dataesr/scientific-paragraphs-categorization huggingface dataset:
This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e. g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.
Symmetry analysis In general, a linear PDE admits an infinity of conservation laws, with integrating multipliers being solutions to the adjoint PDE  [2]. Here we provide an interesting conservation law, which was found using the GeM Maple package  [5] : E 1 - γ x η p t + G x = 0 , * Using modern analytical techniques it is possible to show even sharper results on the solution support, see e. g. [4]. † It is known that both Eulerian and Lagrangian descriptions were proposed by the same person -Leonhard Euler. where E 1 (z) def := ´+∞ 1 e -t z t dt is the so-called exponential integral function  [1]  and the flux G is defined as G (x, p) def := -η e γ x η p -x γ E 1 - γ x η p + η E 1 - γ x η p x. The symmetry group of point transformations can be computed using GeM package as well. The infinitesimal generators are given below: ξ 1 = D t , ξ 2 = p D p , ξ 3 = - e -γ t γ D t + e -γ t x D x -e -γ t p D p , ξ 4 = e γ t γ D t + e γ t x D x - γ e γ t η x p D p , ξ 5 = e (γ + c) t M 1 + c γ , 1, γ x η e -γ x η D p , ξ 6 = e (γ + c) t U 1 + c γ , 1, γ x η e -γ x η D p , where c ∈ R , M (a, b, z) and U (a, b, z) are Kummer special functions  [1, 17]  (see also Appendix C).
The quantity ∆P k can be defined as the arithmetic or geometric mean of two neighbouring discretization steps ∆P k ± 1 2 : ∆P k def := ∆P k + 1 2 + ∆P k -1 2 2 , ∆P k def := ∆P k + 1 2 • ∆P k - 1 2. * We present our algorithm with a constant time step for the sake of simplicity. However, in realistic simulations presented in Section 4 the time step will be chosen adaptively and automatically to meet the stability and accuracy requirements prescribed by the user. To be specific, in our code we implemented the arithmetic mean. The fully discrete scheme can be easily rewritten under the form of a discrete dynamical system: Y n + 1 k = Y n k -η ∆t e γ t n Y n k ∆P k ∆P k + 1 2 Y n k + 1 -Y n k - ∆P k - 1 2 Y n k -Y n k -1 , n 0. Remark 1. We would like to say a few words about the implementation of boundary conditions.
(3) The variable X (P, t) is recovered by inverting (3. 5), i. e. X (P, t) = e -γ t Y (P, t). (4) Thanks to (3. 1) we can deduce the values of p X (P, t), t ∈ [ 0, 1 ] by applying a favourite finite difference formula *. Working with the pseudo-inverse allows to overcome the issue of the retention phenomenon, which manifests as the expanding support of p (x, t) for positive (and possibly large) times t > 0 , t ≫ 1 , since the computational domain was transformed to [ 0, 1 ]. This method is the Lagrangian counterpart of the moving mesh technique in the Eulerian setting  [15, 16]. A simple Matlab code, which implements the scheme we described hereinabove, is freely available for reader's convenience at this URL address: https://github. com/dutykh/Feller/ * In our code we employed the simplest forward finite differences and it lead satisfactory results.
Numerical results In this Section we validate and illustrate the application of the proposed algorithm on several examples. However, first we begin with a straightforward validation test. The only difference with the proposed above algorithm is that we are using a higher order adaptive time stepping for our practical simulations. The explicit first order scheme was used to simplify the presentation. In practice, much more sophisticated time steppers can be used. For instance, we shall employ the explicit embedded Dormand-Prince Runge-Kutta pair (4, 5)  [8]  implemented in Matlab under the ode45 routine  [22]. Conceptually, this method is similar to the explicit Euler scheme presented above. It conserved all good properties we showed, but it provides additionally the higher accuracy order and totally automatic adaptivity of the time step, which matches very well with adaptive features of the Lagrangian scheme in space.
