dataesr/scientific-paragraphs-categorization huggingface dataset:
The TPH+DH set of statistics performs better than all other sets of statistics for all dataset types and bottleneck strengths tested. The power to detect population size reductions of 90% or more is greater than or equal to 0. 95 for all but the worst datasets, whether that be a smaller dataset with higher genetic diversity (Y TPHzDH ~0:95; n~10, l~15, h~0:005), or a larger dataset with lower genetic diversity (Y TPHzDH ~0:95; n~20, l~30, h~0:0015). For smaller datasets with low genetic diversity, however, the power is still low to reject the SNM (Y 0:2N ~0:205; Y 0:1N ~0:373; Y 0:01N ~0:546). To dissect the performance of TPH+DH, we looked at the value of Tajima's D and Fay & Wu's H as a function of the model probabilities for bottlenecks of varying severity. The value of Tajima's D (Figure  4  and Figure  S3 ) decreases with an increase in the severity of the bottleneck.
For small datasets with low genetic variation (n~10, l~15, h~0:0015), the overlap in values of Tajima's D is considerable, even between the SNM (N B ~N) and the most severe bottleneck model (N B ~0:01N), and this is in line with the low levels of power for this type of dataset (Y 0:2N ~0:205; Y 0:1N ~0:373; Y 0:01N ~0:546). Larger datasets (n~20, l~30) reduce the variation, whilst higher levels of genetic variation produce more negative mean values of Tajima's D (large dataset/ low genetic variation: D 0:2N ~{0:40, D 0:1N ~{0:55, D 0:01N ~{0:68; large dataset/high genetic variation: D 0:2N ~{0:55, D 0:1N ~{0:75, D 0:01N ~{0:91). An increase in the severity of the bottleneck causes an overall increase in Fay & Wu's H (Figure  S4 ). There is considerable difference between datasets of low and high nucleotide diversity in the variance of H.
There is just a small shift in the mean of H in datasets with low nucleotide diversity (h~0:0015) as the severity increases, suggest-Table  1. Power and false positive rate for different sets of summary statistics. ing that H is uninformative. However, in datasets with high nucleotide diversity (h~0:005) there is a larger increase in H with increasing bottleneck severity. For the most informative set of statistics (TPH+DH) we performed additional analyses for bottlenecks of different levels of severity (N B ~0:5N and N B ~0:3N) to better understand the relationship between bottleneck severity and the power to reject the SNM (Figure  5A ). The power to detect weak bottlenecks (N B ~0:5N) is low for each of the datasets tested. Contrastingly, for severe bottlenecks with a 99% reduction in the effective population size, all but the most limited datasets have very high power (Y §0:997).
Varying the tolerance We investigated the power of model choice in ABC when the tolerance was varied (Table  S1  and Figure  S5 ). Generally, a stricter tolerance leads to a higher level of power, especially for the TPH set of statistics, where the choice of tolerance is very important. For larger datasets with high nucleotide diversity (n~20, l~30, h~0:005), choosing a tolerance of 0. 001 gives a power of 0. 985 to reject the SNM, whereas using a tolerance level of 0. 005 would result in a much lower power value of 0. 525. Similarly, for large datasets with low nucleotide diversity (n~20, l~30, h~0:0015) there is virtually no power to correctly reject the SNM, except when a tolerance of 0. 0001 is used, which gives a power value of 0. 688. However, a stricter tolerance leads to a higher rate of false positives, with rates reaching a maximum of 1.
7% (n~20, l~30, h~0:005, tol = 0. 0001) and 3. 2% (n~20, l~30, h~0:0015, tol = 0. 0001) for the TPH and SFS5 set of statistics respectively. The choice of tolerance appears to decrease in importance as the summary statistics capture more features of the site frequency spectrum. Tolerance levels of 0. 01, 0. 005 or 0. 001 all give similar levels of power for the SFS5 set of summary statistics, with notable decreases being observed only with the most extreme tolerances (0. 1 and 0. 0001). It is worth noting however Figure  3. The impact of bottleneck severity and dataset quality on model probabilities and summary statistics. The effect of bottleneck strength on the value of summary statistics and model probabilities for larger datasets (n = 20, l = 30) with low (h~0:0015) or high (h~0:005) levels of genetic variation.
