dataesr/scientific-paragraphs-categorization huggingface dataset:
The comparison is performed through an estimation of the RMSE, and the relative absolute percentage error (RApE) between each hidden parameter true and predicted values. To test the quality of VoxNet predictions under contrasted environmental conditions, the test data set was divided into four sub-data sets, according to the severity of light and water stress under which the plant architecture of the example developed. Each training run was tested on the whole test data set as well as on each of the four test sub-data sets (see Results).
Generic modelling of genotype, defining plant sensitivity to environmental constraints Three parameters of each of the six functional axis categories control its death (Sm), branching (Sr) and apical growth ( A l) depending on the current value of the growth factor of the corresponding compartment. Figure  7  shows four examples of the possible use of these three parameter values in the second category of branches (lateral branches). Parameter A l controls apical growth Figure  6. Results of four simulations of random plant architectural development with RoCoCau+TOY FSPM under different environmental water and light conditions. The number of internodes of the functional category of each axis were counted using Xplo Software. For each simulation, the histograms represent the number of internodes in each category compared with the number of internodes of the plant under optimal environmental conditions, i.
Calibration of the three hidden parameters of the TOY first functional shoot category The aim of the calibration method was to assess TOY hidden parameter values. The TOY hidden parameters are the parameters of endogenous growth processes, i. e. the death threshold S m, the branching threshold S r and the apical growth factor A l for each functional axis category (see Table  1 ). Figure  8  shows the results of the training calibration of the three hidden parameters for the shoot first functional category on SubDBStress (A) (see section 2. 2. 3) and on the whole training data set (B). Similar results were obtained for the five other functional categories. With a median RApE of 1. 3 % for A l, 0. 8 % for S r and 4. 2 % for S m, the predictions made by VoxNet trained on SubDBStress are fully accurate for the test examples under water and light stress.
With a median RApE of 1. 3 % for A l, 0. 7 % for S r and 5. 0 % for S m , they are also highly accurate for the test examples under water stress alone. This result underlines the greater sensitivity of the TOY model to water availability than to light availability. Indeed, with a median RApE of 28. 5 % (resp. 37. 6 %) for A l, 19. 2 % (resp. 35. 8 %) for S r and 32. 0 % (resp. 46. 4 %) for S m, the predictions given by VoxNet trained on SubDBStress showed very poor accuracy for the test examples under light stress alone, and were very close to random for the test examples under no stress. Altogether the quality of the predictions made by VoxNet trained on SubDBStress was poor, with a mean RApE on the whole test data set of 24 % for A l, 19 % for S r and 30 % for S m. (b) The quality of the predictions by VoxNet trained on the whole training data set fine-tuned with the weights of the training on SubDBStress was significantly better, with a mean RApE on the whole Methodology for model fitting on simulated data • 13 test data set of 13 % for A l, 14 % for S r and 22 % for S m.
The predictions made by VoxNet trained on the whole data set for example, under water stress alone or under both water and light stress were still slightly more accurate than the predictions made for examples under light stress or no stress at all. However, they were significantly more accurate than the predictions made by the previous VoxNet trained on SubDBStress. The overall improvement in the quality of predictions given by the VoxNet trained on the whole data set was driven by the notable improvement in the quality of the predictions for the test examples under light stress alone and under no stress. Indeed, in comparison with the previous training, the median RApE for the test examples under light stress alone (resp. no stress) decreased significantly from 28. 5 to 7. 5 % (resp. from 37.
Since severe stresses, modelled by low values of the growth factor, are less frequent during and among the simulations that comprise the training data set, it is probably more difficult for VoxNet to learn how to predict the value of the mortality threshold S m. A particularly interesting result is the prediction that VoxNet is able to provide on the examples under limited stress. Even though the prediction is of low quality, the ability of the network to predict plant responses to environmental stresses based on an example in which the plant architecture developed in the absence of stress is quite remarkable. This result requires more detailed investigation. In particular, the definition of stress used to classify the examples is rather vague (decrease of at least 25 % in water (resp. light) availability compared to the optimum).
