dataesr/scientific-paragraphs-categorization huggingface dataset:
Parameter tuning HESA requires 5 parameters: the population size p, the number of greedy randomized solutions gr, the shake strength μ, the tabu tenure t t , and the search depth of tabu search sd. To tune these parameters, we used the "irace" package ( López-Ibáñez, Dubois-Lacoste, Cáceres,  Birattari, & Stützle, 2016 ) , which implements the Iterated F-Race method  ( Birattari, Yuan, Balaprakash, & Stützle, 2010 )  to determine automatically the most suitable parameter settings from a set of possible parameter configurations. For this tun-ing experiment, a set of 15 randomly selected instances from Set I and Set II were used, i. e. , 1-1, 1-3, 3-1, 3-2, 10-1, 11-3, 13-3, 14-2, 14-3, 16-3, 18-2, 23-1, 24-1, 24-2, and 31-2. The tuning budget (the maximum number of runs of the algorithm) was set to 10 0 0 runs, where each run stops after performing a fixed number of 100 generations.
In terms of solution quality, HESA found 44 improved best-known solutions (new lower bounds) (for 9 small instances of Set I, 34 large instances of Set II and the real-life instance). HESA is also computationally effective by reaching equal or better solutions for most tested instances with a shorter time compared with the best reference algorithms. To shed lights on the impacts of the mixed feasible and infeasible search strategy and the knapsack-based crossover operator, we presented additional experiments to investigate these two key components. In addition to the reported computational results that can be useful for future studies on GQMKP, the code of our HESA algorithm that we make publicly available can be used by researchers and practitioners to solve various problems that can be formulated as GQMKP.
Acknowledgments. The authors were partially supported by  ANR   Finite4SoS ANR-15-CE23-0007. A. Koenig is supported by a public grant overseen by the  French National Research Agency (ANR)  as part of the  "Investissements d'Avenir"'s program  of the  Idex PSL  reference  ANR-10-IDEX-0001-02 PSL. H. -M. Nguyen  thanks  Fondation des Sciences Mathématiques de Paris (FSMP)  for the Chaire d'excellence which allows him to visit Laboratoire Jacques Louis Lions and  Mines ParisTech. This work has been done during this visit.
In addition, most population-based studies have investigated brain structural covariance within a relatively limited scope, such as within relatively small samples, over a relatively narrow age window (e. g. , adolescence  2  ), within a single disease (e. g. , Parkinson's disease  3  ), or within datasets lacking sufficient diversity in cohort characteristics or MRI scanner protocols. These have been imposed, in part, by limitations in both available cohort size and in the algorithmic implementation of structural covariance analysis, which has been computationally restricted to modest sample sizes when investigated at full image resolution. Lastly, prior studies have examined brain structural covariance at a single fixed ROI resolution/scale/granularity. While the optimal scale is unknown and may differ by the question of interest, the highly complex organization of the human brain may demonstrate structural covariance patterns that span multiple scales.
Results We summarize this work in three units (I to III) outlined in Fig. 1. In Unit I (Fig. 1A ), we present the stochastic orthogonally projective non-negative matrix factorization (sopNMF) algorithm (Method 1), optimized for large-scale multivariate structural covariance analysis. The sopNMF algorithm decomposes large-scale imaging data through online learning to overcome the memory limitations of opNMF. A subgroup of participants with multiple disease diagnoses and healthy controls (ages 5-97, training population, N=4000, Method 2) were sampled from the discovery set (N=32,440, Method 2); their MRI underwent a standard imaging processing pipeline (Method 3A). The processed images were then fit to sopNMF to derive the MuSIC atlas. We incorporate participants with various disease conditions because previous studies have demonstrated that inter-regional correlated patterns (i.