In this way, we obtained a stable numerical scheme (under not so stringent stability conditions), which turns out to be naturally adaptive as well, since particles move together with the growing support (the rightmost particle position defines the support) and they tend to concentrate where it is really needed. The performance of our scheme was illustrated on several examples. We share also the Matlab code so that anybody can check the claims we made hereinabove and use it to solve numerically the Feller equation in their applications: https://github. com/dutykh/Feller/   2  (right column).
The results show that when children with ASD look at a social scene, they have difficulty looking at actors' eyes. Nevertheless, few studies have compared eyetracking data gathered from children with ASD who have been engaged with both static (such as photos) and dynamic stimuli (such as videos). To the best of our knowledge, only three studies using modern eye-tracking equipment have made a comparison between static photographs and dynamic videos  (Saitovitch et al. , 2013; Shic et al. , 2014; Chevallier et al. , 2015). All three studies showed an effect of stimulus type (dynamic vs. static) on the visual behavior of children with ASD. Shic et al. (2014)  presented stimuli to 6-month-old babies at risk of developing ASD. They presented three types of percepts (images, a video of a female actress smiling, and a video of a female actress smiling and speaking in motherese).
Apparatus and Stimuli The study was carried out with an SMI-RED 250 Hz eye-tracker (SensoMotoric Instruments, SMI) calibrated at 60 Hz. Data and stimuli were recorded in SMI's I View X and Experiment Center software, respectively. They were presented on a 17" screen in 4:3 format, the dimensions of which were 34. 7 × 25. 9 cm. Eye movements were recorded binocularly. The raw data were extracted with Begaze software and fixations were classified using the Gazepath package (van Renswoude et al. , 2018) on R. The Gazepath package takes into account data from both eyes. It averages the x and y coordinates and interpolates the missing data based on the data of the other eye. The velocity threshold is estimated using the same method as  Mould et al. (2012). It is estimated by the distance between the preceding and succeeding points, divided by the time elapsed between them on a trial-by-test basis for each individual.
This allowed for the calculation of the speed of the eye that corresponds to the Euclidean distance between two points divided by the time line. If the data exceed the usual speed of the eye, it is classified as a saccade; otherwise, it is a fixation. According to the literature, saccades are worth about 200 ms  (Nyström and Holmqvist, 2010). When there are successive fixations that follow each other, the package made a correction. In this case, the fixations are merged into one. Finally, the duration velocity thresholds calculated participant by participant that were greater than the optimum duration threshold (that represents the noise) were classified as fixations. After classifying the data as fixations, a posteriori AOI were created with the ks package  (Duong, 2007)  for the mean shift algorithm, and the deldir  (Turner, 2018)  and sp  (Bivand et al.
, 2013)  packages for the Voronoi Tessellation method. All statistical pre-analyses and analyses were done using R software (R Core Team, 2016). Our stimuli and the R script with all the functions allowing the analysis of raw eye-tracker data are available on the Open Science Framework (OSF) platform (https://osf. io/8ewsk/) and are explained in detail in a French article  (Cilia et al. , 2019). The material consisted of a video presented to a raster width of 1,280 pixels and a raster height of 1,024 pixels. A 2 cm-thick black band outlined the stimulus. The audio transmission was at 160 kbit/s. The video image rate was 25 frames per second. The data that were used came from the first 20. 3 s of a 58 s video from which we extracted five video sequences with a duration of 1. 21 to 2. 9 s. In addition, five photos taken as screenshots from the video were presented for the same duration as their corresponding videos.
Procedure During the task, depending on their age and motrice agitation, children were seated comfortably approximately 60 cm from the screen, on a chair, on a parent's lap, or in a highchair. The experimental area was as uncluttered as possible to avoid any distractions. In fact, children faced the screen and were surrounded by two white curtains. Behind each child, the parent or experimenter helped them maintain the optimal position for data recording. During the experiment, the only instruction the children were given was "Look at the screen, " which may have been repeated several times. Babies in the control group and children with autism were not verbal or did not exceed the level of children aged 30 months. Therefore, we did not give them any instructions. Children were invited to sit down and watch the computer screen.
