dataesr/scientific-paragraphs-categorization huggingface dataset:
To validate this model, we tested it on a large dataset of 392 published sequences and experimentally evaluated quadruplex forming potential of 209 sequences using a combination of biophysical methods to assess quadruplex formation in vitro. We experimentally validated the G4Hunter algorithm on a short complete genome, that of the human mitochondria (16. 6 kb), because of its relatively high GC content and GC skewness as well as the biological relevance of these quadruplexes near instability hotspots. We then applied the algorithm to genomes of a number of species, including humans, allowing us to conclude that the number of sequences capable of forming stable quadruplexes (at least in vitro) in the human genome is significantly higher, by a factor of 2-10, than previously thought.
Several tools are available that predict quadruplex forming propensity. Seminal publications from the Balasubramanian and Neidle groups  (14, 15)  describe the first generation algorithms that looked for patterns matching the stereotype [G n N m G n N o G n N p G n ] expected to be favourable for quadruplex formation. In a second-generation algorithm, the group of Maizels looked for the occurrence of runs of G n (n ≥ 2) in a window of a given size. Many vari-Nucleic Acids  Research, 2016 , Vol. 44, No. 4 1747  ations have been proposed and applied to different types of genomic DNA or RNA sequence databases. These algorithms usually identify local enrichment of runs of G above a threshold size (n) of 2 or 3 (see  (16)  for review). Loop size has been (and is still) subject to discussion: initial studies constrained loop size between 1 and 7 nt, later developments allow longer loops, supported by experimental demonstration of formation of quadruplexes with loops of up to 30 nt  (17).
We call this algorithm G4Hunter. To validate this model, we benchmarked it on a large dataset of 392 sequences from the literature (for example:  (17, 20) ) or from unpublished results. We also validated this algorithm by analysis of the human mitochondria genome (16. 6 kb) chosen because of its relatively high GC content and GC skewness as well as biological relevance of sequences with potential to form G4 near instability hotspots  (21). The results of this search were validated using a combination of biophysical methods to accurately assess quadruplex formation of 209 sequences from the human mitochondrial genome in vitro. We then applied the algorithm to a number of species, including human, allowing us to conclude that the number of bona fide G4-prone sequences in the human genome must be very significantly re-evaluated.
Scripting G4Hunter scores were calculated either using Python or R scripts. Genome-wide searches were performed using an R script that takes advantage of existing packages such as GenomicRanges, rtracklayer, BSgenome, Biostrings and GenomicFeatures from BioConductor  (22). Quadparser searches were also performed using a home-built version of a pattern searching script in R based on a previously published script  (16). Receiver Operating Characteristic (ROC) analysis was performed using the ROCR package for R  (23). Examples of script for R are provided as Supplementary Informations.
Genomes analysed G4FS searches were performed on the human mitochondria genome (EF184640. 1), 18 full genomes, including human, mouse, fruit fly and budding yeast, either from BSgenome packages for R  (24)  or from NCBI databases. All genomes analysed are listed in Supplementary Table S4. Script to generate bed or bigwig files allowing visualization in genome browser like UCSC genome browser or IGV genome browser are provided in the script 'ScriptG4Hunter. r' and detailed in the Supplementary Information.
Application of G4Hunter to a reference dataset We performed a literature search for sequences for which G-quadruplex formation was experimentally confirmed or disproven. We added our unpublished data and obtained a dataset of 392 sequences for which G4 formation propensity was known. The G4Hscore was calculated for all the sequences (Supplementary Table  S1 ). Quadparser analysis was performed in parallel using G-runs length setting of 2 or 3 and loop lengths of 7 or 12. We plotted the distribution of the G4Hscore separately for 'G4' sequences and 'not-G4' sequences (Figure  1A ). G4Hscore was significantly higher (P = 9. 5•10 -43 ) for G4 sequences than not-G4 sequences with average G4Hscore values of 1. 64 ± 0. 46 and 0. 16 ± 0. 66, respectively. The significance of the observed distribution differences was evaluated using the non-parametric Wilcoxon rank-sum/Mann-Whitney U-test (null hypothesis: distributions are not different).
