dataesr/scientific-paragraphs-categorization huggingface dataset:
Study region: The study is carried out for northern Tunisia. Study focus: Precipitations are often analysed via intensity or accumulation for a specified timescale (e. g. , annual, seasonal, etc). We propose in this study to analyse regional rainfall variability by adopting a variable time step through the rain event concept. This event-based approach, ensures the integration of information related to rain intermittency, which is one of the fundamental properties of precipitations. This study focuses essentially on wet spells characteristics derived from the aggregation of daily winter dataset over a 50 years period. The multivariate analysis, based on the combination of two clustering approaches, i. e. , self-organizing map and hierarchical clustering, allows the identification of different rainfall regimes.
Study area and dataset description Northern Tunisia is located between 35 • N and 38 • N and covers a total area of about 28,641 km 2 (Fig. 1 ). It is characterized by dry, hot summers and moist, cool winters. We adopt Emberger bioclimatic index  (Emberger, 1930)  which is specific to bioclimatic classification in the Mediterranean region and is based on the total annual rainfall as well as the daily average maximum temperature of the hottest month and the daily average minimum temperature of the coldest month  (Marres, 1972). Accordingly, northern Tunisia is divided into three major bioclimatic regions: humid (H) in the extreme northwest, sub-humid (SH) and semi-arid (SA) in the other parts representing respectively 12,5 %, 28 % and 59. 5 % of the study area (Fig. 1 ). In Tunisia, rainfall is influenced by general atmospheric circulation patterns; the most important are: (1) the Icelandic depression, (2) western Mediterranean depressions (the Gulf of Balearic depression and the Gulf of Genoa depression), (3) eastern Mediterranean depressions (Gulfs of Syrtes depression and Gabes depressions), (4) the Azores anticyclone and (5) the central European anticyclone  (Merzougui and Slimani, 2012).
1 ) over the period 1960 -2009. The database is obtained from the General Directorate of Water Resources of the Agriculture and Water Resources Ministry. Table  1  displays the rainfall stations characteristics, including the geographic position, elevation, starting date of observations, percentage of missing values, December-January-February (DJF) totals and the bioclimatic region. The dataset consists of 3500 DJF seasons (50 years of observations at 70 stations) corresponding to 31,5910 observed days. For a given year, any missing value detected in the DJF daily observations leads to the exclusion of the whole season from the analysis. The number of considered seasons, for each station, is mentioned in Table  1. In total, the number of seasons without missing values is 3137. Note that DJF for year m corresponds to December of year m-1 and January-February of year m.
, 2005). The autocorrelation analysis is based on choosing the time lag on which the autocorrelation coefficient of the rainfall data set converges to zero. This approach is used here to analyse the 50-year DJF daily precipitations for each of the 70 stations. Note that, all days with a rainfall amount greater than zero are considered a rainy day. The minimum rainfall value recorded in the daily timeseries is 0. 1 mm/day. Unlike several studies (e. g. ,  Jiang et al. , 2011) , days with small   rainfall amount or drizzles (<1 mm/day), are not considered as dry days in our study. Indeed, the inclusion of low rainfall events can provide a better characterization of the rainfall intermittency and the events typology over the season. In addition, and for the adopted event-scale, the same rainfall event may include a dry day or days with drizzles, therefore, fixing a threshold may affect the intra-event variability and allows the split of the one single event into separate events.
Self-Organizing Map (SOM) algorithm and parameters A multivariate data analysis using SOM method is proposed to divide the sample of DJF rain-event features observed on the stations network during 50 years into clusters in an unsupervised way. SOM method is defined as a neural network algorithm well-designed for pattern recognition, clustering and dimensionality reduction  (Kohonen, 2013). The SOM algorithm has several advantages that make it a valuable tool in data mining. The main one is that it combines the vector quantization and the vector projection. The vector quantization divides a dataset into subsets of homogeneous data represented by a prototype vector. The prototypes projection and visualization aim to understand the structure of the data to identify the possible clusters structure.