Coding and Analysis This article analyzes visual exploration on the basis of AOI created a posteriori using the Voronoi Tessellation method  (Over et al. , 2006)  based on fixation densities estimated with mean shift clustering  (Santella and DeCarlo, 2004). First, raw data were analyzed with the Gazepath package  (van Renswoude et al. , 2018). Mould et al. (2012)  algorithm was used to classify fixations and saccades. The advantage of this algorithm is that it sets different detection thresholds based on the quality of the raw data. The lower the quality of the data, the more conservative the thresholds used (see  van Renswoude et al. , 2018, for details). Next, the mean shift algorithm enabled us to identify different fixation densities for all children for each photo and corresponding video sequence.
Thus, we obtained coordinates for each participant's visual fixation densities on a Euclidean plane. Generally speaking, mean shift clustering consists in finding the centroid of the data density by creating a vector for each point that will contribute to the local mean. Each centroid makes it possible to identify the distribution density kernel or core. Finally, the algorithm is able to identify clusters, based on the convergence degree of the coordinates in the x and y positions of each fixation point in relation to the density kernel. Finally, we used Voronoi's method  (Over et al. , 2006)  to create AOI that were large enough to be less sensitive to typical eyetracker errors  (Hessels et al. , 2016). This method is used to divide areas centered around a number of points. Each cell represents the area that is closest to one of the points, and lines indicate equidistant locations between points or cell centers.
Statistical Analyses All data analyses and processing were performed using R 3. 6. 0 (R Core Team, 2016). All data and R scripts are available on the Open Science Framework (OSF) platform (https://osf. io/ 8ewsk/). Statistical analyses were performed based on the general linear model, using mixed-design ANOVAs (with Greenhouse-Geisser correction when appropriate). Subsequent comparisons were conducted using Tukey's HSD with Holm's correction for each condition and group when appropriate. Effects sizes were computed using partial eta squared. The normality and homoscedasticity assumptions were checked graphically. The influence of potential outliers was estimated using Cook's distance. According to the recommendations of  Aguinis et al. (2013) , we have determined Cook's distance cutoff using the F distribution with df1 = k -1, df2 = kn -1, and α =.
Comparison with existing integrators We ran the same eccentric and inclined initial conditions using the REBOUND (Rein & Liu 2012) package integrators IAS15  (Rein & Spiegel 2015)  and MERCURIUS  (Rein et al. 2019). IAS15 is an adaptive high-order Gauss-Radau integrator, and MERCURIUS is a hybrid symplectic integrator similar to MERCURY  (Chambers 1999). This choice is motivated because the REBOUND team made recent and precise comparisons with other available integrators  (Rein &   1  to other codes: IAS15, MERCURIUS, and SYMBA. The same initial conditions were integrated. We plot the median of the energy error. Spiegel 2015;  Rein & Tamayo 2015). Moreover, we used a very similar implementation of the Kepler step. We also ran the same tests with the multi-time-step symplectic integrator SYMBA  (Duncan et al.
Identifying a thread of data While we collected data from Facebook, Twitter and YouTube, the Facebook thread of posts was most prominent. The three media complement themselves in the Internet shutdown episode. We looked at Twitter for triangulation and identified cross-posting. While we found posts and tweets of similar content, we reproduce here one tweeted picture and shared on Facebook, that then was extended as a video on Facebook. Therefore, we also collected YouTube videos. For the purpose of this paper, we chose a thread of posts mixing multimedia content starting from the first rumors of Internet shutdown to the "Friday of Anger" protest on the 28 th. We report timestamps, Likes (L) and comments (C) in addition to the posts (Table  2 ). The thread of posts reproduced here aims at showing how the events unfold, and builds on a larger data analysis.
