dataesr/scientific-paragraphs-categorization huggingface dataset:
They correspond to 18. 31% of total number of points in the dataset. For example, consider the tree and the wall in zone C in Figure  24. These points have been manually marked as unclassified, then they have not been taken into account in the evaluation. Table  3  presents the confusion matrix and our classification results for these two categories. Results are presented as percentages with respect to the total number of points in the 3D point cloud (12 million points). Segmentation has been carried out using the method without markers (Section 5). This classification is useful to evaluate the ability of our method segmenting surfaces (façades and ground) while separating other objects connected to them. Using our method, f mean for the surface class is equal to 96. 03% while other are correctly separated from them with f mean equal to 71.
Conclusions In this paper, we have proposed automatic and robust approaches to segment façades from 3D point clouds. Processing is carried out using elevation images and 3D decomposition, and the final result can be reprojected onto the 3D point cloud for visualization or evaluation purposes. Our methods are based on geometrical and geodesic constraints. Parameters are related to urban and architectural constraints. Thus, they are intuitive to tune. The performance of our methods have been proved in our experiments on TerraMobilita databases using 2D and 3D ground truth annotations. Three approaches have been proposed: (i) reconstruction by dilation from markers; (ii) attribute controlled reconstruction from markers and; (iii) maximal elongation image from 3D decomposition (without markers).
Our approach is a research prototype, mainly based on Morph-M library  [55] , the image processing library of our laboratory. This library allows fast prototyping but it is not intended to be a fast library. Optimization of our base operators (erosion, dilation, opening, reconstruction, watershed, and so on), currently under development at CMM, aims at providing optimized operators for real time and/or big image developments. Software (hierarchical queues, structuring elements decomposition, among others) and hardware (SIMD-Single Instruction Multiple Data and parallelization) optimizations are available in SMIL library  [56]  and will be integrated in our future developments.
Introduction The numerical analysis of Markov chains always deals with a tradeoff between complexity and accuracy. Therefore we need tools to compare the approaches, the codes and some well-defined examples to use as a testbed. After many years of development of exact or bounding algorithms for stochastic matrices, we have gathered the most efficient into XBorne, our numerical analysis tool  [8]. Typically using XBorne, one can easily build models with tens of millions of states. Note that solving any questions with this size of models is a challenging issue. XBorne was developed with the following key ideas: 1. Build one software tool dedicated to only one function and let the tools communicate with file sharing 2. If another tool already exists for free and is sufficiently efficient, use it and write the export tool (only create tools you cannot find easily).
3. Allow to recompile the code to include new models. 4. Separate the data and the description of the data. As a consequence, we have chosen to avoid the creation of a new modelling language. The models are written in C and included as a set of 4 functions to be compiled by the model generator. This aspect of the tool will be emphasized in Sect. 2 with the presentation of an example (a queue with hysteresis). The tool decomposition approach will also be illustrated in the paper. XBorne is now a part of the French project MARMOTE which aims to build a set of tools for the analysis of Markovian models. It is based on PSI3 to perform perfect simulation (i. e. Coupling from the past) of monotone systems and their generalizations  [5] , MarmoteCore to provide an object interface to Markov objects and associated methods, and XBorne that we will present in this paper.
Simulation We have added several simulation engines in XBorne, mainly for educational purpose and for verification. All of them define a model with the same functions we have previously presented to design a Markov chain. The modeler just needs to add the simulation time and the seed for the generator when a random number generator is used by the simulation code. Thus, the same model description (i. e. the four C functions) is used for the simulation and the Markov chain generation. Two types of engines have been developed: a simulator with random number generation in C and a trace base version where the random number generation (and generally the random variables generation) are outside the simulation code and previously stored in a file by some statistical packages (typically R). Similarly, the output of the simulations are sample paths which are stored in separate files to be analyzed by state of the art statistical packages where various test algorithms and confidence intervals computations are performed by efficient methods already available in these packages.
This work was partially supported by project MARMOTE (ANR-12-MONU-00019). Y. Ait El Mahjoub is supported by Labex DigiCosme (project ANR-11-LABEX-0045-DIGICOSME) operated by ANR as part of the program Investissement d'Avenir Idex Paris-Saclay (ANR-11-IDEX-0003-02).