Calibration method inversion. Endogenous growth processes are assumed to be identical amongst all individuals of the same plant species. As such, the values of the 18 hidden parameters of the TOY model for endogenous growth are assumed to be associated with the plant species. For a given plant species, once these 18 values have been assessed, phenotypic plasticity between individuals is assumed to be modulated only by the values of the environmental parameters and exogenous growth processes. Since the environment is measurable, the values of the environmental parameters can be assessed using standard calibration methods. However, since it is possible to construct a large data set containing architectural development simulations of an individual of a given species growing in different environmental constraints, it is also possible to train the VoxNet neural network to predict the environmental conditions under which the individual has developed.
Results. The predictions given by the trained VoxNet shown in Fig. 9  are fully accurate for every example of the test data set, with a mean RApE of 1. 5 % for light availability, and of 2 % for water availability. The results of the inversion of the calibration method are therefore conclusive: they demonstrate VoxNet's ability to accurately predict the impact of water and light availability on the architectural development of a given individual of a given species.
2013; Coll et al. 2008; Delagrange et al. 2008; Henry et al. 2010). It could also be improved by adding equations to estimate the amounts of biomass allocated for other essential functions of the tree, i. e. reserve, maintenance, reproduction and defence. The second limitation concerns the branching process, which is mainly managed by the RoCoCau software. Indeed, axes of the first and the second categories can branch into new axes at each time step, the probabilities being fixed by the RoCoCau software. Within RoCoCau+TOY FSPM, the TOY model gives a binary modulation to those branching probabilities. It sets them to zero when the value of the growth factor is below the branching threshold. A first refinement of TOY model could consist in implementing continuous modulation of the branching probabilities, e.
g. a linear decrease in the branching probability following the decrease in the growth factor. A more important refinement however, concerns the branching of the axes of the first functional category, e. g. the trunk and taproot. Indeed, axes of the first functional category can branch into axes of the second or the third category, e. g. branches or short shoots, lateral roots and fine roots, with different degrees of probability. It is likely that trees can modulate the branching process towards the second or the third category, towards exploration or exploitation, depending on the environment. Given that, the two probabilities are fixed by the RoCoCau software, and simultaneously set to zero when the growth factors value drops below the branching threshold, the RoCoCau+TOY FSPM is currently not able to account for new axis strategies, which reduces its genericity.
Analysis We chose a neural network suited to our specific task and improved it. Each plant growth simulation produces a 3D voxel image that contains 10 growth time steps split between the woody and Methodology for model fitting on simulated data • 15 absorbing parts. It is currently possible to predict 6 × 3 hidden TOY parameter values with acceptable accuracy after training on a simulated data set, which is a very promising result. As the input of the network consists in a voxelized representation of the plant, it is independent of the model to be inverted. It is thus possible to keep the same neural network to calibrate future improved versions of TOY. VoxNet was chosen for calibration because of its 3D input and because it is simple to adapt for generative purposes. It is clear that including time series in a single 3D image may not be the most accurate way to calibrate a dynamic model, not to mention including light and water availability in some voxels.
Calibrating TOY parameters for endogenous growth of the tree species on a single phenotype The 18 TOY hidden parameters for endogenous growth are the focus of the calibration method developed in this study (see section 3). Once the RoCoCau simulators and the exogenous growth parameters are calibrated, it is possible to implement RoCoCau+TOY FSPM with random endogenous growth parameters to build a simulated training data set and to train VoxNet neural networks to predict the values of the endogenous growth parameters. Since the output formats of RoCoCau and RoCoCau+TOY FSPM are the same, it is possible to provide the trained VoxNet neural networks with a voxelized density map of the RoCoCau simulation of the tree phenotype measured in vivo (see section 5. 1. 1). The prediction given by the trained VoxNet neural networks for this input are the values of the endogenous growth parameters for the tree species measured in vivo.
