dataesr/scientific-paragraphs-categorization huggingface dataset:
Other directions of developing coalescent modeling involve different scenarios of populations evolution, constant or undergoing expansions or bottlenecks, combined with possible inhomogeneity of their structures  [11, 12] , as well as different models of mutation, infinite size, infinite alleles, recurrent, stepwise. There are also several studies concerning coalescence modeling for populations under selection  [13] [14] [15]. Emergence of large datasets resulting from contemporary sequencing technologies has drawn attention of researchers to problems in the coalescent theory arising in the situation where the coalescent sample size becomes large. There are several areas of analysis of such problems. Below we describe those of them, which are in the scope of our interest in the present paper.
In previous articles such distributions and expectations were estimated on the basis of coalescence simulations or approximate methods. • Computing limit distributions of times to most recent common ancestor in the coalescene tree under different rates of population growth. • Evaluation of accuracy of published large sample approximations  [16]  for times in the coalescence tree and expected allele frequencies. • Estimation of rates of convergence of distributions of times in the coalescence tree to their limits. • Fitting the exponential growth model to DNA polymorphisms data from the whole database of mitochondrial DNA for over 2000 individuals  [22]. In the "Discussion" section we show some other possible applications of the derived results and some possible further directions of the research.
Analysis of mitochondrial DNA dataset The last result, which we show is the analysis of human mitochondrial DNA polymorphisms from the Human Mitochondrial Genome mtDB database  [25]. The mtDB database contains in total 3857 polymorphic sites quantified in 2704 individuals. For our analysis we have chosen only a subset of 3857 polymorphic sites in mtDB, namely those sites whose status was determined for all 2704 individuals and which were diallelic. There were 3213 such segregating sites. Table  2  shows their allelic frequencies. We have fitted the model of exponential growth for the data given in Table  2. Analogously to  [8]  we treated each segregating site as a separate SNP. The model fit is based on maximizing the likelihood function defined in  [8]  (Eq  (24) ). In Fig  6  we present plots of log likelihood functions versus exponential growth product parameter ρ, obtained with the use of exact  method (marked with asterisks) and with the use of approximate expectations of coalescence times proposed by Chen and Chen (2013)  [16]  (marked with open circles).
One can see that plots are quite close one to another, consistently to results presented in subsection "Accuracy of approximate formulae for expected allele frequencies". Maximum likelihood estimate obtained by using the exact method is rexact ¼ 339:3 and the estimate obtained by using the approximate method is rapprox ¼ 341:7. Additionally, we used Hudson's program "ms"  [26]  to perform 1000 coalescence simulations, with appropriate parameters, which allowed us to estimate 95% confidence interval as 285 < ρ < 403. Similar estimates can be obtained on the basis of the likelihood ratio statistics  [8]. The obtained values and bounds of confidence intervals, fit into the range of values (50-500) of exponential growth product parameter of human population, which we estimated in  [8]  on the basis of different datasets.
Discussion In this paper we evaluate the accuracy of the approximations for times in the coalescence tree and expected allele frequencies as proposed by  [16]  and we compute the probability distributions of times in the coalescence tree and their limits. We also use Human Mitochondrial Genome mtDB database to present a comparison of exact versus approximate log likelihood function for solving the inverse problem of estimating population size history from observed allele frequencies  [18, 20, 24]. The presented resuts are based on new approaches described in the "Methods" section. We propose new methods for coalescence computations for large sample sizes, based on inverting the integral transform defined in  [7]  ("Methods" section, Eq (12)) and on using analytical expressions for infinite products for computing limit distributions.
g. , for analyzing statistics of triallelic DNA loci  [28]. In this paper, by large sample sizes n we understand numbers comparable to the present throughput capabilities of experimental techniques for DNA sequencing, i. e. thousands of people, with data publically available in databases in 1000 Genomes Project  [29]  or mtDB  [25]. The sample size is going to increase to hundreds of thousands or even millions in short order, with ongoing projects including UK10K (about 10 thousand human genomes) and the Million Veteran Program (about 1 million human genomes). The computational methods proposed in this paper are likely to be relevant to many aspects of statistical analyses of these datasets. Sequencing data for even larger number of cell samples are already available in the cancer genomics TCGA database  [30].
