dataesr/scientific-paragraphs-categorization huggingface dataset:
Overall, applying a 5% MAF threshold on Pool-Seq data (even with =2. 5 ) to remove false SNPs (see above) allowed recovering the performances similar to that obtained when analyzing datasets with no sequencing error. Finally, it is worth stressing that analyzing Pool-Seq data as allele counts, whatever the coverage or MAF threshold considered, lead to no power in detecting admixture event with f 3 or f 3 based tests due to a strong upward estimation bias. Tables  4  and S3    ii) 15 different Pool-Seq read count data (five mean coverages λ and three sequencing error rates ); and iii) Pool-Seq read count data simulated with = 0 treated as allele counts (corresponding results of this bad practice are highlighted in italics and ). Each TPR was computed from the analysis of 250 independent datasets (generated from the data simulated under Figure  1  demographic scenario) as the proportion of f 3 with an associated Z-score < -1.
Likewise, all FPR remained low (≤ 0. 15%), although increasing with MAF thresholds (more than twice higher for a given type of data when increasing the MAF threshold from 1% to 5%). Overall, sequencing errors and coverage had no impact on the performance of the f 4 -and D-based test of treeness. As expected, analyzing read counts as allele count data did not affect the performance of these tests (see Discussion ii) 15 different Pool-Seq read count data (five mean coverages λ and three sequencing error rates ); and iii) Pool-Seq read count data simulated with = 0 treated as allele counts (corresponding results of this bad practice are highlighted in italics and ). Each TPR was computed from the analysis of 250 independent datasets (generated from the data simulated under Figure  1  demographic scenario) as the proportion of f 4 with an associated absolute Z-score < 1.
Precision of the F 4 -ratio based estimation of the admixture rate α Given the simulated scenario, two different ratios of f 4 estimates could be used to estimate the admixture proportion α = 0. 25 (Figure  1 ), namely α1 = f 4 (P1,P4;P3,P6) f 4 (P1,P4;P2,P3) and α2 = f 4 (P1,P5;P3,P6) f 4 (P1,P5;P2,P3)  (Patterson et al, 2012). The graph. params2symbolic. fstats function (Table  2 ) may also prove useful to identify appropriate quadruplets (Supplementary Vignette V2). We used the compute. f4ratio function to obtain these two estimates from all the simulated datasets together with their 95% CI (defined as α ± 1. 96 σα where σα is the block-jackknife standarderror estimate). Tables  5  and S4  provide the mean of the estimated α1 and α2 respectively over the 250 analyzed datasets for each of the 42 investigated configurations.
Evaluation of graph fitting We further estimated for all the simulated datasets branch lengths in drift units and admixture proportion α with their 95% CIs by fitting the simulated graph with fit. graph. Table  5. Comparison of F 4 -ratio based estimation of the simulated admixture proportion α in Figure  1  scenario for different types of data processing poolfstat analyses. For each MAF threshold (MAF> 1% or MAF> 5%), the table gives the mean of the estimated α = f 4 (P1,P4;P3,P6) f 4 (P1,P4;P2,P3)) (across 250 independent simulated datasets) for 21 different types of analyses relying on i) allele count data; ii) 15 different Pool-Seq read count data (five mean coverages λ and three sequencing error rates ); and iii) Pool-Seq read count data simulated with = 0 treated as allele counts (corresponding results of this bad practice are highlighted in italics and ).
Note that the branches P8 ↔ R and P9 ↔ R that are connected to the root R (Figure  1 ) can only be estimated jointly (as τ P8↔P9 = τ P8↔R + τ P9↔R , R being arbitrarily set in its middle). At the 5% MAF threshold, very similar performance were obtained for the allele count and the different Pool-Seq datasets whatever the simulated read coverage or sequencing error rates (Figures  4A, 4B,  and 4C ). Hence, mostly unbiased branch lengths were estimated for the four leaves (terminal branches) τ P1↔P7 , τ P2↔S 1 , τ P6↔S and τ P3↔S 2. As previously observed with α, the estimated 95% CI's remained too narrow particularly for τ P2↔S 1 for which less than 50% of the CI's contained the true value (Table  S7 ) compared to more than 80% for τ P1↔P7 (Table  S6 ). As expected from the the drift-scaling approximation, the estimated branch lengths tended to be slightly downwardly biased (ca.
