (2000) for California); -the path P (R, f ): takes into account the effects of geometrical spreading, of attenuation and of the increase of duration with distance due to wave propagation and scattering. (24)  with R 0 = 1, R 1 = 40 and p 1 = 0. 5; -the site G( f ): takes into account the effects due to the local site geology and is divided into amplification A( f ) and attenuation D( f )  (25)  where the amplification A( f ) is taken for generic rock in reference  [30]  and the attenuation function D( f ) is defined as the combination of two filters P (R, f ) = Z (R) exp - π f R Q ( f )c Q (23) where c Q = 3.
Results In this study, we recorded spontaneous spiking activity and local field potentials (LFP) from the primary visual cortex of four anesthetized cats (~1 hr/animal) and one awake monkey using 32-channel silicon probes (cats) and a chronically implanted 96-channel Utah array (monkey, 4x10 minutes, total of 40 minutes). To avoid interference of visually evoked activity with the ongoing dynamics all recordings were performed in the dark. Visual inspection of the LFP spectrogram of both cat and monkey datasets showed non-stationary dynamics with prominent power fluctuations in a frequency band between 1 and 15 Hz and stronger alpha oscillations  (9) (10) (11) (12) (13)  in the monkey recordings  (Fig 1A).
State separation In order to account for the variability of cortical dynamics, we attempted to pool short segments of the data into sets which were characterized by a similar frequency composition of the LFP power spectrum. Each set is referred to as a different cortical (or dynamical) state in accordance with previous studies  [35, 38, 41]. We first used a combination of principal component analysis (PCA) and subsequent kmeans clustering to find frequency bands that showed the highest variance across an entire dataset and subsequently cluster data epochs with similar power in these bands (see Materials and methods). The first three principal components (PC) explained 97% (cats) and 99% (monkey) of the variance and corresponded to different bands of the frequency spectrum within a range between 1 and 15 Hz (Fig  1B ).
Each data segment was represented in a three dimensional PC space and we observed a characteristic pattern of segment clusters across cat and monkey datasets. Most segments were concentrated at the origin of the PC space around which the remaining ones were scattered along the three dimensions (Fig  1C ). We performed a k-means cluster analysis to extract different clusters in each dataset. The optimal number of clusters was estimated using a validation procedure based on the Dunn index (DI). On average, the optimal number of clusters, as indicated by a peak in the DI distribution, was found to be five in the cat datasets and four in the monkey recordings (Fig 1D ), each of which corresponded to different cortical states. In order to compare states across different datasets and species, we coded clusters at the same location in the PC space with the same color (see color code in Fig  1C ).
11). In contrast, neurons in the awake monkey fired significantly more vigorously in desynchronized states than during synchronized activity (one-way rm-ANOVA: F 3,9 = 39. 03, p = 0. 0005, ε = 0. 62). To further quantify the relationship between spikes and LFP we computed spike-triggered averages (STA) for each dataset and cortical state (see Fig  2C  for two examples of a cat and a monkey dataset). In all cases, as expected, spikes were associated with the negative trough of LFP deflections, whose area between the negative deflection and the zero baseline (one-way rm-ANOVA: F 4,12 = 7. 26, p = 0. 019, ε = 0. 56 (cat) and F 3,9 = 6. 63, p = 0. 027, ε = 0. 71 (monkey)) varied between states. In desynchronized states the LFP peaks were small and thin, while they increased in amplitude and width in more synchronized states.
The synchronized cluster with faster deflections displayed peaks with the highest amplitude, but its width was smaller than synchronized states with lower frequency fluctuations. These results were confirmed across all datasets and both species  (Fig 2D). To assess the level of correlation in the population spiking activity, we computed the population auto-correlation histograms (pACH) of the population spike trains for each state  (Fig 2E)  which captures all possible correlations either generated intrinsically by neurons (i. e. bursting behavior) or through neuronal interactions. The area of pACH peaks was significantly state dependent (one-way rm-ANOVA: F 4,12 = 15. 91, p = 0. 002, ε = 0. 6 (cat) and F 3,12 = 4. 27, p = 0. 018, ε = 1 (monkey)). The pACH of the Desyn I state had lower amplitude and area compared to the other states, while the pACHs of SynSlow II and SynFast states had the largest peaks.