In our computational examples, presented further in this paper, we have used both these approaches. For numerical integration we have used adaptive Gauss-Kronrod quadrature procedure  [40]  implemented as the Matlab function "quadgk". Advantage of using numerical integration is that the time points can be freely located according to needs, which leads to lower errors. The disadvantage of the method of numerical integration is that it is slower compared to the fast Fourier transform algorithm. t ¼ g À 1 ðtÞ ¼ 1 r ln ð1 þ N 0 rtÞ; ð36Þ The advantage of the fast Fourier transform algorithm is that it its much faster. However, estimating and controlling accuracy is more difficult. Despite problems with controlling accuracy, in the majority of computational examples we have computed Fourier integrals in Eq (35) by using Matlab inverse fast Fourier transform function "ifft", taking advantage of its speed.
For the case of exponential scenarios of population growth we have experimentally verified that a grid with 1000 equidistant time points for τ was sufficient for obtaining relative error 10 -3 for moments of distribution with the transformed time, with n 10 4 and ρ 10 4. As supporting files (S1 File) to this paper we provide Matlab functions and scripts for computing probability distributions of times in the coalescence tree for exponential scenario of population growth, based on the direct method of numerical integration. We have tested these functions for the range of values of the product parameter 0 ρ 10 6 and genealogy sizes n < = 10 4. In the provided programs all parameters are set automatically and the relative errors are 10 -5 or better.
By assuming the value of σ of one or two orders of magnitude higher than true relative round-off errors in computing e j we can obtain the following, conservative, upper bound on MxRelErr MxRelErr < max. The assumed value of σ is approximately of one-two orders of magnitude higher than accuracy of computing e E j in Eq  (21) , which we estimate to be in the range 10 -14 -10 -15. Values of e E j were computed by using Matlab function "expint" with the modification described in  [8] , which allows for obtaining exact function values for wide ranges of argument values. Contemplating values of upper bounds for MxRelErr computed by using Eq (43), shown in Fig  7 , we come to the conclusion that formulae Eqs (  24 ) and (  25 ) for computing allele frequencies f nb can be safely used for sample sizes n up to the range of hundreds of thousands and expect relative errors not higher than 10 -6.
Bound structures are likely formed through conformational selection upon binding, as supported by experimental evidence  [41, 42]. In this study, we will apply RNAsnap along with secondary structure prediction by RNAfold  [43]  to investigate the role of secondary and tertiary structure in temperature adaptation of bacterial rRNA, tRNA, and mRNA. RNAsnap was built based on X-ray structures crystallized at low temperatures. In other words, it is not feasible to determine ASA as a function of temperature. Thus, our investigation of temperature adaptation focused on how RNA sequences encode secondary structure and solvent accessible surface area differently for species with different OGTs. This is a generally accepted practice as there is simple no other alternative to analyze temperature-dependent behavior.
Materials and methods Datasets Three datasets of RNA sequences were built from the bacterial species with known OGTs. We obtained 729 prokaryote species with OGTs compiled by Lobry and Necsulea  [32]  and 131 extremophile species with OGTs available from the BacDive metadatabase  [44]. The scientific names of these species were mapped to NCBI's taxon identifiers (taxids)  [45]. After limiting to bacterial species and only one strain per species, we obtained 536 retrieved taxids to search against the Reference Sequence (RefSeq) database  [46]  for well annotated bacterial genomes. There are 5,507 sequences of 20 tRNA coding genes from 289 species, and 9,624 mRNA sequences from 172 essential protein-coding genes  [47]  in 287 species, and 107 5S rRNA sequences from 107 species (not all the species have the same genes annotated).