Acknowledgments. This work was partially supported by project MARMOTE (ANR-12-MONU-00019). Y. Ait El Mahjoub is supported by Labex DigiCosme (project ANR-11-LABEX-0045-DIGICOSME) operated by ANR as part of the program Investissement d'Avenir Idex Paris-Saclay (ANR-11-IDEX-0003-02).
The Python code used to generate this figure is provided as Jupyter notebook in Supplemental Information 3. The last part of this introduction is dedicated to a motivating example. In 'Kernels of Periodic and Aperiodic Subspaces,' we focus on the construction of periodic and aperiodic kernels and on the associated model decomposition. 'Application to Matérn Kernels' details how to perform the required computations for kernels from the Matérn familly. 'Quantifying the Periodicity t' introduces a new criterion for measuring the periodicity of the signal. Finally, the last section illustrates the proposed approach on a biological case study where we detect, amongst the entire genome, the genes showing a cyclic expression. The examples and the results presented in this article have been generated with the version 0.
Motivating example To illustrate the challenges of determining a periodic function, we first consider a benchmark of six one dimensional periodic test functions (see Fig. 1  and Appendix A ). These functions include a broad variety of shapes so that we can understand the effect of shape on methods with different modelling assumptions. A set X = (x 1 ,. ,x 50 ) of equally spaced observation points is used as training set and a N (0,0. 1) observation noise is added to each evaluation of the test function:   (. ,5). For these plots, one of the kernels variables is fixed to 5. The three graphs on each plot correspond to a different value of the lengthscale parameter ℓ. The input space is D = [0,4π] and the cut-off frequency is q = 20. The Python code used to generate this figure is provided as Jupyter notebook in Supplemental Information 3.
aperiodic portion m a. Our decomposition allows for recognition of both periodic and aperiodic parts. In this case maximum likelihood estimation was used to determine the parameters of the kernel, we recovered (σ 2 p ,ℓ p ,σ 2 a ,ℓ a ) = (52. 96,5. 99,1. 18,47. 79). The Python code used to generate this figure is provided as Jupyter notebook in Supplemental Information 3. notations). We consider three different modelling approaches to compare the facets of different approaches based on harmonic analysis: F i = f (x i ) + ε i (or F = f (X ) + ε with vector • COSOPT  (Straume, 2004) , which fits cosine basis functions to the data, • Linear regression in the weights of a truncated Fourier expansion, • Gaussian process regression with a periodic kernel. COSOPT. COSOPT is a method that is commonly used in biostatistics for detecting periodically expressed genes  (Hughes et al.
Within each cell, protein-coding genes are transcribed into messenger RNA molecules which are used for protein synthesis. To quantify the expression of a specific protein-coding gene it is possible to measure the concentration of messenger RNA molecules associated with this gene. Microarray analysis and RNA-sequencing are two examples of methods that take advantage of this principle. The dataset (see http://millar. bio. ed. ac. uk/data. htm) considered here was originally studied by  Edwards et al. (2006). It corresponds to gene expression for nine day old arabidopsis seedlings. After eight days under a 12 h-light/12 h-dark cycle, the seedlings are transferred into constant light. A microarray analysis is performed every four hours, from 26 to 74 h after the last dark-light transition, to monitor the expression of 22,810 genes.
Edwards et al. (2006)  use COSOPT  (Straume, 2004)  for detecting periodic genes and identify a subset of 3,504 periodically expressed genes, with an estimated period between 20 and 28 h. We now apply to this dataset the method described in the previous sections. The kernel we consider is a sum of a periodic and aperiodic Matérn 3/2 kernel plus a delta function to reflect observation noise: k(x,x ′ ) = σ 2 p k p (x,x ′ ) + σ 2 a k a (x,x ′ ) + τ 2 δ(x,x ′ ). ( 21 ) Figure  4  Distribution of the periodicity ratio over all genes according to the Gaussian process models. The cut-off ratio determining if genes are labelled as periodic or not is represented by a vertical dashed line. Although the cycle of the circadian clock is known to be around 24 h, circadian rhythms often depart from this figure (indeed circa dia is Latin for around a day) so we estimated the parameter λ to determine the actual period.