As shown in the histogram of the score distributions for this reference dataset (Figure  1B ), a threshold of 1 (dotted green line) resulted in a good discrimination of G4 versus not-G4 sequences. In order to evaluate the quality of our scoring system, we performed an ROC analysis. The ROC curve is characteristic of a good estimator with pronounced convexity toward true positive results. The area under the ROC curve (AUC) estimates the accuracy with which the algorithm discriminates between G4 and not-G4 sequences to more than 0. 96 (an area of 0. 5 represents a non-discriminating value whereas an AUC of 1 indicates a perfect prediction). To estimate the threshold 'quality', we evaluated the ROC results for five different thresholds between 1 and 2 and the position of the ROC analysis for three settings commonly used for Quadparser.
7 and 15. 4% for G4H1 and G4H1. 2 respectively. We next evaluated the precision by determination of the fraction of sequences that formed a G4 detected experimentally among the sequences found by Quadparser or with a G4Hscore above a threshold (Figure  1D ). For all the settings of Quadparser or for threshold above 1 for G4Hunter, the prediction is very robust with a precision above 95%. We may thus conclude that G4Hunter is as good as Quadparser to predict G4 formation on this dataset, keeping in mind that this library is heavily biased towards G4FS (76% of library sequences) and towards G4FS that fit the 'classical' definition (50% of sequences). The symbols represent positions of the corresponding ROC values after applying Quadparser algorithm on the reference dataset with the following settings: runs of 2Gs and loop lengths between 1 and 7 (QP27, green dot), runs of 3Gs and loop lengths between 1 and 7 (QP37, blue triangle) and runs of 3Gs and loop lengths between 1 and 12 (QP312, red diamond).
Application of G4Hunter to the human mitochondria genome To evaluate G4Hunter on a less biased (or more accurately, differentially biased) dataset, we chose the human mitochondrial genome (release EF184640. 1 from NCBI) because it is compact (16. 6 kb circular DNA molecule) and GC-rich (and therefore potentially prone to G4 formation). The first eukaryotic genome to be sequenced  (30) , the mitochondrial genome encodes for mitochondrial subunits I, II, III, IV and V. The genome consists of a heavy (H) strand, rich in guanine bases and a complementary light (L) strand, which is rich in cytosines. The first G4 motif analysis was performed on the yeast mitochondrial DNA  (31). Several studies found correlations between transcription termination, primer formation and R-loop stability and the presence of G4 structures  (32).
Computational analyses have correlated mitochondrial DNA deletions with non-B DNA propensity  (33). Mitochondrial DNA deletions are observed in patients with human genetic disorders, and Quadparser-predicted mitochondrial G-quadruplexforming sequences are located near known deletion breakpoints  (21, 34). A striking feature of the human mitochondrial genome is its GC skewness; this is reflected by the average G4Hscore value (-0. 4). We first calculated G4Hscores using sliding windows of 25 nt. We chose this window size as it is a close match to the mean length (26 nt) of the oligonucleotides in the G4FS reference dataset. Based on results from the analysis of the reference dataset, a threshold of 1 was chosen. Thus, we selected every sequence for which the G4Hscore was above 1 in absolute value in order to identify G4FS on both strand simultaneously.
In order to obtain a reliable answer to the seemingly simple question, 'Does this oligonucleotide form a quadruplex in vitro?' we had to combine the results of up to six different techniques (IDS, TDS, UV-melting, CD, NMR and the thioflavin fluorescence assay). Taken individually, none of methods gave a satisfactory answer in all cases (IDS and NMR were the most reliable techniques). The experimental results for all sequences tested are presented in supplementary information ('Biophysical data' file): each page contains data on a single sequence. Based on the conclusions from these tests, these sequences were classified as G4 (n = 71), unstable G4 ('UG4'; n = 63) and not-G4 (n = 75). The data were subjected to the same statistical analyses as were performed on the reference dataset. Results are summarized in Supplementary Figure  S2A -F and discussed in the Supplementary Information.
For these sequences, the G4Hunter discriminating score appears to be 1. 2 (Supplementary Figure  S2F ). The G4Hscores are less dispersed than those from the reference dataset; this is not unexpected as most of the sequences tested were selected based on a score >1. This analysis indicated that for an actual genomic sequence, the G4Hunter score is a good estimator of the ability of a sequence to fold into a G-quadruplex when analysed in vitro. On the other hand, for sequences with a G4Hscore between 1. 2 and 1. 5, the conclusion is not so straightforward. To evaluate the ability of G4Hunter to identify 'true' (at least in vitro) G4FS, we adjusted the G4Hunter results to avoid redundancy by merging overlapping sequences using thresholds ranging from 1 to 2. We obtained 96, 67, 25, 19 and 7 hits for threshold values of 1, 1.