Here, we chose 5S rRNA to represent rRNA because 16S and 23S rRNAs were annotated in less than 20 bacterial species. However, the number of 5S RNA sequences is still much smaller than those of mRNA and tRNA. To increase the statistics of 5S rRNA, additional sequences were retrieved manually from the NCBI nucleotide database using the scientific names of bacteria species with available OGT in the BacDive metadatabase. The final set has 158 sequences of 5S rRNA from 158 species. In addition to natural sequences, we also generated random RNA sequences with the same dinucleotide frequencies. Using dinucleotide frequencies, rather than mononucleotide frequencies, for generating random sequences is necessary because RNA secondary structure depends on pairwise stacking energies  [48]. Using Ushuffle  [49] , we randomly shuffled dinucleotide within each original RNA sequence to obtain the corresponding random RNA sequence.
RNA secondary and solvent accessibility prediction We downloaded and installed RNAfold from the ViennaRNA Package 2  [43]. RNAfold predicts the minimum free energy (MFE) of a single RNA sequence using the algorithm of Zuker and Stiegler  [50]  and calculates equilibrium base pairing probabilities using the partition function  [51]. The base pairing probabilities are employed to obtain the percentage of paired nucleotides. All default parameters were employed. The solvent accessible surface area (ASA) of RNA was predicted by the online server of the RNA SolveNt Accessibility Prediction (RNAsnap) at http://sparks-lab. org  [39].
Illustration of predicted and actual ASA values for tRNA and rRNA Before we apply RNAsnap to monitor the relation between OGT and ASA, it is necessary to get a sense of the performance of RNAsnap in predicting ASA by using illustrative examples. We employed Escherichia coli's lysine-tRNA and Thermus thermophilus 5S rRNA, both from PDB 5IB8. This structure was deposited in February 22, 2016 and released in May 25, 2016  [52]. We found that the newly deposited tRNA and rRNA sequences are not in sequencehomologous relation to any RNA chains employed in the training RNAsnap  [39]  based on sequence similarity determined by the software CD-HIT-est  [53]. Thus, it can be considered an independent test example for RNAsnap. and independent test (44 RNA chains) in the original RNAsnap method paper  [39]  and, thus, provided the confidence for our intended analysis on temperature adaptation of solvent accessibility of rRNA and tRNA.
Discussion In this paper, we investigated the dependence of primary, secondary, and tertiary structures (solvent accessible surface area) of structural (tRNA and rRNA) and informational (mRNA) RNAs on OGT. The newly developed program RNAsnap provides an opportunity to examine how RNA sequences code RNA structures differently for species with different OGTs. Different temperature adaptation schemes are observed. The observed role of RNA tertiary structures in temperature adaptation relies heavily on the accuracy of the ASA predictor RNAsnap. We demonstrated its accuracy by applying it to a newly solved crystal structure containing 5S rRNA, Lysine-tRNA structures and a mRNA segment (Fig  3 ). The correlation coefficients between predicted and actual ASA of RNAs are 0. 6 and 0. 7, respectively, consistent with the reported accuracy using larger cross-validation and independent test sets  [39].
Acknowledgments This work was supported in part by  National Natural Science Foundation of China  ( 61671107 ) to YY and JW, by the  Taishan Scholars Program of Shandong province of China, National Natural Science Foundation of China  ( 61540025 ), and  National Health and Medical Research Council  ( 1059775  and  1083450 ) of Australia to YZ. We also gratefully acknowledge the use of the  High Performance Computing Cluster "Gowonda"  to complete this research. This research/project has also been undertaken with the aid of the research cloud resources provided by the  Queensland Cyber Infrastructure Foundation (QCIF).
In addition, assumptions are made about the symmetry of the eyes in research, for example in studies that analyse retinal vascular morphology. These assumptions may not be correct, and in fact, there may be a consistent pattern of asymmetry between our eyes and visual pathways. We now have access to tools that are capable of reliable and precise measures of ocular structure, such as optical coherence tomography (OCT) of the retina, and automated software analysis of the retinal vascular morphology revealed by fundus imaging. We can therefore begin to challenge assumptions of anatomical symmetry by analysis of sophisticated ocular measurements from large studies utilising these tools. Simultaneously, clues to the patterning of the neuroretina are emerging from advances in developmental genetics, with immediate relevance to our understanding of the pathology of ocular disease, as well as how we use statistics to investigate the impact of new treatments on these diseases.