2%) for the two other leaves (τ P4↔P9 and τ P5↔P9 ) but the estimated 95% CI displayed similar characteristics since from 48. 0% to 87. 6% contained the true values, the proportion increasing in Pool-Seq datasets when coverage and sequencing error decreased (Tables  S10  and S11 ). Conversely, the internal branch lengths tended to be upwardly biased from a slight (ca. 2%) for τ S 1↔P7 , τ P7↔P8 and τ S 2↔P8 (Tables  S12  to S14 ), to a moderate amount (ca. 20%) for the root including branch τ P8↔P9 , the true value being then always outside the estimated 95% CI's (Table  S15 ). Yet, when analyzing data with a lower MAF threshold of 1%, this bias almost completely vanished (Figure  S4  and Table  S15 ). For the other branches, the estimates had similar characteristics (yet with a slightly decreased performance for the τ P4↔P9 and τ P5↔P9 leaves) for allele count data or Pool-Seq data simulated without sequencing error (Fig-  ure S4A ).
Evaluation of graph construction To provide insights into the reliability of graph construction, we evaluated the performance of the add. leaf function in positioning the admixed population P6 on the underlying (((P1,P2),P3),(P4,P5)) tree (Figure  1 ) for the different types of simulated datasets. Table  S16  gives the proportion of correctly inferred admixture graphs (i. e. , corresponding to the simulated scenario) with a ∆ BIC > 6 support with all other tested graphs over the 250 analyzed datasets for each of the 42 investigated configurations. As the reference tree with rooted topology (((P1,P2),P3),(P4,P5)) consists of eight branches, P6 may be connected with either i) nine non-admixed edges (connection to either one of the eight branches or as an outgroup) or; ii) 8 2 -1 = 27 admixed edges from two-way admixture events.
Structuring of genetic diversity across the 14 populations Overall, the estimated global F S T across the 14 populations was 7. 03% (95% CI; [6. 90%; 7. 32%]). Estimates of all the pairwise-population F S T confirmed that populations tended to cluster according to their geographic area of 29   S1 ). In D), the read count data were analyzed as allele counts which corresponds to a bad practice. Note that the two branches coming from the root are combined since the position of the root is not identifiable by the model (i. e. , τ P8↔P9 = τ P8↔R + τ P9↔R ). Note that the box plots obtained from the analysis of count data are replicated in each panel for comparison purposes. For each branch, a red dotted line indicates the underlying simulated value. For Pool-Seq data, the overall MAF was estimated from read counts.
2017 ) also provides several alternative valuable utilities for the fitting (based on a slightly different approach), the manipulation, and the visualization of admixture graphs together with utilities for the plotting of the statistics with their confidence intervals or the symbolic derivation f -statistics (as poolfstat). Overall, our effort of developing with poolfstat a self-contained, efficient and user-friendly R package capable of performing the entire workflow for f -statistics based demographic inference from both standard allele count and Pool-Seq read count data will hopefully make such a powerful framework accessible to a wider range of researchers and biological models.
As a result, simply increasing the threshold on the overall MAF (computed from read counts over all the pool samples) to 5% allowed to remove all the spurious SNPs and recover accurate estimates of the parameters at the lowest read coverages. In agreement with original observations made for allele count data  (Patterson et al, 2012) , all the f -statistics based analyses (i. e. , three-population test of admixture, four-population test of treeness, F 4 -ratio estimation of admixture proportions or admixture graph fitting) remained remarkably robust to a MAF-based ascertainment process. From our simulation study, discarding lowly polymorphic SNPs was only found to increase the bias of the drift-scaled length estimates of internal branch in admixture graph. In practice, cost-effective designs consisting of sequencing pools of 30 to 50 individuals at a 50-100X coverage and applying MAF threshold of 5% to filter the called SNPs are expected to provide good performance for all the different f -statistics based inference methods we presented here.
In D), the read count data were analyzed as allele counts which corresponds to a bad practice. Note that the two branches coming from the root are combined since the position of the root is not identifiable by the model (i. e. , τ P8↔P9 = τ P8↔R + τ P9↔R ). Note that the box plots obtained from the analysis of count data are replicated in each panel for comparison purposes. For each branch, a red dotted line indicates the underlying simulated value. For Pool-Seq data, the overall MAF was estimated from read counts. 30.