But if only high confidence (stable) G4 are seeked (excluding UG4, see Supplementary Information for a discussion regarding this point), the threshold for G4Hunter has to move up to 1. 5 to get a FDR < 10%. This nevertheless comes to the cost of a reduced number of sequences identified. If an even lower FDR is required, increasing the threshold to 1. 7 eliminate (for this dataset) all false positive result. On the other hand, QP312 and QP37 are also very good in ignoring false positive, but the results then miss half (for QP312) or three-fourth (for QP37) of the results found with G4H1. 7. We studied the impact of window size on G4Hunter performance. We computed the G4Hscores using windows ranging in length from 15 to 100 nt. The lower limit of 15 nt corresponds to the length of one of the shortest known stable intramolecular G-quadruplexes that is formed by the thrombin binding aptamer (TBA, d-GGTTGGTGTGGTGG).
Thus, although there are 3. 1•10 9 bases in the human genome, our analysis was performed on 2. 86•10 9 bases. To evaluate metrics (ii) and (iii), we computed the total coverage of the feature on the genome by dividing the sum of the length of the feature by the size of the genome. This is referred to as the global background. To better reflect the actual genome composition, G4FS lists were randomized 1000 times in the available and annotated genome using an R script (gaps of more than 20 were avoided). This allowed us to generate 1000 lists with the same strand, width and chromosomal distribution as G4FS lists. We call this the resampled background. Promoters. Using genomic annotation from UCSC Known Genes list, we defined a promoter region as the 1 kb upstream of a transcription start site (TSS) of an unambiguous transcript.
Interestingly, although stringent versions of Quadparser gave an excellent false positive rate (0 in the mitochondria dataset: i. e. , all sequences predicted experimentally form G4 do), a large majority of true G-quadruplex forming motifs were missed. QP27 identified more true G4 but at the cost of accuracy (48%, Figure  2B ). Interestingly, G4Hunter with a threshold of 1. 2 has a higher precision (63%) with a comparable number of hits. In other words, the number of false positives is reduced with G4H1. 2 as compared to QP27 (23 and 37 respectively). Provided a reasonable G4Hscore threshold is chosen, the number of hits found at the genome wide level is higher than QP37. Given the data described here, the number of G4prone sequences found in the human genome should therefore be significantly revised upwards compared to the commonly accepted figure of 376 000 G4FS.
This facilitates calculations when large genomes are analysed. However, there is no reason not to consider fractional values for these parameters, and we are currently investigating this possibility. Given our large database of sequences of known structure, we should be able to calculate accuracy for various values of n. Further, our scoring of A, T and C are context independent. This is obviously an approximation: for example, a GGGCGGGN. NGGGCGGG can form a very stable quadruplex with loops of single cytosine. The G4 formed is more stable with loops of single cytosine than with loops of single thymine or adenine  (49). Our use of a negative score for C and null for A and T is not justified for this family of sequences. We therefore hope that our work will stimulate further studies aimed at improved G4Hunter! G4Hunter was designed to take into account C with negative values both to disfavour regions rich in alternative G/C and to score both strand of a DNA duplex simultaneously.
ACKNOWLEDGEMENTS We are grateful to the  Genotoul Bioinformatics Platform Toulouse Midi-Pyrenees  for computing and storage resources. L. L. wishes to thank all the Cuvier team, in particular P. G. P. Martin ,  G. Micas ,  Y. Visser  and  W. T. Jones  for support using  R. P. G. P. Martin  also participated in this work by providing code and advices regarding Bioconductor and R. J. L. M. and L. L. dedicate this work to the memory of  Bruno Faucon  and  Ian Fraser Kilmister.
FUNDING Fondation ARC (subvention libre to J. L. M. );  Conseil régional d'Aquitaine Fellowship  (to A. B. );  Agence Nationale de la Recherche  ' OligoSwitch ' [ ANR-12-IS07-0001 ], ' Quarpdiem ' [ ANR-12-BSV8-0008-01 ], ' VIBBnano ' [ ANR-10-NANO-04-03  to J. L. M. ];  Université de Toulouse 'PISAAN'  [ AO1-2013  to L. L. ]. Funding for open access charge: Inserm.