Cortical states and criticality To study criticality in spiking activity, we first applied a classical analysis  [13]  that is based on binning point processes like spike trains and extracting clusters defined as consecutive bins with a number of spikes above a predefined threshold (Fig 3A, threshold ! 1). Bin-sizes were given by the average inter-spike interval of each state (see Table  1  for detailed values). Sufficiently sampled critical dynamics underlying the generated spikes predicts power laws in the cluster size distributions, i. e. a straight line in log-log plots. Such analysis was consequently performed for each cortical state separately and the full datasets for comparison (Fig  3B ). The distributions in the most desynchronized states (black solid lines) did not follow a power law, albeit not being as curved as expected from shuffled data (Fig 3B  , dashed lines ).
(Fig 3B, solid black line) To quantify these tails, we fitted both lognormal and power law distributions to the cluster size distributions. Lognormal functions are more flexible and support different degrees of heavytaildness as opposed to power laws with extreme tails. Thus, comparing the goodness of fit between both distributions provides a relative quantification of how closely a distribution approaches a power law. We performed comparisons using loglikelihood ratios (LLR) with positive values indicating superior power law fit and negative values giving more evidence for lognormal fits with reduced tails  [22, 52]. In our recordings, LLRs were in general negative across all states in both cat and monkey datasets (all datasets: p < 0. 001), indicating that tails were less pronounced than expected by a power law.
However, how much each state deviated from a power law varied between states as indicated by the absolute values of the LLR. These were more negative during desynchronized states and when analyzing the full datasets, while the discrepancy between lognormal and power law fit was less pronounced during states with more synchronization (Fig  3C ). We repeated this analysis using different thresholds for avalanche detection (see Methods and material)  [22, 53]. In the cat, significant state differences (rm-ANOVA: p < 0. 05) were found for all but the lowest and highest thresholds, which only yielded a trend (p < 0. 1) or were non-significant, respectively. In the monkey, state differences were found for all thresholds (see example in We also determined the exponent of the fitted power law distributions for all states which yielded values for each species close to the theoretically expected and experimentally found value  [13, 54]  of -1.
Lifetime distributions Another signature of criticality is a power law in the distribution of lifetimes, i. e. the duration of neuronal event clusters (Fig 5A ), which decays with a characteristic exponent of -2. This theoretically obtained result  [54]  was indeed found in neuronal networks in vitro and in vivo using LFP events and spiking activity  [13, 22]. Here, we also calculated lifetime distributions and assessed their closeness to power laws by comparing LLRs between power laws and lognormals across different states. Similar to the cluster size distributions, LLRs indicated a generally better lognormal fit (all datasets: p < 0. 001). However, LLR values during synchronized states were significantly less negative during synchronized states compared to desynchronized states and the full datasets (Fig  5B ).
Inter-spike interval distributions Previous studies reported heavy tails in the inter-spike interval distributions of individual neurons  [56, 57]  and spike trains of neuronal populations  [20, 58]. In this study, we also compared inter-spike interval distributions of population spike trains (ISI pop ) for each state quantifying differences through the coefficient of variation (CV = std(ISI pop ) / mean(ISI pop )). In both cat and monkey recordings the distributions of desynchronized states and the entire datasets were clearly curved (Fig.
Δt was chosen to obtain homogeneous averaged activation rates across datasets and cortical states (Fig 7A, see also Table  2 ). We aimed at obtaining the probability distribution PðsÞ over the 2 N possible binary patterns. For this, we used a Maximum entropy model (MEM) to find PðsÞ by maximizing its entropy under the constraint that the activation rates (<σ i >) and the pairwise correlations (<σ i σ j >) are preserved (see Methods). The resulting distribution is PðsÞ / e À EðsÞ , where EðsÞ is the energy of the pattern s, and EðsÞ ¼ À X N i ½h i s i þ 1 2 X N j J ij s i s j , where h i represents the intrinsic tendency of site i towards activation and J ij represents the effective interaction between sites i and j (see Methods). Note that energies are proportional to the patterns' minus log probabilities, or "surprise".