e. , depicting a network) show variations in both healthy and diseased populations, albeit to a differing degree. 7  Multi-scale PSCs of MuSIC (volumetric measures in this study), which serve as the flexible set of ROIs for this atlas, were then extracted across the entire population and statistically harmonized 8 (Method 3B). Unit II (Fig. 1B ) investigates the harmonized data for 2003 MuSIC PSCs (13 PSCs have vanished in this process for C=1024; see Method 1) in a broad range of brain structural covariance analyses. Specifically, we performed: i) PSC-wide association studies (PSC-WAS, Method 4) with respect to various clinical phenotypes, including cognitive measures (N=10) and disease diagnoses or risk conditions (N=39); ii) genome-wide association studies (GWAS, Method 5) that sought to discover associations of PSCs at single nucleotide polymorphism (SNP), gene, or gene set-level; and iii) pattern analysis via machine learning (Method 6) to derive imaging signatures for the quantification of individualized disease vulnerability.
These novel associations might indicate subtle neurobiological processes that are captured thanks to the biologically relevant structural covariance expressed by MuSIC. Notably, MuSIC was able to identify many novel associations compared with prior large-scale GWAS using conventional atlases (Supplementary eTable 3). The Automated Anatomical Labeling (AAL) atlas  21  with the current data set and by previous GWAS  22, 23  identified a smaller number of SNPs, largely matched or in linkage disequilibrium with those identified by the MuSIC PSCs (Supplementary eTable 3, eFile 6, 7, and 8). Constraining these associations to the lead SNPs (Method 5C and Supplementary eMethod 5), we found that 915 SNPs had 3791 SNP-PSC pairwise significant associations with 924 PSCs after Bonferroni correction (Supplementary eFile 4).
BRIDGEPORT: bridging knowledge across brain imaging, genomics, and clinical phenotypes We integrated the PSC-WAS and GWAS results using the MuSIC atlas into an online resource. The web portal allows researchers to interactively browse the MuSIC atlas in 3D, query our experimental results via variants, MuSIC PSCs, or clinical phenotypes, and download the GWAS summary statistics for further analyses. In addition, we allow users to search via conventional brain anatomical terms (e. g. , the right thalamus proper) by automatically annotating traditional anatomic atlas ROIs, specifically from the MUSE atlas  37  (Supplementary eTable 6), to MuSIC PSCs based on their degree of overlaps (Supplementary eFigure 7). Open-source software dedicated to image processing,  37  genetic quality check protocols, MuSIC generation with sopNMF, and machine learning  34  is publicly available in BRIDGEPORT (see Code Availability for details).
Discussion This study depicted the phenotypic landscape and genetic architecture of human brain structural covariance at multiple scales from an unprecedented large-scale population: 50,699 people with numerous brain diseases and cognitively healthy individuals across the entire lifespan. We developed a novel stochastic multivariate implementation of structural covariance that enabled its application at the full resolution of the MRI scan. The BRIDGEPORT online portal disseminates our experiment results, the MuSIC atlas, and open-source software, serving as a knowledge hub for the research community. The mechanisms underlying structural covariance are not yet fully understood. A commonly accepted belief is that the mechanisms involve an interplay between common underlying genetic expression, shared susceptibility to risk factors, connectivity, and network effects, resulting in coordinated brain morphological changes.
Glasser and colleagues 41 adopted a semi-automated parcellation procedure to create a multimodal cortex atlas from 210 healthy individuals. Although this method was successful in integrating multimodal information from cortical folding, myelination, and functional connectivity, this semi-automatic approach requires significant resources, some with limited resolution. MuSIC allows flexible, multiple scales for delineating macroscopic brain topology; the inclusion of patient samples exposes the model to sources of variability that may not be visible in healthy controls. Another pioneering endeavor is the Allen Brain Atlas project,  42  whose overarching goals of mapping the human brain to gene expression data via existing conventional atlases, identifying local gene expression patterns across the brain in a few individuals, and deepening our understanding of the human brain's differential genetic architecture, are complementary to ours -characterizing the global genetic architecture of the human brain, emphasizing pathogenic variability and morphological heterogeneity.
