dataesr/scientific-paragraphs-categorization huggingface dataset:
This was attributed to the denominator of F-wPLI being different from that of F-ICOH and less sensitive to (residual) volume conduction effects  (Stam et al. , 2007; Vinck et al. , 2011). These arguments straightforwardly extend to W-wPLI and W-ICOH, and they thus likely explain the enhanced ability of W-wPLI to assess functional connectivity from fractal dynamics compared to W-ICOH. Interestingly, the numerical simulations conducted in section 2. 3 on synthetic fGn/fBm data showed only a moderate superiority of W-wPLI over W-ICOH to quantify functional connectivity from fractal dynamics, except for slightly improved estimation (RMSE) performance. This suggests that fGn/fBm, even with delays, correlations, and possible additive trends, are not rich enough models to account for all the difficulties encountered in modeling real MEG data.
It was confirmed that wPLI outperforms ICOH, as commonly observed, and that COH is not suited for functional connectivity assessment. While Fourier-based tools are natural to use to assess functional connectivity in band-limited rapid oscillatory rhythms, it was shown, using simulated synthetic data and mostly on MEG data, that the assessment of functional connectivity for large-band slow scale-free cross-temporal dynamics is better achieved by complex wavelet based indices. Therefore, Fourier and complex waveletbased spectral estimation must be regarded as complementary, rather than as mutually exclusive, tools. Complex wavelet-based analyses of functional connectivity assessment from fractal dynamics conducted on MEG data recorded on 36 participants at rest and during a visual discrimination task with individualized training, yielded several key conclusions.
These spatiotemporal modulations are reinforced with intensive and individualized training for the task. Routines (in MATLAB) to synthesize (correlated and delayed) bivariate fractional Gaussian noise, to perform Fourier and complex-wavelet based analysis and to compute indices quantifying functional connectivity from fractal dynamics, on synthetic or MEG data, have been developed by ourselves and will be made publicly available at the time of publication. Such tools could further be used to examine the relevance of functional connectivity assessed from fractal dynamics in the context of network physiology, and networks of networks, relating brain activity to other physiological functions (heart rate, respiration, sleep, ocular, and motor systems, etc. ) (cf. e. g. ,  Bartsch and Ivanov, 2014; Bartsch et al.
Finding Population Structure in Hybrid Breeding Populations Due to the considerable diversity, we then tried to identify whether the population structure within the dataset should be considered  (Lyra et al. , 2018). Population structure arises mainly due to geographical isolation and natural/artificial selections. Individuals are distributed into a few to several distinct subgroups that display different allele frequencies (Figure  1A ). In a genome-wide association study (GWAS), individuals within the diversity panel present a specific phenotype of one or more lines that may generate misleading estimates on the linkage imbalance. As a result, whenever a phenotype is correlated with a subpopulation, this phenotype will probably show spurious associations. Although these associations are a major concern for GWAS, the use of highly structured subgroups in hybrid prediction could influence the achievement of reliable estimates of genomic estimated breeding values (GEBVs) for quantitative traits  (Larièpe et al.
For this purpose, we used the algorithm proposed by  Akdemir et al. (2015)  with predefined population size. Therefore, to predict the FD, we used the NCII, the testcross (TC), and OTS as the TS with sizes of 32 (with the same size of the TC data set), 152, 272, and 393 hybrids (with the same size as the NCII data set). Following the same idea of aiming to predict NCII, we used the TC and OTS with 32, 152, and 272 hybrids. Our results suggest that TC is the worst genetic design to be used as a TS to predict simple maize crosses that must be obtained through FD or NCII. On the other hand, NCII is the best TS for the prediction of hybrids taken from FD. In addition, combinations from FD or NCII can be well predicted using OTS, thus reducing the total number of crosses to be made. However, the number of parents and crosses per parent in the ST should be maximized.