Finding the optimal dataset size In population genetic studies of natural populations there may be limitations on the quality of the dataset available for sampling. It is therefore of interest to ask how many samples or loci need to be obtained in order to have a 95% power to detect a bottleneck. We therefore extended our analyses, using the most informative set of summary statistics (TPH+DH), to include datasets with samples of between 5 and 40 individuals, where the number of loci varied between 1 and 60 and the level of genetic variation was low (h~0:0015). Figure  5B  shows the power as a function of the product of the number of samples (n) and loci (l) as this can be seen as being proportional to the sequencing cost of a study. The relationship between Y and nl is sigmoidal, with the addition of loci and samples increasing the power above 95% when nl §600.
However, the contributions of the number of samples and loci to the power is not equal, with datasets having more power when lwn. Figure  5  also shows the power to reject the SNM in favor of a BNM for a different number of samples when the number of loci are limited (l~15 or 30; Figure  5C ) and for a different number of loci when the number of samples is limited (n~10 or 20; Figure  5D ). When the number of loci are limited to 15 the power to reject the SNM remains well below 95%, even for large sample sizes (Y n~40 ~0:762), and the relationship appears to be asymptotic. Increasing the number of loci to 30 greatly increases the power such that sampling more than 20 individuals means that the power is greater than 95%. When the number of samples are limited 95% power is reached when *50 and 30 loci are used for sample sizes of 10 and 20 individuals respectively.
Parameter estimation To assess the ability of ABC to estimate parameters of a BNM in limited datasets, we performed parameter estimation using the local linear regression method described in  [1]. Figure  6  and Table  3  summarize the distribution of the means of the posterior distributions for each replicate under a BNM for large datasets (n~20, l~30). The parameter h is estimated well by three of the four sets of summary statistics. SFS3, however, gives a very poor estimate of h (0. 00413) in low diversity samples, whilst the estimate is far better in high diversity samples (0. 00475). The time of the bottleneck (T) was estimated better in the high diversity samples than in the low diversity samples, with an increase in nucleotide diversity also decreasing the variance of the posterior means.
The effective population size during the bottleneck (N B ) is estimated well for TPH+DH in both the low and high diversity datasets. For the rest of the sets of summary statistics, samples with high nucleotide diversity give better results. Table  S2  shows the proportion of replicates where the true value lies within the 90%, 50% and 10% credible intervals of the parameter posterior distributions. One notable observation is that, for SFS3, the proportion of replicates in which the true value lies within the credible intervals is surprisingly high. This is particularly striking for high levels of variation and 10% credible intervals where a proportion of 0. 578 was found for SFS3, compared to much smaller values for the other summary statistics  [7]. It is also interesting to note that, for each parameter for TPH+DH, the proportion of replicates where the true value lies within the credible intervals is better for low nucleotide diversity (h~0:0015) than for high nucleotide diversity (h~0:005).
While our results generally support this, we do find some limited evidence to the contrary in datasets with low genetic diversity where the power is lower for T+SFS3 compared to the SFS3 set of summary statistics. Accordingly, a number of methods have been established for identifying informative summary statistics in relation to estimating parameters. For example,  [20]  weight statistics according to the information they give for a parameter of interest, whilst  [21]  implement a partial least-squares transformation of the summary statistics and  [22]  apply a machine learning technique (boosting) to find the most informative summary statistics. More recently, research has moved towards identifying summary statistics for model choice. [19]  use logistic discriminant analysis to process summary statistics before model choice,  [23]  weight the summary statistics for model choice after a preliminary regression step and  [24]  derive conditions under which summary statistics are sufficient for selecting the true model.
While we find PCA to be a highly informative way of summarizing the data, it may not be enough to simply perform PCA and look for patterns in the summary statistics. Some results of our analyses were counter-intuitive, such as the finding that the T+SFS3 set of summary statistics performed worse than SFS3 in datasets with low genetic diversity. This suggests that there can be a complex relationship between some summary statistics and the parameters of the model. This may be the case in the above example where Watterson's h only adds noise rather than any additional information to the low diversity datasets and could, as discussed above, be due to the curse of dimensionality. However, the SFS3 set of statistics estimates the parameter h poorly. This may be due to the use of the relative instead of the absolute site frequency spectrum, as information in the absolute SFS regarding h is lost when it is re-scaled.