The model parameters O = {h; J} were estimated from the data using a gradient descent algorithm (see Methods). We constructed pairwise-MEMs for each dataset and each cortical state separately and analyzed the obtained models. Here, we present analyses of the joint activity of N = 6 electrodes for both cat and monkey datasets-but, as shown below, we found consistent results for models of larger size for the cat datasets, for which larger ensembles were recorded (see Table  2 ). We first evaluated the importance of correlations by comparing the performance of the pairwise-MEMs to the performance of independent-MEMs for which only the activation rates (<σ i >) are preserved (i. e. , only h is optimized). Specifically, we compared the prediction and the empirical estimation of the probabilities of spiking patterns in each cortical state.
This is the expected behavior close to a critical point where both order and  disorder coexist  [59]. In conclusion, a maximal heat capacity close to the operating point (i. e. , T max = 1, corresponding to the model of the real data) suggests that the system is likely to be close to a critical state. We calculated the heat capacity C as a function of T for each cortical state (Fig 7F  -7I ). We found that the peak of C is located at different temperatures for different cortical states: in all 4 cat datasets and in all 4 monkey datasets the temperature T max at which C is maximal is significantly cortical-state-dependent (p < 0. 01, one-way rm-ANOVA, Fig 7F  and 7G ) and is the highest for the most desynchronized cortical state and the lowest (approaching T max % 1) for the most synchronized cortical state (Fig 7H  and 7I ).
We further studied the collective dynamics for different ensemble sizes N. For increasing N the heat capacity of the data grows and the peak temperature decreases for all cortical states, except for the most desynchronized state for which T max increases (Fig 8A  and 8B ). Notably, the heat capacity of the data significantly grows even when it is normalized by N, as expected close to a critical point  [59] , for all but the desynchronized states (Fig  8B ). Lastly, as a consequence of the relation between entropy and C (see Methods), the entropy of the spiking patterns significantly depends on the cortical state (p < 0. 05, rm-ANOVA) and it is higher in synchronized states (Fig  8C ). The mean entropy differences between SynSlow II and Desyn I is ΔS = 0. 428 bits (average over all cat and monkey datasets, for N = 6); this is a substantial change, since this implies that the pattern repertoire is reduced 2 NΔS % 6-fold from the synchronized to desynchronized states.
In the latter studies, invariant deviations from power law were found across several species, brain areas and stages of the sleep wake cycle after averaging criticality measures across entire datasets. However, after having separated statistics for various cortical states, we have shown that the cortex is indeed capable of transiently generating dynamics that come close to criticality. Moreover, our analyses using the MEM confirm that cortical states have consistently different second-order statistics and demonstrate that cortical states are truly different physical states in the sense of statistical physics. Our results are in line with a previous study which reported fluctuations of criticality measures in spiking activity recorded in the barrel cortex of rats under urethane anesthesia  [44].
For each cat we acquired one dataset lasting between 3900 and 6000 seconds, while four datasets of 600 seconds each were obtained in the monkey on four different days. The monkey was sitting in the complete dark, head fixated. For subsequent analysis the LFP was filtered between 1 and 100 Hz. Spikes were detected by manually setting a one-sided threshold that would result in a signal to noise ratio larger than ~2. Action potential waveforms were sorted and separated from remaining noise using the T-EM clustering algorithm and manual cluster cutting (Offline Sorter, Plexon Inc, Dallas, USA). In the cat, simultaneous recordings of spiking activity were extracted from an average of 21. 5±6. 7 channel sites and in the monkey 8. 75±1. 9 channels sites. Note that no attention was paid to extract single units, as during later analysis spikes from each electrode were pooled together into one population spike train.
The mean firing rate per site ranged between 0. 61 Hz and 1. 44 Hz (1. 01±0. 38) in the cat and between 4. 95 Hz to 7. 32 Hz (6. 31±1. 08) in the monkey recordings. The rates for the entire recordings were 20. 64±7. 9 Hz for the cat data and 54. 24±10. 57 Hz for the monkey. The cat recordings were performed in uniform scotopic illumination level, while any source of light was eliminated during the monkey recordings. During three recording sessions in the monkey we obtained eye tracking data using the Eyelink 1000 system (SR research, sampling frequency 1000Hz).