3. 1. 3 Figure 3. 133 Figure 3. Comparison of poolfstat and AdmixTools estimates across 250 simulated allele count datasets (AC m≥1% ). A) All estimates of the 15 basis f -statistics taking P1 as the reference population and corresponding to 5 f 2 of the form (P1,Px) and the 10 f 3 of the form (P1;Px,Py) (with x = 2,. , 6; y = 3,. , 6 and y > x). B) All Block-jackknife estimates of the covariance matrix Q of the 15 basis f -statistics (15 error variances and 105 error covariances). C) All estimates of the 60 f 3 (scaled f 3 ) and their associated Z-scores (D). E) All estimates of the 45 D-statistics (scaled f 4 ) and their associated Z-scores (F). For each comparison, the Mean Absolute Difference (MAD) between the parameter estimates of the two programs are given on the upper left corner of the plots.
5 in panel B) and C) respectively (TableS1). In D), the read count data were analyzed as allele counts which corresponds to a bad practice. Note that the two branches coming from the root are combined since the position of the root is not identifiable by the model (i. e. , τ P8↔P9 = τ P8↔R + τ P9↔R ). Note that the box plots obtained from the analysis of count data are replicated in each panel for comparison purposes. For each branch, a red dotted line indicates the underlying simulated value. For Pool-Seq data, the overall MAF was estimated from read counts. 30.
Furthermore, as detailed in Supplementary Material, we assume a snapping heuristic to existing infrastructures to keep a consistent network. This infrastructure optimization problem considerably increases the operational computational cost, and we use an heuristic exploring a fixed number N I of randomly chosen infrastructures. In practice, we take N I = 50 which gives a reasonable coverage of possible choices with a realistic computational time for each model run. Low values for N I will lead to random infrastructure choices, while high values will imply an exhaustive search, ensuring that the infrastructure segment is optimal. The model is open-source, and its implementation is available on the open repository of the project at https: //github. com/JusteRaimbault/TransportationGovernance.
Simulation results used in this paper are available on the Dataverse repository at https://doi. org/10. 7910/DVN/V3KI2N and our modelling framework is thus reproducible by external readers. Regarding technical requirements to run the model, no specific constraints in terms of memory or number of cores exist to simply run the model with reasonable world sizes (less than a width of 50). To run numerical experiments described below, and in particular calibration, high performance computing infrastructures are needed as a high number of model runs (often more than 10,000) are required. All model parameters are summarised in Table  1. We describe here only the parameters which have not been explicitly fixed previously, and these will be the privileged parameters on which the exploration and the application of the model will be done.
Model exploration and validation In this section, we detail the validation and exploration of the theoretical model for: land-use module only (to control the sprawl speed), governance module only (to test for the influence of coordination between planning actors), and both modules activated (co-evolution), to test the condition of emergence of a coordination at MCR scale. The idea is to proceed to elementary experiments by making either land-use, or network, or both, evolve, and studying the consequences on the different aspects. Numerical experiments are realised using the OpenMOLE model exploration software  (Reuillon et al. , 2013) , which (i) can embed any model as a black box; (ii) integrates state-of-the-art methods for the exploration, calibration, and validation of simulation models; (iii) provides a transparent access to high performance computing environments such as clusters and computation grids.
Furthermore, our contribution opens new perspectives towards systematic testing of governance structures: for instance it can be used to assess the spatial organization at MCR level that are the most likely to be associated with the emergence of an integrated governance, following work by Le  Néchet (2019) , and in line with the work of  Nowak et al. (1994)  on stable cooperation configurations in game theory. A fundamental limitation to such developments however remains the sparsity of spatial and dynamical databases covering both land-use and the evolution of transportation networks. Historical land-use data are already widely used to calibrate LUTI and land-use change models, but they generally cover shorter time spans than required to grasp the evolution of infrastructure. The construction of open and harmonised databases for the dynamics of transportation networks on long time scales is still an ongoing research issue.