The SOM can be applied to a large and complex dataset. Moreover, it is robust to missing data  (Vatanen et al. , 2015). The SOM map or Kohonen map is a grid of units (neurons), usually a two-dimensional (2D) grid where each neuron is associated to a reference vector (prototype) in the learning data set and thus corresponds to a cluster of rainfall events having common characteristics. The neurons are connected and a topological relationship is defined among neighbourhood neurons. The SOM algorithm preserves the topology of the data, i. e. , neighbour neurons on the SOM map are connected to neighbour cluster in the original space  (Haykin, 2009; Kalteh et al. , 2008; Hannachi, 2021). The structure of the SOM map consists of two layers: the input layer contains the Fig. 2. Median and mean variation of autocorrelation coefficients calculated for 70 stations over the study area from 1-day to 5-day lags.
In the literature, the hierarchical agglomerative clustering (HAC) is commonly combined with SOM in different contexts. For example,  Gueye et al. (2010)   2021 ) provide a robust decomposition of Mediterranean into bio-regions using remote sensing observations. This SOM-HAC procedure exposed in these different studies have shown the relevance of the combined SOM-HAC approach to extract information on spatial and temporal variability from multivariate datasets. These studies in various application domains have in common to deal with data of geophysical nature and which present a significant natural hazard. This two level-approach SOM-HAC is equally adopted in this study. Indeed, SOM ensures a first clustering and a visual inspection of the rainfall features as a first step. This step reduces the DJF season number where seasons with similar rainfall event properties are grouped and represented by a single, more significant prototype season.
Hierarchical clustering analysis The hierarchical clustering procedure starts by calculating the interpoint matrix proximity between all singleton clusters  (Vesanto and Alhoniemi, 2000). To merge two clusters, different types of linkage criteria can be used. Ward 's linkage distance  (Ward, 1963)  is used here because of its ability to minimize the total within-cluster variance or error sum square  (Murtagh and Legendre, 2014). The hierarchical clustering produces a tree-based representation named dendrogram that highlights the hierarchical links between different clusters. The dendrogram is composed of root, merging nodes and branches. The root is linked to the whole dataset, the merging node reflects the distance between the two merged clusters, the height of the branches corresponds to the increase in the Fig.
Kohonen map analysis To analyse the feature matrix previously obtained, we first use SOM map. Fig. 8  displays the mapping obtained by SOM using the parameters of Table  3 , and shows the projection of the 6 variables on the topological map and the corresponding U-matrix (Fig. 8a ), observation number by units' (Fig. 8b ), and the neurons classification (Fig. 8c ). The Fig. 8b  shows that, after training, the number of observations represented by each neuron is between 0 and 20. The color coverage, in Fig. 8b , reflects the number of observations by each neuron. Only 2 % of the neurons are empty, i. e. , they don't represent any data from the feature space. The U-matrix (Fig. 8a , first row and column) enables understanding and interpretation of the structure of the original data, as it represents distances between adjacent neurons.
With the assumption of an extra cluster, the five-class model (not shown) results in splitting the bigger class of Fig. 9c  into three clusters, but these are no longer discerned in the data image. With larger number of clusters, the discernability is completely lost. Thus, the combination of the dendrogram and the data image analysis favors a partition into three or four clusters. Although the three-class model is equally likely, given the good contrast obtained in Fig. 9d , we will focus the discussion here on the four-class model in order to take into account the nuance that exists in the large class of Fig. 9c. The clusters can be easily identified on the topological map, as the latter is based on proximity. In fact, Fig. 8c  shows the repartition of the four clusters on the SOM map obtained by the HAC.
Conclusions This paper investigates the temporal and spatial variability of a 50-year long data set of rainfall events in the winter season DJF in northern Tunisia. The data used consist of observed rainfall time series taken from 70 rain gauge stations during DJF 1960-2009. The analysis begins by changing daily rainfall to a sequence of DJF rainfall events and then to seasonal DJF features. These features are clustered using a two level-approach: the SOM combined with hierarchical clustering. The obtained clusters are identified and their space-time regionalization is carried out. Each class characterizes the rain event types and take into account the rain intermittent character at both seasonal and event scales. The rainfall regime was found overall to be dominated by classes describing drought, lack of rain, and intermittent weak events.