CON CLUSION RoCoCau is a new structural whole-plant growth model (describing shoot and root growth and their interactions at the same time). It includes an approach using the architectural unit concept and relies on structural axis categories. Basic functions that explain growth (apical growth, branching, death and self-pruning) are adapted to our specific field of knowledge and experimental measurements made in the shoot and root compartments  (Taugourdeau et al. 2012). The RoCoCau simulator can produce 3D mock-ups that are botanically accurate. The functional TOY module is dynamically linked to RoCoCau to express shoot-root compartment dependencies for: -biomass production that requires carbon, water and light; -partitioning to balance shoot and root compartments absorbing contributions and modulating further growth.
The combination RoCoCau+TOY produces an FSPM that can express a variety of growth strategies and reveal plant plasticity under varying environmental conditions. It is possible to fit RoCoCau to a particular species thanks to measurements on both compartments but most of the 25 parameters of TOY are hidden parameters with values that can only be calibrated using numerical tools. It is possible but unlikely that such a large number of values can be discovered using standard methods, which is why we tested the capability of neural networks to accomplish this task. To this end, we adapted the well-known VoxNet convolutional neural network and tested the quality of its predictions using simulated plant data sets for training and validation. The input of the network consists in a 3D voxel representation of split woody and absorbing parts of the The next steps in this project will consist in improvements in two complementary directions.
A. L. M. mainly cared about the calibration part and VoxNet input/ output data content. He also helped about RoCoCau+TOY check and improvement. E. N. and Y. C. brought their knowledge about plants. P. B. brought his knowledge about neural network theory and technical management. J. -F. B. built RoCoCau+TOY model and simulator according to E. N. and Y. C. knowledge, provided the training/validation databases and coordinated the study.
This abdominal window permits in vivo imaging for several weeks up to one month; however, the insertion of such an imaging window requires invasive surgery and is associated with chance of inflammation. Moreover, imaging windows are sometimes lost and tissue necrosis can occur  [102]. Obviously, this imaging modality is not translatable into clinical practice. An interesting alternative to monitor capillary blood flow non-invasively at the bedside is achievable since the introduction of hand-held vital microscopy (HVM) into clinical practice  [104]. Even though this imaging modality is based on an entirely different technology, i. e. , side stream and incident dark field video-microscopes, it offers real time assessment of superficial located capillaries. Novel clinical implemented algorithms, known as MicroTools software packages enable automated microvascular imaging analysis of total and perfused vessel density for accessing angiogenesis, vessel dilation/constriction, and fluid balance, as well as oxygen delivery capacity based on capillary hematocrit and velocity of erythrocytes  [105].
In this note, we consider a compartmental epidemic mathematical model given by a system of differential equations. We provide a complete toolkit for performing both a symbolic and numerical analysis of the spreading of COVID-19. By using the free and open-source programming language Python and the mathematical software SageMath, we contribute for the reproducibility of the mathematical analysis of the stability of the equilibrium points of epidemic models and their fitting to real data. The mathematical tools and codes can be adapted to a wide range of mathematical epidemic models.
Although the difficulty of this analysis depends on the complexity of the model under study, part of it is common to the majority of the models and may become simplified if we use adequate mathematical software. In this paper, we show how to use free and open-source software for the mathematical analysis of the models. We focus on the mathematical software SageMath (version 9. 2)  [22]  and Python programming language  [20] , version 3. 8, and the Python Libraries: Numpy (version 1. In this note, we consider a SAIRP model, given by a system of five ODE's, for the transmission of SARS-CoV-2, first proposed in  [26]  and after generalized to piecewise constant parameters and complex networks model in  [25]. We provide all the codes that allow us to compute the equilibrium points, basic reproduction number, visualize the global stability of the equilibrium points and by considering piecewise constant parameters.
Moreover, we provide the Python code that allows to estimate some of the piecewise constant parameters and fit the model to the real data of COVID-19 transmission in Portugal, from March 2, 2020 until April 15, 2021. It is important to note, that all the codes are elementary and thus can be easily adapted to other compartmental models, see e. g. [3, 6, 9, 17, 24, 30]. The paper is organized as follows. In Section 2, the SAIRP model, given by a system of ODE's, is described. The equilibrium points of the SAIRP model are computed in Section 3 and their global stability is illustrated using SageMath (version 9. 2)  [22]  and Python (version 3. 8)  [20]. The generalized SAIRP model with piecewise constant parameters is presented and the Python code for the model fitting to COVID-19 Portuguese real data is given, in Section 4.