Finally, the approach we adopted, using intensive computation and model simulation, also shed a light on more general issues of model validation for interaction models between transport and territories. Crucial research directions in this field indeed include (i) a more systematic benchmark and validation of existing models, in the spirit of  Bonnel et al. (2014) ; (ii) the development of new methods to evaluate and calibrate interaction models, since existing examples such as methods developed by  Capelle (2017)  rely on model-specific techniques. On the contrary, methods included in the OpenMOLE model exploration software  (Reuillon et al. , 2013)  are generic and provide a new type of knowledge on complex simulation models.
They have greatly participated to revealing the importance of the so-called ocean mesoscale and submesoscale dynamics, which typically refer to horizontal scales from a few hundreds of meters to hundreds of kilometers. While satellite altimetry data cannot solve scales below ∼100 km due to narrow-swath sampling patterns, other technologies have been developed such as drifters, high-frequency (HF) radar technologies or SAR imaging  [6]. Their space-time sampling however involve some limitations to fully inform sea surface dynamics on a global or even regional scale. Following  [2, 3] , this work further explores the potential of AIS data streams to infer sea surface dynamics. The irregular space-time sampling of AIS data, the complex relationships between ship trajectories and sea surface conditions as well as the absence of a consistent ground-truth dataset of fully observed fields make this objective particularly challenging.
• Numerical experiments for a real dataset demonstrate the relevance of the proposed approach with respect to state-of-the-art approaches. As case-study region, we focus on the Aghulas current off South Africa. This region involves challenging and complex sea surface dynamics for altimetry products. We report significant improvements up to 40% w. r. t. state-of-the-art altimetry-derived assimilation-based products  [8, 9]. The paper is organized as follows. Section 2 briefly reviews related studies and presents the considered observation model. We describe the proposed learning-based approach in Section 3. In Section 4 we report numerical experiment and benchmark with state-of-the-art product on a real case-study and Section 5 provides concluding remarks.
• Y the available set of AIS messages over a time period [0, T]; • U the spatio-temporal sea surface current field we aim to reconstruct; • V an external dataset of sea surface current fields that we consider realistic such as reanalysis product or numerical simulations. We state the reconstruction of fields U from observation data Y as the solution of the following optimization problem: U * , Θ * = arg min U,Θ J(U, Y) + λ U R Θ (U) + λ V R Θ (V) (3) where J(U, Y) is the observation term derived from the linear observation model, R Θ a regularization term with trainable parameters Θ, which applies to unknown state U and R Θ a regularization term with the same trainable parameters as R Θ , which applies to external dataset V. λ U and λ V are weight parameters balancing the regularization terms w.
Trainable Regulatization Terms The considered space-time dynamical prior falls in the category of deep generative models  [31]. Variational learning techniques, especially VAE schemes, are among the state-of-the-art methods to train generative models. Broadly speaking, VAEs aim to model the distribution of random variables x using latent variables z. The joint distribution of (x, z) is stated as p(x, z) = p(x|z)p(z) where p(z) and p(x|z) are given by some parametric forms. Under this framework, we would typically aim to maximise the likelihood of the observations w. r. t. model parameters. This would lead to the computation of the likelihood of the observed data as p(x) = p(x, z)dz. However this integral is generally intractable. To address this problem, VAE frameworks  [32]  introduce an inference model q(x|z), which is trained such as q(x|z) approximate the true posterior p(z|x).
Training and Evaluation Phase Given variational formulation Equation (  2 ) and the neural-network-based components introduced in the previous sections, we end up with an end-to-end learning framework. Given some AIS dataset Y, the training phase aims to solve minimization Equation (3) w. r. t. both sea surface currents U and all model parameters Θ. For the training phase, we may emphasize that Equation (3) includes a regularization term R Θ (V) computed over a representative dataset of exemplars of sea surface current fields. As AIS data streams involve an irregular and sparse space-time sampling of the space-time domain conditioned by maritime traffic routes, such exemplars shall provide additional information to constrain the space-time variability encoded by the latent ODE representation.
In our implementation for minimization (3), we use Adam optimizer for model parameters and a fixed step gradient descent for retrieving initial conditions of Equation  (5). Given a trained model with parameters Θ, we may solve minimization (2) to reconstruct the sea surface currents associated with any new AIS dataset. Similarly to the training phase, we consider a fixed-step gradient descent optimizer. We may point out that in this case term R Θ (V) may be dropped from minimization (3).
