dataesr/scientific-paragraphs-categorization huggingface dataset:
This new matrix was transformed into grayscale with contrast and brightness increased by 20% and 5% respectively. To determine the spatial distribution of collagen fibres, a two-dimensional Fourier transformation was performed on the image. This data was transformed from cartesian to polar coordinates by grouping predominant frequency-component orientations of the fibres in 1-degree increments from 0 to 180 degrees. The total intensity at each angle was calculated by summing the grayscale intensity values of each pixel contained within the group. Large intensity values represented the summation of multiple sinusoidal waves with large amplitude signifying major fibre alignment along the respective orientation. From this data, a comparative analysis can be conducted whereby the dot product was calculated using each permutation of resulting vectors (parallel vectors would provide a dot product of 1, with orthogonal vectors presenting a dot product value of -1).
Endothelial Tube Formation Assay Matrigel (50 μL/well) (BD Matrigel Basement Membrane Matrix, BD Biosciences) was added to the wells in a 96-well plate and allowed to polymerize at 37 °C for 30 min. HMEC-1 cells, an immortalised human microvascular endothelial cell line (28) (15,000 cells) previously transfected with siRNA-control or siRNA MC1R were added to the top of the Matrigel and treated with MC1R agonist BMS-470539. After incubation for 8 hr, tube formation was assessed by acquiring four randomly microscopic fields (magnification ×10) by using Nikon Eclipse Ti inverted microscope. Total tube length and branching points were assessed by Angiogenesis Analyzer for ImageJ analysis software (29). For confocal imaging, cells were fixed (4% PFA, 15 m), blocked ( ) and stained (phalloidin, ; DAPI, ).
Acknowledgments: We acknowledge the support of the  QMRI SURF  facilities for histological services and  BVS (Bioresearch and Veterinary Services) , especially  Dr Nacho Vinuela-Fernandez  for assistance with animal studies. We thank  Professor Ian Jackson  for providing the MC1Re/e mouse line and  Dr Andrew Tambyraja  and  Professor Keith Harding  for helpful insights on chronic wounds from a clinical perspective and  Professor Paul Martin  for general discussions. We thank  Dr Alison Munro  of the  Institute of Genetics and Cancer (IGC ) for running nanostring assays and  Wolfson Bioimaging Facility  for assistance with Incucyte experiments. Thanks also to  Prof Stuart Forbes ,  Prof David Dockrell  and  Prof Julia Dorin  for mentorship.
Introduction Throughout the history of neuroscience, the analysis of single neuron morphologies has played a major role in the classification of neuron types and the study of their function and development. The NeuroMorpho. Org database  [1, 2] , which collects and indexes neuronal tracing data, currently hosts more than one hundred thousand arbors of diverse neurons from various animal species. Technological advances in large-scale electron  [3] [4] [5] [6]  and fluorescence microscopy  [7] [8] [9] [10] [11]  facilitate the exploration of increasingly large volumes of brain tissue with ever improving resolution and contrast. These tridimensional (3D) imaging approaches are giving rise to a variety of model-centered trace sharing efforts such as the MouseLight (http:// mouselight. janelia.
This scale is quite small for a very straight trace, and larger when the trace displays a complex and convoluted pattern over longer distances. We then propose examples and applications on several published neuronal trace datasets that demonstrate the interest of this metric to describe arbors, compare the arbors of individual neurons and extract morphological features reflecting local changes in neurite behavior. Finally we use it for a more thorough analysis of the local morphology of single neurites across the region of the whole brain of a zebrafish larvae. Implementation of the nAdder algorithms along with an array of geometry routines and functions are made available in the recently published GeNePy3D Python library  [36] , available at https://genepy3d. gitlab. io. Code to reproduce all figures in this study, exemplifying its use, is available at https://gitlab.