This draws to attention an interesting problem concerning the choice of summary statistics in ABC. A set Figure  5. The effect of sample size and the number of loci on power. The power to reject the SNM, for the TPH+DH set of summary statistics, as a function of (A) the bottleneck severity (expressed as the relative effective population size N B ), (B) the product of the number of loci and the number of samples (N B ~0:1N, h~0:0015), (C) the number of samples (N B ~0:1N, h~0:0015), and (D) the number of loci (N B ~0:1N, h~0:0015). In B, C and D the dotted line corresponds to a power of 0. 95. doi:10. 1371/journal. pone. 0099581. g005 Figure  6. Parameter estimation for different sets of summary statistics. Boxplots showing the distribution of mean values of the 1000 posterior distributions for the replicates for the population scaled mutation rate (h), the time of the bottleneck (T) and the strength of the bottleneck (N B ) for datasets with low (h~0:0015) and high (h~0:005) genetic variation.
ABC in non-model organisms The amount of data available for genetic studies of non-model organisms is often limited, and so it is important that sequencing and sampling efforts are directed towards maximizing the amount of information available for ABC. Specifically, we find that there are a number of factors that govern the power to distinguish between two competing models. In particular, the level of genetic variation is important and this inevitably has consequences on the number of loci and samples required. Here, we considered the power afforded to sequence data, but other types of markers, such as microsatellites, are more variable and would give more information. For our low variation datasets (h~0:0015), around 20 individuals and 30 loci would be required in order to have a 95% power to detect a strong bottleneck (N B ~0:1N).
In the more variable dataset (h~0:005), around 10 individuals and 15 loci would give the same power. In general, and in agreement with expectations of the coalescent  [26] , we find that sampling more loci rather than individuals is of greater benefit in increasing the power. It is also important to acknowledge that there is a limit to what one can say with a limited dataset. Our analyses dealt with relatively strong bottlenecks, and these represent quite drastic demographic events. Weaker events will undoubtedly affect genetic data in a subtler way that is harder to detect and therefore requires more data, whether that be more loci, individuals or more variable markers. However, in general we find that the power to detect a bottleneck increases with the severity of the bottleneck. Large samples of loci and individuals are required to detect mild bottlenecks and this is likely to generalize to parameters in other models.
Similarly,  [27]  found that there is lower power to detect a weaker migration rate in an isolation-with-migration model. However, even if bottlenecks with a reduction in the population size of 99% or more can de detected with the correct summary statistics, it is unclear how often bottlenecks of this magnitude occur in natural populations. There are examples (e. g. [9] : *3% of current size;  [28] : *1:5% of current size), especially in domesticated species (e. g. [29] : *0:5% of current size), where drastic reductions in the effective population size have been inferred. However, it may be the case that weaker bottlenecks, or more subtle temporal variation in the effective population size, are more frequent but that we simply do not have enough power to detect them with the datasets at hand.
In general, the approach of ABC in summarizing the data into summary statistics is relatively reliable for estimating parameters  [8]. Although this seems to be true in most cases, we find that this does not hold in cases where the summary statistics are less informative. This is exemplified by the poor estimate of h by the SFS3 set of summary statistics. This appears to be resulting from the priors, that are uniformly distributed between 0 and 0. 01. When the summary statistics offer no information on the parameters of interest then the expected value of the parameter will be the mean of the prior distribution. In this case, the parameter estimate of h would approach 0. 005 as the summary statistics become less informative, and would explain the poor estimate of h in low diversity samples (0.
00413). A sensitivity analysis might therefore be an important step in determining the influence of the prior over the posterior distribution. This may also be influencing the other parameters. T and N B appear to be overestimated when the data or summary statistics are insufficient, and so these parameters could tend to the mean of the prior distribution if the dataset or summary statistics are insufficient. There are a number of ways that the estimation of parameters and model choice can be improved. The euclidean distance metric is most commonly used for assessment of the fit of the simulated data to the observed data, but other metrics may provide a better measure. Another common step is to even out the contribution of each of the summary statistics through a normalization step that conforms them to the same standard deviation, and this could lead to improvements in parameter estimation.