CRediT authorship contribution statement Sabrine Dérouiche: Data analysis, SOM and HAC analysis, Writingoriginal draft. Cécile Mallet SOM coding and SOM interpretation, Writingreview & editing. Abdel Hannachi event definition, image method's coding, writingreview & editing. Zoubeida Bargaoui Database, event definition, statistical analysis, Writingreview & editing.
Acknowledgements ZB would like to thank the  General Directorate of Water Resources (DGRE, Tunisia)  for providing daily precipitation data. This study was supported by  University Tunis El Manar  ( UTM, Tunisia ) with providing travel and accommodation fees for SD to visit LATMOS France and the  Department of Meteorology, Stockholm University, MISU, Sweden. This study was supported  IMI  for inviting ZB to visit MISU. This study was supported by ( UTM ) for inviting CM to visit ENIT.
5 mK/ √ Hz/pixel/array. By combining the two arrays, and taking into account that each beam is sampled by more than two pixels, we should in the end achieve NET ≤ 1 mK• √ s per beam. These values are in agreement with our initial sensitivity forecasts  [6]. The next step in the technical commissioning was to set up CONCERTO in the final observing condition, that includes software and data format compat-ibility with the APEX observatory. During these sessions, second half of April 2021, we have performed a number of observations, mostly technical routines like focus, pointing, sky dips, interferometer tests. We report in figure  4  an example among the very first results. We focus for now, due to space constraints in these proceedings, on the photometric mode. In particular, we show the projected geometries of both arrays, and a pointing map.
Acknowledgements We thank the electronics, mechanics, cryogenics and administrative groups at  Institut Néel, LPSC  and  LAM. We thank  Florence Picchiottino ,  Karina Celedon  and  Lilia Todorov  for taking care of the shippings. For the outstanding technological and human support we thank the whole APEX staff. Among them, the telescope operators  Juan Pablo Perez ,  Edouard Gonzalez ,  Mauricio Martinez. Thank you all, it was a unique experience !We acknowledge financial support from the  European Research Council  ( ERC grant   788212 ), the  Aix-Marseille University-A*Midex  and the  LabEx FOCUS.
We will start by giving a concise (and by no means complete) overview of the field to introduce the two frameworks and then explain how to compute both well-established and newer metrics on resting-state functional magnetic resonance imaging. We use an open-source language (Python) and provide an accompanying publicly available Jupyter Notebook that uses the 1000 Functional Connectomes Project dataset. Moreover, we would like to highlight one part of our notebook dedicated to the realistic visualisation of high order interactions in brain networks. This pipeline provides three-dimensional (3-D) plots of pairwise and higher-order interactions projected in a brain atlas, a new feature tailor-made for network neuroscience.
Various imaging modalities are available to reconstruct the brain network  (Hart et al. 2016; Bullmore and Sporns 2009). The focus of this hands-on paper will be resting-state functional MRI (rsfMRI). As the name suggests, rsfMRI indirectly measures brain activity while a subject is at rest (i. e. , does not perform any task). This type of data provides information about spontaneous brain functional connectivity  (Raichle 2011). Functional connectivity is often operationalised by a statistical dependency (usually a Pearson correlation coefficient) between signals measured from anatomically separated brain areas  (Rosen and Savoy 2012; Smith et al. 2013 ). An in-depth explanation of rsfMRI and functional connectivity is out of the scope of our manuscript. However, considering the focus on this type of data here, we recommend readers who are not familiar with this imaging method to read  Lee et al.
We offer a theoretical and experimental background of these metrics and include code blocks in each section to explain how to compute the different metrics. We also list several additional resources (Tables  1  and 2 ) of personal preference (and by no means complete), including a Jupyter Notebook that we created to accompany this hands-on tutorial publicly available on GitHub and Zenodo (Centeno and Santos 2021) (see Table  1 , under the Jupyter Notebooks section-Notebook for network and topological analysis in neuroscience). Our work differs from previous literature  (Hallquist and Hillary 2018; Otter et al. 2017 ) since we describe the concepts central to graph theory and TDA and provide an easy-to-grasp step-by-step tutorial on how to compute these metrics using an easily accessible, open-source computer language.