The trace will then locally transform to 2D or 1D for scales higher than that local 3D scale. An example of local 3D scale calculation is shown in Fig 1B. This computation is done at the level of curves; to apply it to whole neuronal arbors, we decompose these arbors into curves by considering, for each 'leaf' (terminals), the curves that link it to the root (i. e. the cell body), averaging values when needed  (Fig F in S1 Text). The result is an algorithm that computes a local 3D scale metric for full neuronal arbors, which we term nAdder (see Methods for more details on the algorithm). and Having defined a new metric and evaluated it on simulated traces, we subsequently used our algorithm to reanalyze published datasets in order to explore its capacity to extract biologically meaningful anatomical insights.
Application of nAdder to characterize neuronal arbors To test our approach, we first examined the local 3D scales of different types of neurons presenting dissimilar arbor shapes, using traces from the NeuroMorpho. Org database (Fig  2A ). We studied a mouse striatal D2-type medium spiny neuron reconstructed by  [39]   The local 3D scale computed with nAdder showed a range of values coherent with local neurite behavior, like a lower local 3D scale in straight vs. curved neurites (compare for instance region (i) and (ii) of the spiny neuron in Fig  2A1 , with respective values of �40 μm and �100 μm), or a small local 3D scales in different axon portions (�35 μm in region (iii) of the retinal ganglion neuron axon in Fig 2A2, as it runs directly towards the optic nerve head to leave the retina, compared to �160 μm in the proximal region (iv)).
To evaluate the relevance and usefulness of the local 3D scale measure to answer more biologically meaningful questions, we then applied nAdder to compare neuronal arbors at different stages of their development and in normal vs. experimentally altered contexts. We selected data from  [26]  hosted in the NeuroMorpho. Org database which describe the expansion of the dendritic arbors of the Xenopus laevis tectal neuron during development and the effect of altering the expression of Down syndrome cell adhesion molecule (DSCAM). In this study, the authors showed that downregulation of DSCAM in tectal neuron dendritic arbors increases the total dendritic length and number branches, while overexpression of DSCAM lowers them. We reanalyzed neuronal traces generated from the dendritic arbors in this study by computing their local 3D scale using nAdder.
Local 3D scale of individual neurites across the whole larval zebrafish brain We next sought to test nAdder over a large-scale 3D dataset encompassing entire long-range axonal projections. A database including 1939 individual neurons traced across larval zebrafish brains and co-registered within a shared framework has been published by  [12]. Here, we reanalyzed this dataset by computing the local 3D scales of all available neuronal traces, focusing on projections linking distinct brain regions (i. e. that terminated in a region distinct from that of the cell body), interpreted as axons. We then explored the resulting whole-brain map of the geometric complexity of projection neurons. Local 3D scale variations across brain regions. Processing of the 1939 traces of the larval zebrafish atlas with nAdder resulted in a dataset where the local 3D scale of each inter-region projection (i.
This observation is consistent with the idea that the proximal axonal path and terminal arbor differ in their complexity, as related to their developmental assembly and function. When comparing local 3D scale with number of branching points and axonal length across brain regions, we found potentially significant correlations for axons having soma in the region (. This suggests that highly branched and long axons could exhibit more complex shapes than short and no-branched axons. Another class of axons we chose to focus on are commissural axons, that cross the midline. They play a major role by interconnecting the two hemispheres and have been well studied, in particular for the specific way by which they are guided across the midline  [42]. Examining axonal arbors intersecting the midline in the whole larval fish dataset, we found that a majority (71%) crossed only once, making a one-way link between hemispheres, while a significant proportion crossed multiple times, with 10% traversing the midline more than 5 and up to 24 times (Fig 3F.
This is consistent with the existence of two populations of commissural axons in the vertebrate brain, the hindbrain being home to neurons following complex trajectories across the midline with many short and convoluted branches, and forebrain commissural neurons forming longer and straighter axons crossing fewer times and often only once. Given the lack of clear link between the length and local 3D scale of crossing branches (Fig M panel C of S1 Text) the full picture is most likely more complex and would need more complete study including functional data to be clarified. and Together, these results show that the local 3D scale computed with nAdder is informative at the whole brain level, adding a new level of description for analyzing connectomic datasets.