The final parametrisation of k is based on six variables: (σ 2 p ,ℓ p ,σ 2 a ,ℓ a ,τ 2 ,λ). For each gene, the values of these parameters are estimated using maximum likelihood. The optimization is based on the standard options of the GPy toolkit with the following boundary limits for the parameters: σ p , σ a ≥ 0; ℓ p , ℓ a ∈ [10, 60]; τ 2 ∈ [10 -5 ,0. 75] and λ ∈  [20, 28]. Furthermore, 50 random restarts are performed for each optimization to limit the effects of local minima. Eventually, the periodicity of each model is assessed with the ratio S given by Eq. (  20 ). As this ratio is a random variable, we approximate the expectation of S with the mean value of 1,000 realisations. To obtain results comparable with the original paper on this dataset, we labeled as periodic the set of 3,504 genes with the highest periodicity ratio.
6B  that there is always at least one observation associated with each spike, which ensures that the behaviour of the Gaussian process models cannot simply be interpreted as overfitting. The reason COSOPT is not able to identify these signals as periodic is that it is based on a single cosine function which makes it inadequate for fitting non sinusoidal periodic functions. This is typically the case for gene expressions with spikes as in Fig. 6B , but it can also be seen on the test functions of Fig. 1. This comparison shows very promising results, both for the capability of the proposed method to handle large datasets and for the quality of the results. Furthermore, we believe that the spike shape of the newly discovered genes may be of particular interest for understanding the mechanism of the circadian clock.
Figure2Examples of decompositions of a kernel as a sum of a periodic and aperiodic sub-kernels. (A) Matérn 3/2 kernel k(. ,5). (B) Periodic sub-kernel k p (. ,5). (C) Aperiodic sub-kernel k a (. ,5). For these plots, one of the kernels variables is fixed to 5. The three graphs on each plot correspond to a different value of the lengthscale parameter ℓ. The input space is D = [0,4π] and the cut-off frequency is q = 20. The Python code used to generate this figure is provided as Jupyter notebook in Supplemental Information 3.
Algorithm 1 shows the pseudo-code of MAP-Elites. Given a performance measure performance(x), where x represents a candidate solution, the user chooses N behavioral dimensions that are measured by behavioral descriptors. For instance, the dimensions for evolving robot morphologies could be the height and weight of the robot. Each dimension of variation is then discretized based on user preference or available computational resources, leading to an N -dimensional grid where each cell can be seen as a niche-a different type of solution-that MAP-Elites will try to fill with the best performing solution of that type. MAP-Elites starts by randomly generating G genomes and determining the performance and phenotypic features of each. Those genomes are placed into the cells to which they belong in the behavior space (if multiple genomes map to the same cell, the highest-performing one per cell is retained).
The total number of CPG parameters generatively encoded by the CPPN is 23 (12 intrinsic amplitudes and 11 phase biases, for details see  [26] ) ANNs with CPPNs (HyperNN). The second generative encoding scheme is a simplified version of the HyperNEAT indirect encoding, in which NEAT is replaced by a basic direct encoding for neural networks. The CPPNs encode the weights of input-hidden and hidden-output neuron connections of a fixed topology, single-layer feedforward ANN. ANN neurons are positioned in the substrate to reflect the hexapod robot morphology (details in  [26] ). For each connection, these locations are input to the CPPN and it specifies the weight of that connection (details in  [26] ). The ANN inputs are the previously requested angles for each of the 12 pivot joints of the 6-legged robot.
Linear Solvers All linear solvers used in this study were implemented in the publicly available numerical package Parallel Toolbox (pt)  [72, 44, 73]. The cardiac bidomain equations and the nonlinear deformation equation were solved in parallel using the Cardiac Arrhythmia Research Package (CARP)  [118]  as an outer framework which was interfaced with the pt library. Technical aspects have been described elsewhere  [80]. CARP makes use of the MPI based library PETSc [7] as the basic infrastructure for handling parallel matrices and vectors. Parallel partitioning of unstructured grids relies upon the graph based domain decomposition ParMetis  [54, 55]. Details on the methods employed for solving the bidomain equations in parallel have been reported previously  [92, 119, 80]. Briefly, the elliptic portion of the bidomain equations is solved using the algebraic multigrid preconditioner ptAMG  [72]  with an iterative CG solver method (ptAMG-PCG).