General requirements The following Python 3 packages are necessary to perform the computations presented below. The accompanying Jupyter Notebook can be found on GitHub (Table  1 ) or Zenodo  (Centeno and Santos 2021). The imaging technique used to measure brain activity by detecting brain blood flow changes, i. e. , blood-oxygen-leveldependent (BOLD) signal k-clique A subset of k vertices in an undirected graph in which all vertices are connected to each other k-simplex Geometrically, it is the generalisation of the region delimited by a tetrahedron to an arbitrary dimension k, which can be done in many ways  (Zomorodian 2005). In this work, a k-simplex is a complete graph of k + 1 vertices. For example, 0-simplex is a point (or vertex), 1-simplex is a line segment (or edge), 2-simplex is a triangle, and so on Simplicial complex A simplicial complex K is a finite set of k-simplexes (e.
When the edges' weights (e. g. , correlation values in rsfMRI connectivity) are maintained, the network will be weighted (Fig. 1d  and f ). Another approach is to use an arbitrary threshold or density, e. g. , only keep and binarise the 20% strongest connections (Fig. 1a  and b ). There is currently no gold standard for the weighting issue in rsfMRI matrices  (Fornito et al. 2016; Jalili 2016 ) and may also be dependent on the dataset or proposed analysis  (van den Heuvel et al. 2017). Brain network data are often analysed using a specific thresholding procedure (or criteria). These thresholded brain networks often display ubiquitous signatures of the brain as a complex system, such as skewed degree distributions, clustering, Giant components, small wordness, and short average path lengths, to name a few  (Eguíluz et al.
2005). However, some of these properties, considered signatures of complex networks, are observed, even when one threshold normally distributed data  (Cantwell et al. (2020). Yet, some brain network properties are not robust towards changes in the threshold  (Garrison et al. 2015). Those results raised the awareness for using methods of network analysis that are independent of thresholding, such as minimum spanning trees (van  Dellen et al. 2018; Stam et al. 2014)  or topological data analysis  (Phinyomark et al. 2017 ), as we will discuss below. Please see Chapter 11 in  Fornito et al. (2016)  and van Wijk et al. (  2010 );  Simpson et al. (2013)  for a more in-depth discussion on the issue of matrix thresholding and statistical connectomics. Another relevant discussion about rsfMRI matrices is the interpretation of negative weights or anticorrelations.
2011; Zhan et al. 2017; Fornito et al. 2016; Hallquist and Hillary 2018). In this tutorial, we will use an undirected, absolutised (positively) weighted matrix. In our Jupyter notebook tutorial on GitHub (Centeno and Santos 2021), we provide an example matrix which is an average of all connectivity matrices available in our repository. To follow the steps below, we assume that rsfMRI was already pre-processed and converted to a matrix according to some atlas. Steps and explanations on data pre-processing and atlas choices are beyond the scope of this paper; please see  Strother (2006)  or the NI-edu course materials (Table  1 ) for further information. Details on our Jupyter Notebook's dataset pre-processing can be found in  Brown et al. (2012) ;  Biswal et al. (2010).
Code example The minimum spanning tree The minimum spanning tree is the backbone of a network, i. e. , the minimum set of edges necessary to ensure that paths exist between all vertices without forming cycles  (Stam et al. 2014; van Dellen et al. 2018). A few main algorithms are used to build the spanning tree, with Kruskal's algorithm being implemented in NetworkX  (Kruskal 1956 ). Briefly, this algorithm ranks the distances between vertices, adds the ones with the smallest distance first, and at each added edge, it checks if cycles are formed or not. The algorithm will not keep an edge that results in the formation of a cycle.
Topological data analysis In this section, we will use TDA on our rsfMRI adjacency matrices. TDA can identify different network characteristics by addressing the high-order structure of a network beyond pairwise connections as used in graph theory (Carlsson 2020;  Battiston et al. 2020; Kartun-Giles and Bianconi 2019). TDA generally uses topology and geometry methods to study the shape of the data  (Carlsson 2009). A core feature of TDA is the ability to provide robust results compared with alternative methods, even if the data are noisy (Blevins and Fig. 6  Euler characteristic in convex polyhedra. Note that there are no cavities in their shapes for convex polyhedra, and the Euler characteristic is always equal to two Fig. 7  The Euler characteristic in polyhedra with cavities. The Euler characteristic of a cube with a cavity is equal to zero, just as the torus.