That method gives partially overlapping curves; thus, we compute the average of the values when needed; we verified that the standard deviations were small. Next, the local 3D scale is computed for each extracted sub-branch within a scale interval of interest. The scale is defined as the radius of curvature and can be selected based on the size of the branches or that of the region studied. For example, in the case of Xeonopus Laevis tadpole neurons (Fig 2B ), we selected scales from 1 to 60 μm which was sufficient to study neuronal branches of about 180 μm in length (i. e. a 60 μm radius of curvature corresponds to a semicircle with length equal to 60π � 180 μm). In the case of the zebrafish brain dataset (Fig  3 ), we selected scales from 1 to 100 μm based on the length of the largest region, which was about 300 μm.
Toolset for neuronal traces manipulation We provide an open source Python toolset for seamless handling of 3D neuronal traces data. It supports reading from standard formats (swc, csv, etc), visualizing, resampling, denoising, extracting sub-branches, calculating basic features (branches, lengths, orientations, curvatures, torsions, Strahler order  [53] , etc), computing the proposed intrinsic dimension decompositions and the local 3D scales. The toolset is part of the open source Python library GeNePy3D  [36]  available at https://genepy3d. gitlab. io/ which gives full access to manipulation and interaction of various kinds of geometrical 3D objects (trees, curves, point cloud, surfaces).
Importantly, an implementation of the proposed algorithms, along with all codes to reproduce the figures, is openly available, making it a potential immediate addition to computational neuroanatomy studies. Specifically, nAdder is part of GeNePy3D, a larger quantitative geometry Python package providing access to a range of methods for geometrical data management and analysis. More generally, it demonstrates the interest of geometrical mathematical theories such as spatial statistics, computational geometry or scale-space for providing some of the theoretical concepts and computational algorithms needed to transform advanced microscopy images into neurobiological understanding. from 1 to 100 μm and the scale with the largest accuracy (optimal scale) is chosen. (B) Comparison of estimated intrinsic dimensions at four different noise levels.
Funding: EB received funding from  Agence Nationale de la Recherche  (https://anr. fr/) under contract  ANR-11-EQPX-0029 Morphoscope2  and  ANR-10-INBS-04   France BioImaging  JL received funding from  Fondation pour la Recherche  Medicale (https://www. frm. org/) ( DBI20141231328 ) and  Agence Nationale de la Recherche  (https://anr. fr/) under contracts  LabEx LIFESENSES  ( ANR-10-LABX-65 ) and  IHU FOReSIGHT  ( ANR-18-IAHU-01 ) EB and JL received funding from  European Research Council  ( Horizon 2020 programme , grant No  951330 HOPE ) The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
This under-determined system has one free variable. Choosing Q 1 as the free variable, the equations reduce to Q 2 = 3 /4 -Q 1 Q 3 = 1 /3 -Q 1 Q 4 = -1 /12 + Q 1. (2) A symbolic solution can be obtained by using Wolfram Mathematica's Reduce[] function  [5]  as shown in Figure  1. In this code snippet, the three equations can be recognized as well as the positivity condition. The solution is 1 /12 ≤ Q 1 ≤ 1 /3. ( 3 ) With this solution the probability table can be filled in as in Table  4.
(47) This is a non-linear problem in three unknowns. Solving the Lagrange parameters usually requires an advanced numerical approximation technique. The Legendre transform provides such a method, which is described in detail by  Blower ([4] , Ch. 24), and demonstrated in the code example in Figure  4. In some cases, the λ j can be obtained exactly, as we will see below. Our four models are distinguished only by their constraint function average, F 3 = Q 1 , in (39). The details are shown in Table  13. The constraint function vectors are shown in the second column. The three Lagrange parameters are shown in the third column. From this column one can learn that all three Lagrange parameters λ j vary, even when only the value of F 3 is varied. Substituting these (λ 1 , λ 2 , λ 3 ) in (  46 ), the probability distributions Q i of the last column are obtained.