Training Populations Using Public Databases-An Alternative Due to the scarcity of resources in the initial phases, we addressed the possibility of incorporating public databases in the composition of our training populations  (Morais et al. , 2020). Small-scale public and private programs with limited budgets often lack the financial ability to genotyping a considerable number of individuals to apply GP efficiently. In this regard,  Morais et al. (2020)   These databases contained phenotypic information regarding plant height (PH, in cm), ear height (EH, in cm), and the SNP markers data. A total of 29 training populations (TPs) were defined and divided into four scenarios to determine the best strategy to apply public databases to predict lines. The best predictions were achieved with the strategy of the TP composed by candidates selected with an optimization algorithm from all the public database and private lines, even at the smallest TP sizes evaluated (81 and 281 TP sizes).
On the other hand, the lowest predictive abilities were achieved using only the Tropical USP database as training and validation populations (VP), due to its lack of genetic variability and reduced population size, hindering prediction. The results of all four scenarios of TP formation showed that the predictive ability increased with the increase of TP size, the relationship rate between TP and VP, and genetic variability. (Rife et al. , 2018)  revealed a similar potential of GP to predict wheat traits using historical data across several public breeding programs, reinforcing the possibility of using external data for model training. The optimization of the training population proposed by  Akdemir et al. (2015)  showed promising results, even when the training population size was reduced.
For example, small groups of individuals (250) selected in public panels are enough to achieve predictive abilities of over r = 0. 44 and r =0. 53, for PH and EH, respectively. Optimizing the TP can increase the representation of the subpopulation, allowing for an efficient and controlled updating of the training population over the years  (Akdemir et al. , 2015). Nevertheless, what is the real reason to use public databases, and how does it fit into a breeding framework? The use of public data aims to an early-start GP with reduced costs and over the years, to setup a more complex GP training population. The number of individuals from the program genotyped and phenotyped will increase as time goes on, reducing the participation of public databases in the training population and thus paying off the costs of genotyping the population in training over the years.
For example, the total cost of the training population could be divided over 5 years, with the public database replacing 20% per year of the training population with individuals from the program. Considering a training population that is 10 times bigger than the VP, this strategy should be conducted as follows: in the first year, (a) genotyping and phenotyping of the germplasm program, composing 10% of TP, along with external individuals selected by optimization procedures (90% of TP), (b) out of 10%, established as the VP (new progeny with no phenotyping data), (c) validation and prediction of GEBV. In the second year, (a) genotyping and phenotyping of individuals from the germplasm program (10% of the TP), (b) once again, new individuals are to make up the VP (10% of TP), while the remaining individuals from the germplasm program are to be a part of TP, with the TP composed by 70% of external individuals selected from optimization procedures and 30% of internal individuals genotyped previously, (c) validation and prediction of GEBV.
, 2018; Darrier et al. , 2019; Negro et al. , 2019; Chu et al. , 2020)  (Table  1 ). In this context, we studied how SNP markers obtained from two genotyping platforms (616K SNP-array and GBS) affect the GP in our germplasm  (Sabadin, 2020). We also attempted to verify the effect of the use of different reference genomes in SNP calls via GBS (i) using the most common reference genome, line B73 (GBS-B73), (ii) using a simulated reference genome built with GBS data, considering all inbred lines (GBS-Mock-All), and (iii) using a simulated reference genome built with GBS data from a single line, our heterotic pool tester L56 (GBS-Mock-L56). For this purpose, we used the USP data set mentioned above (see section above "Training populations using public databases"). To build the simulated genome, we used a pipeline developed by  Melo et al.
Therefore, assessing the genomic relationship is more important than the polymorphism resolution, which was confirmed when we evaluated the additive genomic relationship matrix (Ga) and the genomic dominance matrix (Gd). For the Ga matrices, high correlations were observed between the SNP-array, GBS-B73, and GBS-Mock-All SNP data sets (r = 0. 88), revealing that these approaches estimate the additive genomic relationship between hybrids in a similar way. However, for the Gd matrices, lower correlations were observed among all SNP data sets, which show that the polymorphism captured by these platforms estimated the dominance effects differently. GBS-Mock-L56 displayed low correlations with other SNP data sets and had a low performance for all downstream analyses, proving that it is an erroneous alternative to sample polymorphism within the population, since only polymorphisms between L56 and other individuals were identified.