In order to find segments with similar power spectra, we applied a k-means clustering algorithm with a different number of clusters (2-10 clusters) after normalization of each principal component to a value of 1. To determine the optimal number of clusters we validated the clustering results with the Dunn index  [82]  according to the following formula: DI ¼ min with distance d(i, j) between the centers of clusters i and j and distance d'(k) between the center and elements of cluster k. This equation evaluates the compactness of clusters by calculating the ratio between the minimal distance between clusters to the maximal distance within clusters. The Dunn index was computed for each dataset and then averaged separately across all cat datasets and all monkey datasets. The Dunn index reaches a maximum at the optimal cluster number and we identified five clusters for each cat dataset and four clusters for each monkey dataset (Fig 1C  and 1D ).
In order to allow a comparison between different datasets and species, these measures were normalized such that the cortical state with the maximum value for each dataset was set arbitrarily to one. We also estimated the correlation between spiking activity and the LFP by constructing spike triggered averages (STA) for each cortical state of a given dataset. The STAs of all clusters and datasets showed a negative deflection. LFP was z-scored and STAs were quantified by calculating the amplitude of the deflection peak and the integral of the negative deflection with respect to the zero crossings. Like for the ACH, these two measures were normalized to the cortical state with the maximum value which was set to one.
Maximum entropy models (MEMs). We further studied the patterns of the ensemble spiking activity from N recording sites during the different cortical states in the framework of statistical mechanics. The ensemble activity was binarized in non-overlapping time bins of 50 ms for anaesthetized cat data, and 10 or 20 ms for awake monkey data (different time bins were chosen to compensate for the different averaged activation rates between datasets and cortical states; see Table  2  and Fig 7A ). In a time bin Δt, a single electrode site i either did (σ i = +1) or did not (σ i = -1) generate one or more spikes, thus, the state of the neural ensemble is described by a binary pattern s ¼ ½s 1 ; s 2 ;. ; s N. We used a Maximum entropy model (MEM) to estimate the distribution PðsÞ of each of the 2 N possible patterns, i.
Right, the entropy S(T) increases with T and the heat capacity C(T) peaks at a given temperature T max (for this particular example neural ensemble T max = 1). (F-G) Heat capacity as a function of the temperature parameter (T), for each cortical state, for two example anesthetized cat datasets (F) and two example awake monkey datasets (G) (10 random choices of groups of N signals were used; trace thickness indicates SEM). Inset: Peak temperature (T max ) for each neuronal ensemble and for each cortical state. T max significantly depends on cortical state (p: p-value, rm-ANOVA). (H-I) T max averaged over all cat datasets (H) and over all monkey datasets (I) for each cortical state (rm-ANOVA: H: F 4,156 = 25. 03, p < 0. 001, ε = 0. 34; I: F 3,117 = 59. 60, p<0. 001, ε = 0. 90). Error bars indicate SEM.
Funding: GH, CM and YF were supported by the  CNRS , the  Agence Nationale de la Recherche  (ANR:  V1-Complex ) https://www. cnrs. fr. GH and GB were financed by the  initial training network program  FACETS-ITN ( PITN-GA-2009-237955 ) http://facets. kip. uni-heidelberg. de/ITN/. APA was supported by  SEMAINE ERA-Net   NEURON  Project and by a  Juan de la Cierva  fellowship (IJCI-2014-to the vigilance state. 21066) from the  Spanish Ministry of Economy and Competitiveness. CM, GD and YF received funding from the  EC grants BrainScales  ( FP7-2010-IST-FETPI 269921 ) and the flagship  Human Brain Project  (n. 604102) https://www. humanbrainproject. eu/. The Utah array recordings were made possible through a loan by  S. Gru ¨n  ( Research Center Ju ¨lich, INM6, Germany ) and were part of a collaborative work with  S.