A small set of images generated by combining information of a different nature will be used in the localization instead of the global map of the environment. In the example of Cobzas  [24] , a panoramic image memory is created by combining the images acquired by the camera with depth information extracted from a laser scanner. In this image database, only the information essential to the navigation process will be retained  [25]. This allows to obtain homogeneous results with the same properties (accuracy, convergence, robustness, etc. ) as the original global map when performing localization. Several works have confirmed the interest and efficiency of this imagebased memory method. That is why we have chosen to adopt this strategy to summarize our initial mesh. However, in the literature, several techniques can be used to build this image-based memory.
They have proposed curvature as a main criterion for calculating saliency and selecting optimal viewpoints. In  [39] , a method for mapping between different mesh areas has been proposed. Each mesh part is geometrically represented using a descriptor based on its curvature and the variation of this curvature in relation to its environment. Several works have been done to find the optimal viewpoint in a scene. Among these works, we mention the work of  [40]. In this work, the authors proposed a method for calculating saliency on a 3D surface by detecting protruding regions. They compare the different patches of a 3D surface with a database built by several salient patches classified according to their belonging to the same object. In  [41]  a method of predicting the saliency in a mesh has been proposed using ''Schelling Points'' on the 3D surface.
A database of these points is built from data collected as part of a coordination set where users choose the points they think they will be selected by other users. An ther work  [42]  proposes to use region distinction to extract salient areas based on the fact that human beings are attracted to differences. Unlike most previous approaches, which only consider local distinction, this work takes into account global distinction. In addition, the author considers the fact that visual shapes may have one or more centers of gravity on which the shape is organized, this may influence the search criterion for saliency. Generally speaking, the extremities are often considered as protruding by humans, which is why they have chosen to calculate the projection on extreme vertices of a mesh. The salient vertices are those whose geometry is unique.
In an iterative way, the edges of this graph are discretized in a set of points. We keep only the points that maximize the two criteria Entropy and Visibility. The optimization algorithm consists in selecting a start point and an end point on the initial graph T. Starting from the start point, we select points of view with entropy greater than a threshold α and covering some uncovered vertices of the visibility polygon Σ. The value of this threshold α is chosen in an empirical way. To do that, we have built our ground truth dataset. For each point in the this dataset, we have manually attributed a label {0: irrelevant for localization, 1: relevant for localization} based to their geometric shapes. Then, we have computed Recall and Precision  [57]  with different values of α. We have found that the choice of the α has an impact on the relevance of the 3D points in the summary map and consequently on the recall and the precision.
We have chosen follows (Eq. (  7 )): CR = (1 - S f S i ) * 100 (7) S i is the size in bytes of the initial 3D map. S f is the size of the spherical images in the final navigability graph. This graph is the result of the summary process of the initial map. For the first database, we have obtained 10 RGB-D-L spheres summarizing the 3D mesh. We have obtained 52 spherical images summarizing the second database. The compression ratio of this map is 98. 7%. The Fig. 5  shows an example of an RGB-D-L sphere. We have applied our summarizing method on several databases and we have achieved significant compression ratios, consistently above 89%. However, these compression ratios are strongly related to the resolution of the chosen RGB-D-L spheres. Generally a resolution of 2000 × 1000 pixels is sufficient to have a compromise between spherical image quality and compression ratio.
Other classes have been removed such as the sky class. As a result, we have eliminated about 20%  of pixels in each spherical image. The Table  2  groups all the results obtained with each database. To evaluate the registration results, we have calculated the score of successful localization (LS) and the mean localization error MLE. The localization is considered successful if the localization error is less than 1 m. By applying this threshold, we have calculated the score of successful localization.
Ensure: Mark all vertices in Σ as uncovered Mark all vertices in Σ visible from C s and C e as covered X ← {C s , C e } q ← C s γ k ← the edge in γ whose starting point is q while ∃x an uncovered point in Σ do Π(γ k ) =Discretization of the edge γ k p ← first point in Π(γ k ) to the right of q such that p cover some uncovered x ∈ Σ and E(p) ≥ α X ← X ∪ {q} Mark all points ∈ x as covered q ← p if q ∈ C then γ k ← the edge in γ whose starting point is q end if end while return X mobile mapping vehicle  [63]. The 3D mesh contains three types of information: radiometric (RGB from images and reflectance from LiDAR), geometric (from LiDAR), and semantic (from machine learning) The first input database (Fig. 4 ) contains more than 5 million triangles (faces). The second database is larger than the first one and contains more than 30 million of triangles.