Computing equilibrium points and basic reproduction number in SageMath The model  (1)  has two equilibrium points: • disease-free equilibrium, denoted by Σ 0 , given by Σ 0 = (S 0 , A 0 , I 0 , R 0 , P 0 ) = Λ (ω + µ) µ (pφ + µ + ω) , 0, 0, 0, φ pΛ µ (pφ + µ + ω) ; (3) • endemic equilibrium, Σ + , whenever R 0 > 1, given by Σ + = (S + , A + , I + , R + , P + ) with S + = Λ(ω + µ) (pφ + µ + ω)µ R -1 0 , A + = Λ ν + µ R -1 0 (R 0 -1) , I + = Λν (ν + µ)(δ + µ) R -1 0 (R 0 -1) , R + = δΛν (ν + µ)(δ + µ)µ R -1 0 (R 0 -1) , P + = Λφp (pφ + µ + ω)µ R -1 0 , ( 4 ) where the basic reproduction number, R 0 , is given by R 0 = β (1 -p) (δ θ + µ θ + ν) (ω + µ) (δ + µ) (ν + µ) (pφ + µ + ω). ( 5 ) The SageMath code reads as follows: var('S','A','I','R','P','phi','mu','nu','delta',\ 'omega','Lambda','theta','beta','p','lambdat'); The output sol gives the two biological meaningful equilibrium points Σ 0 and Σ + given by (  3 ) and (4), respectively.
Stability analysis The following theorems hold and are numerically illustrated in Figure  1. Theorem 1  ([25] , Local stability of the DFE). The disease-free equilibrium, Σ 0 , is locally asymptotically stable whenever R 0 < 1. Theorem 2  ([25] , Global stability of the DFE). If R 0 < 1, then the disease-free equilibrium, Σ 0 , is globally asymptotically stable in Ω. Theorem 3  ([25] , Global stability of the EE). The compact region Γ defined by Γ = x = (S, A, I, R, P ) T ∈ R + 5 ; S + A + I + R + P = Λ µ is positively invariant under the flow induced by system  (1). It contains the disease-free equilibrium, Σ 0 , and the endemic equilibrium, Σ + , if R 0 > 1. Furthermore, if R 0 > 1, then the endemic equilibrium Σ + is globally asymptotically stable in Γ. The Python code to generate Figure  1  is given below.
Model fitting to real data with Python In order to fit the real data of active infected individuals by SARS-CoV-2 (detected by test) daily provided by the health authorities in Portugal  [31] , we use the model  (8)  with piecewise constant parameters and use the programming language Python (version 3. 8)  [20] , and the Python Libraries: Numpy (version 1. 18. 5), Pandas (version 0. 25. 3), Scipy (version 1. 4. 1) and Matplotlib (version 2. 0. 0). The real data are available in  [31]  or, for example, in the data repository site, see e. g. [32]. In what follows we explain the goal of each code block. First we need as previously to import several Python scientific libraries.
#! / u s r / b i n / env python3 import numpy as np from scipy. integrate import odeint import pandas as pd import matplotlib. pyplot as plt from scipy. optimize import curve fit We consider the real data from  [31, 32] , here denominated data-pt-covid19 with extension. xlsx. To read the real data one can use the following code. Next, we subdivide the time window of the total 410 days into 9 subintervals. This specific subdivision is related to the increase/decrease of the transmission of the virus in the community, the public health measures implemented by the Portuguese authorities and the human behavior, that changes over time. In order to solve the model (  6 ) we need to define the initial conditions, for t = 0, that correspond to the number of individuals in each class on March 2, 2020.