As far as predictive abilities are concerned (Figure  3 ), genotyping platforms and reference genomes do not affect the additive model, except for GBS-Mock-L56. Furthermore, the use of a reference genome historically unrelated to the evaluated germplasm, such as the B73 genome (temperate maize), seems to be enough to capture the additive relationship of the genotypes within the population. This situation can change greatly when we consider the effects of dominance to estimate genetic values. In our study, except for GBS-Mock-L56, small differences in predictive capabilities were observed among SNP data sets, when we performed the GBLUP additive-dominance model. Furthermore, the differences were more remarkable for GY, supporting the fact that the inclusion of the dominance effects of GP models is more relevant for complex traits.
, 2019). These ECs can be collected from in-field sensors or public databases (for more details, see the next section) and also consider stress-covariates derived from crop growth models (CGM)  (Heslot et al. , 2014; Rincent et al. , 2017). For the latter, a more robust single-step approach relies on the integrated use of GP with CGM, which was successful in predicting the performance of DH maize lines on water-stressed environments  (Cooper et al. , 2016)  and across a large target region of the breeding program in the United States  (Messina et al. , 2018). For low-budget breeding programs that are unable to invest in large phenotyping for ecophysiology traits (e. g. , biomass accumulation during crop life) need to improve accuracy in training CGM. An alternative can be in the exploring of the environmental relatedness or EC-specific regressions, which increases the accuracy of GP in hybrid prediction more simply  (Costa-Neto et al.
OPEN-SOURCE R PACKAGES TO FACILITATE THE ADOPTION OF GENOMIC PREDICTION Since the first work on GP, published approximately 20 years ago  (Meuwissen et al. , 2001) , a wide number of computational solutions have been developed to process data and run prediction models, such as BGLR (Pérez and de los Campos, 2014), rrBLUP  (Endelman, 2011), and sommer (Covarrubias-Pazaran, 2016). For plant breeding, most of these solutions were implemented in R, an open statistical-computational environment. Nowadays, these software solutions can offer the processing of genotyping data  (Granato et al. , 2018b) , fit marker regressions or genomic wide association analysis  (Endelman, 2011) , run GP accounting for several multi-trait multi-environment approaches  (Pérez and de los Campos, 2014; Covarrubias-Pazaran, 2016; de los Campos and Gr?neberg, 2016; Granato et al.
, 2018a; Montesinos-López et al. , 2019) , and integrate envirotyping sources in the reactionnorm modeling of G × E  (Costa-Neto et al. , 2021). Here, we briefly discuss three software developed by the Allogamous Plant Breeding Laboratory of the University of São Paulo as part of our experience in the field of genomic-enabled prediction of maize hybrids. To deal with genotyping data, we developed the package snpReady  (Granato et al. , 2018b) , which helps the user with quality control and the recoding of markers. In addition, it helps obtain some parameters of population genomics. This package implements a pipeline of conversion, imputation of missing data, and preparation of genotyping data for genomic analysis, outputting matrices in appropriate formats for different software. These applications are simple and enough to be integrated into the breeding pipelines or coupled with other environments, such as shiny  (Matias et al.
, 2021). Three modules of envirotyping are offered in this package, namely (i) the collection of raw environmental information from public platforms, requiring only the geographic and temporal coordinates of the experiments and processing data set, (ii) environmental characterization based on the use of the processed environmental covariables to describe the typology of the environments, and (iii) the implementation of GP models enriched with ecophysiological parameters, considering three different structures of reactionnorm, and subsequently incorporate them into the prediction models under a Bayesian framework in the same way as in BGGE.
Finding Research Partnerships to Expand the Field-Testing Network Most of the applications described in the last section consider datasets with at least four environments and almost one thousand entries (lines, DH, and hybrids), which represent the reality for at least a small-scale breeding program. As discussed in the previous sections, with the increase in the availability of data, the computational demand and the power of cuttingedge testing hypotheses in maize breeding also increase  (Rogers et al. , 2021). We envisage that maize hybrid breeding programs can take advantage of historical multi-environment testing data  (Dawson et al. , 2013)  to explore the environmental impacts on the plasticity of germplasm, collecting during this process data from enviromics, and other sources of data useful to train accurate models.
