dataesr/scientific-paragraphs-categorization huggingface dataset:
Allowing computations in both double-double and quad-double precision requires setting -D precision-QD=all. The default is none. • integrals: Choose whether or not to compile the master integrals of the module IntegralLibrary. The default is none which means that no master integrals are compiled. If goncharovs is selected, GiNaC  [63]  is required. If pentagons is selected the PentagonLibrary  [47]  is required. 3 The choice all compiles both representations of the master integrals. • lapack-path: If necessary, specifies the path of Lapack if meson is unable to find the path to the library. Beyond these, there are a number of options mainly useful for development: • caravel-debug: Enable a dynamic handling of debugging information from specific source files. To use this feature, simply place a file named debug.
e. a 0 = g 0 , where g 0 = √ 4πα s. For Einstein gravity amplitudes, instead, a 0 = κ 0 /2, where κ 0 = √ 32πG N and G N is Newton's constant. In this section we will often refer to the index L in M (L) n as the loop order, as for the examples we will consider the two numbers are aligned. L = 0 corresponds to tree-level amplitudes. As already stated in section 2, see in particular eq. (  1 ), Caravel computes the coefficients A n we must specify several of our conventions and this is done in detail in Appendix A. These conventions are important for defining the output of the example programs described in this section. The example programs we provide compute tree-level, one-loop and twoloop amplitudes. While the tree-level example program allows one to evaluate amplitudes with an arbitrary number of particles, the one-loop and two-loop example programs evaluate at most five-point amplitudes, up to order ǫ 2 for one loop and ǫ 0 for two loops.
Tree level The program treeamp evaluates tree-level amplitudes for a variety of processes. It can be executed by specifying the corresponding amplitude with a Particles list (see section 5. 2). For example: >. /treeamp "Particles[Particle[. ],. ,Particle[. ]]" The program randomly generates a phase-space point and prints the value of the specified tree-level amplitude as well as the point. In Appendix A. 2 we provide details about the normalization employed for external helicity states, which are necessary to specify our phase conventions. If treeamp is to be used to evaluate N-graviton scattering amplitudes, Caravel must be configured with the option -D gravity-model=Cubic Instead of evaluating the amplitudes on randomly-generated phase-space points the user can also provide external momenta by placing a file with the name treeampPSP.
>. /treeamp "Particles[. ]" "HighPrecision[prec]" where prec is either HP for double-double or VHP for quad-double precision. Finally, the program can be used to compute tree amplitudes using finitefield arithmetic (-D finite-fields=true required). In this case the cardinality of the finite field has to be passed as a parameter to the program >. /treeamp "Particles[. ]" "Cardinality[p]" where p is a prime number smaller than 2 31 and larger than 2 30 , such as p = 2 31 -1 = 2147483647. For finite-field evaluations, the program does not randomly generate phase-space points and so the user must provide a set of valid external momenta using a file named treeampPSP. dat as explained above. Notice that in the case of finite-field evaluations we use a spacetime metric with alternating signature (+, -, +, -) to enhance performance.
3, see in particular eq. (A. 17). On the first evaluation of each amplitude, the program performs a warm-up run, as described in sections 2. 2 and section 2. 4. By default, the program runs on phase-space points defined in ref. [10]  and can be used to reproduce the results presented in the tables 1 and 2. As at one-loop, this example program is restricted to the Euclidean region of phase space, as master integrals are so far included only for this region. In order to enable this example the Caravel library has to be configured with the following options: -D finite-fields=true -D field-ext-fermions=true -D integrals=all The program can be executed in an analogous way to what was described in the previous example in section 5. 3. 2. Additionally, the user can pass the argument Verbosity[All] in order to print to the standard output extra information on the computations performed.