2019 ). To create the 3-D plots, we used mesh algorithms available in Plotly (Inc. 2015), together with a mesh surface of the entire brain available in  Fan et al. (2016) ;  Bakker et al. (2015). In Fig. 5 , we display an example of 3-D visualisation of 3-cliques in the 1000 Functional Connectomes data. When we increase the filtration density d, we obtain more connections, and more 3-cliques arise. In Fig. 5 , only 3-cliques are shown; however, the same can be done for higher-dimensional cliques like a tetrahedron, et cetera. In Supplementary Material 1, we offer filtration in a functional brain network up to 4-cliques. In the Jupyter Notebook, we can also visualise the clique complex at arbitrary sizes, up to computational limits. The computation is not shown here as code blocks due to its size and complexity (see the Jupyter Notebook).
A similar approach was used in an Alzheimer's disease dataset by  Kuang et al. (2019). More considerations on how TDA can be used in brain imaging big data and resting-state functional connectivity analyses can be found in Phinyomark et al. (  2017  Notably, limitations and other relevant points should be kept in mind when working with these metrics. Firstly, it is common in network neuroscience to use null models for comparison with real data. The idea is to show that the results are different from what one would obtain by chance (or randomly). The generation and comparison with null models must be performed differently for graph theory and TDA, and it is crucial to define what propriety should be kept constant (e. g. , the density of the network or degree distribution). For instance, in  Viger and Latapy (2005) , if one wants to generate null models with a prescribed degree sequence.
( 4 ) Γ is the Grüneisen parameter (unitless); µ a and µ s are, respectively, the absorption and scattering coefficients (cm -1 ); g is the anisotropy factor (unitless); Φ is the fluence (W•cm -2 ). For simplicity, Γ is supposed to be known and equal to 1 in this study. If needed, it has been shown that spectroscopic measurements allow one to account for it  [17, 18]. With this simplification, the measurement p 0 meas = ΓH meas is referred to as H meas from this point. The anisotropy coefficient g is supposed to be equal to 0. 9 in the IVD and to 1 in water. Monte Carlo simulations are accurate at solving the radiative transfer equation, provided sufficient statistics are considered, and this method was chosen here to compute the fluence Φ, with the versatile MCmatlab software  [19].
Defining the Morphology and Optical Properties The morphology of the IVD was obtained from proton density-weighted MRI imaging of the IVD of a 4 month old pig taken from  [11, 12]  (see Figure  2 ). The imaged disc was approximately 0. 8 cm × 2. 5 cm × 3. 5 cm. The 3D morphology was integrated in a 512 × 512 × 512 voxel grid in MATLAB. The reconstructions were performed on a different grid of size 256 × 256 × 256 voxels to avoid the inverse crime. The surrounding medium was set to be water to fulfil the impedance matching condition needed for PA imaging. The spatial resolution in each direction was set to 0. 02 cm. We differentiated the NP from the AF by modelling the NP as a simple cylinder at the centre of the disc, as presented in Figure  2. The laser illumination configuration used is presented in the same figure.
( 9 ) The simplified expression of the gradient using this decomposition is: d dµ a = -Φ(H meas -H) + ∞ ∑ l=0 l ∑ m=-l i lm (r)i * lm (r), (10) where i * lm corresponds to the SH coefficients of the adjoint radiance L *. The decomposition in SH implies the use of an infinite sum, but because of the finite computation time and memory, we stopped the decomposition at the degree of SH l = 3. The radiances L and L * were calculated by modifying MCmatlab and using the SH decomposition. The photons' directional information s (which was not stored in the original code) was taken into account by using the SH: the radiance L(r, s) is computed by storing the weight of photons going through the voxel at position r in the corresponding SH Y lm (s). The gradient descent scheme step size was chosen to be that of the Barzilai-Borwein step  [20].