dataesr/scientific-paragraphs-categorization huggingface dataset:
4 ). The preparation of input data is straightforward (Supplementary Note 3), and the results are equally relevant for fundamental vestibular research 1 or practical applications assessing species-specific sensory specialization, for example in relation to diverse locomotor behaviors  20, 22, 26, 28, 38, 39. Ariadne consists of 19 executable modules written in C that perform all the computational work required to analyze inputted data. Some of these executables require the free software packages GMSH  40  (http://geuz. org/gmsh/) and Elmer (https://www. csc. fi/web/elmer/) to be installed. Each executable can be launched independently, or in combination with others using batch files. The user can thus choose either to press one button to get all the morphological and biomechanical results as output, or to launch each executable individually to scrutinize the output in sequential steps.
Visualization of biomechanical data can be done optionally through the use of two Scilab (http://www. scilab. org/) scripts provided in the Ariadne package. Ariadne comes with a manual that details the function of all executables, batch files and algorithms that are implemented (Supplementary Note 2). c, d ), rhesus macaque (b,e,g) and squirrel monkey (a,f) specimens. Aa, Ap, Al, anterior, posterior and lateral ampullae, respectively; Ca, Cl, anterior and lateral cupulae (artificially shrunk); CC, common crus; CD, cochlear duct; Cra, Crp, Crl, anterior, posterior and lateral cristae ampullares; S, sacculus; Sa, Sp, Sl, slender parts of the anterior, posterior and lateral semicircular ducts; Sm, macula sacculi; ST, scala tympani; SV, scala vestibuli; Ua, anterior utriculus; Um, macula utriculi.
Values thus obtained are 5. 73 ± 0. 23 s for the squirrel monkey  50  and 7 s for the rhesus macaque  51. That Ariadne calculated a very similar value for the squirrel monkey cannot be used as independent validation because the neurophysiological results for this species were used in the software to calibrate the default shear modulus of the cupulae (γ = 1. 44 Pa). However, the good match between the values for the rhesus macaque does independently corroborate the result calculated by Ariadne. The value of the long time constant of human semicircular ducts remains uncertain as it cannot be obtained through neurophysiological experiments. Biomechanical studies estimated its average value to be around 10 s  18  , but recent experimental analysis based on the slow phase of the angular vestibulo-ocular reflex, measured from the response to steps of rotation about a yaw axis, provided a value of 4.
Validation of the biomechanical analyses currently implemented is perforce constrained by the limited independent evidence that is available, testament of the great difficulty of accessing the functioning inner ear. However, where comparisons can be made the results obtained for the three primate species examined here are consistent with neurophysiological and oculometric studies. In particular, the match between experimentally measured and independently computed long time constants gives credit to the capability of Ariadne to compute such parameters, endorsing the accuracy of the visualization approach on which the software directly depends. The observed intra-and inter-observer variation of reconstructing the semicircular duct system results in small fluctuations of the biomechanical parameters calculated by Ariadne.
By examining multiple specimens per species the intraspecific variation of these biomechanical parameters can be quantified. Within a clinical setting, standards can be developed for normal variation of the human semicircular duct system, and the membranous labyrinth in general. Based on post-mortem analyses, attempts can be made to link specific vestibular disorders both morphologically and functionally with unusual duct systems, leading to a better understanding of the biological basis of pathology. The development of Ariadne is intended as an ongoing project in which researchers in the field of vestibular physiology can expand and modify the current modules and develop new ones as our understanding of inner ear function improves over time. Table  3. Mechanical sensitivity and radius of curvature.