XGBoost has the benefit or advantage that it can capture interactions in the model (e. g. , interactions between covariates, between PGS, as well as between PGS and covariates). We apply our multi-PGS framework to the Lundbeck Foundation Initiative for Integrative Psychiatric Research (iPSYCH)  22, 23  , one of the largest datasets on the genetics of major psychiatric disorders. These disorders are genetically correlated with many other psychiatric and neurological disorders as well as other behavioral phenotypes  24, 25  , which are precisely the circumstances under which the proposed multi-PGS might boost the polygenic prediction accuracy. We benchmark the multi-PGS against each phenotype's respective single PGS prediction and compare it with an existing re-weighting method that does not train on individual-level data, wMT-SBLUP  8.
We demonstrated in practice how these multi-PGS could be generated for various psychiatric sub-diagnoses and case-case prediction, including classification of ADHD and ASD with relatively high prediction accuracy. This study and the multi-PGS approach has several limitations. First, as we performed a 5fold cross-validation in the iPSYCH (individual-level) data when training and testing the multi-PGS, it is possible that some of the prediction accuracy gain is due to overfitting. However, the multi-PGS also resulted in multiple null predictions despite having large training sample sizes (APGAR score and gestational age) suggesting that overfitting is small. To further avoid overfitting we restricted the analyses to a set of unrelated individuals of European ancestry to control for population structure.
PGS library construction A detailed description of the PGS library construction and file filtering process is provided as Supplementary Text and all code used will be available. A number of resources were used to obtain an initial list of GWAS summary statistics for generating the PGS library. The majority of the GWAS summary statistics were downloaded from publicly available databases (GWAS Catalog  39  , GWAS Atlas 40 , the Psychiatric Genomics Consortium Website (https://www. med. unc. edu/pgc). For the specific PGC GWAS summary statistics where iPSYCH was used in the discovery dataset, we used in-house GWAS results where these samples were excluded from the calculation. The GWAS files were specifically selected to be based on European ancestry individuals, to not be overly redundant (only the latest GWAS for each same phenotype) and to not contain iPSYCH samples.
From an original list of 6,206 files (ST1), this filtering resulted in 1,377 files to download. We developed a pipeline for downloading, parsing, reformatting and doing a quality control filter on the list of files. We created a GWAS summary statistic column-name library (SF1) to ease file parsing, and after re-formatting and removing corrupted files, this step resulted in 1,005 files. We restricted the number of SNPs to the overlap of the iPSYCH imputed variants with the HapMap3 variants and the LD reference provided by LDpred2, resulting in a maximum of 1,053,299 SNPs per GWAS summary statistics file. Filtering SNPs with a large discrepancy in standard deviation between the genotyped/imputed data and the GWAS summary statistics can increase the robustness and prediction accuracy of PGS  41.
For each file, we created a QC plot for visual inspection of the QC SNP filtering (Example in SF2). The set of 952 GWAS summary statistics that passed QC and kept over 200,000 SNPs were used to derive PGS with LDpred2-auto  16. Polygenic scores were derived using LDpred2-auto, a method within the LDpred2 framework  16  that does not require a validation dataset to fit the hyperparameters (SNP-h2; SNP-based heritability estimate and p; proportion of causal SNPs), but these are fitted as part of the Gibbs sampler instead. We used the provided European-ancestry independent LD blocks as reference panel  41. For each GWAS summary statistics file, LDpred2-auto was run with 30 Gibbs sampler chains, 800 burn-in iterations and 400 iterations. The SNP-h2 initial value was set to the LD score regression estimate 42 from the GWAS summary statistics after.