The program automatically verifies that all poles in ǫ cancel exactly, rationally reconstructs the special function coefficients in the finite remainder and subtraction term, and evaluates the special functions. The program then prints the values of the subtraction term, the remainder and the amplitude. We refer to ref. [17]  for the precise definition of our subtraction conventions. We note that the run-time of this program is comparable to that of the two-loop amplitude evaluation program. In order to enable this example Caravel has to be configured with the following options:   [2] ]" in order to compute the finite remainder for the color-ordered two-loop amplitude A (2) [2] (1 + g , 2 + g , 3 + g , 4 + g , 5 + g ). As in the two previous examples, the phase-space point can be specified in the command-line input as a list with the head TwistorParameters.
Program output The two analytic reconstruction example programs share common output features, which we describe here. Both programs perform the analytic reconstruction over a single finite field and attempt to rationally reconstruct the result. The computation in the finite field is saved as a text file in the local directory analytics/amplitudes XY/, where XY refers to the relevant cardinality. The master-integral coefficients are then rationally reconstructed employing only the single finite-field evaluation performed. This rational reconstruction is cross checked against a numerical computation at a single phase-space point in a second finite field. In the case of a successful reconstruction, the amplitude is saved in a text file under NumeratorLabel Master-integral numerator analytics/amplitudes rational/.
Univariate amplitude reconstruction As a simple example of the two-loop analytic reconstruction capabilities of Caravel, the program 4parton 2loop analytics MPI analytically computes the reduction to master integrals. The massless four-point amplitudes depend only on the Mandelstam variables s = (p 1 + p 2 ) 2 and t = (p 2 + p 3 ) 2. By setting s = 1 and x = t/s the amplitude depends only on a single parameter. Its analytic dependence on x is reconstructed from exact numerical evaluations of the master-integral coefficients over a finite field, which are then fed into Thiele's interpolation formula. The dependence on s is then recovered by dimensional analysis. To enable this example, Caravel has to be configured with the options.
Multivariate amplitude reconstruction The program computes the analytic form of five-parton one-loop amplitudes, using multivariate functional reconstruction. The five-parton amplitudes depend on five twistor parameters x 0 ,. , x 4 , see Appendix B. The problem is reduced to a four-dimensional reconstruction by setting x 4 = 1. The dependence on x 4 is recovered from dimensional analysis. In order to enable this example, Caravel has to be configured with the options.
Conclusions We have presented Caravel, a C ++ framework for the computation of multi-loop amplitudes through the multi-loop numerical unitarity method. This is the first publicly available program of its kind. We have provided a series of example programs which showcase the main functionalities of Caravel. In particular, these examples give access to all details of the calculation of the planar two-loop five-parton scattering amplitudes  [16, 17]  and the two-loop four-graviton scattering amplitude in Einstein gravity  [19]. In its current form, Caravel is not meant to be able to automatically evaluate arbitrary two-loop multi-leg amplitudes. Rather, it is meant as a framework to do so, which should be complemented with process-specific information such as, for instance, the master integrals.
Acknowledgments We gratefully acknowledge contributions to Caravel made by  Matthieu Jaquier  during the initial stages of the development. We also wish to thank  Mao Zeng  for discussions. The work of S. A. is supported by the  Fonds de la Recherche Scientifique-FNRS ,  Belgium. The work of F. F. C. is supported by the  U. S. Department of Energy  under grant  DE-SC0010102. The work of V. S. is supported by the  European Research Council (ERC)  under the European Union's  Horizon 2020 research and innovation programme , Novel structures in scattering amplitudes (grant agreement No. 725110 ). The work of B. P. is supported by the  French Agence Nationale pour la Recherche , under grant  ANR-17-CE31-0001-01. M. S. R. 's work is funded by the  German Research Foundation (DFG)  within the  Research Training Group GRK 2044.
Introduction Functional data are encountered in many fields, a multitude of examples can be found in the books by  Ferraty and Vieu (2006) ;  Ramsay and Silverman (2002, 2005). When analyzing functional data it is of particular interest to provide answers to the questions: (i) is there a common main (mean) functional pattern to be distinguished?; (ii) can we quantify the significant individual fluctuations with respect to such a mean pattern? While the common functional mean is capturing main features such as peaks and valleys, differences between individual curves are often exposed via differences in phase and in amplitude of the main features. In Figure  1  the Pinch Force data are depicted. These data were collected as part of an experiment to investigate the force (measured in Newton) exerted by thumb and forefinger when pinching a 6 cm width force meter.