Preparation of input data. To use Ariadne, input data have to be prepared following specific protocols that are summarized below, and are described in Supplementary Note 3 in the form of tutorials. We currently use Geomagic Studio 12 (Raindrop Geomagic Inc, Morrisville, NC, USA) and Avizo 7. 1 (Visualization Science Group, Burlington, MA, USA) to implement these protocols. However, other software can be used for data preparation as long as general guidelines and naming conventions described in the tutorials are followed. Data preparation involves six main steps. First and foremost, the semicircular duct system has to be segmented, excluding neighboring structures like the saccule and the cochlear duct (Supplementary Note 3 -Section I. i). In the stack of CT images the areas that are filled with endolymph have to be delineated, being careful to not include surrounding membranes into the selection.
Overview of Ariadne. At present Ariadne consists of 19 executable files, 8 batch files and 2 Scilab scripts. It runs on Windows NT platforms and needs the freeware software packages Gmsh (http://geuz. org/gmsh/) and Elmer (https://www. csc. fi/web/elmer/) to be installed on the computer. After preparing the primary input files, the use of Ariadne only requires some basic information, such as specimen name and spatial resolution, and subsequently the results of the morphological and biomechanical analyses are provided in specific folders. Descriptions of algorithms implemented in Ariadne and in-depth explanation of using the software is provided in Supplementary Note 2. After loading the input files Ariadne performs five main tasks: (1) the preparation of the cupula meshes for finite element analysis (Supplementary Note 2 -Section I.
Acknowledgements We are grateful to  R. Allain ,  J. Droulez ,  L. Halpern ,  J. -J. Hublin ,  P. Janvier  and  P. Taquet  for support and encouragement. We thank  I. Bechmann ,  K. Mueller  and members of the  Institutes of Anatomy and Veterinary Pathology at Leipzig University  for access to specimens, and  D. Plotzki  and  H. Temming  for CT scanning. This work was supported by the  Max Planck Society  and the  European  Project  CLONS  ( FP7-ITC-2007. 8. 0. Project 225929 ).
The potential conclusion 'Life on Mars' would be promptly challenged by the planetary science community and it would fail, if just one single argument (among the many arguments required) was not solid, e. g. due to instrument artefacts, contamination issues, possible inorganic pathways, conflicting datasets, lack of reproducibility of a given experiment etc. The question 'Life on Mars?' cannot be separated from the question on the origin of 'Life on Earth'. Hence, answering the question 'Life on Mars?' may well become a long scientific process of defining appropriate experimental techniques and protocols and developing plausible and safely applicable life criteria for ancient (terrestrial or Martian) sediments. However, by virtue of its science payload and its drill capability, the ExoMars rover mission will provide new types of data that will promote this process.
, 2011; Schyns et al. , 2009]. The methods we present enable study of the representation, processing, and communication in the brain of multiple features of the external world  [Ince et al. , 2015]. Furthermore, they also enable the study of the relationships between representation in different signals  [Kriegeskorte et al. , 2008]. Overall, this new estimator provides the basis for a useful and flexible multivariate statistical framework for the analysis of neuroimaging data. In this article, we first introduce the concepts of entropy and MI within a neuroimaging context, and briefly review current MI estimation methods. We also describe higher order information theoretic quantities and possible neuroimaging applications (Section 2). We then present our novel MI estimator (Section 3) and demonstrate its statistical performance when combined with a permutation-based null-hypothesis testing framework, with simulations and examples on several datasets (Section 4).
This is a desirable property for a neuroimaging statistic as it ensures that any signal processing or feature extraction applied to the recorded responses (for example spectral analysis) cannot artificially inflate the measured effect size, provided it is applied across the whole dataset without incorporating knowledge of the stimulus. Given the above, we suggest there are two views that can be adopted when applying MI in practice  [Nelken and Chechik, 2007]. The first relies on the coding interpretations of MI, and therefore requires accurate and bias-free estimates; this view has driven most neuroscience applications of MI to date. The second view considers MI more like a conventional statistical hypothesis test of independence, comparable to a t test or correlation. With this view, accurate bias-free values are less important, but determining statistical significance, including accounting for the problem of multiple comparisons, is crucial.