Making Inferences From the analyses and interpretation of data, theoretical explanations still need to be formulated. We analyzed the data in 2016, five years after the events took place and went back into the analysis in 2018 and 2019 knowing how the outcomes and the current situation eventually evolved (overcoded abduction). We explicitly coded pictures and texts according to semiotics approach developed in the previous section (undercoded abduction). Detailed examples of this coding, including User loaded images and text are shown in Figure  7. 2)  6. 5. 1. Going through the ladder Despite the shutdown, people still rallied the protest sites (social world). Therefore, we looked for traces explaining the massive turnout, which are the acts of communication (physical world). We worked the dimensions of the semiotic ladder to investigate.
Rigor arises by bringing structure into the analysis of unstructured, rich social meanings in representationally complex data and by making explicit the inference mode (i. e. abductions). This rigor is extended by explicating the researcher's analytical commitment in making interpretations. Researchers can better demonstrate the trustworthiness of their conclusions by applying our semiotic toolkit to their perceptions and understandings of observed phenomena. Furthermore, using the semiotic toolkit to code data and the researcher's analysis integrates systematic jottings  (Miles et al. , 2014)  to strengthen the coding process itself. The trustworthiness of the SEANT is still to be demonstrated in future research. Moreover, the complementarity between insights driven from big data analytics and insights from semiotics is still an unexplored area.
Big data covers a range of analytical techniques to study large datasets; semiotics investigates interpretations. There are limits to datasets and there are limits to questions such datasets can answer through applied mathematics. These limits do not call for richer data but for richer analyses. These limitations open the path for mixed method research  (Mingers, 2001). In comparison to other techniques, SEANT has merits in the way it integrates visual and textual materials together for data analysis. SEANT has some shortcomings in the study of emergent and largescale phenomena like the Arab Spring. Defining the extent of data collection can be challenging because it is hard to pin down the beginning of the events. Consequently, the researcher often ends up with a subset of the data. Lacking guidelines for data collection, we proceeded by following concordant items of evidence that led us to specific posts and tweets that identified specific Facebook pages and hashtags.
Video and image data are regularly used in the field of benthic ecology to document biodiversity. However, their use is subject to a number of challenges, principally the identification of taxa within the images without associated physical specimens. The challenge of applying traditional taxonomic keys to the identification of fauna from images has led to the development of personal, group, or institution level reference image catalogues of operational taxonomic units (OTUs) or morphospecies. Lack of standardisation among these reference catalogues has led to problems with observer bias and the inability to combine datasets across studies. In addition, lack of a common reference standard is stifling efforts in the application of artificial intelligence to taxon identification. Using the North Atlantic deep sea as a case study, we propose a database structure to facilitate standardisation of morphospecies image catalogues between research groups and support future use in multiple frontend applications.
We also propose a framework for coordination of international efforts to develop reference guides for the identification of marine species from images. The proposed structure maps to the Darwin Core standard to allow integration with existing databases. We suggest a management framework where high-level taxonomic groups are curated by a regional team, consisting of both end users and taxonomic experts. We identify a mechanism by which overall quality of data within a common reference guide could be raised over the next decade. Finally, we discuss the role of a common reference standard in advancing marine ecology and supporting sustainable use of this ecosystem.
g. [37, 38]. Imaging has also been applied to detecting and assessing temporal variation  [22, 39]. Estimates of organism densities from seafloor imagery have proven more accurate than those obtained by physical sampling methods, such as trawling. For instance, densities derived from seafloor imagery provided a 10-50 fold increase in accuracy in comparison to trawling in the Porcupine Abyssal Plain in the North East Atlantic  [40]. However, it is likely that diversity is underestimated as a result of difficulties of identification of the taxa to lower taxonomic levels from imagery  [21]. The use of images to collect faunal data brings with it the challenge of identifying taxa from image data. Identification of physical specimens is usually achieved using taxonomic keys that have been developed by experts working on specific taxonomic groups.