Lastly, Schaefer and colleagues  5  proposed a multi-scale atlas using functional MRI data guided by a local abruption and global similarity approach, widely used in functional MRI studies but less suited for structural analyses. Bridging knowledge across the brain imaging, genomics, and machine learning communities is another pivotal contribution of this work. BRIDGEPORT, together with MuSIC, provides a platform to lower the entry barrier for whole-brain genetic-structural analyses, foster interdisciplinary communication, and advocate for research reproducibility. 34, [43] [44] [45] [46]  The current study demonstrates the broad applicability of this large-scale, multi-omics platform across a spectrum of neurodegenerative and neuropsychiatric diseases. With the availability of MuSIC, BRIDGEPORT, large-scale imaging and genetics consortia,  [47] [48] [49]  and "big data" analytics,  50  we anticipate that the current work provides a springboard for future research to uncover the underlying mechanisms of human brain diseases.
Methods Method 1: Structural covariance patterns via stochastic orthogonally projective nonnegative matrix factorization The sopNMF algorithm is a stochastic approximation built and extended based on opNMF  6, 51. We consider a dataset of 𝑛𝑛 MR images and 𝑑𝑑 voxels per image. We represent the data as a matrix X where each column corresponds to a flattened image: 𝑿𝑿 = [𝑥𝑥 1 , 𝑥𝑥 2 , … , 𝑥𝑥 𝑛𝑛 ], 𝑿𝑿 ∈ ℝ ≥0 𝑑𝑑×𝑛𝑛. The sopNMF algorithm factorizes X into two low-rank (𝑟𝑟) matrices 𝑾𝑾 ∈ ℝ ≥0 𝑑𝑑×𝑟𝑟 and 𝑯𝑯 ∈ ℝ ≥0 𝑟𝑟×𝑛𝑛 under the constraints of non-negativity and column-orthonormality. Using the Frobenius norm, the loss of this factorization problem can be formulated as ‖𝑿𝑿 -𝑾𝑾𝑯𝑯‖ 𝐹𝐹 2 subject to 𝑯𝑯 = 𝑾𝑾 𝑻𝑻 𝑿𝑿 , 𝑾𝑾 ≥ 0 and 𝑾𝑾 𝑻𝑻 𝑾𝑾 = 𝑰𝑰 (1) where I stands for the identity matrix. The columns 𝑤𝑤 𝑖𝑖 ∈ ℝ 𝑑𝑑 , ‖𝑤𝑤 𝑖𝑖 ‖ 2 = 1, ∀ 𝑖𝑖 ∈ {1.
𝑟𝑟} of the socalled component matrix 𝑾𝑾 = [𝑤𝑤 1 , 𝑤𝑤 2 , … , 𝑤𝑤 𝑟𝑟 ] are part-based representations promoting sparsity in data in this lower-dimensional subspace. From this perspective, the loading coefficient matrix 𝑯𝑯 represents the importance (weights) of each of the features above for a given image. Instead of optimizing the non-convex problem in a batch learning paradigm (i. e. , reading all images into memory) as opNMF,  6  sopNMF subsamples the number of images at each iteration, thereby significantly reducing its memory demand, by randomly drawing data batches 𝑿𝑿 𝒃𝒃 ∈ ℝ ≥0 𝑑𝑑×𝑏𝑏 of 𝑏𝑏 ≤ 𝑛𝑛 images (b is the batch size); this is done without replacement so that all data goes through the model once (⌈𝑛𝑛/𝑏𝑏⌉). In this case, the updating rule can be rewritten as 𝑾𝑾 𝑡𝑡+1 = 𝑾𝑾 𝑡𝑡 �𝑿𝑿 𝒃𝒃 𝑿𝑿 𝒃𝒃 𝑻𝑻 𝑾𝑾� 𝑡𝑡 (𝑾𝑾𝑾𝑾 𝑇𝑇 𝑿𝑿 𝒃𝒃 𝑿𝑿 𝒃𝒃 𝑻𝑻 𝑾𝑾) 𝑡𝑡 (2) We calculate the loss on the entire dataset at the end of each epoch (i.