Convergence was said to be reached when the difference in norm between estimated parameters in two consecutive iteration steps was less than 10 -2. We also would like to mention that in our simulation study we use a rewritten Matlab version of the original Table  1 : Evaluation criteria for the estimation tasks. Gervini and Carter (2014) , since the latter was no longer running properly. The use of the Matlab code can make computations a bit slower. quantity of interest evaluation criterion µ ∆ µ = T -1 j=1 [μ(t j ) -µ(t j )] 2 (t j+1 -t j ) w ∆ w = T -1 j=1 [w -1 (t j ; θ0 ) -t j ] 2 (t j+1 -t j ) Σ U ∆ U = Tr( ΣU -Σ U ) Σ θ ∆ θ = Tr( Σθ -Σ θ ) σ 2 ε ∆ ε = |σ 2 ε -σ 2 ε | code used in The elastic square-root slope is a promising framework, so we include a comparison with the method developed in  Tucker et al.
(2013). We use the default settings: no elasticity, Karcher mean, do not smooth the data and at most 20 iterations. We use the code available in the R package fdasrvf. Bayesian methods are also of interest, and we choose to compare with  Cheng et al. (2016) , also available in the R package fdasrvf. Also here we considered the default settings: 150000 iterations and a uniform prior distribution. Finally, we compare the performances with that of the algorithm of  Sangalli et al. (2010) , available in the R package fdakma, that allows for clustering misaligned data. We assume that there is no cluster, consider affine alignment and compute the similarity through the cosine of the angle between the two function. Since the available inference in those studies does not fully match our modeling inference, we can only report on the comparison related to estimating µ.
On model M 1 , the method fdakma performs the best, with a very low variance, but it has a comparable performance (in terms of bias) to the proposed method for M HD 1. On models M wCDG 2 and M wGC 2 , our method has particularly good results in mean, but with a larger variance. As GC's method is very slow (i. e high computational cost) and does not provide very good results whereas the modelling is close to the proposed one, we restrict further comparisons, for Models M 3 , M HD 3 , M 4 and M HD 4 , to the other three methods. On all models M 3 , M HD 4 , M 4 and M HD 4 , fdakma performs the best among the competitive methods, followed by the Bayesian warping method (method (3)), but both are less good than the proposed method in terms of bias. Finally, we see that the elastic square-root slope method (method (4) in the table) does not perform well on those simulated datasets.
Real data analysis We analyze the Pinch Force dataset, available in the R package fda. These data were described and analyzed in  Ramsay et al. (1995). The data consist of measurements, at every second millisecond, on the exerted force (in Newton) during a period of 0. 3 seconds. The resulting measurements consist of 20 curves recorded on 151 points in [0, 0. 3]. See Figure  1. For convenience the data were rescaled to the domain [0, 1]. We analyzed these data, using B-splines of degree 2 for µ and U (i. e. p µ = p Ui = 2), with interior knots {0. 25, 0. 50, 0. 75}, resulting in six B-spline basis functions. For the function determining the warping in (5) we use B-splines of degree 3 (i. e. p h = 3) and the same set of interior knots {0. 25, 0. 50, 0. 75}, leading to seven B-spline basis functions for h -1.
The survey was accessed via a SurveyMonkey© website link in the email. The survey was available for three months, and two reminders for participation were sent via the original method of communication. The estimated total number of residents who could have participated is 1,560. Responses were tallied and data was compiled for analysis. A Likert-type scale was used to provide ordinal ranks for perceptions of the importance of global health and the likelihood to participate in global health experiences. We utilized standard descriptive statistics, including the Spearman's rank correlation coefficient, the Mann-Whitney test and Pearson's chi-squared tests using GraphPad Prism (version 7. 0a, www. graphpad. com), which was used for the preparation of figures. A p-value of <0. 05 was considered significant for all data endpoints.
