dataesr/scientific-paragraphs-categorization huggingface dataset:
Conclusion Here we propose a method for determining a threshold for the interpretation of values obtained with semantic measures. We applied this method to obtain the similarity and particularity thresholds for BP, MF and CC branches of GO and the similarity threshold for the ChEBI ontology. These new thresholds provide new insight on semantic measure results. Using the new thresholds, we showed that the results of comparisons in the HomoloGene database were classified into very different patterns. These new thresholds also better separated orthologs and paralogs in the multigene PPAR family. The new thresholds we proposed are not absolute. As the curves used to define them were rather flat around the minima, we can pick our thresholds from within a relatively large range. The precise threshold values proposed here are only the minimum values of this range.
Similarity threshold variations considering full and partial datasets (Lin's measure). This table summarizes the similarity thresholds obtained considering each complete dataset or all the groups of a dataset except one, when using Lin's similarity measure. The numbers given for FP and FN are the proportions of false-positives and false-negatives that the threshold admits in the These thresholds minimize the proportions of non-informative "+ + +" or "---" patterns according to Table1.
The necessary mathematical results have recently been developed  (Lambert 2010; Lambert and Stadler 2013) , and our aim here is to implement and test a computational framework for application to data. The manuscript is organized as follows. We first describe the model, present the mathematical likelihood expressions, and explain our computational approach. Though already-existing mathematical results are more general  (Lambert 2010) , we confine ourselves here to lifetimes described by gamma distributions, a family of unimodal distributions where both mean and variance can be controlled independently. This family contains as a special case the exponential distribution, corresponding to a constant (ageindependent) death/extinction rate, to which we compare our results. We apply the inference method to simulated trees to rigorously confirm the method's accuracy, investigate power, and identify biases to be expected when age dependency in the death rate is neglected.
W is a differentiable function defined by its Laplace transform: L(W)(y) := ∞ 0 exp(-ys)W(s)ds = 1/ (y) fory > where (y) := y - ∞ 0 g(x)(1-exp(-yx))dx for y ≥ 0 is called the Laplace exponent. Incidentally, the net diversification rate is a root of (see Equation (  3 )) and W(t) is the expected number of species extant at time t conditional on there being at least one  (Lambert 2010). Taking g to be the gamma density given by Equation (1), we can write in closed form as: (y) = y -1-(1+y) -k Numerical Evaluation of the Likelihood Analytical expressions for the scale function W, and in turn the likelihood, are available in the special case k = 1 (exponentially distributed lifetimes; Lambert and Stadler 2013), but not for general k. We thus implement a numerical computational method in Matlab.
A numerical inverse Laplace transform method has previously been developed for stability in calculating scale functions of spectrally negative Lévy processes  (Surya 2008) , which includes the scale function W required here  (Lambert 2010). As a basis we use the Matlab code provided in  Surya (2008) , with parameters of the inverse Laplace transform itself (controlling numerical error in W) set as chosen there. The derivative of W is then approximated with a central difference, where numerical error is controlled through the spacing between points at which W is evaluated. We take 500 grid points evenly spaced on the interval [0,T] (see Supplementary Text), where T is either the stem age, T s , or the crown age, T c , according to the choice of conditioning in the likelihood formula. Node depths in a tree (simulated or constructed from real data) are rounded to the nearest grid point value, thus rounding errors in W are also controlled by grid spacing.
Availability of Code in Matlab and R Our numerical method of likelihood evaluation and optimization is implemented in Matlab. We additionally compile the necessary functions (using 'mcc' in Matlab) into stand-alone applications, which can be used on compatible systems without requiring a Matlab license, thanks to the Matlab Compiler Runtime (MCR) freely available from Mathworks at http:// www. mathworks. com/products/compiler/mcr/. Our Matlab source code and compiled application files are available to download from https://github. com/ cevo-public. We further provide an interface to call these functions in R, included in the package TreePar v3. 2  (Stadler 2011 ) available on CRAN. The steps to set up MCR and apply our method in R are described in the R help pages of the relevant functions  ('create.
Simulated Trees To analyze performance of the inference method, we simulate trees under constant speciation rate and gamma-distributed species lifetimes, the key assumptions of the model described above. We could study performance as a function of either tree size (number of tips, i. e. , sampled extant species) or tree age. We argue that the former is a more informative analysis for empirical systematists, because the number of sampled species is unequivocally known in real data. Sets of simulated trees with a given number of tips are generated using the R package TreeSimGM  (Hagen and Stadler 2013). The package allows two options for obtaining trees with a fixed number of tips; we typically use the more computationally efficient option (denoted 'gsa=FALSE'), which is expected to introduce a slight bias in parameter estimates that decreases with tree size.