Existing Methods for Calculating Mutual Information There are several different practical approaches for calculating MI from experimental observations, which we briefly review here from a neuroimaging perspective. MEG, fMRI bold signal amplitude) one commonly used approach for such signals consists of quantizing the continuous valued observations into a set of discrete categories or bins. We therefore briefly review methods for estimating information values on discrete spaces. There are two main strategies for the quantization step: either bins are set with equal spacing, or bins are sized to have approximately equal occupancy (i. e. , if using four bins, each data sample is labeled according to the quartile of the empirical distribution in which it lies). For data that are approximately normally distributed, the second method is preferable, as fixed width bins result in the extreme bins having few samples, which exacerbates the limited sampling problem.
This is particularly useful given that MI is an unsigned quantity-all participants could have similar levels of MI but with opposite signs of effect. It can also help to identify situations where group significance is driven by a strong effect in one or a few participants, rather than a consistent effect across the group. This is something that is not considered with most existing group statistics. Third, is the effect significant if the data is pooled (pooled-G, equivalent to MI)? This means overall, the data recorded across all participants deviates from the null hypothesis. This allows the identification of cases where there is a weak but consistent effect across participants, which might not suffice to produce a significant CMI value. While this approach requires further development and testing we mention it here to motivate some of the wide range of potential applications for CMI within neuroimaging.
By the probability integral transform, the empirical CDF values of the data sample are uniformly distributed and so this transformation produces a dataset that has perfect standard normal marginals. This transformed dataset preserves the same empirical copula as the original data (right); in other words, the rank-relationships between the variables are preserved. In practice, the empirical CDF is not computed explicitly; instead the rank of each sample is obtained and normalized by N 1 1, where N is the number of samples. This results in a uniform distributed sample taking values in the range 1 N11 ; N N11 Â Ã at which the inverse standard normal CDF is directly evaluated. Transformations of this type are sometimes referred to as inverse normal transformations and have been used in fields such as genetics  [Beasley et al.
One option is to form the mixture model from the class-conditional parametric fits and numerically integrate this to obtain the entropy (since there is no closed form expression for the entropy of a Gaussian mixture). A second option is to fit a separate parametric model of the same form to the full dataset and use that to estimate the unconditional entropy. Figure  9  r Gaussian Copula Mutual Information r r 1555 r illustrates these issues with an example of data generated under a Gaussian model with different means for each of two discrete stimulus conditions (Fig. 9A ). Figure  9B  illustrates the two different models that can be used to estimate the unconditional entropy term, the actual mixture density (solid line) or a Gaussian fit (dotted line). Whichever strategy is used, MI is obtained as the difference between the entropy of the chosen unconditional model, and the average of the entropies of the class-conditional distributions (Fig.
9C ). It is not clear if either of these is more appropriate than the other-each preserves a different interpretation of MI. The first leads to an MI estimate more consistent with the Kullback-Leibler divergence expression of MI; it is the property of a single distribution (the fitted parametric mixture distribution) and measures the deviation of that distribution from a surrogate independent model. The second leads to an MI estimate more consistent with a statistical testing viewpoint, comparing an unconditional Gaussian fit to class-conditional Gaussian fits (cf. ANOVA). Fortunately, the use of the copula transform removes this dichotomy. Motivated by the previous section, we apply the same copula transform to the unconditional data to obtain a surrogate dataset with a standard normal distribution (Fig.
Since the conditional entropy terms are subtracted in Eq. (  4 ) this ensures GCMI is again a lower bound on the true MI. As in the continuous case, this method can be applied whatever the original distribution of the data; it does not require Gaussian classes as in the example shown here. The key feature is that the copula transform preserves the rank-class relationships and results in a dataset to which the parametric Gaussian entropy estimates can be applied. Note that while the unconditional entropy H(X) itself is not invariant to the copula normalization transform, as in the continuous case, the MI, as a difference of entropies, is invariant to marginal transformation.