g. [41, 42] , but they are rare for depths beyond recreational SCUBA diving capability (>30 m) (hereinafter referred to as deep-water species). Good field guides are usually underpinned by a comprehensive understanding of the species pool for the region of study. For most deep-water regions, this understanding is lacking. Notable exceptions include the Monterey Canyon  [43]  and the soft sediment (trawlable) habitats of the North Atlantic. The lack of comprehensive field guides for deep-water marine organisms presents a significant challenge to those faced with the interpretation of image data from poorly known regions or habitats, such as seamounts, ridges, or other areas of hard and high-relief substrates that are not conducive to trawling surveys. In the absence of a good knowledge of the taxonomy of many groups and regional field guides, a common practice in the interpretation of image data is the development of a morphospecies reference image dataset (Fig  1 ) and the use of operational taxonomic unit (OTU) numbers.
Thus, following traditional methods of sample analysis, all observed species would be assigned the level Porifera or Alcyonacea, resulting in a significant loss of it clear that one of the co-authors is employed by a commercial company (Gardline Limited). This company provided support in the form of salary, travel and subsistence for Michael Thompson to attend the workshop held to discuss end user needs and database structure, as well as to contribute to the preparation of the manuscript. We would also like to make clear that this commercial affiliation does not alter our adherence to all PLOS ONE policies on sharing data and materials.
Competing interests: We would like to make it clear that one of the co-authors is employed by a commercial company (Gardline Limited). We would also like to make clear that this commercial affiliation does not alter our adherence to all PLOS ONE policies on sharing data and materials. resolution in the data. However, use of a morphospecies reference image catalogue allows the observer to assign morphologically different (and in most cases, likely taxonomically distinct) forms to a unique OTU number, which can then be assigned to the taxon (e. g. Porifera msp. 1, Porifera msp 2 etc. ) if needed, thereby retaining taxonomic resolution in the data. The problem with this approach is that each study or group uses a different naming convention for morphospecies. It then becomes impossible to compare or combine datasets between studies.
The most promising of these techniques is supervised machine learning to automatically detect and classify taxa  [53, 58, 61]. However, consistent interpretations by humans are initially required, providing 'gold standard' classifications, with as much data as possible, which can be used to train these algorithms. Moving forward, developments in AI and CV approaches that combine the use of visible morphological characteristics with deep learning, would benefit significantly from the development of a standard image-reference dataset. For those taxonomic groups in which the morphological characteristics commonly used to differentiate taxa are not discernible in images (e. g. sponges, anemones, zoanthids and plexaurid gorgonians), these types of combined approaches will first require development of novel visual multi-access keys, which themselves can only be created from a high-quality reference image dataset and skilful determination of characteristics differentiating taxa.
While there are a variety of on-line open-access databases that are designed to archive biological and ecological information, including genetic data (for example GenBank), species occurrence records (for example the Global Biodiversity Information Facility GBIF) and even images of taxa (for example Morphbank), there are few that provide a reference guide to support the interpretation of image-based datasets. Table  1  provides a list of existing field guides and morphospecies reference image catalogues for deep-water species of the Atlantic Ocean that are currently publicly available. However, many more are un-published or inaccessible to others, and are held as a mixture of printed and electronic materials. Recently there have been attempts to make morphospecies reference image catalogues associated with specific research programmes or projects available to others (for example  [43, 47, 62, 63, 64, 65, 66]  to mention a few).
In addition classification based approaches to this issue have also been developed  [67]. While useful, this 'piece-meal' approach will not solve the challenges outlined above. There is a clear need for the development of a standard reference guide to support the use of image-based sampling. Failure to develop appropriate tools will ultimately hinder progress in marine ecology, particularly in deep-sea marine ecology where images are frequently one of the few collected datasets. In order to improve data quality and comparability, realise the benefits of new technologies in both image data collection and interpretation, and ultimately raise standards of taxonomic identification within academia, government, and industry, we must move towards the use of standard reference guides, quality controlled and curated by experts in both taxonomy and field identification.