During this step, it is possible to integrate some simulation platform capable of generating reliable environmental scenarios  (Millet et al. , 2016)  or phenotypic landscapes  (Bustos-Korts et al. , 2019) , such as CGM. The use of public databases to test hypotheses, train models, or import datasets for your own purposes that might reduce costs and provide a guideline to follow. However, as we have pointed out in section Germplasm Characterization, the implementation of a well-conducted field trial for phenotypic, genotypic, and envirotypic characterization of the so-called "Modern Plant Breeding Triangle"  (Crossa et al. , 2021) , is crucial for providing good quality data to test a wide number of hypotheses. Another interesting option is to establish partnerships with other small-scale breeding programs and public institutions in order to create a large network of field data, such as the successful partnership of public institutions in the United States-The Genome to Field Project  (McFarland et al.
have evaluated the usefulness of incorporating public database panels to compose tropical GP training populations. In this context, the following public databases were used: (a) ASSO-Nested Association Mapping Population (NAM) combined with the Maize Association Panel 282 (166 + 282 endogamic lines, respectively); (b) NCRPIS-United States Department of Agriculture-Agricultural Research Service (USDA-ARS), North Center Regional Plant Introduction Station (2. 046 endogamic lines); (c) USP-tropical endogamic lines of the University of São Paulo (64 endogamic lines).
The entire design and optimization procedure are coded on the computer program "scilab. " Numerical examples are presented to demonstrate the efficiency of the developed approach, and the results are analyzed. The rest of the paper is structured as follows. Section 2 details the methodology developed for both full and partially prestressed sections under service and ultimate limit states. Section 3 is a description of the optimization using Genetic Algorithms. Section 4 defines the optimization problem and states all design variables and constraints. In section 5, a numerical example is presented with parametric studies on several variables (span length, truck live loads, steel ratio ρ and compressive strength f ck ) followed by a cost sensitivity analysis and a comparison between the results obtained with fully and partially prestressed sections.
Optimization methodology using scilab The algorithm is coded on the computer program "scilab"; fully prestressed and partially prestressed sections are coded on two separate programs. All input parameters are provided in an Excel spreadsheet read by the program, and each constraint is introduced as a "scilab function" along with the objective cost function. The procedure is as follows. The GA generates random populations of the design variables h and b w respecting the upper and lower bounds provided as input. The initial population size is set to 100 and the number of generations to 50. The genetic operators of selection, crossover and mutation are defined in the program with the corresponding probabilities: elitism selection, crossover with a rate of Pc = 0. 6 and continuous variable mutation with a rate of Pm = 0.
Design variables The design variables (Table  1 ) include the heel dimensions since this part of the section is responsible for the placement of the tendons and the passive reinforcement with a minimum addition of concrete volume. For the dimensioning of the heel, a data table including all possible tendon configurations for 1 to 10 tendons and passive steel reinforcement is included in the program (see Fig. 9 ). Passive reinforcement is placed at a location lower than the tendons, closer to the bottom concrete fiber. The number and configuration of steel tendons is computed so as to ensure a maximum steel reinforcement ratio of 1% with a maximum of 2 bundled layers.
Conclusion In this paper, the structural optimization of partially and fully PC bridge T-shaped girder with heels is addressed as a single-objective optimization problem solved using genetic algorithms coded on the computer program "scilab". For this purpose, an optimization-oriented dimensioning approach for prestressed concrete is set forth in accordance with the  [13] , provisions, introducing a new pivot rule, similar to the one used in reinforced concrete, but based on the stress limitations instead of the strains. The permissible domain of the prestressing force P and the bending moment M * is represented demonstrating the benefit of partial prestressing in extending this domain and significantly decreasing P for the same section dimensions. The following conclusions can be drawn based on the numerical example.