Gru  ¨n and  A. Riehle  ( INT, Marseille ). AK received funding from the  German Federal Ministry of Education and Research  ( BMBF 01GQ0420  to  BCCN Freiburg  and  01GQ0830  to  BFNT Freiburg/Tu  ¨bingen) https:// www. bmbf. de/en/. GD is supported by the  ERC  Advanced Grant: DYSTRUCTURE (n. 295129), by the  Spanish Research  Project  PSI2016-75688-P  and by the the European Union's  Horizon 2020 research and innovation programme  under grant agreement n. 720270 ( HBP SGA1 ). GD obtained support from the  ERC Advanced Grant DYSTRUCTURE  (n. 295129) gustavodecolab. com/dystructure/ and the Spanish Research Project  PSI2013-42091-P. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Determination of possible steady states A semi-analytical method (first described by  Welander (1967)  but applied here to a more general case) is used to find the steady states of the system of Equations (  10 )-(  13 ). The method consists in: (1) determining analytically the steady-state distribution of temperature θ e and salinity S e as a function of the loop velocity, (2) computing the equilibrium buoyancy torque B e (w) from steady-state temperature and salinity distributions using the EOS, (3) finding the velocity values for which the scalar momentum balance (10) is satisfied. A Matlab code is provided as Supplementary Material for computing the steady-state tracer distribution and the equilibrium buoyancy torque. For any given value of velocity w, steady-state distributions of temperature and salinity can be determined analytically by solving the advective-diffusive balance equation: -w ∂ X e ∂φ + R ∂ 2 X e ∂φ 2 + F X = 0 (16) where X e (φ) is the steady-state distribution of either temperature or salinity.
The next step consists in computing the eigenvalues and eigenvectors of the Jacobian, J X = XD (22) The matrix X = [x 1. x 2N ] contains the 2N eigenvectors (or modes) which form an orthogonal basis of decomposition for any perturbation vector x. Each eigenvector x k is associated with a complex eigenvalue σ k = σ Re k + iσ I m k , found in the diagonal matrix D. Several algorithms exist to decompose the Jacobian, such as the QZ algorithm. In this study, we used the function eig of Matlab which automatically selects an optimal algorithm. For each eigenvector, the solution to equation (  21 ) is of the form, x k = c k e (σ Re k +iσ I m k )t (23) where c k is the projection of the initial perturbation on the considered eigenvector. Dynamical system theory shows that 1) the system is linearly stable if none of the Jacobian eigenvalues has a positive real part and 2) the system is at a bifurcation point if at least one of the eigenvalues has a null real part.
Objectives To quantify the relationship between exposure to lacosamide monotherapy and seizure probability, and to simulate the effect of changing the dose regimen. Methods Structural time-to-event models for dropouts (not because of a lack of efficacy) and seizures were developed using data from 883 adult patients newly diagnosed with epilepsy and experiencing focal or generalized tonic-clonic seizures, participating in a trial (SP0993; ClinicalTrials. gov identifier: NCT01243177) comparing the efficacy of lacosamide and carbamazepine controlled-release monotherapy. Lacosamide dropout and seizure models were used for simulating the effect of changing the initial target dose on seizure freedom. Results Repeated time-to-seizure data were described by a Weibull distribution with parameters estimated separately for the first and subsequent seizures.
gov identifier: NCT01243177)  [7]  was conducted with the aim of demonstrating at least a similar benefit-risk balance for LCM compared with an acknowledged standard AED at individually optimized dosages using clinically relevant endpoints. The choice of carbamazepine controlled release (CBZ-CR) as the standard AED was based on the 2006 treatment guidelines of the International League Against Epilepsy  [8]. Over 800 patients with newly diagnosed epilepsy were randomized and results indicated that LCM met the primary endpoint, based on the proportion of patients remaining seizure free for 6 consecutive months following stabilization at the last evaluated dose, LCM was non-inferior to CBZ-CR  [7]. LCM was also generally well tolerated in this patient population  [7]. The aim of the present work was to identify an exposure-response relationship under the challenging setting of a trial design where patients move to a higher dose level if their response is insufficient (i.