This expectation was confirmed by a limited set of simulations repeated with the computationally intensive 'gsa=TRUE' option (see Supplementary Text for details). The TreeSimGM package currently only allows complete sampling (p = 1). To generate an incompletely sampled tree with n sampled tips and given sampling fraction p < 1, we first simulate a tree with n/p tips, then select n tips uniformly at random. This sampling procedure is much more computationally efficient than Bernoulli sampling (where each tip is sampled independently with probability p) when a particular number of sampled tips is desired, and is not expected to yield substantially different patterns in the tree structure. For each final sampled tree, the stem age and list of node depths (including the crown age) are recorded and used for maximum likelihood inference as described above.
Nightshades Data Analysis We analyze a previously constructed phylogeny of 356 extant nightshade species, including 135 SI species and 221 SC species  (Goldberg et al. 2010). This phylogeny represents sampling fractions of p = 0. 162 among SI species and 0. 150 among SC species (see Supplementary Material of  Goldberg et al. 2010 ; we follow these authors in assuming independent sampling). The previous study used a model that assumes speciation and extinction rates depend only on the character state (SI/SC) and incorporates transitions between states. Since our model does not incorporate transitions, we separate SI and SC species in the maximum likelihood tree for our analysis. While transitions from self-incompatibility to self-compatibility are common, there is strong evidence that reverse transitions have not occurred within the family (Goldberg and Igić 2012 and references therein).
We therefore consider the subtree of SI species obtained simply by pruning all SC clades. The end of a species lifetime on this subtree should thus be interpreted as either extinction or a transition to self-compatibility. We treat each clade consisting of only SC species as an independent realization of a fixed model (i. e. , with the same parameter values for all SC clades) arising from one event of losing self-incompatibility. The overall likelihood of the parameters given all SC data is thus taken as the product of the likelihood of the 73 individual clades. SC clade size ranges from 1 to 21 species, and since many (35) clades are singletons, we conduct two analyses: one including all clades with likelihood conditioned on stem age, and one including only nonsingleton clades with likelihood conditioned on crown age as usual.
The total log likelihood of the full (six-parameter) model is obtained, under the assumption of independence, simply by summing the log likelihoods of the SI and SC data as previously determined individually. For each restricted model, we optimize the likelihood jointly over both the SC and SI data sets with the focal parameter restricted to be the same in both. We again obtain results conditioning likelihood on either stem age or crown age of SC clades. We compare each restricted model to the full model using the likelihood ratio test with one degree of freedom.
To fit our age-dependent extinction model to a real data set of interest, the "user" needs a reconstructed phylogenetic tree along with an estimate of the fraction of extant species in the clade that have been sampled. The tree can be derived from any application (though we have focused here on trees of extant species), as long as it is ultrametric, i. e. , all sampling occurs effectively at one time point. More precisely, the information about the tree required by our inference method is the stem or crown age, together with a list (in any order) of speciation times leading to the sampled extant species in the tree. Given this tree information, our freely available Matlab code or corresponding functions in the R package TreePar v3. 2 (see "Methods" section) can be used to obtain MLEs of model parameters (speciation rate and lifetime distribution parameters) and the maximum likelihood value for use in model comparison.
2015). However, a statistical inference method accounting for age-dependent speciation is currently lacking, as trees generated under such a model can no longer be represented by a coalescent point process, and thus the likelihood cannot be derived with previously used mathematical approaches  (Lambert and Stadler 2013). Our second data analysis, involving a phylogeny of self-incompatible (SI) and self-compatible (SC) nightshades, extended previous results concerning the species-level disadvantage of self-compatibility. Our results suggested that the lifetime of SC species not only has a significantly lower mean than that of SI species, in agreement with previous results  (Goldberg et al. 2010; Goldberg and Igić 2012) , but also that it has a higher variance-to-mean ratio. Among SC species, the exponential lifetime distribution (constant rates) model was rejected in favor of a gamma lifetime distribution model where extinction rate decreases with age.
This result is surprising in light of the hypothesis that selfing or asexual species face increasing extinction risk with age due to the accumulation of deleterious mutations  (Johnson et al. 2011). One possible explanation is that the accumulation of mutations in a parent species, though not hindering speciation, continues to have deleterious effects on daughter species; that is, age of the entire clade and not only of the individual species is relevant. Our analysis may also be limited by the small size of the data set and our method of considering each SC clade independently; thus, these initial results should be interpreted with caution. We are not aware of any existing larger reconstructed trees containing both asexual/selfing and sexual/nonselfing species that are suitable for our analysis.
ACKNOWLEDGMENTS We thank  Jeff Joy  and  Sally Otto  for assistance obtaining and interpreting appropriate data sets,  Louis Du Plessis  for technical assistance in making our code distributable, and members of the  Institute for Integrative Biology at ETH Zürich  for helpful comments on this work. We also thank the  Editor-in-Chief ,  Frank Anderson ; the Associate Editor,  Edward Susko ; and several anonymous reviewers, for excellent suggestions that helped us to improve this manuscript.