The most important factor for improving strong scalability was the grouping of parallel data at the intermediate multigrid levels onto fewer active computing units, as described in Section 4. 2. The reduction in communication density and the increase in average message size turned out to be beneficial for N p > 320. This effect was even greater for N p > 640, above which scalability stalled with a group size of g = 1, meaning data redistribution was turned off (Fig. 7 ). In terms of overall solving time, a group size of g = 2 proved to be optimal; a more aggressive reduction of the computing units g = 3, 4 was not beneficial. The performance of the linear solver in terms of convergence and cost of individual solver steps was monitored by recording iteration count, N it , and time per iteration, T it.
Acknowledgements This project has received funding from the  Austrian Science Fund (FWF)  within the  SFB Mathematical Optimization and Applications in Biomedical Sciences  and from from the  European Union 's  Seventh Framework Programme  for research, technological development and demonstration under grant agreement no. 611232. We acknowledge  PRACE  for awarding us access to resource SuperMUC based in Germany at  LRZ  (grant CAMEL), and, partially, ARCHER based in the UK at  EPCC  (project  e348 ). This research was supported by the grants  F3210-N18  from the  Austrian Science Fund (FWF) ,  NIH   1RO1 HL 10119601l  and the  EU  grant  CardioProof 611232. We acknowledge  PRACE  for awarding us access to resource SuperMUC based in Germany at  LRZ  (grant CAMEL), and, partially, ARCHER based in the UK at  EPCC  (project  e348 ).
Computing the Maximal Anti-Exponent Procedure MaxAntiExp(z, w, ẽ) is designed to compute the maximal antiexponent of zw by considering gapped palindromes uv u such that u occurs in z, u is inside w, and whose anti-exponent is at least ẽ. In particular, at each position of z, the procedure finds the factors of zw beginning in this position that have the form uvũ with ũ inside w and updates the current maximal antiexponent with the value of |uv u|/|uv|. Before detailing the procedure, we present the suffix automaton data structure which is the fundamental algorithmic tool used by MaxAntiExp. The suffix automaton of string w, denoted S(w), is the minimal partial deterministic finite automaton whose language is the set of suffixes of w (see  [5, Section 6. 6 ] for more description and for efficient construction); an example is given in Fig.
Targeted RNA sequencing (CaptureSeq) uses oligonucleotide probes to capture RNAs for sequencing, providing enriched read coverage, accurate measurement of gene expression, and quantitative expression data. We applied CaptureSeq to refine transcript annotations in the current murine GRCm38 assembly. More than 23,000 regions corresponding to putative or annotated long noncoding RNAs (lncRNAs) and 154,281 known splicing junction sites were selected for targeted sequencing across five mouse tissues and three brain subregions. The results illustrate that the mouse transcriptome is considerably more complex than previously thought. We assemble more complete transcript isoforms than GENCODE, expand transcript boundaries, and connect interspersed islands of mapped reads. We describe a novel filtering pipeline that identifies previously unannotated but high-quality transcript isoforms.
In this set, 911 GENCODE neighboring genes are condensed into 400 expanded gene models. Additionally, 594 GENCODE lncRNAs acquire an open reading frame (ORF) when their structure is extended with CaptureSeq. Finally, we validate our observations using current FANTOM and Mouse ENCODE resources. [Supplemental material is available for this article. ] Advances in sequencing technology have permitted rapid highthroughput sequencing of cDNA and the discovery of novel genes and transcript isoforms. This has also fostered the rapid accumulation of annotated long noncoding RNAs (lncRNAs)  (Bussotti et al. 2013)  and further recognition that the vast majority of genes express alternative isoforms  (Katz et al. 2015). Current estimates of human lncRNA loci range from 58,648 from a large compendium of RNA-seq data sets  (Iyer et al.