The meaning of this finding remains unclear and requires additional investigation. Additionally, the data from this study show that prior experience begets interest in future experiences. This is similar to the data from studies conducted in the field of general surgery and a few other surgical sub-specialties. A 2005 survey of UCSF general surgery residents showed that 40% had participated in an international health experience prior to residency, and 90% expressed an interest in an elective in a developing country during residency. A 2009 survey of resident members of the American College of Surgeons found that 92% of the 724 individuals surveyed were interested in international outreach opportunities, and 82% would prioritize these opportunities over other electives  [17]. Finally, a study conducted by Aziz et al.
Background: RNA-seq is being increasingly adopted for gene expression studies in a panoply of non-model organisms, with applications spanning the fields of agriculture, aquaculture, ecology, and environment. For organisms that lack a well-annotated reference genome or transcriptome, a conventional RNA-seq data analysis workflow requires constructing a de-novo transcriptome assembly and annotating it against a high-confidence protein database. The assembly serves as a reference for read mapping, and the annotation is necessary for functional analysis of genes found to be differentially expressed. However, assembly is computationally expensive. It is also prone to errors that impact expression analysis, especially since sequencing depth is typically much lower for expression studies than for transcript discovery.
Results We propose a shortcut, in which we obtain counts for differential expression analysis by directly aligning RNA-seq reads to the high-confidence proteome that would have been otherwise used for annotation. By avoiding assembly, we drastically cut down computational costs -the running time on a typical dataset improves from the order of tens of hours to under half an hour, and the memory requirement is reduced from the order of tens of Gbytes to tens of Mbytes. We show through experiments on simulated and real data that our pipeline not only reduces computational costs, but has higher sensitivity and precision than a typical assembly-based pipeline. A Snakemake implementation of our workflow is available at: https://bitbucket. org/project_samar/samar Conclusions: The flip side of RNA-seq becoming accessible to even modestly resourced labs has been that the time, labor, and infrastructure cost of bioinformatics analysis has become a bottleneck.
It is only likely that RNA-seq will continue to rapidly proliferate while high-quality reference databases grow at a slow pace. The conventional strategy to adapt standard referencebased RNA-seq analysis workflows to the case of nonmodel organisms, has been to first compute a de-novo transcriptome assembly by pooling all reads and to annotate the assembly against a high-confidence protein database. Since assemblers typically do not provide a read-to-contig mapping, the subsequent step is to map the reads to the assembly. This is followed by a quantification step in which reads mapping to each contig are counted. The count data is used for statistical testing of differential expression. Since the number of differentially expressed genes tends to be quite large, inference of biological function is done computationally by using the annotations to perform GO-term enrichment or pathway analysis.
Finally, in special cases such as comparison of gene expression across species, it might not even be reasonable to compute a single assembly. We provide an alternative strategy that circumvents the need for assembly and annotation. The first step of our proposed pipeline uses LAST  [28, 29]  to directly align RNA-seq reads to the high-confidence protein set which would otherwise have been used for annotation. This is followed by a simple counting step that employs a traditional rescue strategy to resolve multimaps  [30]. The counts can be fed into standard count-based differential gene expression analysis tools, e. g. DESeq2  [31]. Our main proposition here is that since functional analyses in non-model organisms rely on a database of homologous proteins in order to draw conclusions, it might be more reasonable to directly allocate reads to those homologous proteins using DNA-protein alignment, instead of introducing an error-prone yet computationally heavy intermediary step of assembly.
The main and obvious advantage of our method is that it drastically brings down computational costs. For example, for a typical RNA-seq study containing 2 groups of 3 replicates each and 20 million paired-end reads per replicate, our approach takes under half an hour, whereas computing an assembly would take several tens of hours. Additionally we show, through experiments on simulated and real RNA-seq datasets, that our method is more accurate in identifying differentially expressed genes than an assemblymapping-quantification pipeline. Another advantage is that it is easier to interpret results, as each homologous gene is reported as differentially expressed or not, along with associated statistical measures. In contrast, with assembly-based pipelines, there might be a need to consolidate results across several fragmented contigs.