RESULTS Our primary intention is to present our new GCMI estimator as the effect size for a practical statistical test for neuroimaging, that can be considered as a drop-in replacement for a number of different established statistical measures (Table  I ). In this section, we therefore first validate the performance of the new estimator when employed as a statistical test and provide some example applications. The data used for the simulation and examples in this section are available in  [Ince et al. , 2016]. We then demonstrate the bias and mean-square error of the GCMI estimator compared to other MI estimators on simulated systems as well as the example datasets (Section 4. 4).
Discrete Experimental Condition With Continuous EEG Response: Face Detection We performed a number of analyses in order to evaluate the performance of the continuous-discrete GCMI estimator (Section 3. 2) as a statistical test for neuroimaging applications. We consider EEG data collected from a single subject within an event-related design (Section 2. 3), with presentation of two classes of images: faces and noise textures. Data were band-pass filtered between 1 and 30 Hz and the current source density transformation was applied  [Rousselet et al. , 2014a]. We calculated GCMI independently for each time point and sensor using samples collected from the repeated presentations (Fig. 4A ). A common approach with neuroimaging studies is to apply a permutation test together with the method of maximum statistics in order to correct for multiple comparisons [Holmes   r Gaussian Copula Mutual Information r r 1557 r et  al.
, 1996; Nichols and Holmes, 2002]. We calculated the two-sample Kolmogorov-Smirnov (KS) test statistic  [Massey, 1951]  for each time point and sensor from all the available 1000 trials and used this as the ground-truth to evaluate tests performed with smaller numbers of trials (Fig. 11A , top left, color plot). We performed the calculation over all sensors and time points 1,000 times, randomly permuting the stimulus class labels each time. We took the maximum value over sensors and time points for each of these permutations, and used the 99th percentile of these maximum values as the threshold for significance (Fig. 11A , top left, black and white plot). This procedure corrects for multiple comparisons and provides a Family-Wise Error Rate (FWER) of 0. 01. We then repeatedly subsampled smaller sets of trials from the full dataset and repeated the mass-univariate analysis for various statistics, together with the permutation approach.
The MEG signal was obtained from a 248magnetometer whole-head MEG system (MAGNES 3600 WH, 4D Neuroimaging). We band-pass filtered in the range 2-12 Hz (third order noncausal Butterworth), downsampled to 50 Hz and then computed the planar gradient tangential to the head at each magnetometer  [Bastiaansen and Kn€ osche, 2000]. This potentially simplifies interpretation of sensorlevel data because it typically results in maximal signal directly above the corresponding source  [H€ am€ al€ ainen et al. , 1993]. We analyze 450 s of recording (22,500 samples at 50 Hz) during which the subject listened to a spoken story. Similar to a cross-correlation of two signals we calculate the relationship between the speech envelope and the MEG signal over a range of delays (0-350 ms). The resulting planar gradient signal consists of a 2d magnetic field vector (tangential to the head) at the position of each magnetometer.
We therefore take the view that considering the gradient together with the voltage (Fig. 13E ) provides a substantial advantage: these artifactual dips are smoothed out, providing a clearer picture of the time window over which the EEG signal is modulated by the changing stimulus. We suggest that including the gradient of recorded neuroimaging signals could be a useful principle across a range of different analyses. For example, returning to the MEG dataset under continuous speech stimulation (Section 4. 2), including the temporal derivative of each planar gradient component (resulting in a 4d response) has the same effect of smoothing out the artifactual MI zero resulting from a change of sign in the effect (Fig. 13G ). Again, this gives a clearer, smoother picture of the range of delays over which the amplitude of the speech envelope modulates the MEG signal, which is made possible with the use of a multivariate statistic.