Introduction Modern machine learning and artificial intelligence methods are revolutionizing many fields of science today, such as medicine, biology, engineering, high-energy physics and sociology, where large amounts of data have been collected due to the emergence of new high-throughput computerized technologies. Historically and methodologically speaking, many machine learning algorithms have been based on minimizing the mean squared error potential, which can be explained by tractable properties of normal distribution and existence of computationally efficient methods for quadratic optimization. However, most of the real-life datasets are characterized by strong noise, long-tailed distributions, presence of contaminating factors, large dimensions. Using quadratic potentials can be drastically compromised by all these circumstances: therefore, a lot of practical and theoretical efforts have been made in order to exploit the properties of non-quadratic error potentials which can be more appropriate in certain contexts.
However, as it is the case in any nonquadratic metrics, the resulting components can be non-orthogonal or even not invariant with respect to the dataset rotation. Moreover, unlike L 2 -based principal components, the Algorithm 3 does not always converge to a unique global minimum; the computed components can depend on the initial estimate of V. The situation is somewhat similar to the standard k-means algorithm. Therefore, in order to achieve the least possible approximation error to the linear subspace, V can be initialized randomly or by data vectors x i many times and the deepest in PQSQ approximation error (1) minimum should be selected. How does the Algorithm 1 serve a more abstract version of the Algorithms 2,3? For example, the 'variance' function m( x) = 1 N j u( x j -x) to be minimized in Algorithm 2 uses the generating functions in the form Q = {b k ji + k a k ji (x k -x k j ) 2 } , where i is the index of the interval in  (2).
Nonlinear methods: PQSQ-based Principal Graphs and Manifolds In a series of works, the authors of this article introduced a family of methods for constructing principal objects based on graph approximations  (e. g. , principal curves, principal manifolds, principal trees), which allows constructing explicit nonlinear data approximators (and, more generally, approximators with non-trivial topologies, suitable for approximating, e. g. , datasets with branching or circular topology)  [28, 29, 30, 31, 11, 8, 7, 32]. The methodology is based on optimizing a piece-wise quadratic elastic energy functional (see short description below). A convenient graphical user interface was developed with implementation of some of these methods  [33]. S i |x i -x| S i u PQSQ-L1 (x i -x) Let G be a simple undirected graph with set of vertices Y and set of edges E.
For k ≥ 2 a k-star in G is a subgraph with k + 1 vertices y 0,1,. ,k ∈ Y and k edges {(y 0 , y i ) | i = 1,. , k} ⊂ E. Suppose for each k ≥ 2, a family S k of k-stars in G has been selected. We call a graph G with selected families of k-stars S k an elastic graph if, for all E (i) ∈ E and S (j) k ∈ S k , the correspondent elasticity moduli λ i > 0 and µ kj > 0 are defined. Let E (i) (0), E (i) (1) be vertices of an edge E (i) and S For any map φ : Y → R m the energy of the graph is defined as U φ (G) := E (i) λ i φ(E (i) (0)) -φ(E (i) (1)) 2 + + S (j) k µ kj k i=1 φ(S (j) k (i)) -kφ(S (j) k (0)) 2. For a given map φ : Y → R m we divide the dataset D into node neighborhoods K y , y ∈ Y. The set K y contains the data points for which the node φ(y) is the closest one in φ(y). The energy of approximation is: U φ A (G, D) = y∈Y x∈K y w(x) x -φ(y) 2 , ( 14 ) where w(x) ≥ 0 are the point weights.
22: goto repeat till convergence Application of PQSQ-based potential is straightforward in this approach. It consists in replacing  (14)  with U φ A (G, D) = y∈Y x∈K y w(x) k u(x k -φ(y k )), where u is a chosen PQSQ-based error potential. Partitioning of the dataset into {K y } can be also based on calculating the minimum PQSQ-based error to y, or can continue enjoying nice properties of L 2 -based distance calculation.
Implementation We provide Matlab implementation of PQSQ approximators (in particular, PCA) together with the Matlab and R code used to generate the example figures in this article at 'PQSQ-DataApproximators' GitHub repository 1  and Matlab implementation of PQSQ-based regularized regression with build-in imitations of L 1 (lasso-like) and L 1 &L 2 mixture (elastic net-like) penalties at 'PQSQ-regularized-regression' GitHub repository 2. The Java code implementing elastic graph-based non-linear approximator implementations is available from the authors on request.