, 2008). However, all the above studies used the older and less precise time-domain OCT (TD-OCT) technology. There is an unfortunate paucity of large population-based studies of healthy individuals using the more precise SD-OCTwith its superior resolution -and little comment on interocular symmetry amongst those that have been published. The Beaver Dam Eye Study was a large population-based observational cohort study of persons aged 43-86 years. 1544 of the participants received SD-OCT examination in 2008-2010, of which 977 were found to be healthy and free of retinal pathology  (Myers et al. , 2015). Unfortunately, no data on interocular symmetry from this dataset of healthy OCT scans has been published. The largest resource of OCT data is the UK Biobank, a long-term cohort study following 500,000 volunteers aged between 40 and 69 years in the UK, of which 67,321 participants have had SD-OCT examination with the Topcon 3D-OCT (Topcon, Tokyo, Japan)  (Keane et al.
although it is of note that RNFL and INL showed the lowest correlation coefficients, with the outer layer unification of posterior photoreceptor, RPE and Bruch's membrane next lowest in right-left concordance (Table  1 ). The weakness of the study is that it preceded the software upgrade on the Spectralis SD-OCT that enabled automatic segmentation of the individual layers. Therefore, the authors manually segmented the layers in image analysis software, before computing layer thicknesses. Nevertheless, it remains the only study to have attempted this interocular symmetry investigation of the full retinal layers. There are far fewer studies investigating the symmetry of outer retinal layers. In part, this is due to a limitation of OCT technology. The reflectance image produced by a SD-OCT machine is often misinterpreted as corresponding exactly to the anatomical neuronal layers.
OCT machine normative databases: Normative databases within the software of SD-OCT machines provide useful visual references of normality for individual patient scanning episodes. However, these normal databases have been incorporated with the assumption of complete retinal symmetry. For example, the Heidelberg Spectralis (Heidelberg Engineering, Heidelberg, Germany) device normative database for macular thickness is based upon a study of 201 healthy volunteers, where one eye was used and the machine now uses that same normative spread identically for each eye,  (Grover et al. , 2009)  Data on the normative database for the Spectralis SD-OCT nSite RNFL thickness protocol is not expressly published, but can be retrieved from the device by generating multiple varied-age hypothetical subjects on the device.
Retinal vasculature software analysis VAMPIRE (Vessel Assessment and Measurement Platform for Images of the REtina) is an international initiative led by the Universities of Edinburgh and Dundee (Scotland, UK). The main software tool is interactive and allows operators to measure efficiently more than 100 morphometric parameters of the retinal vasculature per image in large numbers of fundus camera images. Measurements include classic retinal biomarker candidates like summative measures of vessel calibre near the optic disc, estimates of vessel tortuosity, and the fractal dimension of the vascular network, computed by zone, quadrant and vascular tree. Figure  2  shows intermediate structures computed by the tool, namely the production of a binary map of the vessels, and the analysis of the arteriole and venule size and morphometry.
Images are processed in batches and results saved in tabulated spreadsheets. Further VAMPIRE software tools enable a similar semiautomatic analysis of the retinal images produced by scanning laser ophthalmoscopes, such as Heidelberg Spectralis SLO  (Cameron et al. , 2016)  and the ultra-widefield-of-view retinal images acquired by Optos SLO  (Pellegrini et al. , 2014).
We found only moderate correlations between left and right eyes (r = 0. 403 -0. 582)  (Taylor et al. , 2015). Other features of the retinal vasculature are also thought to reveal abnormalities or have the capacity to demonstrate deviation away from the optimal or healthy network arrangement, and may thus be indicative of disease. We have previously studied vessel tortuosity and branching geometry in the context of right and left eye asymmetry with data from the UK Biobank  (MacGillivray et al. , 2015). We accessed fundus camera images for a subset of participants (n=957). Using VAMPIRE software, 4 operators measured, per image, tortuosity for the 2 thickest arterioles and 2 thickest venules as well as branching geometry for 3-5 arteriolar and 3-5 venular bifurcations from locations detected automatically.