Conclusions Our analysis of the power of ABC model choice in limited datasets suggests that careful consideration of the number of loci and samples is critical when designing a study. Even in scenarios as simplistic as the one examined here, under some conditions, there is simply not enough information contained in the data to confidently separate two distinct models. While ABC in principle allows testing for very complex demographic histories, the amount of information that can be extracted from a given dataset is likely to limit power to make more subtle inferences. However, certain parameters, such as the number of samples, the number of loci and the level of genetic variation, can be used fairly reliably to predict the power of a study to separate different models. What's more, if suitably informative summary statistics are used together with an appropriately large dataset then, in general, ABC model choice is relatively powerful and quite conservative with regard to the false positive rate.
Demographic models and simulated datasets We test the power of ABC by comparing two simple population genetic models, each simulated under a coalescent model. The coalescent is a backward in time simulator of a population of gametes that can be subjected to a number of evolutionary forces. The genetic variation in a population of gametes is determined by the mutation rate per generation (m), and the effective population size (N). The level of genetic variation in a population is then defined as the product of these two parameters: h~4Nm. Two coalescent models were considered, the first of which consisted of a population of effective size N (haploid individuals) that remain constant through time (SNM). For the second scenario, a bottleneck model (BNM) was considered where an instantaneous reduction in the population size occurs at 0.
2 coalescent time units (t) in the past (measured in 4N generations), and persists for a period of 0:2t before returning to its original size. For each demographic model, 1000 datasets were simulated whereby the levels of nucleotide diversity (assuming an infinite sites model) and number of samples and loci were varied. For the majority of analyses, we considered a sample size (n) of 10 or 20 individuals (where a population consists of 2N gametes), with 15 or 30 loci sequenced (750 bp each in length) and two levels of genetic variation with per base pair scaled mutation rates of h~0:0015 or h~0:005 (where h~4Nm). For the majority of simulations in the BNM, the relative population size during the bottleneck (N B ) was 0:1N, although we also varied this parameter (0:5N, 0:3N, 0:2N, 0:1N and 0:01N) to assess the performance of ABC in detecting bottlenecks of varying severity.
The population scaled recombination rate, r~4Nr, was set to 0. 01/bp in each model. For each of these simulated datasets the mean, standard deviation and 5% and 95% quantiles across loci were calculated for  Watterson   [34] ) and the number of segregating sites (S, S sd , S 05 , S 95 ). The relative site frequency spectrum (SFS) was also summarized by the average proportion of segregating sites that occur within each of three or five evenly sized frequency classes (s1, s2, s3, s4, s5). These represent population genetic statistics that are thought to summarize population sequence data in the most informative way (see for example,  [17, 25, 26] ). For the analysis of the power and false positive rate of ABC we combined a number of summary statistics: TPH (h W , p, H e ), SFS3 (folded site frequency spectrum in 3 bins), T+SFS3 (h W , folded site frequency spectrum in 3 bins), SFS5 (folded site frequency spectrum in 5 bins) and TPH+DH (h W , p, H e , D, H).
Model choice, power and parameter estimation Joint posterior densities were simulated for each of the two ABC models using 10 6 draws from uniformly distributed priors. The prior bounds for the SNM and BNM were (0, 0. 01) and (0, 0. 02) for h and r, respectively. Time was measured on a scale of 4N generation. For the BNM, the time (T) of the bottleneck (looking backwards in time) was sampled from a prior with bounds (0, 1. 5), with the relative population size during the bottleneck (N B ) having bounds of (0, 1). The relative ancestral population size and the duration of the bottleneck were fixed as 1 and 0:2t respectively. ABC was performed using the python library EGGLIB  [37] , which implements the Euclidean distance-based, local linear regression method described in  [1]. Model choice was performed using the rejection-based method implemented in EGGLIB, with model probabilities being defined as the proportion of simulations belonging to each model after the ABC rejection step.