Experimental Setting As case study region, we consider a region off South Africa, which involves a dense maritime traffic. This area associated with the Aghulas current exhibits complex upper ocean dynamics and is considered as a challenging region for current estimation using satellite altimetry  [34]. The collected AIS dataset covers 240 days in 2016 with more than 4 millions of AIS messages. Figure  3  provides an illustration of the daily sampling pattern of the AIS data. To account for the seasonal variability of upper ocean dynamics in the case study area, we apply and evaluate the proposed approach to three different distinct periods of 80 days, namely • a summer period from 1 January to 20 March; • a transition period from 9 April to 28 June; • a winter period from 29 June to 16 September.
We consider two state-of-the-art operational products for benchmarking purposes and as external complementary dataset of numerical examplars V during the training phase: namely, GLORYS (the GLORYS reanalysis product used for the experiment is available at https://marine. copernicus. eu/ (accessed on 6 May 2021)) reanalysis product (ref. [9]  and altimetry-derived AVISO product (we refer the reader to the following link for additional information on altimeter-derived AVISO sea surface currents. https:// www. aviso. altimetry. fr/en/data/products/sea-surface-height-products. html (accessed on 6 May 2021)). GLORYS product relies on the variational assimilation of an ocean circulation model based on coupled Navier-Stokes equations, using different sources of observation data especially sea surface temperature (SST) and altimeter-derived sea level anomaly (SLA).
This dataset results in a 22-year time series from 1993 to 2016. By contrast, AVISO product is a purely observation-driven dataset based on the analysis of altimeter data from multiple satellite missions using optimal interpolation. For benchmarking purposes, besides AVISO and GLORYS sea surface currents, we also include a AIS-derived product combining an expert-based processing and optimal interpolation (OI)  [2] , referred to as AIS-OI. Hereafter, we refer to the different configurations of proposed approach as VAE-NODE-AIS, VAE-NODE-AIS-GLORYS and VAE-NODE-AIS-AVISO. Regarding the evaluation framework, we exploit an independent in situ datasets issued from drifters as depicted on Figure  4  to evaluate the relevance of the reconstructed sea surface currents. As performance metrics, we focus on the mean square error (MSE) of the estimated sea surface current along drifters' trajectories.
Results The results obtained from independent in situ data are reported in Table  1  (lowest MSE are in bold). The proposed method is denoted as VAE-NODE and trained either using solely AIS data or using both AIS data and external datasets (GLORYS, AVISO and OI). Among the different configurations of the proposed VAE-NODE framework, we report the best performance for all periods using a training with GLORYS data as external dataset V in Equation (  3 ). It may be noted that using AIS alone or using AVISO data as external dataset significantly lessens the performance (e. g. , 0. 05 for VAE-NODE-AIS+GLORYS setting vs. 0. 40 (resp. 0. 14) for VAE-NODE-AIS+AVISO (resp. VAE-NODE-AIS) setting for the summer period). The mean reconstruction performance is also significantly better than that of AIS-OI scheme.
Interestingly, the proposed approach outperforms GLORYS and AVISO products for summer and autumn periods, with a significant relative gain, up to 28% w. r. t. GLO-RYS products and 57% w. r. t. AVISO. For the winter period, we reach a reconstruction performance similar to AVISO product and slightly better than GLORYS product. We provide an illustration of the reconstructed velocity fields on 16 January 2016 in Figure  6. The sea surface current estimated by VAE-NODE-AIS+GLORYS depicts information at fine scales (e. g. , the width of the current coming from the north-east of the area) and sharp gradients compared with the altimeter-derived AVISO method. Whereas the AIS-OI baseline involves local artifacts, which relate to noise patterns of the AIS dataset and local outliers for simplified observation model (1), the proposed framework retrieves more consistent space-time dynamics.
This is regarded as a direct outcome of the considered regularization through the proposed latent ODE representation. When using both AIS and GLORYS data in the training phase, we retrieve much larger velocity values along the high-current area. As the VAE-NODE-AIS and VAE-NODE-AIS+GLORYS configurations reach similar values for training loss J, this suggests that the additional use of GLORYS data greatly improves the interpolation capabilities of the trainable latent ODE representation.