Hence, two different pixels with values  [2, 3]  will attain a lower diversity with respect to two pixels with values [0,100]. For instance, to make an ecological parallel, this is somewhat similar to the phylogenetic distance between two species: the values [2,3] would be equivalent to two sister species closely related on the tree of life while  [1, 100]  would be equivalent to two very distant species on the tree of life. The aim of this paper is thus to propose, for the first time, a parameterization of Rao's quadratic entropy in order to provide a generalized entropy that accounts for both relative abundances and distances among pixel values. The proposed approach is now part of the rasterdiv R package, a package dedicated to diversity measures of spatial matrices, increasing its capability to discern among different diversity measures by a single formula.
, 2020;  https://CRAN. R-proje ct. org/packa ge=raste rdiv). The calculation of different Q by automatically changing the range of potential values is done by the function paRao, as: where x is the input data set, which can be a RasterLayer or a matrix class object, and alpha is the parameter of Equation  4 , which can be a single value or a vector of integers. In the example above, is a vector of integers ranging from 0 to 4, plus Inf, which in the R language is a reserved word representing positive infinity ( → ∞). The option method decides if paRao is calculated with one single layer (classic) or with more than one layer (multidimension). With method="multidimension" then x must be a list of objects. The argument dist_m is the type of distance considered in the calculation of the index, and can be set to any distance class implemented in the R package proxy, such as "euclidean", "canberra" (3) Q = N ∑ i,j = 1 p i p j d ij = N ∑ i,j = 1 1 N × 1 N d ij (4) Q = N ∑ i,j = 1 ij d ij = N ∑ i,j = 1 1 N × 1 N d ij = N ∑ i,j = 1 1 N 2 d ij (5) Q = N ∑ i,j = 1 ij d ij 1 = N ∑ i,j = 1 1 N 2 d ij 1 (7) M d = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ d 1 , 1 d 1 , 2 d 1 , 3 ⋯ d 1 , n d 2 , 1 d 2 , 2 d 2 , 3 ⋯ d 2 , n d 3 , 1 d 3 , 2 d 3 , 3 ⋯ d 3 , n ⋮ ⋮ ⋮ ⋱ ⋮ d n , 1 d n , 2 d n , 3 ⋯ d n , n ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ (6) or "manhattan".
If np > 1 then the doParallel package will be called for parallel calculation, and cluster. type will indicate the type of cluster to be opened (default is "SOCK", "MPI" and "FORK" are the alternatives). The diag argument refers to the diagonal term of Equation (  6 ). It will have no effect on the function for  > 0, while it will nullify the value of Q if set to TRUE, as previously explained in Equation (  6 ). In the next section, we provide an ecological example of the application of the spatio-parametric Rao's Q, done at regional scale to allow a comparison with in-situ data on species diversity. Supporting Information Appendix S2 provides an example at worldwide spatial scale.
| Case study: the diversity of vegetation greenness and the ecoregions of California A comparison between in-situ and remotely sensed diversity at worldwide scale might be difficult due to known biases in, for example, sampling effort, taxonomies, spatial uncertainty (Rocchini   2017 ). We chose California as a case study due to its high ecological diversity as well as to the availability of plant species field-data for this region. In practice, we aimed at visualizing and describing differences in both diversity and structure of vegetation for the state of California, USA. First, an NDVI raster layer was derived from Copernicus Sentinel-2 data (European Space Agency, reference period: January 2017 to July 2018) and processed through Google Earth Engine to filter out cloud cover, select the greenest pixel of the time series and resample at 100 m pixel resolution.
In this paper, the examples provided were based on a single NDVI layer since (a) it is a valuable index of vegetation health and (b) it is freely available in the rasterdiv package to reproduce the code proposed in this paper (see Supporting Information Appendix S2 for an application at worldwide spatial scale based on the Copernicus Proba-V NDVI freely available in the package). We are aware that NDVI has very limited capacity to track diversity in some habitats like dense forests, because it is saturated at dense vegetation  (Mutanga & Skidmore, 2004). From this point of view, imaging spectroscopy offers higher information content, also enabling plant functional trait retrievals  (Jetz et al. , 2016; Schneider et al. , 2019)  as well as structural traits by LiDAR data  (Schneider et al. , 2020).