Another application of the GCMI framework allows us to directly quantify the emergence of novel MI over time. For each time point, we calculate the MI about the stimulus feature available in the (bivariate) EEG response at that time point. We then subtract the MI that is redundant with that at the previous time point, leaving only the amount of new MI about the stimulus arriving at that time. Mathematically, this is equivalent to calculating the Performance of GCMI as a statistical test for MEG data with continuous stimuli in a continuous design. A. GCMI is calculated between the speech envelope and the full 2D planar gradient response (top), the amplitude (middle), or the direction (bottom) of the planar gradient vector, for each sensor and time point (left colored image plots). Significance is determined with block permutation testing and the method of maximum statistics (black and white image plots).
With real data this is not necessarily the case. We performed similar analysis of the bias of the estimator with the experimental data presented in Sections 4. 1 and 4. 2. Bootstrap sampling (with replacement) is not suitable for use with the nearest-neighbor-based KSG estimator due to the effects of repeated data points on the nearest-neighbor calculation  [Abadie and Imbens, 2008]. We therefore subsample datasets without replacement. Figure  14C  shows the results for the two-class event-related EEG dataset considered in Section 4. 1 with the same channel as Figure  11B. Here we apply the Kozachenko and Leonenko nearestneighbor entropy estimator  [Kozachenko and Leonenko, 1987]  to the class-conditional and unconditional dataset and calculate MI following Eq. (3). Due to the combinatorial properties of subsampling from the 1,078 trials, there is less variation in the largest data sample: the value there is close to that measured from the entire dataset.
The GCMI measure produces similar estimates to the four-bin discrete method, with similar asymptotic value, but lower variance and much lower bias at small samples. The k-NN method does produce a slightly higher estimate suggesting that there maybe some non-Gaussian copula dependence in this dataset. However, as shown in Section 4. 1, the GCMI still provides an effective and sensitive statistical test when combined with permutation testing and the method of maximum statistics. Figure  14D  shows a similar subsampled analysis for the continuous MEG dataset, using the channel and optimal delay lag shown in Figure  12B. Here GCMI provides a higher estimate than either of the binned methods, with reduced bias (but similar variance). The KSG method appears to reach a slightly higher asymptotic value than the GCMI, but it is difficult to determine this without a larger dataset.
One variable represented the stimulus and was correlated to a varying degree (0. 2, 0. 4, and 0. 6) with each of the response variables (which were themselves weakly correlated with r 5 0. 1). C. Five hundred subsamples of different sizes were drawn from the two-class event-related EEG dataset described in Section 4. 1. Plot shows mean (error bars show 25th to 75th percentiles). D. Five hundred subsamples of 5 s blocks were drawn from the continuous MEG dataset described in Section 4. 2. Plot shows mean (error bars show 25th to 75th percentile). r Gaussian Copula Mutual Information r r 1567 r together with tutorial examples covering the analyses presented here. The major advantage of our method over traditional statistical approaches is that it unifies a variety of applications (continuous, discrete, and multidimensional variables) in a framework with a common effect size, and quantities like conditional mutual information and interaction information allow novel interpretations that are not available with other approaches.
Again it uses a common scale, provides the ability to relate MI in different signals (e. g. , between EEG sensor array linear discriminant output and single-trial fMRI voxel beta activations, see below), and allows us to condition out correlated features. Other approaches to estimating MI in higher dimensional response spaces include extensions to the nearest-neighbor method with specifically chosen distance measures that preserve the appropriate structure of the high-dimensional space. For example, in fMRI a distance based on correlation between voxel time courses can be used to estimate MI between a statistical parameter map and a high-dimensional whole brain validation dataset  [Afshin-Pour et al. , 2011].
ACKNOWLEDGMENTS We thank  Arno Onken ,  Daniel Chicharro , and  Stefano Panzeri  for useful discussions. JG and PGS are supported by the  Wellcome Trust. GAR, PGS, BG, and CK are supported by the  UK Biotechnology and Biological Sciences Research Council (BBSRC). CK is supported by the  European Research Council  ( ERC-2014-CoG ). The authors report no financial conflict of interest.