Taking g to be the gamma density, we have a constant extinction rate (a) = 1/ if and only if k = 1, i. e. , in the special case of an exponentially distributed lifetime. When k = 1, there is no explicit formula for (a), but it can be shown (see Supplementary Text available on Dryad at http://dx. doi. org/10. 5061/dryad. 7894h) that for k < 1 the extinction rate decreases with age, while for k > 1 the extinction rate increases with age. In the limiting case where k →∞ and → 0 simultaneously, with k → , the distribution approaches a Dirac delta, i. e. , lifetimes have a fixed duration of. The choice of a gamma lifetime distribution therefore captures qualitatively different extinction patterns, while containing the previously studied case of constant extinction rate (exponentially distributed lifetime), over which it introduces just one additional parameter.
We introduce a rotated coordinate system in which r i = R ji r j , such that r 1 is along the particle symmetry axis (see Appendix B). This change of basis enables integration of one spatial coordinate. After this operation 260 terms still remain which we program Mathematica R to express in spheroidal coordinates (Appendix C) and integrate over the remaining two spatial coordinates. As a consistency check we have also evaluated the volume integral numerically over all three spatial dimensions by converting to spheroidal coordinates and choosing a specific value of λ. For extreme values of λ the numerics are difficult, nevertheless they serve as a check for a wide range of aspect ratios (see markers in Fig. 2 ).
Although EISCAT_3D will probably not be able to observe the radar gap, the new radar will make important inputs to understanding the coupling processes which occur there, by observing winds and waves in the mesosphere (above) and in the lower stratosphere and troposphere (below), as well as the energetic particles reaching the mesosphere, and looking for evidence of fine-scale structure which would indicate the presence of turbulent mixing. Measuring the dynamics of the atmosphere above and below the stratosphere provides information on which waves are being dissipated at stratospheric heights, while observing energetic particles constrains the modelling of chemical processes which can modulate ozone. Combining EISCAT_3D data with other inputs such as satellite observations of stratospheric dynamics and photometric measurements of ozone content will lead to an improved understanding of the energy balance in the polar middle atmosphere.
EISCAT_3D has a different frequency than most other lower atmosphere radars, and its troposphere/stratosphere observations would therefore be complementary to data obtained by other radars in northern Scandinavia, as well as by satellites and balloon-borne sounders. The volumetric capabilities of EISCAT_3D can also be used at these altitudes, for example to make measurements of wind vorticity on scales of about 10 km. This could be an important parameter for meteorological studies, since it has been suggested that vorticity on this scale may trigger storms  (Schumann and Roebber 2010). The physics of the low-altitude scattering mechanism at these frequencies is also an interesting issue which should be studied, including issues such as the radar cross-section and the spectral index of atmospheric turbulence and its scattering properties, such as aspect sensitivity.
In the future, new multi-satellite missions are expected. The Magnetospheric Multiscale Mission (MMS) is a NASA mission to study the Earth's magnetosphere using four identical spacecraft flying in a tetrahedral formation, building upon the successes of the ESA Cluster mission. The MMS mission was launched successfully on March 12 th 2015. Phased array incoherent scatter radars provide us with comprehensive ionospheric data locally and over medium and small scales. EISCAT_3D is designed to create this opportunity in the Scandinavian sector complementing the existing phased array incoherent scatter radars PFISR in Alaska and RISR in Canada, but providing multi-scale and multi-static observations of plasma parameters, including ionospheric conductivities and electric fields, which can be used to calculate the 3D currents.
In the early 1990s, the EISCAT UHF became the first ISR system to be deliberately applied to the study of meteor head echoes (Pellinen-Wannberg and  Wannberg 1994 , Wannberg et al. 1996). Soon thereafter, all the world's leading ISR facilities joined in. The present EISCAT has offered a possibility to study the properties of the micrometeor population that cannot be resolved by any other radar system. The most important of these has been the tristatic geometry of the UHF radar, which has made it possible to derive the full velocity vector of the radar targets with very high accuracy. Observations have contributed to the database of micrometeor orbits with a view to eventually determining the 3D distribution of sub-millimetre particles at 1 AU with good statistics. However, the UHF system has not by any means been ideal for this purpose, since the scattering cross-section is strongly inversely proportional to radar frequency and hence the number of orbits has been relatively small.
In order to achieve these aims, considerable amounts of computing power will need to be devoted to the signal processing and analysis of the EISCAT_3D data  (Mann et al. 2013). Because the low-level EISCAT_3D data will be very large, some of this capability will need to be deployed at the radar sites and will be devoted to data decimation, data combination, short-term storage, and event detection. Many of these functions will have to be automated, since the volume of data is so large as to be beyond the ability of a human operator to interpret them in real time. Because of this, it is also desirable to store data at the lowest level possible for a limited period, so that decisions made automatically can be revised in the light of later reconsideration, for example if interesting events are found to develop from initially unpromising conditions.