2008; Cabili et al. 2011 ) by de novo transcript detection. Many of these issues can be addressed using targeted RNA sequencing (CaptureSeq). CaptureSeq utilizes magnetic bead-linked oligonucleotide probes to dramatically enhance the abundance of selected transcripts. Targeted cDNAs hybridize to the probes facilitating the purification of the RNA of interest prior to conventional RNA sequencing  (Mercer et al. 2011). Previously, we used the CaptureSeq strategy to enrich and sequence targeted fractions of the human transcriptome  (Clark et al. 2015). This allowed the discovery of novel transcripts, expressed beneath coverage restrictions usually imposed by RNA-seq and the joining of previously fragmented annotations. In human leukemia cell lines (K562), 42. 1% of the transcriptome was expressed below 0.
0366 attomole/µL and was better quantified by CaptureSeq  (Clark et al. 2015). This fraction of the transcriptome was enriched in cancer and other disease associated loci  (Clark et al. 2015). Given the advantages of CaptureSeq to characterize and quantitate poorly annotated, lowly expressed and high tissue-specific human lncRNAs  (Mercer et al. 2011; Clark et al. 2015) , we applied this method to the much less annotated mouse transcriptome. We prepared a CaptureSeq design with 190,689 probes comprising 28,228 known and predicted mouse lncRNAs annotations. Additionally, we created a second CaptureSeq design with 154,281 probes designed to target annotated splice junctions. We used these two probe designs to profile transcriptome complexity in five mouse tissues (including three brain subregions), revealing both novel lncRNA and coding transcripts and simultaneously correcting previous annotations.
Results The two CaptureSeq probe designs were used to perform targeted sequencing of the splice junctions and lncRNA loci of the mouse genome. The lncRNA design was generated considering a combination of annotated and predicted loci (Methods). This data set spanned 28,228 transcripts, an increase of ∼2. 8-fold with respect to lncRNAs annotated in GENCODE (M4). Transcript coordinates and an accompanying annotation table of targeted lncRNAs are provided (Supplemental Data S1, S2, respectively). We used probes designed to perform targeted sequencing in five mouse tissues: brain, heart, kidney, liver, and testis. Typically lncRNAs are highly tissue specific and enriched in brain and testes  (Cabili et al. 2011). Furthermore, distinct neuronal populations have characteristic lncRNA expression landscapes  (Kadakkuzha et al.
S3B ). The mapped reads together with GENCODE (M4) annotations were used to guide assembly of the transcriptome. Annotations of both lncRNA and splice junction CaptureSeq experiments were merged together to generate a comprehensive assembly of 59,206 genes encoding 137,562 transcripts. The resulting data set incorporated the full GENCODE (M4) annotations together with the genes defined in the CaptureSeq experiments. As the CaptureSeq design included monoexonic ESTs and cDNAs (Methods) derived from sense intronic regions of the genome, this comprehensive assembly includes a higher fraction of unspliced transcripts with respect to GENCODE (24. 4% versus 17. 0%). When considering the spliced component only, the average number of isoforms per gene was comparable with GENCODE annotations (3. 8 versus 3.
2010). This comprehensive unfiltered transcriptome assembly is freely available to the community as Supplemental Data S3. We next sought to curate a high quality selection of novel transcripts (HQ set) by applying consecutive filtering steps to remove any mapping and assembly artifacts and to exclude previously annotated isoforms (Fig. 1 ). Initially, we excluded transcripts mapping to unplaced mouse contigs (Methods). Then, we selected only those transcripts whose exons overlap at least one CaptureSeq probe (either in the lncRNA or splice junction design). Transcripts overlapping solely to control probes were discarded. Next, we discarded any poorly supported transcript isoforms. We utilized the known quantities of RNA spiked-in controls to set a threshold below which we consider the expression readings and transcript assemblies likely unreliable.
The spike-in controls used were External RNA Controls Consortium (ERCC) RNAs  (Baker et al. 2005). These consist of a set of unlabeled, polyadenylated transcripts of differing sizes and concentrations in order to measure against defined performance criteria. These controls have become widely accepted for normalization and quantitation of RNA samples. Previous reports demonstrated that transcript models with at least eightfold sequence coverage can be confidently assembled  (Jiang et al. 2011). Thus, for each sample, we estimated the known concentration and the FPKM for which the ERCC controls reach a lower limit of 8× sequence coverage (Supplemental Figs. S5, S6). Transcripts consistently expressed below the established sample-specific FPKM thresholds were discarded. We next removed all transcripts for which Cufflinks/Cuffmerge failed to predict the transcript orientation.