Method 5: Genetic analyses Genetic analyses were restricted to the discovery and replication set from UKBB (Method 2). We processed the array genotyping and imputed genetic data (SNPs). The two data sets went through a "best-practice" imaging-genetics quality check (QC) protocol (Method 5A) and were restricted to participants of European ancestry. This resulted in 18,052 participants and 8,430,655 SNPs for the discovery set, and 15,243 participants and 8,470,709 SNPs for the replication set. We reperformed the genetic QC and genetic analyses for the combined populations for BRIDGEPORT, resulting in 33,541 participants and 8,469,833 SNPs. Method 5G details the correction for multiple comparisons throughout our analyses. (A): Genetic data quality check protocol. First, we excluded related individuals (up to 2 nddegree) from the complete UKBB sample (N=488,377) using the KING software for family relationship inference.
69  We then removed duplicated variants from all 22 autosomal chromosomes. We also excluded individuals for whom either imaging or genetic data were not available. Individuals whose genetically-identified sex did not match their self-acknowledged sex were removed. Other excluding criteria were: i) individuals with more than 3% of missing genotypes; ii) variants with minor allele frequency (MAF) of less than 1%; iii) variants with larger than 3% missing genotyping rate; iv) variants that failed the Hardy-Weinberg test at 1x10 -10. To adjust for population stratification,  70  we derived the first 40 genetic principle components (PC) using the FlashPCA software  71. The genetic pipeline was described elsewhere,  72  and documented online: https://www. cbica. upenn. edu/bridgeport/data/pdf/BIGS_genetic_protocol.
(D): Gene analysis for gene-level associations. We performed gene-level association analysis using MAGMA. 76  First, gene annotation was performed to map the SNPs (reference variant location from Phase 3 of 1,000 Genomes for European ancestry) to genes (human genome Build 37) according to their physical positions. The second step was to perform the gene analysis based on the GWAS summary statistics to obtain gene-level p-values between the pairwise of 2003 PSCs and the 18,097 protein-encoding genes containing valid SNPs. (E): Gene set analysis for biological pathway enrichment. Using the gene-level association pvalues, we performed gene set enrichment analysis using MAGMA. Gene sets were obtained from Molecular Signatures Database (MsigDB, v7. 5. 1),  77  including 6366 curated gene sets and 10,402 ontology gene sets.
All other parameters were set by default for MAGMA. (F): Genetic correlation estimates between PSCs and complex clinical traits. LDSC  78  was used to estimate the pairwise genetic correlation (rg) between each PSC and the pre-selected clinical traits. To this end, we used the precomputed linkage disequilibrium scores provided by the LDSC software from the 1000 Genomes of European ancestry. As regards the clinical traits, six were pre-selected: autism spectrum disorder (ASD), attention-deficit/hyperactivity disorder (ADHD), obsessive-compulsive disorder (OCD), major depressive disorder (MDD), bipolar disorder (BPD), and schizophrenia (SCZ) (Supplementary eTable 4). The two-step inclusion criteria ensured the suitability of the GWAS summary statistics: once to ensure the available study population was predominantly of European ancestry and a second time to guarantee the quality of the corresponding GWAS summary statistics.
Code Availability The software and resources used in this study are all publicly available: • sopNMF: https://pypi. org/project/sopnmf/, MuSIC, and sopNMF (developed for this study) • BRIDGEPORT: https://www. cbica. upenn. edu/bridgeport/, (developed for this study) • BIGS: https://www. cbica. upenn. edu/bridgeport/data/pdf/BIGS_genetic_protocol. pdf, genetic processing protocol (developed for this study) • MLNI: https://pypi. org/project/mlni/, machine learning (developed for this study) • MUSE: https://www. med. upenn. edu/sbia/muse. html, image preprocessing • Clinica: http://www. clinica. run/, machine learning and image preprocessing • PLINK: https://www. cog-genomics. org/plink/, GWAS • GCTA: https://yanglab. westlake. edu. cn/software/gcta/#Overview, heritability estimates • LDSC: https://github.
com/bulik/ldsc, genetic correlation estimates • MAGMA: https://ctg. cncr. nl/software/magma, gene analysis • GWASRAPIDD: https://rmagno. eu/gwasrapidd/articles/gwasrapidd. html, GWAS Catalog query • MsigDB: https://www. gsea-msigdb. org/gsea/msigdb/, gene sets database.