Implementation of our proposed method We have implemented our proposed strategy as a Snakemake pipeline  [32] , which is available at https: //bitbucket. org/project_samar/samar. The first step in the workflow aligns RNA-seq reads to a reference set of proteins. For this we use the DNA-protein alignment feature of LAST  [28, 29, 33]. We chose LAST over numerous other aligners capable of DNA-protein alignment -BLASTX  [34]  being a prominent example -for its unique combination of features. It scales well to high-throughput sequencing data. The probabilistic framework for incorporating paired information from paired-end reads, which was originally designed for read-to-genome alignment  [35] , works out of the box for the case of read-to-proteome alignment. It allows training the substitution matrix and gap penalties to reflect the sequence divergence between the (translated) RNA-seq reads and the reference proteome  [36].
Benchmarking We perform benchmarking on both real and simulated RNA-seq read datasets from the protein-coding transcriptome of the fruit fly D. melanogaster. We chose this extensively studied transcriptome since the transcripts and protein products associated with each gene is known for a huge number of protein-coding D. melanogaster genes. Such a mapping between Flybase ID and UniProt ID can be obtained from Ensembl, UniProt, Flybase  [37] , etc. , and can be used for evaluation of our workflow. The simulated RNA-seq read dataset was generated as follows. We downloaded the transcripts of proteincoding genes from the fruit fly assembly BDGP6. 28 obtained from Ensembl Genes 101. After removing sequence duplicates and transcripts with no corresponding protein entries, there were 28,692 transcripts of 13,320 genes.
From this transcriptome, we simulated 2 groups of RNA-seq reads with 3 replicates per group using Polyester  [37]. In the first group, the mean expression levels of the transcripts were set to be proportional to the FPKM values computed from an arbitrarily chosen poly-A+ enriched real RNA-seq data (Ar-rayExpress E-MTAB-6584). The FPKM values were estimated using RSEM  [38]  on Bowtie2  [39]  alignments of the reads to the transcriptome. In the second group, a subset of roughly 30% of the transcripts were set to be differentially expressed at varying levels of up-and down-regulation: 1. 5, 2, and 4-fold. The transcripts were chosen by randomly selecting genes and setting only the highest expressing isoform to be differentially expressed. Since inference of differential expression is typically done at the gene level, having at most one isoform to differentially expressed simplifies the evaluation process  [40]  as we can define a gene to be differentially expressed if one of its transcripts was differentially expressed.
DNA-protein alignment attains similar performance to using a transcriptome reference We first demonstrate, under ideal conditions, the soundness of our idea of aligning RNA-seq reads to a proteome reference for differential gene expression analysis, by comparing our performance to that of the traditional case of using an established transcriptome reference. We aligned the fruit fly simulated RNA-seq reads (described earlier in the Implementation section) to the UniProt D. melanogaster proteome UP0000 00803, which contains 1 representative protein sequence per gene, and fed the counts obtained by our method to DESeq2  [31]  for differential analysis. To serve as baseline for comparison, we additionally ran a typical pipeline consisting of Bowtie2  [39]  for read alignment to the D. melanogaster transcriptome, followed by RSEM for transcript quantification, tximport  [40]  for gene-level aggregation of counts, and finally DESeq2  [31]  for differential analysis at the gene level.
The evaluation process described below uses the mosquito proteome as reference; but to calibrate the effect of the degree of evolutionary and sequence divergence, we repeated the process described below with reference proteomes of closer relatives of D. melanogaster: D. ananassae and D. grimshawi. We compared our performance to that of a typical assembly-based pipeline consisting of: Trinity  [43]  for de-novo transcriptome assembly, followed by Bowtie2 for mapping the reads to the assembly, RSEM for counting, tximport for gene-level aggregation using the gene-to-transcript mapping provided by Trinity, and finally DESeq2 for differential analysis. We used the Dammit pipeline  [44]  to annotate the assembly against the mosquito proteome. Details of the two pipelines are provided in the Supplementary Material.