The remainder of the EISCAT_3D storage and computing capabilities will be provided off-site, utilising the power of supercomputing and archiving centres in the various participating countries. These centres will provide the Web-based remote control, data visualisation, and experiment design capabilities required for the operation of EISCAT_3D, as well as the intelligent technology that will make it possible for the radar to respond adaptively to changing conditions, e. g. by changing its aperture characteristics, look directions, coding schemes, and data recording rate. The following sub-sections discuss some specific applications which, while impossible with the current generation of EISCAT radars, will form a fundamental part of the observing capabilities of EISCAT_3D. In each of these applications, EISCAT_3D will serve as a "pathfinder" instrument, where new techniques will be developed into standard observing applications for implementation in the next generation of software radars.
As with volumetric imaging, changes in conditions will imply changes in the required resolution, especially if the ionosphere changes from a relatively quiet state to one having a high degree of horizontal and vertical structure. This type of change is very likely at the auroral latitudes where EISCAT_3D will operate. Another circumstance requiring an adaptive approach to beam forming would be the need to study a particular region of interest as it propagates through an observing region illuminated by a known transmitter pattern. It is worth re-iterating that, in contrast to the changes in volumetric imaging philosophy discussed above, these changes in beam forming strategy can be achieved simply by data postprocessing. The challenge is equivalent to an inversion problem in which the measured set of all samples from every radar antenna is inverted in an optimal way to recover the large-scale structure of the scattering ionosphere, subject to certain constraints on temporal and spatial resolution imposed by the measurement strategy.
33  (see, for example,  Schlatter et al. 2013). The existence of a distributed receiving array, as planned for EISCAT_3D, with receiving elements located up to 2 km from the array centre, allows the reconstruction of ionospheric targets down to tens of metre scales, significantly smaller than the beam widths of the current generation of incoherent scatter radars (La Hoz and Belyey 2011). As before, the most significant part of the imaging challenge lies in data post-processing, since the ensemble of samples from the distributed array elements will already exist but will need to be inverted to recover the small-scale structure. One of the key aspects of this technique, therefore, consists of determining when it is actually needed, in other words determining when (and where within the viewing area) any small-scale structures exist.
For example, although the radar might devote a substantial proportion of its duty cycle to a predefined mode of ionospheric observation, a fraction of its observing time could be simultaneously devoted to other applications such as space debris, while some of its receiver beams could be used for radio astronomy observations, e. g. for solar wind studies via interplanetary scintillation. A major issue, which will drive the development of techniques for all phased array radars of this type, is the question of how these interleaved experiments should change as conditions alter. This question has many aspects: not only how the experimental modes themselves should change, in terms of beam direction, modulation Fig. 35  Schematic showing how the motion of a space debris object, indicated by the red line, could be tracked by using multiple quasisimultaneous beams, as will be available in EISCAT_3D (courtesy of Dr J Vierinen) scheme, or transmitted power, but also how the division of observing time should be re-assigned between competing applications, how the computing resources should be re-distributed between different kinds of data processing, and, perhaps most importantly, the identification of what circumstances would trigger such changes in the observational philosophy.
EISCAT_3D will have a capacity to serve scientists and science in a better way than the present EISCAT has by enabling a more flexible radar scheduling system. While it will still be possible to assign time in advance to pre-defined modes, there will be considerable emphasis on a conditiondependent response to changing conditions. This requires the development of a strong set of criteria specifying what conditions would trigger a change of mode, or what class of phenomenon would require an interruption of "normal" observations, or a significant re-distribution of resources, in order to make detailed observations of its development. One method of achieving this, which should be pioneered using EISCAT_3D, is to make a very strong connection between data and models, with radar (and other) data being assimilated to models in real time and used to predict the future development of the geophysical processes which, in turn, will trigger new modes of observation.
Radar coding and data analysis methods One of the most prominent contributions which the EIS-CAT community has made over the whole 30-year operation of the facilities has been the development of new methods of coding and data analysis to optimise the scientific return from the radars. These include the operational development of techniques such as the flexible re-use of radar samples in correlation (the GEN system, Turunen 1986), the use of modulations based on Walsh codes (alternating codes, e. g. Häggström et al. 1989 , Wannberg 1993 , Lehtinen et al. 1998) , and analysis based on the principles of statistical inverse theory  (GUSDAP, Huuskonen and Lehtinen 1996; Lehtinen and Huuskonen 1996). Many of these techniques are in use, not only at EISCAT but also elsewhere in the worldwide network of incoherent scatter radars.