Ray tracing and image orders We performed general-relativistic ray tracing in the Kerr spacetime with the model described in Sect. 2. We used the opensource code Gyoto  (Vincent et al. 2011)  to trace null geodesics backwards in time from a distant observer. The code integrates the radiative transfer equation along the null geodesics to evolve the specific intensity I ν across the accretion flow. The output is an image, that is, a map of I ν. As discussed in Appendix D, the Gyoto integration parameters are chosen to ensure the highest possible numerical precision for the ray tracing and radiative transfer computations, while maintaining a reasonable computation time. We will frequently differentiate between image orders. The 0th-order (n = 0) primary image is defined as the image produced by selecting the part of each null geodesic that extends from the observer screen to its first angular turning point (following the ray backwards into the geometry).
Acknowledgements. F. H. V. thanks  F. Roy  from  Paris Observatory-LUTH  for his help in compiling the Gyoto code on the MesoPSL cluster. We thank  Alejandro Cárdenas-Avendaño ,  Hadrien Paugnat , and  George Wong  for helpful comments and discussions. George Wong also provided the data for the green curve in Fig. 1, and  Alejandro Cárdenas-Avendaño  computed the equatorial horizon images in Figs. 3 and4 using AART (Cárdenas-Avendaño et al. , in prep. ). This work was supported in part by  NSF  grant  PHY-1752809  to the  University of Arizona. It was also granted access to the HPC resources of MesoPSL financed by the  Région Île-de-France  and the project  Equip@Meso  (reference  ANR-10-EQPX-29-01 ) of the  Programme d'Investissements d'Avenir  supervised by the  Agence Nationale pour la Recherche.
One benefit of this procedure is to avoid the case where the decay products of the D 0 -meson candidate fill the dead-cone region. A jetfinding algorithm was then used to cluster the particles (tracks and the D 0 -meson candidate) in the event, in order to reconstruct the parton shower by sequentially recombining the shower particles into a single object (the jet). The jet containing the D 0 -meson candidate was then selected. The four-momentum of the jet is a proxy for the four-momentum of the charm quark initiating the parton shower. The jet-finding algorithm used was the anti-k T algorithm  [18]  from the Fastjet package  [19] , which is a standard choice for jet reconstruction due to its high performance in reconstructing the original parton kinematics. More details on the jet finding procedure can be found in the Methods section.
• • Figure 2. Dumbbell graph Among the many other interesting recent results on nonlinear quantum graphs, we mention the flower graphs studied in  [35] , graphs with generals operators and nonlinearities  [33] , periodic graphs  [45] , etc. On the numerical side, however, the literature devoted to nonlinear quantum graphs is very sparse. Finite differences on graphs have been implemented in a library developed in Matlab by R. H. Goodman, available in  [28]  and which has been used in particular in  [27, 36]. The work  [40]  is one of the rare work containing numerical computation of nonlinear ground states on graphs. In our case, we have implemented a finite difference discretization scheme (see Section 4. 2) in the framework of the Grafidi library  [17] , a Python library which we have developed for the numerical simulation on quantum graph and which is presented in the companion paper  [18].
Using the matrix [H], we may also compute the energy. For instance, in the case where g(z) = z, by using the standard 2 inner product on the graph, we obtain  To illustrate our methodology, we give below an example of a star-graph with 3 edges (see Figure  7   Remark 4. 4. We have implemented this space discretization in the framework of the Grafidi library  [17] , a Python library which we have developed for the numerical simulation on quantum graph and which is presented in  [18]. Note that finite differences on graphs have also been implemented in a library developed in Matlab by R. H. Goodman, available in  [28]  and which has been used in particular in  [27, 36]. E(ψ n ) = 1 2 ([H]ψ n , ψ n ) 2 - 1 4 (ψ n ) 2 , (ψ n ) 2 2. (33).