# T o t a l p o p u l a t i o n , N N = 10295894 + 2 + 2/0. 15 The parameters β, p and m are assumed to be piecewise constant. Moreover, we estimate the parameter β for all t ∈ [0, 410] days and the parameters m and p in some of the sub-intervals, using scipy. optimize. curve_fit from Python, see  [33]  for more details, that uses non-linear least squares method to fit a function to data. print ("\n beta1 : ",beta1 ) ret = odeint ( sairp model , y0 , tf1 , args =(N ,\ beta1 ,theta ,p1 ,phi ,w,nu ,q,delta ,m1 ,Lambda ,mu )) S, A, I, R, P = ret. T #2 sub-i n t e r v a l o f time y2 = ret. T[0][72] , ret. T  [1] [72] , ret. T  [2] [72] , ret. T  [3] [72] , ret. T  [4] [72] def fit odeint2 (tf2 ,beta ):.
Conclusion In this note, we provided a complete toolkit for performing both a symbolic and numerical analysis of a recent epidemic model, presented in  [25] , introduced in order to study the spreading of the COVID-19 pandemic. This innovative compartmental model takes into account the possible transmission of the virus by asymptomatic individuals, as well as the possibility to protect a fraction of the affected population by public health strategies, such as confinement or quarantine. Since the public health policies have a strong influence on the spreading of the epidemic, we have also considered a piecewise constant parameters extension of the initial autonomous system, which have proved its ability to fit with real data. Once the mathematical analysis of such a complex compartmental model can be tedious, we have presented a computational approach, which is intended to support the theoretical analysis: • using the free and open-source software Sagemath, we have first computed the symbolic expressions of the basic reproduction number R 0 (equation (  5 )), of the disease-free equilibrium Σ 0 (equation (  3 )) and of the endemic equilibrium Σ + (equation (  4 )), which highlight the role of each parameter of the model; • using the scientific libraries numpy, scipy and matplotlib of the free and open-source language Python, we have integrated the epidemic model, in order to illustrate the theoretical stability statements (see Figure  1 ); • finally, we fitted the piecewise constant parameters extension of the initial model with recent real-world data (see Figure  2 ).
These include data generation, discovery and new knowledge generation, resource development (research and ethics guidelines, infrastructure, capacity strengthening through skills development and biobanks with biospecimens, development of bioinformatics tools and pipelines), information for health policy development and targeted interventions, patents and peer-reviewed publications. Importantly, the H3Africa Consortium contributes large African genome datasets from populations across the continent to explore insights into demographic histories of migration and admixture across Africa. These data are available to the global scientific community for further analysis. In this chapter, we have limited ourselves to assessing the publications oeuvre of the H3Africa Consortium (January 2013 to February 2020) under specific themes that reflect the areas of substantive activity.
Identification of Publications and Categorization We performed a PubMed database (https://www. ncbi. nlm. nih. gov/pubmed) search for publications potentially originating out of the H3Africa Consortium. We used "H3Africa" as a search term along with a list of NIH grant IDs associated with NIH funded H3Africa projects. The grant IDs searched were -HG006938, DK116913, AI110398, HG007479, HG006947, HG007480, HG009826, HL141011, HG009824, MH096754, AI136677, MH115484, HG009784, HD094658, HG007044, MH115485, HG008226, HG008222, HG008224, HG009810, HG009790, HG007008, HG007438, HG007051, HG006941, HG009780, TW010677, TW010672, TW010673, TW010679, HG006939, AI110398, HG007480, AI110422, HG007465, AI110466, HG007472, HG007459, HG007628, HG007654, HG007092, HG006941, HG010273, HG010275 and HG009822.
Epidemiological Studies on Diseases, Traits and Risk Factors An important outcome of the H3Africa Consortium is the development of large patient-control cohorts and population cross-sectional cohorts that provide an opportunity to assess the prevalence and distribution of cardiovascular and metabolic diseases and associated traits across the continent. In this section we describe 25 publications that examined and compared the distributions of several traits and associated risk factors, including body mass index (BMI), obesity, stroke, carotid intima-media thickness (cIMT) and hypertension. A series of publications described the BMI distribution and obesity in older adults in a population cross-sectional study by the AWI-Gen group, and included data from over 10,000 individuals sampled from six centres, both rural and urban, across four African countries,  (Ramsay et al.