Performance/stability trade-off benchmarking of L 1 -based PCA In order to compare the computation time and the robustness of PQSQ-based PCA algorithm for the case u(x) = |x| with existing R-based implementations of L 1 -based PCA methods (pcaL1 package), we followed the benchmark described in  [26]. We compared performance of PQSQ-based PCA based on Algorithm 3 with several L 1 -based PCA algorithms: L1-PCA*  [25] , L1-PCA  [23] , PCA-PP  [34] , PCA-L1  [24]. As a reference point, we used the standard PCA algorithm based on quadratic norm and computed using the standard SVD iterations. The idea of benchmarking is to generate a series of datasets of the same size (N = 1000 objects in m = 10 dimensions) such that the first 5 dimensions would be sampled from a uniform distribution U (-10, 10).
σ = 0 if and only if the first five components do not have any non-zero loadings in the dimensions 6,. , 10. The results of the comparison averaged over all 1300 test sets are shown in Figure  6. The PQSQbased computation of PCA outperforms by accuracy the existing heuristics such as PCA-L1 but remains computationally efficient. It is 100 times faster than L1-PCA giving almost the same accuracy. It is almost 500 times faster than the L1-PCA* algorithm, which is, however, better in accuracy (due to being robust with respect to strong outliers). One can see from Figure  6  that PQSQbased approach is the best in accuracy among fast iterative methods. The detailed tables of comparison for all combinations of parameters are available on GitHub 3. The scripts used to generate the datasets and compare the results can also be found there 4.
Comparing performances of PQSQ-based regularized regression and lasso algorithms We compared performance of PQSQ-based regularized regression method imitating L 1 penalty with lasso implementation in Matlab, using 8 datasets from UCI Machine Learning Repository  [35] , Regression Task section. In the selection of datasets   1 ). All table rows containing missing values were eliminated for the tests. We observed up to two orders of magnitude acceleration of PQSQ-based method compared to the lasso method implemented in Matlab (Table  1 ), with similar sparsity properties and approximation power as lasso (Figure  7 ). While comparing time performances of two methods, we've noticed that lasso (as it is implemented in Matlab) showed worse results when the number of objects in the dataset approaches the number of predictive variables (see Table  1 ).
In order to test this observation explicitly, we took a particular dataset ('Crime') containing 1994 observations and 100 variables and compared the performance of lasso in the case of complete table and a reduced table ('Crime reduced') containing only each 10th observation. Paradoxically, lasso converges almost two times slower in the case of the smaller dataset, while the PQSQ-based algorithm worked slightly faster in this case. It is necessary to stress that here we compare the basic algorithms without many latest technical improvements which can be applied both to L 1 penalty and its PQSQ approximation (such as fitting the whole lasso path). Detailed comparison of all the existent modifications if far beyond the scope of this work. For comparing approximation power of the PQSQ-based regularized regression and lasso, we used two versions of PQSQ potential for regression coefficients: with and without trimming.
PQSQ-based approximators can be less accurate than the exact algorithms for optimizing L 1 -based functions utilizing linear programming: however, they are several orders of magnitude faster. PQSQ potential can be applied in the task of regression, replacing the classical Least Squares or L 1 -based Least Absolute Deviation methods. At the same time, PQSQ-based approximators can imitate a variety of subquadratic error potentials (not limited to L 1 or variations), including fractional quasinorms L p (0 < p < 1). We demonstrate that the PQSQ potential can be easily adapted to the problems of sparse regularized regression with non-quadratic penalty on regression coefficients (including imitations of lasso and elastic net). On several real-life dataset examples we show that PQSQ-based regularized regression can.
Figure6: Benchmarking several algorithms for constructing L 1 -based PCA, using synthetic datasets representing 'true' five-dimensional linear manifold contaminated by noise and outliers (located in other five dimensions). The abscissa is the error of detecti tnghe 'true' manifold by a particular method and the ordinate is the computational time relative to the standard SVD (L 2 -based PCA) computation, in logarithmic scale. The computational cost of application of linear programming methods instead of simpler iterative methods is approximately shown by an arrow.