The software calculated the median for each set of measurements in order to summarise arteriolar and venular indices. Ocular bilateral agreement was assessed using intraclass correlation coefficient (ICC) (2-way mixed model) analysis. Single measure coefficients and 95% confidence intervals (CI) are reported. Spearman's correlation coefficient was also used to examine correspondence between right and left eye measurements. Statistical analyses were performed using SPSS software version 22. 0 (SPSS Inc, Chicago, Illinois, USA). While positive but low correlations (<0. 223) were present and significant (<0. 05) for all variables, ICC agreement between retinal parameters measured in separate eyes was poor (<0. 142) (Table  2 ). Bland-Altman analysis revealed average differences between right and left eyes close to zero for all measurements (Table  2 ).
Interocular differences in IOP  (Cartwright and Anderson, 1988; Levine et al. , 2006; Williams et al. , 2013) , optic disc characteristics  (Armaly, 1969; Ong et al. , 1999) , OCT measurements of cpRNFL and macular thickness  (Gugleta et al. , 1999; Sullivan-Mee et al. , 2013) , and visual field sensitivity  (Greenfield et al. , 2007; Levine et al. , 2006 ) are all features that raise suspicion of glaucoma. Indeed an interocular difference in cup-disc ratio of more than 0. 2 has long been quoted as a diagnostic criterion for glaucoma  (Armaly, 1969). The detection of interocular asymmetry in optic nerve or macula parameters has some possible diagnostic advantages over using isolated measures from one eye. For example, OCT normative databases are often used to classify cpRNFL thickness as normal, borderline or outside normal limits, however, normative databases consist of relatively few subjects, and these subjects have homogenous ocular and systemic characteristics  (Realini et al.
, 2015)  (Figure  9 ). Parameters such as cpRNFL thickness exhibit wide overlap between healthy subjects and those with early glaucoma and are influenced by patient-specific factors including age, gender and ethnicity, increasing the chances of patients with different characteristics to those included in the normative database being misclassified. As many of these factors are intrinsic to the individual and will not influence interocular asymmetry, using the fellow eye of the same individual for comparison may overcome some of these limitations  (Sullivan-Mee et al. , 2013). Eye-specific factors such as axial length, which also exhibit wide inter-individual variation, and influence structural measurements, are also likely to be similar between eyes and so have less influence on interocular asymmetry  (Li et al.
, 2013). A patient's fellow eye could therefore serve as a useful comparative reference for the index eye. Several investigators have examined whether assessment of macular or optic nerve asymmetry is useful for discriminating between glaucomatous and healthy eyes and asymmetry analysis is now incorporated in commercial OCT software for glaucoma detection. The Blue Mountains Study, which also examined asymmetry in optic disc parameters in healthy compared to glaucomatous subjects found interocular asymmetry of vertical cup-disc ratio to be more common in those with glaucoma than healthy controls  (Ong et al. , 1999). 24% of those with glaucoma had cup-disc ratio asymmetry of ≥ 0. 2 compared to only 6% of healthy subjects. 10% of those with glaucoma had cup-disc ratio asymmetry ≥ 0. 3 compared to only 1% of healthy subjects.
, 2015). Performance of asymmetry indices is therefore likely to be worse in advanced disease, however in advanced disease, the diagnosis of glaucoma is usually straightforward without recourse to imaging or asymmetry analyses. Detection of early glaucoma is more challenging and in equivocal cases, recognition of asymmetric structural change may prove a useful aid to diagnosis, albeit, used in parallel with raw measurements from each eye. A further limitation of current asymmetry metrics is the lack of a database of ranges of interocular asymmetry in healthy subjects that could inform decision-making regarding likelihood of disease. Jacobsen and colleagues have gone some way to addressing this problem by using the PPAA-protocol to obtain normal values for asymmetry in 105 healthy subjects aged 18 to 45 years  (Jacobsen et al.