This work was supported by the  European Community 's  Seventh Framework Programme  ( FP7/20072013 ), under grant agreement  211868  ( Project Noveltree ) and the  Eranet Biodiversa LINKTREE  and TIPTREE projects. M. Siol  and  S. De Mita  were funded by  Agropolis Fondation. The research trip of M. Stocks to IRD was funded by the  EBC  graduate school on Genomes and Phenotypes at  Uppsala University. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Acknowledgments We would like to thank  Marcos Alexandrino ,  Vicente Cortés ,  Thomas Grimm ,  Nigel Hitchin ,  Dominic Joyce ,  Ruben Minasian ,  David Morrison ,  Raffaele Savelli ,  Dirk Töben ,  Daniel Waldram  and  Frederik Witt  for useful discussions. This work was supported in part by the  ERC  Starting Grant 259133 -ObservableString, and by projects  MTM2011-22612  and  ICMAT Severo Ochoa   SEV-2011-0087  (Spain) and  Pesquisador Visitante Especial  grant  88881. 030367/2013-01 ( CAPES/Brazil ).
PLUTO 04005-p. 2 EPJ Web of includes optically thin radiative losses modeled with a cooling function Λ(T ) that depends on temperature T , and that is derived from the APED V1. 3 atomic line database  [21] , assuming complete ionization of the plasma. The accretion column is modeled with a 2D axisymmetric simulation, from which we have built a 3D structure by rotation around the accretion direction represented by a z-axis. MHD equations and details on the basic physical modeling are described in  [10]. The accretion stream is perpendicular to the chromosphere. The magnetic field is strong (500 G), so that the plasma β parameter (β = p gas /p magnetic < 1). Figure  1  shows the structure of the accreting column and its surrounding environment. We propose to determine the radiative components of the momentum and energy conservation equations, by solving the 3D RTE with the IRIS code  [22].
Acknowledgments It is a pleasure to thank  Giulio Bonelli ,  Davide Fioravanti ,  Domenico Orlando ,  Vladimir Rubtsov  and  Maxim Zabzine  for discussions, and  Maxim Zabzine  and  Jian Qiu  for sharing a version of their paper in preparation. The work of F. P. is supported by a  Marie Curie International Outgoing  Fellowship FP7-PEOPLE-2011-IOF, Project n o 298073 (ERGTB). A. T. thanks  EPSRC  for funding under the  First Grant  project  EP/K014412/1  " Exotic quantum groups, Lie superalgebras and integrable systems ", and the  Mathematical Physics group  at the  University of York  for kind hospitality.
Acknowledgements. Some work on this paper was undertaken during a visit of AS and SW to the  University of Leeds in June 2012 , funded by  EPSRC  grant  EP/I026819/I. They thank the faculty of the  School of Mathematics  for their hospitality. The authors would also like to thank  Jan Cameron ,  Caleb Eckhardt ,  David Kyed ,  Roland Vergnioux  and the anonymous referee for valuable comments and advice.
Acknowledgements. This work was partially funded by the  ANR-08-JCJC-013-01  project  M3RS , headed by  Céline Grandmont , and by the  ANR-11-TECS-0006  project  OxHelease , coordinated by  Caroline Majoral. BG  and FS also want to acknowledge the  Reo  project-team from  Inria Paris-Rocquencourt , for its hospitality which allowed to carry out this article.
Background: Alirocumab is a fully human monoclonal antibody to proprotein convertase subtilisin kexin type 9 (PCSK9) under investigation for treatment of hypercholesterolemia and reduction of cardiovascular events. Methods/design: The COMBO studies, part of the Phase 3 ODYSSEY clinical trial program, are designed to evaluate the efficacy and safety of alirocumab as add-on therapy to stable, maximally tolerated daily statin, with or without other lipid-lowering therapy (LLT), in a planned 966 patients with hypercholesterolemia at high cardiovascular risk. COMBO I (http://clinicaltrials. gov/show/NCT01644175) is placebo-controlled, with a double-blind treatment period of 52 weeks, and 306 planned patients who may receive other LLTs in addition to statin therapy. COMBO II (http://clinicaltrials.