It was also observed by COR2 and C2 (see Fig. 3d ) at approximately the same PA. Besides these features in the CME core, we also tracked the LE of the CME as observed by FSI304 (Fig. 2a ), LASCO C2 (Fig. 3a ), and STEREO/COR1 and COR2. L5, page 2 of 11  The 3D positions were calculated using triangulation, except for the LE, for which we used graduated cylindrical shell (GCS) model reconstruction  (Thernisien et al. 2009 ). The triangulation method requires identification of the same point in the two images (tie-pointing; see  Inhester 2006). The 3D positions of lines of sight passing through a point that is visible in the two images are calculated, and the position of the intersection point in 3D space is determined using the scc_measure. pro program of SolarSoft  (Thompson & Reginald 2008).
A. 5. Observations of the associated flare There are no direct observations of the source region of this farside eruption. Helioseismograms 2 (see  Zhao et al. 2019) , based on the data taken by the Helioseismic and Magnetic Imager  (Schou et al. 2012)  aboard SDO, indicate a substantial active 2 http://jsoc. stanford. edu/data/timed/index. html region present on 15-16 February 2022 about 60 • behind the east limb as seen by SDO. This region corresponds to the location of the old sunspot group complex NOAA AR 2936-2938. NOAA 2936 was a rather big sunspot region that showed considerable flux emergence while rounding the north-west solar limb on 5 February. A post-eruption system of loops is observed by EUVI in the 195 Å passband at the limb starting at ∼23:30 UT on 15 February. The flare is occulted, and hence no X-ray emission is seen from either of the GOES X-ray Sensor (XRS) channels, as shown in This means that the observed emission is most likely thermal soft X-ray emission from the corona (perhaps with a small nonthermal contribution), either from the flare arcade or from the hottest part of the erupting CME.
Acknowledgements. Solar Orbiter is a space mission of international collaboration between  ESA  and  NASA , operated by  ESA. The EUI instrument was built by  CSL ,  IAS ,  MPS , MSSL/UCL, PMOD/WRC, ROB,  LCF/IO  with funding from the  Belgian Federal Science Policy Office (BELPSO) ; the  Centre National d'Etudes Spatiales (CNES) ; the  UK Space Agency (UKSA) ; the  Bundesministerium für Wirtschaft und Energie (BMWi)  through the  Deutsches Zentrum für   L5 , page 7 of  11 A&A 662 ,  L5 (2022 ) Luft-und Raumfahrt (DLR); and the  Swiss Space Office (SSO). We acknowledge the use of PROBA2/SWAP,  SDO/AIA ,  GOES-16/SUVI ,  SOHO/LASCO , and  STEREO EUVI ,  COR1 ,  COR2  data. I. C. J and J. M. acknowledge funding by the  BRAIN-be project SWiM (Solar Wind Modelling  with EUHFORIA for the new heliospheric missions).
The ROB team thanks the  Belgian Federal Science Policy Office (BELSPO)  for the provision of financial support in the framework of the  PRODEX Programme  of the  European Space Agency (ESA)  under contract numbers  4000134474 ,  4000134088 , and 4000136424. M. M. would like to thank  J. Dudik  for fruitful discussions on filament eruption mechanisms and  S. Willems  for updating the missing data on the local servers. E. P. acknowledges support from  NASA  HTMS grant no. 80NSSC20K1274. S. J. acknowledges the support from the  Slovenian Research Agency  No. P1-0188. D. M. L. is grateful to the  Science Technology and Facilities Council  for the award of an  Ernest Rutherford Fellowship  ( ST/R003246/1 ). P. H. was supported by grant No. 22-34841S  of the  Czech Funding Agency  and acknowledges support from the grant No.